multiplication and division basic math packet july 2010

Multiplication and Division Basic Fact Strategies

Office of Elementary Education 2010‐2011

Washington County Public Schools 2010 ‐ 2011

Office of Elementary Education 2

Table of Contents

PageBasic Fact Philosophy 3

Program Overview 5

Fact Remediation for Upper Grade Students 6

Description of Multiplication Math Fact Strategies 7

Strategy Overview 9

Parent Letter: Description of Strategies 11

Fact Strategy Assessments: Multiplication & Division 16

Classroom Assessment Recording Sheet 21

Multiplication: Twos Facts (Doubling) 31

Multiplication: Fives Facts 55

Multiplication: Ones Facts 85

Multiplication: Zeros Facts 103

Multiplication: Nines Facts 117

Multiplication: Helping Facts 137

Multiplication: Helping Facts x 3 143





Internet Sites for Strategic Facts Practice 193

Multiplication Mixed Practice: all strategies mixed on each game 195

Multiplication: Children’s Literature 217

Division Fact Acquisition 220

Types of Division 221

Fact Strategy Assessments: Division 222

Classroom Assessment Recording Sheet: Division 223

Division Introductory Lessons 229

Division: Twos Facts 249

Division: Fives Facts 257

Division: Zeros and Ones Facts 261

Division: Nines Facts 273

Division: Helping Facts 281

Division: Games for all strategies: one strategy per game 291

Division: Spinners 312

Division: Mixed Practice: all strategies mixed in each game 321

Division: Children’s Literature 327

Appendix 329

Division Flash Cards 331



Basic Fact Philosophy Mastery of basic facts means that a child can give a quick response (in about 3 seconds) without resorting to non‐efficient means, such as counting. All children are able to master the basic facts—including children with learning disabilities. Children simply need to construct efficient mental tools that will help them. The following information on facts is an excerpt from Teaching Student‐Centered Mathematics by John Van de Walle: Development of Efficient Strategies An efficient strategy is one that can be done mentally and quickly. The emphasis is on efficient. If drill is undertaken when counting is the only strategy available, the result is faster counting. Two Approaches to Fact Strategies

1. Plan lessons or short activities that promote development of specific strategies. There are two basic types of lessons suggested for this purpose.

Use simple story problems designed so that students are most likely to develop a strategy as they solve it. These are worthwhile tasks that do not require a full period to do and discuss. Rathmell, Leutzinger, and Gabriele (2000) suggest a simple story problem and discussion in a 5 to 10 minute period to start every day. Teachers report that students develop and use a variety of effective strategies for mastering basic facts. In the discussion of these solution methods, you can focus attention on the methods others have developed.

A more direct approach is to plan a lesson that is centered on a special ‘collection’ of facts for which a particular type of strategy is appropriate. The teacher can facilitate discussion regarding how the facts may be alike in some way. The teacher could also suggest an approach and see if students are able to apply it to similar facts.

There is a huge temptation simply to tell students about a strategy and then have them practice it. Though this can be effective for some students, many others will not personally relate to your ideas or may not be ready for them. Continue to discuss strategies invented in your class and plan lessons that encourage strategies. Drill of Efficient Methods and Strategy Selection Practice refers to problem‐based activities in which students are encouraged to develop (invent, consider, try—but not master) flexible and useful strategies that are meaningful. The types of lessons just described can be thought of as practice lessons. Whether from story problems or from consideration of a collection of similar facts, students are wrestling with the development of strategies that they can use themselves. Drill refers to repetitive non‐problem‐based activity. Drill activity is appropriate for children who have a strategy that they understand, like, and know how to use but have not yet become facile with it. Drill with an in‐place strategy focuses student’s attention on that strategy and helps to make it more automatic. Drill plays a significant role in fact mastery, and the use of old‐fashioned methods such as flash cards and fact games can be effective if used wisely.



Avoid Premature Drill It is critical that you do not introduce drill too soon. Suppose that a child does not know the 9 + 5 fact and has no way to deal with it other than to count fingers or use counters. These are inefficient methods. Premature drill introduces no new information and encourages no new connections. It is both a waste of time and frustrating to the child. Drill should only be used when an efficient strategy is in place. Overview of the Approach For each particular strategy, from development to eventual drill, when the strategy is well understood, the general approach for instruction is very similar. Make Strategies Explicit in the Classroom As has been discussed, your students will develop strategies as they solve word problems or as they investigate a category of facts you present. When a student suggests a new strategy, be certain that everyone else in the room understands how it is used. You can ask another student to explain what the student has just shared with the class. This requires students to attend to ideas that come from their classmates. Then, explore with the class to see what other facts would work with the student’s suggested strategy. Don’t expect to have a strategy introduced and understood with just one word problem or one exposure such as this. Try on several successive days problems in which the same type of strategy might be used. Children need lots of opportunities to make a strategy their own. Many children will simply not be ready to use an idea the first few days, and then all of the sudden something will click and a useful idea will be theirs. It is a good idea to write new strategies on the board or make a poster of strategies students develop. Give the strategies names that make sense. (Doubles and add on one more set. Helen’s idea. Use with 3s. Include an example.) No student should be forced to adopt someone else’s strategy, but every student should be required to understand strategies that are brought to the discussion. Drill Established Strategies When you are comfortable that children are able to use a strategy without recourse to physical models and that they are beginning to use it mentally, it is time to drill it. You might have as many as ten different activities for each strategy or group of facts. File folder or boxed activities can be used by children individually, in pairs, or even in small groups. With a large number of activities, children can work on strategies they understand and on the facts that they need the most. Flashcards are among the most useful approaches to fact strategy practice. For each strategy, make several sets of flash cards using all the facts that fit that strategy. On the cards, you can label the strategy or use drawings or cues to remind the children of the strategy.

Text from Teaching Student Centered Mathematics Grades K‐3, John Van De Walle Pages 94‐98

Program Overview



The structure of the program is based on a hierarchy of teaching groups of facts. The instruction should follow the concrete‐pictorial‐abstract model. For students who do not have strong number sense, beginning with concrete experiences is essential. As the students’ number sense increases, the activities move from concrete to pictorial and then to abstract. Research shows that the most effective way for students to learn the basic facts is to arrange the facts into groups. Each group contains centers/activities (which move through the concrete‐pictorial‐abstract stages of learning) to help students learn all of the facts in that group. The order in which the groups are taught is of great importance. The thinking involved in learning one group of facts is a prerequisite to learning the next group. Before beginning the instruction of multiplication facts, it is imperative that students completely understand the communicative property. (If needed, please see page 66, figure 2.16 in Van de Walle for further clarification.) Also, please be mindful that the strategies presented are just suggestions, not rules, and that the most general approach with children is to have them discuss ways that they can use to think of facts easily. This booklet is divided into 2 main sections (Multiplication and Division) with groups and subsections below each. See the Table of Contents for more information.



Fact Remediation with Upper‐Grade Students Students who have not mastered their basic facts by the fifth grade are in need of strategic instruction other than more drill. They have certainly seen and practiced facts countless times in previous grades. There is no reason to believe that the drills you provide will somehow be more effective than last year’s. These students need something better. The following key ideas can guide your efforts to help these older students.

1. Recognize that more drill will not work. Van de Walle defines drill as “repetitive, non‐

problem‐based exercises designed to improve skills or procedures already acquired” (Elementary and Middle School Mathematics, 7th edition). Students’ fact difficulties are due to a failure to develop or to connect concepts and relationships, not a lack of drill. At best, more drill will provide temporary results. At worst, it will cause negative attitudes about mathematics.

2. Inventory the known and unknown facts for each student in need. Find out from each

student what facts are known quickly and comfortably and which are not. Fifth and sixth‐grade students can do this diagnosis for you. Provide sheets of all facts for one operation in random order and have the students circle the facts they are hesitant about and answer all others. Suggest that finger counting or making marks in the margin is not permitted.

3. Diagnose strengths and weaknesses. Find out what students do when they encounter one of their unknown facts. Do they count on their fingers? Add up numbers in the margins? Guess? Try to use a related fact? Write down times tables? Are they able to use any of the relationships that might be helpful? Some of this you may be able to accomplish by having students write about how they approach two or three specific facts. More efficiently, you should conduct a 15‐minute diagnostic interview with each student in need.

4. Provide hope. Children who have experienced difficulty with fact mastery often believe that

they cannot learn facts or that they are doomed to finger counting forever. Let these children know that you will help them and that you will provide some new ideas that will help them as well.

5. Build in success. As you begin a well‐designed fact program for a child who has experienced

failure, be sure that successes come quickly and easily. Begin with easy strategies, and introduce only a few new facts at a time. Even with pure rote drill, repetitive exposure to five facts in three days will provide more success than introducing 15 facts in a week. Success builds success! With strategies as an added assist, success comes even more quickly. Point out to children how one idea, one strategy, is all that is required to learn many facts. Use fact charts to show what set of facts you are working on. It is surprising how the chart quickly fills up with mastered facts. Keep reviewing newly learned facts and those that were already known.



Description of Multiplication Math Fact Strategies Doubles Facts: These are facts that have 2 as a factor and are equivalent to the addition doubles (e.g., 7 + 7) and should already be known by students who know their addition facts. The major problem is realizing that not only is 2 x 7 double 7, but so is 7 x 2. Five Facts: This group consists of all facts with 5 as the first or second factor. Zeros and Ones: Thirty‐six facts have at least one factor that is either 0 or 1. These facts, though apparently easy, tend to get confused with “rules” that some children learned for addition. Above all else, avoid rules that sound arbitrary and without reason such as “Any number multiplied by zero is zero”. We’ll be using story problems to help student develop understanding for these facts. Building Down and Building Up Nifty Nines: Facts with a factor of 9 include the largest products but can be among the easiest to learn. Three patterns are useful for mastering the nines:

1) The tens digit of the product is always one less than the “other factor (the one other than 9). 2) The sum of the 2 digits in the product is always 9.

3) Use your 10 fingers as a tool. For single digit multiplication we always mark the number by folding the

finger down as a marker (referred to as the “space” between the digits). In this example 3 x 9, the third finger was bent. So the answer to the first digit is the # of fingers before the bend which is 2 and the second digit is the # of fingers after the bend which 7, therefore the answer for 3 x 9 is 27.

Six Facts: Build on the known facts of 5 and think:

“_ x 6 is only _ more than _ x 5” (fill in blank with same factor) For example: “2 x 6 is only 2 more than 2 x 5” “4 x 6 is only 4 more than 4 x 5”

Helping Facts : There are only 15 remaining facts to learn after the previous facts have been mastered.

Double and Double Again: (Fours Facts) This approach is applicable to all facts with 4 as one of the factors. For 4 x 8, double 8 and then double 16 to get 32. Double and One More Set: (Threes Facts) This approach is a way to think of facts with one factor of 3. With an array or a set picture, the double part can be circled, and it is clear that there is one more set. Two facts in this group involve difficult mental additions. Half Then Double: (Sevens Facts) This approach can be used if either factor is even. Select the even factor and cut it in half. If the smaller fact is known, that product is doubled to get the new fact. (For 6 x 7, half of 6 is 3. 3 x 7 is 21. Double 21 is 42.)



Add One More Set: (Sixes Facts) Many children prefer to go with a fact that is “close” and then add one more set to this known fact. For example, think of 6 x 7 as “6 sevens”. 5 sevens is close: That’s 35. 6 sevens is one more seven, or 42. When using 5 x 8 to help with 6 x 8, the set language “6 eights” is very helpful in remembering to add 8 more and not 6 more.

Text from Teaching Student Centered Mathematics Grades K‐3, John Van De Walle



Strategies Overview

Office of Elementary Education

2010‐2011



Multiplication Fact Strategy Hundred’s Chart Multiplication facts should be mastered by relating new facts to existing knowledge (addition, subtraction, skip counting, etc…). The chart below shows the strategy that relates to each multiplication problem. Refer to Van de Walle pages 88‐93 for more information.

0 1 2 3 4 5 6 7 8 9

0 Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

Zeros Fact

1 Zeros Fact

Ones Fact

Twos Fact

Ones Fact

Ones Fact

Ones Fact

Ones Fact

Ones Fact

Ones Fact

Ones Fact

2 Zeros Fact

Twos Fact

Twos Facts

Twos Fact

Twos Fact

Twos Fact

Twos Fact

Twos Fact

Twos Fact

Twos Fact

3 Zeros Fact

Ones Fact

Twos Fact

Helping Fact

Helping Fact

Fives Fact

Helping Fact

Helping Fact

Helping Fact

Nines Fact

4 Zeros Fact

Ones Fact

Twos Fact

Helping Fact

Helping Fact

Fives Fact

Helping Fact

Helping Fact

Helping Fact

Nines Fact

5 Zeros Fact

Fives Fact

Twos Fact

Fives Fact

Fives Fact

Fives Fact

Fives Fact

Fives Fact

Fives Fact

Fives Fact

6 Zeros Fact

Ones Fact

Twos Fact

Helping Fact

Helping Fact

Fives Fact

Helping Fact

Helping Fact

Helping Fact

Nines Fact

7 Zeros Fact

Ones Fact

Twos Fact

Helping Fact

Helping Fact

Fives Fact

Helping Fact

Helping Fact

Helping Fact

Nines Fact

8 Zeros Fact

Ones Fact

Twos Fact

Helping Fact

Helping Fact

Fives Fact

Helping Fact

Helping Fact

Helping Fact

Nines Fact

9 Nines Fact

Nines Fact

Twos Fact

Nines Fact

Nines Fact

Fives Fact

Nines Fact

Nines Fact

Nines Fact

Nines Fact



Dear Parents, In the weeks to come, our class will be focusing on learning our multiplication and division math facts. I wanted to make you aware of some of the strategies we will be using so that you can help to reinforce these same strategies at home.

1. Doubles Facts that have 2 as a factor are equivalent to the addition doubles and should already be know by students who know their addition facts. The major problem is realizing that not only is 2 x7 double 7, but so is 7 x 2. Parents can help by making flash cards with the related addition fact or use the word double as a cue.

2. Five Facts This group consists of all facts with 5 as the first or second factor. Parents can help

children by practicing counting by fives to at least 45.

3. Zeros and Ones Thirty‐six facts have at least one factor that is either 0 or 1. These facts, though apparently easy, tend to get confused with “rules” that some children learned for addition. We’ll be using story problems to help student develop understanding for these facts.

4. Building Down and Building Up

Six Facts Build on the known facts of 5 and think: “_ x 6 is only _ more than _ x 5” (fill in blank with same factor)

For example: “2 x 6 is only 2 more than 2 x 5” “4 x 6 is only 4 more than 4 x 5”

Nifty Nines Facts with a factor of 9 include the largest products but can be among the easiest to learn. Three patterns are useful for mastering the nines:

The tens digit of the product is always one less than the “other factor (the one other than 9).

The sum of the 2 digits in the product is always 9.

Use your 10 fingers as a tool. For single digit multiplication we always mark the number by folding the finger down as a marker (referred to as the “space” between the digits). In this example 3 x 9, the third finger was bent. So the answer to the first digit is the # of fingers before the bend which is 2 and the second digit is the # of fingers after the bend which 7, therefore the answer for 3 x 9 is 27.



5. Helping Facts There are only 15 remaining facts to learn after the previous facts have been mastered.

Double and Double Again This approach is applicable to all facts with 4 as one of the factors. For 4 x 8, double 8 and then double the result (16) to get a product of 32. Many children prefer to go with a fact that is “close” and then add one more set to this know fact. For example, think of 6 x 7 as 6 sevens. Five sevens is close: That’s 35. Six sevens is one more seven, or 42. When using 5 x 8 to help with 6 x 8, the set language “6 eights” is very helpful in remembering to add 8 more and not 6 more.

Division facts prove to be more difficult than multiplication. Division as Think Multiplication The main strategy that will be used with division facts is division as “think multiplication”. When done in this think‐multiplication manner, the child uses known multiplication facts to find the answer. When your child sees 25 5, you want them to think spontaneously, “Five times what equals 25?”. If you have any questions, please feel free to contact me. I look forward to working with you and your child on this new and exciting adventure!

Sincerely,

Information from Teaching Student Centered Mathematics Grades, John Van De Walle



Dear Parents, We are continuing to practice our multiplication and division math facts in our classroom. I have assessed all of the students to determine their level of fact mastery. When I use the term “mastery” that simply means that students are able to produce an answer for that particular fact in less than 3 seconds. I will be sending home activities to support your child’s individual fact level. Please use these activities as part of your fact practice each night. At the end of each week your students will take a quick assessment which will determine if he/she is able to move to the next level.

The strategies that we will be using are listed below: (M) Mastered (C) Currently Working on

Strategy – Multiplication

Doubles: Facts that have 2 as a factor are equivalent to the addition doubles and should already be know by students who know their addition facts. The major problem is to realize that not only is 2 x7 double 7, but so is 7 x 2. Parents can help by making flash cards with the related addition fact or word double as a cue.

Five Facts: This group consists of all facts with 5 as the first or second factor. Parents can help children by practicing counting by fives to at least 45.

Zeros and Ones: Thirty‐six facts have at least one factor that is either 0 or 1. These facts, though apparently easy, tend to get confused with “rules” that some children learned for addition. We’ll be using story problems to help student develop understanding for these facts.

Nifty Nines: Facts with a factor of 9 include the largest products but can be among the easiest to learn. Three patterns are useful for mastering the nines:



Using your 10 fingers as a tool. For single digit multiplication we always mark the number by folding the finger down as a marker (referred to as the “space” between the digits). In this example 3 x 9, the third finger was bent. So the answer to the first digit is the # of fingers before the bend which is 2 and the second digit is the # of fingers after the bend which 7, therefore the answer for 3 x 9 is 27.

Helping Facts: There are only 15 remaining facts to learn after the previous facts have been mastered. Use strategies such as “build up, build down”, double and double again, etc…



(M) Mastered (C) Currently Working on

Division as Think Multiplication: The main strategy that will be used with division facts is division as “think multiplication”. When done in this think‐multiplication manner, the child uses known multiplication facts to find the answer. When your child sees 25 5, you want them to think spontaneously, “Five times what equals 25?”.

Division as Think‐Multiplication for Doubles

Division as Think‐Multiplication for Fives

Division as Think‐Multiplication for Zeros and Ones

Division as Think‐Multiplication for Nines

Division as Think‐Multiplication for Helping Facts

Thank you for your support in this area. Sincerely,



Fact Strategy Assessments The attached fact strategy assessments and student tracking chart were developed so that teachers can diagnosis which strategies the students have mastery of and which strategies still need to be explored. These assessments should not be used as practice sheets. They should be used sparingly only to diagnosis the strategies that students have and have not mastered. Each fact strategy assessment contains 10 questions. Students should have 3 seconds to answer each question, for a total of 30 seconds per ten question assessment. “If there is any defensible purpose for a timed test of basic facts it may be for diagnosis—to determine which combinations are mastered and which remain to be learned.”

Teaching Student Centered Mathematics

John A. Van De Walle Page 119



Student: __________________________ Date: _________________

(1) Twos Facts Write the answers as fast as you can.

8 2 = ____ 2 9 = ____

1 2 = ____ 6 2 = ____

2 2 = ____ 3 2 = ____

2 5 = ____ 2 4 = ____

4 2 = ____ 7 2 = ____

(2) Fives Facts Write the answers as fast as you can.

5 4 = ____ 1 5 = ____

9 5 = ____ 5 6 = ____

5 8 = ____ 3 5 = ____

4 5 = ____ 7 5 = ____

5 5 = ____ 5 2 = ____

(3) Zeros and Ones Facts Write the answers as fast as you can.

1 1 = ____ 0 5 = ____

7 1 = ____ 3 0 = ____

1 6 = ____ 0 0 = ____

9 1 = ____ 0 7 = ____

1 4 = ____ 2 0 = ____

(4) Nines FactsWrite the answers as fast as you can.

9 x 6 = ____ 4 x 9 = ____

2 x 9 = ____ 5 x 9 = ____

9 x 7 = ____ 9 x 8 = ____

9 x 9 = ____ 3 x 9 = ____

9 x 1 = ____ 9 x 0 = ____



(5) Helping Facts Write the answers as fast as you can.

3 x 3 = ____ 3 x 8 = ____

4 x 7 = ____ 8 x 4 = ____

6 x 6 = ____ 7 x 6 = ____

7 x 8 = ____ 7 x 7 = ____

8 x 6 = ____ 8 x 8 = ____

(7) Fives Facts Write the answers as fast as you can.

20 ÷ 5 = ____ 5 ÷ 1 = ____

10 ÷ 2 = ____ 30 ÷ 5 = ____

35 ÷ 5 = ____ 25 ÷ 5 = ____

20 ÷ 4 = ____ 15 ÷ 3 = ____

45 ÷ 9 = ____ 5 ÷ 5 = ____

(6) Twos FactsWrite the answers as fast as you can.

6 ÷ 2 = ___ 18 ÷ 2 = ___

2 ÷ 1 = ___ 14 ÷ 7 = ___

4 ÷ 2 = ___ 6 ÷ 3 = ___

16 ÷ 8 = ___ 8 ÷ 2 = ___

12 ÷ 2 = ___ 16 ÷ 2 = ___

(8) Zeros and Ones Facts Write the answers as fast as you can.

3 ÷ 1 = ____ 0 ÷ 5 = ____

9 ÷ 1 = ____ 0 ÷ 3 = ____

6 ÷ 1 = ____ 0 ÷ 6 = ____

6 ÷ 6 = ____ 0 ÷ 8 = ____

7 ÷ 1 = ____ 0 ÷ 1 = ____



(9) Nines Facts Write the answers as fast as you can.

45 ÷ 9 = ____ 63 ÷ 7 = ____

18 ÷ 2 = ____ 81 ÷ 9 = ____

54 ÷ 6 = ____ 9 ÷ 9 = ____

72 ÷ 9 = ____ 27 ÷ 3 = ____

36 ÷ 9 = ____ 54 ÷ 9 = ____

(10) Helping Facts Write the answers as fast as you can.

24 ÷ 3 = ____ 21 ÷ 7 = ____

32 ÷ 8 = ____ 24 ÷ 4 = ____

42 ÷ 6 = ____ 18 ÷ 3 = ____

56 ÷ 8 = ____ 49 ÷ 7 = ____

28 ÷ 4 = ____ 64 ÷ 8 = ____



Dear Parents, We are continuing to practice our multiplication and division math facts in our classroom. I have assessed all of the students to determine their level of fact mastery. When I use the term “mastery” that simply means that students are able to produce an answer for that particular fact in less than 3 seconds. I will be sending home activities to support your child’s individual fact level. Please use these activities as part of your fact practice each night. At the end of each week your students will take a quick assessment which will determine if he/she is able to move to the next level.

The strategies that we will be using are listed below: (M) Mastered (C) Currently Working on

Strategy – Multiplication

Doubles: Facts that have 2 as a factor are equivalent to the addition doubles and should already be known by students who know their addition facts. The major problem is to realize that not only is 2 x7 double 7, but so is 7 x 2. Parents can help by making flash cards with the related addition fact or word double as a cue.

Five Facts: This group consists of all facts with 5 as the first or second factor. Parents can help children by practicing counting by fives to at least 45.

Zeros and Ones: Thirty‐six facts have at least one factor that is either 0 or 1. These facts, though apparently easy, tend to get confused with “rules” that some children learned for addition. We’ll be using story problems to help student develop understanding for these facts.

Nifty Nines: Facts with a factor of 9 include the largest products but can be among the easiest to learn. Three patterns are useful for mastering the nines:



Helping Facts: There are only 15 remaining facts to learn after the previous facts have been mastered. Use strategies such as “build up, build down”, double and double again, etc…



(M) Mastered (C) Currently Working on

Division as Think Multiplication: The main strategy that will be used with division facts is division as “think multiplication”. When done in this think‐multiplication manner, the child uses known multiplication facts to find the answer. When your child sees 25 5, you want them to think spontaneously, “Five times what equals 25?” .

Division as Think‐Multiplication for Doubles

Division as Think‐Multiplication for Fives

Division as Think‐Multiplication for Zeros and Ones

Division as Think‐Multiplication for Nines

Division as Think‐Multiplication for Helping Facts

Thank you for your support in this area. Sincerely,



Classroom Recording Sheet – Multiplication & Division

Student

1 2 3 4 5 6 7 8 9 10

Twos Facts

Fives Facts

Ones & Zero Facts

Nines Facts

Helping Facts

Division – Twos Facts

Division –Fives Facts

Division – Ones & Zero Facts

Division – Nines Facts

Division – Helping Facts



Alternate Set of Multiplication/Division

Assessments

Timing: 3 seconds per question



Name: __________________________________

Twos Facts Write the answers as fast as you can.

2 3 = ____ 2 9 = ____ 8 2 = ____ 6 2 = ____

1 2 = ____ 3 2 = ____

2 2 = ____ 2 4 = ____

2 7 = ____ 2 8 = ____

9 2 = ____ 2 6 = ____

4 2 = ____ 7 2 = ____

2 1 = ____

Name: __________________________________


2 3 = ____ 2 9 = ____ 8 2 = ____ 6 2 = ____

1 2 = ____ 3 2 = ____

2 2 = ____ 2 4 = ____

2 7 = ____ 2 8 = ____

9 2 = ____ 2 6 = ____

4 2 = ____ 7 2 = ____

2 1 = ____

Name: __________________________________


2 3 = ____ 2 9 = ____ 8 2 = ____ 6 2 = ____

1 2 = ____ 3 2 = ____

2 2 = ____ 2 4 = ____

2 7 = ____ 2 8 = ____

9 2 = ____ 2 6 = ____

4 2 = ____ 7 2 = ____

2 1 = ____

Name: __________________________________


2 3 = ____ 2 9 = ____ 8 2 = ____ 6 2 = ____

1 2 = ____ 3 2 = ____

2 2 = ____ 2 4 = ____

2 7 = ____ 2 8 = ____

9 2 = ____ 2 6 = ____

4 2 = ____ 7 2 = ____

2 1 = ____



Name: __________________________________

Fives Facts Write the answers as fast as you can.

5 4 = ____ 1 5 = ____

2 5 = ____ 5 6 = ____

5 9 = ____ 5 8 = ____

5 5 = ____ 7 5 = ____

5 1 = ____ 5 3 = ____

8 5 = ____ 9 5 = ____

5 7 = ____ 5 2 = ____

3 5 = ____ 6 5 = ____

4 5 = ____

Name: __________________________________


5 4 = ____ 1 5 = ____

2 5 = ____ 5 6 = ____

5 9 = ____ 5 8 = ____

5 5 = ____ 7 5 = ____

5 1 = ____ 5 3 = ____

8 5 = ____ 9 5 = ____

5 7 = ____ 5 2 = ____

3 5 = ____ 6 5 = ____

4 5 = ____

Name: __________________________________


5 4 = ____ 1 5 = ____

2 5 = ____ 5 6 = ____

5 9 = ____ 5 8 = ____

5 5 = ____ 7 5 = ____

5 1 = ____ 5 3 = ____

8 5 = ____ 9 5 = ____

5 7 = ____ 5 2 = ____

3 5 = ____ 6 5 = ____

4 5 = ____

Name: __________________________________


5 4 = ____ 1 5 = ____

2 5 = ____ 5 6 = ____

5 9 = ____ 5 8 = ____

5 5 = ____ 7 5 = ____

5 1 = ____ 5 3 = ____

8 5 = ____ 9 5 = ____

5 7 = ____ 5 2 = ____

3 5 = ____ 6 5 = ____

4 5 = ____



Name: __________________________________

Zeros and Ones Facts Write the answers as fast as you can.

1 3 = ____ 0 4 = ____

7 1 = ____ 8 0 = ____

5 0 = ____ 1 6 = ____

1 9 = ____ 0 7 = ____

0 2 = ____ 6 0 = ____

0 9 = ____ 1 7 = ____

6 1 = ____ 0 1 = ____

3 0 = ____ 9 1 = ____

1 1 = ____ 3 1 = ____

Name: __________________________________


1 3 = ____ 0 4 = ____

7 1 = ____ 8 0 = ____

5 0 = ____ 1 6 = ____

1 9 = ____ 0 7 = ____

0 2 = ____ 6 0 = ____

0 9 = ____ 1 7 = ____

6 1 = ____ 0 1 = ____

3 0 = ____ 9 1 = ____

1 1 = ____ 3 1 = ____

Name: __________________________________


1 3 = ____ 0 4 = ____

7 1 = ____ 8 0 = ____

5 0 = ____ 1 6 = ____

1 9 = ____ 0 7 = ____

0 2 = ____ 6 0 = ____

0 9 = ____ 1 7 = ____

6 1 = ____ 0 1 = ____

3 0 = ____ 9 1 = ____

1 1 = ____ 3 1 = ____

Name: __________________________________


1 3 = ____ 0 4 = ____

7 1 = ____ 8 0 = ____

5 0 = ____ 1 6 = ____

1 9 = ____ 0 7 = ____

0 2 = ____ 6 0 = ____

0 9 = ____ 1 7 = ____

6 1 = ____ 0 1 = ____

3 0 = ____ 9 1 = ____

1 1 = ____ 3 1 = ____



Name: __________________________________

Nines Facts Write the answers as fast as you can.

9 x 3 = ____ 1 x 9 = ____

2 x 9 = ____ 5 x 9 = ____

9 x 6 = ____ 8 x 9 = ____

9 x 9 = ____ 3 x 9 = ____

9 x 1 = ____ 9 x 7 = ____

9 x 8 = ____ 9 x 4 = ____

9 x 5 = ____ 0 x 9 = ____

7 x 9 = ____ 9 x 2 = ____

4 x 9 = ____ 6 x 9 = ____

Name: __________________________________


9 x 3 = ____ 1 x 9 = ____

2 x 9 = ____ 5 x 9 = ____

9 x 6 = ____ 8 x 9 = ____

9 x 9 = ____ 3 x 9 = ____

9 x 1 = ____ 9 x 7 = ____

9 x 8 = ____ 9 x 4 = ____

9 x 5 = ____ 0 x 9 = ____

7 x 9 = ____ 9 x 2 = ____

4 x 9 = ____ 6 x 9 = ____

Name: __________________________________


9 x 3 = ____ 1 x 9 = ____

2 x 9 = ____ 5 x 9 = ____

9 x 6 = ____ 8 x 9 = ____

9 x 9 = ____ 3 x 9 = ____

9 x 1 = ____ 9 x 7 = ____

9 x 8 = ____ 9 x 4 = ____

9 x 5 = ____ 0 x 9 = ____

7 x 9 = ____ 9 x 2 = ____

4 x 9 = ____ 6 x 9 = ____

Name: __________________________________


9 x 3 = ____ 1 x 9 = ____

2 x 9 = ____ 5 x 9 = ____

9 x 6 = ____ 8 x 9 = ____

9 x 9 = ____ 3 x 9 = ____

9 x 1 = ____ 9 x 7 = ____

9 x 8 = ____ 9 x 4 = ____

9 x 5 = ____ 0 x 9 = ____

7 x 9 = ____ 9 x 2 = ____

4 x 9 = ____ 6 x 9 = ____



Name: __________________________________

Helping Facts Write the answers as fast as you can.

3 x 3 = ____ 8 x 8 = ____

3 x 6 = ____ 4 x 3 = ____

3 x 7 = ____ 8 x 3 = ____

4 x 4 = ____ 4 x 6 = ____

4 x 7 = ____ 4 x 8 = ____

6 x 3 = ____ 6 x 4 = ____

6 x 6 = ____ 6 x 7 = ____

6 x 8 = ____ 7 x 3 = ____

7 x 7 = ____ 7 x 8 = ____

Name: __________________________________


3 x 3 = ____ 8 x 8 = ____

3 x 6 = ____ 4 x 3 = ____

3 x 7 = ____ 8 x 3 = ____

4 x 4 = ____ 4 x 6 = ____

4 x 7 = ____ 4 x 8 = ____

6 x 3 = ____ 6 x 4 = ____

6 x 6 = ____ 6 x 7 = ____

6 x 8 = ____ 7 x 3 = ____

7 x 7 = ____ 7 x 8 = ____

Name: __________________________________


3 x 3 = ____ 8 x 8 = ____

3 x 6 = ____ 4 x 3 = ____

3 x 7 = ____ 8 x 3 = ____

4 x 4 = ____ 4 x 6 = ____

4 x 7 = ____ 4 x 8 = ____

6 x 3 = ____ 6 x 4 = ____

6 x 6 = ____ 6 x 7 = ____

6 x 8 = ____ 7 x 3 = ____

7 x 7 = ____ 7 x 8 = ____

Name: __________________________________


3 x 3 = ____ 8 x 8 = ____

3 x 6 = ____ 4 x 3 = ____

3 x 7 = ____ 8 x 3 = ____

4 x 4 = ____ 4 x 6 = ____

4 x 7 = ____ 4 x 8 = ____

6 x 3 = ____ 6 x 4 = ____

6 x 6 = ____ 6 x 7 = ____

6 x 8 = ____ 7 x 3 = ____

7 x 7 = ____ 7 x 8 = ____



Multiplication Basic Fact Strategies

Office of Elementary Education 2010‐2011



Twos (Doubles) Facts Facts that have 2 as a factor are equivalent to the addition doubles (e.g., 6 + 6) and should already be known by students who know their addition facts. It is important to realize that 2 x 7 is double 7 as is 7 x 2. Be sure to expose students to problems where 2 is the number of sets as well as the size of the set.

0 1 2 3 4 5 6 7 8 9

0 0

1 2

2 0 2 4 6 8 10 12 14 16 18

3 6

4 8

5 10

6 12

7 14

8 16

9 18



The Twos Facts (Doubles)

Two is very fast and fun, Quickly double and you’re done.

What’s that you say, be more precise? Okay then, just add it twice!

The Best of Times by Greg Tang



Twos Facts: Lego Multiplication

Objective: Students will be able to connect doubling to multiplying by 2. Activity Type: Groups of 2 students Materials: (each group will need the following)

Bag of Legos (of various sizes)

Recording sheet for each pair of students

Directions: 1. Have each student choose a Lego (larger than 2 x 2). Ask them how they can count the knobs on the top of their

piece without counting each individual knob. Ask students to draw pictures to represent how they could count them. (For example, they might skip count by 2, count 1 row and double, make equal groups horizontally or vertically, etc…)

2. Have students show and explain their representations. Talk about strategies for doubling or multiplying by 2. Be sure students can write a numerical representation for their Lego piece. For example if they had a piece that was 2 knobs wide and 4 long they could represent the knob with the expression 2 x 4 or 4 x 2.

3. Pose the following open ended question to students: Jimmy put his Lego blocks on a flat. His design had 60 knobs. What might his design look like? How could you prove that your design used 60 knobs without counting each knob?

Variations: The page that follows could be used in addition to or instead of the activity in #3 above. It is recommended that you cut apart the questions and have each group select several to solve. Note: It is not recommended that every student complete the entire sheet.



Lego Multiplication Facts Can you find a Lego to represent 2 x 1? Draw a picture of the Lego below.

Can you find a Lego to represent 2 x 2? Draw a picture of the Lego below.








Choose any Lego and draw it below. How could you use multiplication to determine the total number of knobs?



Doubles Concentration

Objective: Students will match the doubles fact (twos fact) and the product. Activity Type: Groups of 2 ‐ 3 students Materials: (Each group will need)

A set of cards copied on card stock and cut out. The doubles facts should be copied on 1 color paper, twos multiplication fact on another color paper, and finally the product copied on a third color paper. By copying each on different colors students know to pick up one of each color on a turn.

Directions: First time playing – reviews the double fact adding

1. Players layout the cards with the doubles and product/sum. 2. On their turn, players pick up one card of each color. If the doubles fact matches the sum/product card they

picked up then they keep the cards and take another turn. If they do not match the cards are returned face down.

3. The player with the most matches at the end wins.

Second time playing – matches the doubles and twos fact

4. Players lay out the cards with the doubles and multiplication facts (no products). 5. On their turn, players pick up one card of each color. If the doubles fact matches the multiplication card

they picked up then they keep the cards and take another turn. If they do not match the cards are returned face down.


Third time playing – matches the twos fact and the product

7. Players layout the cards with the twos facts and product cards. 8. On their turn, players pick up one card of each color. If the doubles fact matches the sum/product card they

picked up then they keep the cards and take another turn. If they do not match the cards are returned face down.


Fourth time playing – matches doubles fact, twos fact, and product/sum

10. Players lay out all cards. 11. On their turn, players pick up one card of each color. If all three cards match, they keep them. If not, they

return all cards face down onto the table.




Doubles Concentration Cards

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

7 + 7

8 + 8

9 + 9

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

7 + 7

8 + 8

9 + 9



Twos Facts Concentration Cards

2 x 2

2 x 3

2 x 4

2 x 5

2 x 6

2 x 7

2 x 8

2 x 9

2 x 2

3 x 2

4 x 2

5 x 2

6 x 2

7 x 2

8 x 2

9 x 2



Product/Sum Concentration Cards

4

6

8

10

12

14

16

18

4

6

8

10

12

14

16

18



Product/Sum Concentration Cards



Twos Facts: Doubling 4 in a Row

Objective: Students will be able to connect doubling to multiplying by 2. Activity Type: Groups of 2‐3 students Materials: (each group will need the following)

Game board

Cube with the faces labeled: 4, 5, 6, 7, 8, and 9 (or the spinner below)

Each child needs approximately 10 counters of 1 color

Directions: 1. The first player rolls the number cube (or spins the spinner). They double the number, state the related

multiplication fact, and then cover the sum on the game board. For example, if a student rolled 6 they would say “6 doubled is 12 or 6 x 2 is 12”.

2. Each player continues to roll and cover the sum. If the double rolled is already covered the player loses his/her

turn. Play continues until 1 player gets 4 counters in a row. Variations: If a player’s sum is already covered they could remove the opponents chip from that square and replace it with their own.

4 5

6 7 8

9



Doubling 4 in a Row

8 18 12 8 10 14

16 12 14 10 14 8

18 10 14 18 12 16

16 14 16 8 18 10

8 16 18 10 16 12

12 18 14 12 8 10



Twos Facts: Double Cross Off Game

Objective: Students will use the doubling strategy to multiply by 2 Activity Type: Groups of 2 students Materials: each group will need the following

Game board inside a clear plastic sheet protector (By placing the game board into a plastic sheet the student can write on it with a dry erase marker allowing the game to be played many times on 1 board).

Dry erase marker (each student)

Directions: 1. The first player spins the spinner (with a paper clip and pencil). The student then states the multiplication fact and

uses the doubling strategy to find the product. The student then crosses off that product. 2. Play continues until a player has crossed off all the numbers. The player that crosses off all the numbers first is the

winner.



2 16

8 18

14 10

16 10

12 4

12 20

18 6

14

8 14

4

10

16

12

20

10

18

2 18

16

8

12

6



Doubles Checkers

Objective: Students will use the doubling strategy to multiply by 2. Activity Type: Groups of 2 students Materials: each group will need checkers and a game board Directions: 1. Math checkers is played like regular checkers.

2. Students set up the game board as shown below. 3. For a player to move a piece, they must first correctly answer the fact on the corresponding space.

4. In order to be “kinged”, a player must explain how they found the answer to the problem on the corresponding

space.



Doubles Checkers

8 x 2 2 x 1 10 x 2 2x 6 8 x 2

7 x 2 2 x 6 3 x 2 2 x 2 2 x 9

2 x 4 8 x 2 2 x 1 10 x 2 2 x 4

2 x 2 2 x 6 8 x 2 2 x 5 9 x 2

1 x 2 2 x 3 9 x 2 2 x 6 7 x 2

9 x 2 2 x 6 2 x 10 2 x 8 2 x 3

6 x 2 2 x 1 5 x 2 2 x 10 2 x 2

2 x 7 5 x 2 2 x 9 6 x 2 2 x 2

2 x 6 7 x 2 2 x 8 4 x 2 2 x 5

2 x 1 3 x 2 2 x 7 6 x 2 2 x 4

7 x 2 2 x 2 2 x 8 9 x 2 2 x 9



Merry – Low ‐ Round

Objective: Students will use the doubling strategy to multiply by 2. Activity Type: Groups of 2 students Materials:

Each player will need a copy of the game board in a plastic sheet, a dry erase marker, and several chips (no more than 10 each).

Spinner (one for each group)

Directions:

1. The first player spins the spinner. They write down the doubles fact, twos fact, and the answer for that number. 2. The second player spins the spinner. They write down the doubles fact, twos fact, and the answer.

3. The players then compare their answers for that round. The player with the smallest product puts a chip by that

round. Note: if the player writes down an incorrect fact or answer they automatically lose that round.

4. Play continues in the same way for all 10 rounds. At the end of 10 rounds, the player with the most chips wins the game.



Merry – Low – Round Spinner



Merry – Low – Round Game Board

Round

Addition Fact

Multiplication Fact

Answ

er

Place a chip in this column if you have the lowest product

for this round

1

2

3

4

5

6

7

8

9

10



Order, Order

Objective: Students will use the doubling strategy to multiply by 2. Activity Type: Groups of 2 students Materials: (Each group will need)

A game board in a plastic sheet protector (or laminated)

Dry erase marker for each student

Spinner

Directions: Object of the game: To be the first player to have all the boxes filled with products from least to greatest.

1. The first player spins the spinner. They then multiply the number by 2 (doubles the number). 2. The player then chooses a box in which to put their product. Once a number is written in a box it may not be

moved.

3. The next player spins, multiplies, and places a number.

4. On each players turn they must place the product so that all of their numbers are in order from least to greatest. If they cannot place a number, they lose a turn.

5. The first player to fill all the boxes with their numbers from least to greatest wins.



Player 1 Player 2



Three for All x2

Objective: Students will use the doubling strategy to multiply by 2. Activity Type: Groups of 2 students Materials: (Each group will need)



Chips (a different color for each player)

Directions: Object of the game: To be the first player to have 3 chips in a row (vertically, horizontally, or diagonally)

1. Players take turns choosing 2 numbers in the box (crossing them off with a dry erase marker) to make a multiplication fact.

2. If their answer is in a circle, they place a chip on it.

3. Numbers in the box may only be used 1 time.

4. The first player to get 3 chips in a row wins.



2 2 6 2 4 9 2 2

8 2 4 3 7 6 2 9

3 2 7 2 2 2 2 2

2 6 9 10 4 2 1 2

2 5 9 2 2 2 2 2

8 14 8 3 10

6 12 16 20 12

8 14 18 16 2

12 18 4 18 18

2



12

Twos Facts

22

Twos Facts

32

Twos Facts

42

Twos Facts

52

Twos Facts

62

Twos Facts

72

Twos Facts

82

Twos Facts

92

Twos Facts

21

Twos Facts

23

Twos Facts

24

Twos Facts



25

Twos Facts

26

Twos Facts

27

Twos Facts

28

Twos Facts

29

Twos Facts

20

Twos Facts

02

Twos Facts



Fives Facts

This group consists of all facts with 5 as the first or second factor. We can help children by practicing counting by fives to at least 45. The fives facts can also be related to the tens facts (as most students can count by tens with ease) by multiplying by ten and taking half.

0 1 2 3 4 5 6 7 8 9

0 0

1 5

2 10

3 15

4 20

5 0 5 10 15 20 25 30 35 40 45

6 30

7 35

8 40

9 45



Fives Facts

Five will yield the right amount, If by 5’s you always count. Or else just multiply by 10, Half will get you there again!




Fives Facts Introduction

Objective: Students will be able to identify real world situations that involve 5. This identification will help students make connections between fives facts and their application. Activity Type: Whole Class Activity Materials: none needed Directions:

1. Ask, what are some everyday situations that involve five? Write down the students ideas on chart paper. Encourage the students to think of a range of situations, for example, the number of school days in one week or the age of a younger sibling.

2. Repeat the discussion using multiples of 5, such as 25 and 15. Write the ideas the students suggest on the

board.



# of People

Count by 10’s

Count by 5’s

10 100 50

9

8

7

6

5

4

3

2

Fives Facts Physical Model

Objective: Students will discover that the fives facts are half of the tens fact. Activity Type: Whole Class Activity (at least 10 students) Materials: 10 students Directions:

1. Invite ten students to stand at the front of the class. Instruct the other students to count by tens. As they say each number, the students raise both of their hands (to represent 10).

2. Once the students have counted to one hundred, direct them to count by fives from 0. Instruct students to raise

only one hand as each five is counted. When the count reaches fifty, ask, what do you notice about the two totals we counted? (Fifty is half of one hundred).

3. Begin the following chart on the board (a template follows this lesson).

Continue to have students’ model problems with different numbers of students. Record the answers when counting by 10 and counting by 5. It is not necessary to do these in order.

4. Ask students about the patterns they notice. (Counting by 5 is half of

10.)

5. Have students solve real‐world problems with students modeling at the front of the room (with their hands/fingers). For example, Susan has 4 bags of candy. Each bag had 10 pieces of candy. How many pieces of candy did she have altogether?

Note: Another quick representation of the 10’s facts is to use the base ten rods. Students can see quickly that if you have 3 groups of 10 that it equals 30. Then they can cover half with an index card and see the related 5’s fact.



# of People

Count by 10’s

Count by 5’s

10

9

8

7

6

5

4

3

2

1

What patterns do you notice? How does counting by 10’s relate to counting by 5’s?



Five and Ten Fact Dot Cards

Objective: Students will use arrays to connect the tens facts to the fives fact. Activity Type: Whole Class, Small Groups, or Individuals Materials: Dot cards (cut out, assembled, and laminated) Directions:

1. Begin with the 1x10 card. Hold the card so that the flap is open. Say, how many rows of dots do you see? (1). How many dots are in each row? (10). If students need to count at first, let them. What multiplication sentence can we use to represent this? What is the turnaround fact for this multiplication sentence? Have student find the 10’s fact by skip counting by tens and then find half to determine the fives fact.

2. Repeat with the other cards. Challenge students to give a real world example of some of the facts.



Five & Ten Fact Relationship Dot Cards

Make a set of use‐tens cards shown on the following pages. Be sure to cut out the “upside down card”, paste it on the back of the flap, and then laminate.

When the bottom flap is unfolded the card shows a tens fact. When the flap is folded the card shows a fives fact. These cards show that the fives facts are half of the tens fact. Ask students questions like “What do you see?”, “How can you figure out the total number of dots?”. Encourage the students to use the known tens fact to figure out the fives fact. Ten Fact Card Five Fact Card





1 10 = _____

10 1 = _____

Cut out the box below. Paste it on the back of the dot card in the same location as the multiplication problems on the front. That way when you flip the card up, you see the times 5 fact.



2 10 = _____

10 2 = _____





3 10 = _____

10 3 = _____





4 10 = _____

10 4 = _____




5 10 = _____

10 5 = _____




6 10 = _____

10 6 = _____




7 10 = _____

10 7 = _____




8 10 = _____

10 8 = _____




Fact Clock Connection

Adapted from Teaching Student Centered Mathematics by John Van de Walle

Objective: Students will connect time with fives facts. Activity Type: Whole class Instruction and a pairs game Materials: 1 set of concentration cards for each pair (clocks on 1 color cardstock and facts on another color cardstock) Directions: 1. Display a clock face with moveable hands. Move the minute hand to 6, directing the students to count each

multiple of five. Say, six lots of five minutes is thirty minutes. What multiplication fact could we use represent this? (6 x 5) What is the turn around fact of 6 x 5? (5 x 6) Move the minute hand to 9. Ask a volunteer to describe the matching number facts (9 x 5 = 45). Repeat with other positions on the clock face.

2. Play Clock Fact Concentration with pairs.

a. Each pair of students lays the cards face down. b. The first player picks up 1 card of each color. If they cards match (the fact or its turnaround) and they can

say the answer to the fact, they keep the cards. If they have a match and the answer they take an extra turn.

c. Players alternate turns until all the cards have been picked up.

d. The player with the most cards is the winner.



Clock Face Concentration

1 x 5 2 x 5 3 x 5

4 x 5 5 x 5 6 x 5

7 x 5 8 x 5 9 x 5

10 x 5 11 x 5 12 x 5



Clock Face Concentration



Fives Spinner Game

Objective: Students will use fives fact strategies to solve multiplication problems. Activity Type: Groups of 2‐3 students Materials: each group will need the following

1 spinner

A game board for each student Directions: 1. The first player spins. The player multiplies the number they spin by 5 and says the multiplication fact. The player

writes the fact and its turnaround beside the matching product on their sheet of paper. 2. The other player takes a turn. 3. As the game continues, the player misses a turn if they spin a number they have already used.

4. The first player to write the matching facts for each product wins.



Fives Spinner Game

Fives Fact Fives Fact Turnaround

5

10

15

20

25

30

35

40

45

Student: _______________________________________



Fives Spinner Game

12 3

4 5 6

7

8 9

Spin Again



Fives Fact Connect Three Game

Objective: Students will use fives fact strategies to solve multiplication problems. Activity Type: Groups of 2‐3 students Materials: each group will need the following

1 game board for each player

Fives spinner from the “Fives Spinner Game”

Counters for each student Directions:

1. Players take turns spinning the spinner and multiplying by the number five. If the answer is on their board, the player can cover it with a counter.

2. The first player to get 3 counters in a row (diagonal, horizontal, or vertical) wins.

3. After they have played several times, have them point to the numbers on the board that end in zero. Ask, what numbers did you roll to get these answers? Invite a number of responses. Ask, what did you notice about these numbers?

Note: 4 different variations of the game board are included to use with groups up to 4 players.



The Fives Fact

Connect 3 Game

40 25 15

35 20 35

15 40 30



The Fives Fact Connect 3 Game

40 5 15

35 20 25

45 10 30




15 35 20

30 5 40

25 45 10




20 35 5

10 40 25

30 45 15



The Fives Connect 3 Game

45 15 20

40 10 25

35 5 30



15

Fives Facts

25

Fives Facts

35

Fives Facts

45

Fives Facts

55

Fives Facts

65

Fives Facts

75

Fives Facts

85

Fives Facts

95

Fives Facts

51

Fives Facts

53

Fives Facts

54

Fives Facts



56

Fives Facts

57

Fives Facts

58

Fives Facts

59

Fives Facts

05

Fives Facts

50

Fives Facts

52

Fives Facts



Zeros and Ones Facts

Children should be given the opportunity to find their own reasoning as to why a number multiplied by zero is equal to zero and that a number multiplied by one is equal to that number. They should not be explicitly told these rules but should be able to explain why this is so. Upon gaining this knowledge, they will know 36 facts of single‐digit multiplication.

0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2

3 0 3

4 0 4

5 0 5

6 0 6

7 0 7

8 0 8

9 0 9



Ones Facts

One is simple as can be, it’s known as the identity. The answer is identify,

it’s the one you multiply!




Ones Real World Introduction

Objective: Students will be able to identify real world situations that involve 1. Activity Type: Whole Class Activity Materials: none needed Directions:

1. Ask, What are some everyday situations that involve one group, stack, or set? Write down the student’s ideas on chart paper. Encourage the students to think of a range of situations, for example, the number of school days in one week or the age of a younger sibling.

2. Write, “One row of _____ “on the board. Have students choose a situation that was listed on the board and

draw a picture of the situation.

3. Hang up the illustrations. Ask students what patterns they notice when we multiply by one. If they struggle finding the pattern, write down some of the facts they illustrated on the board, and ask, what do all the multiplication facts we created using 1 have in common? Or can you finish my statement “When I multiply a number by one _______.”? The key is to ask questions to help students discover that when you multiply by 1 the answer is the number you multiply by 1.



Ones Fact Match Walk

Objective: Students will be able to match the written real world problem with its equation. Activity Type: Whole Class Activity Materials:

Set of cards, cut out for students

Another set of the same cards, cut out in a bag for the teacher. Directions: Overview: In this activity student will rotate in a circle around the cards until music stops. When the music stops the teacher pulls out a card. The students look at the cards at their feet and the student who believes they have the answer raises their hand. If they are correct – they get to carry something until the next match is made (something that the students find fun to have).

1. Hand out 1 card to each student. 2. Have students form a circle. When the circle is formed, have them face the center of the circle. Then

students should put the card at their feet. Let the students know that when you begin playing music, the circle is going to start moving in a clockwise direction. Then, when the music stops you will pull out a card and put it on the document camera/overhead.

3. The students look at the cards where they stopped (at their feet). If they believe they have the match

they raise their hand. Check to see if it is correct. If it is, they get the fact match prize. Repeat – each time the correct match carries the “fact match prize”.

4. Ex. Music stops and you pull out the phrase “One cake needs 4 eggs”. The student who has a picture of

1 group of 4 is the match. Variations:

Instead of having a “Fact Match Walk”, hand out the cards and have them find their match. Then have each pair read their statement and equation to check. Have students’ trade cards while you play music. When the music stops, they find their match.

Play a concentration game with the cards.



Fact Match Walk

Laken has 1 lunch box.

Rachel has 2 stickers in her desk.

Aaron has 3 pencils in his box.

Trey has 4 buttons on his shirt.

Braden has 5 cookies in his lunch.

Susan has 6 roses in a vase.

Kristin has 7 cats in her house.

Jasmine has 8 markers in her desk.

Leo has 9 books in his room.



Fact Match Walk

Michael has 1 ball.

Two girls each have 1 yo‐yo.

Three boys each have 1 hat.

Four girls each have 1 flower.

Five boys each have 1 book.

Six girls each have 1 bag.

Seven boys each have 1 piece of gum.

Eight girls each have 1 bike.

Nine boys each have 1 jacket.



Once Around x1 Game Adapted from Basic Games by Marcy Cook

Objective: Students will be able to multiply numbers involving 1. Activity Type: Groups of 2‐3 Materials:

Marker for each player

Game board

Paper clip for spinner Directions:

1. On their turn, students spin the spinner, state the problem and product. They then move their marker to the next square on the game board with that product.

2. Students continue until a student reaches the last space.

Variation:

On each turn have students draw a picture of the multiplication problem they have to solve on their turn in addition to finding the answer.



Once Around x1 Game Adapted from Basic Games by Marcy Cook



Cover Up x1 Game Adapted from Basic Games by Marcy Cook

Objective: Students will be able to multiply numbers involving 1. Activity Type: Groups of 2 Materials:

Chips (different color for each player)

Game board


1. On their turn, players spin the spinner. They multiply the number on the spinner by 1 and then cover one space on the board that matches that product.

2. Players continue taking turns spinning and marking their product until all the spaces are filled. If there are no

more spaces for a student’s product, they lose their turn.

3. At the end the student with the most chips, wins.



one 3 seven 7

0 zero 6 three

six 2 nine

9 two 8

5 4

eight five

four 1

Adapted from Basic Games by Marcy Cook



01

Ones Facts

11

Ones Facts

21

Ones Facts

31

Ones Facts

41

Ones Facts

51

Ones Facts

61

Ones Facts

71

Ones Facts

81

Ones Facts

91

Ones Facts

10

Ones Facts

12

Ones Facts



13

Ones Facts

14

Ones Facts

15

Ones Facts

16

Ones Facts

17

Ones Facts

18

Ones Facts

19

Ones Facts



Zero Facts

Zero is a cinch to do, the answer is right in front of you. For every problem it’s the same,

zilch or zero is its name!




Zero Real World Introduction

Objective: Students will be able to identify real world situations that involve 0. Activity Type: Whole Class and group activity Materials:

Chart paper

Markers Directions:

1. Write “O” and “zero” on the board. Ask the students to suggest other words for zero. Write their suggestions on the board. Examples may include, none, nothing, nil, empty, naught, all gone, and no more.

2. Ask, what are some multiplication stories that involve zero?” List the student’s ideas on chart paper.

Encourage the students to think of a range of situations, for example, the number of empty rows of seats at a football game. If students are stuck use the posters on the next two pages of this guide.

3. Put students into groups or pairs. Assign each group a 0 multiplication fact (such as 0 x 4 or 5 x 0). On large

chart paper, have each group write down their O fact, write a situation to go with it, draw an illustration, and find the answer.

4. Hang up the illustrations. Ask students what patterns they notice when we multiply by zero. If they struggle

finding the pattern, write down some of the facts they illustrated on the board, and ask, what do all the multiplication facts we created using 1 have in common? Or can you finish my statement “When I multiply a number by zero _______.”? The key is to ask questions to help students discover that when you multiply by 0 the answer is zero.



______ x 0 = ______

There are six nests for chickens. I went to collect the eggs. Each nest was empty. How many eggs were

there?



0 x ______ = ______

Jim went to buy three red shirts. There were no red shirts on the shelf. How many red shirts were

there?



Zero Facts – Another Model

Objective: Students will be able write a number sentence given a real world problem. Activity Type: Whole Class and group activity Materials:

5 transparent cups

20 chips Directions:

1. Place 5 cups in a row in the front of the class. 2. Select a student to place 4 chips in each cup. Invite the students to suggest a food item (such as a lollipop) that

each chip could represent. Ask a volunteer to write a multiplication sentence to model the number of lollipops (5 x 4 = 20).

3. Say, one lollipop goes missing from each jar every night. Remove one chip from each cup. Ask, how many

lollipops are there now? How do we know? What multiplication sentence could we write to represent the amount of lollipops left now? (5 x 3 = 15).

4. Repeat the previous steps until no chips remains in each cup. Ask, how many lollipops are there total now? How

many lollipops in each group? What number sentence can we write to describe this situation? (5 x 0 = 0).

5. Repeat this activity with other numbers of chips and a new situation.



The Zero Risk Game

Objective: Students will be able to multiply numbers by 0 and 1. Activity Type: Pairs activity Materials:

Game board laminated or in a plastic sheet protector for each student

Cube with the numbers 0, 0, 1, 1, 1, and 1 on the faces

Dry erase marker Directions:

1. The first player rolls the cube and spins the spinner.

2. The player multiplies the number on the cube by the number on the spinner. They then write down the produce in the round 1 box.

3. The player can then choose to end their turn or roll and

spin again to get a new product. They write the new product beside the first product in the round 1 box. The player can continue to roll and spin as long as they want and can choose to stop when they want. But, if a student has a product of 0 they lose their score for the entire round. If they stop the round, before they get a product of 0, then they add up their score for that round.

4. Each of the other players has a turn at round 1

(continuing with the same directions as in step 3).

5. At the end of ten rounds, each player adds their ten final products. The player with the greatest total wins.

Connection to Probability: As students are playing this game and in discussion afterward, ask question such as:

Which numbers have an equal probability of being rolled/spun in this game?

Which numbers are you less likely to roll/spin?

Which numbers are you most likely to roll/spin?

What is the probability of rolling/spinning a 2?

What is the probability of rolling/spinning a 1?



The Zero Risk Game

Round Score Total Round Score

Round One

Round Two

Round Three

Round Four

Round Five

Round Six

Round Seven

Round Eight

Round Nine

Round Ten

Total Score

Final Total



1

0

1

0 1 1

Cube or Spinner for The Zero Risk Game



Zero and One Product Game

Objective: Students will be able to multiply numbers by zero and one. Activity Type: Groups of 2‐4 students Materials: (each group needs)

Game board

Spinners (1‐6 and 0 and 1 spinner)

Different color chip for each player Directions: Object of Game: To be the first player to land on the end space.

1. The first player spins both spinners and multiplies the two numbers. They then move their chip to the nearest space with that product. The next player spins the spinners, finds the product, and then moves their chip to the nearest space with that product. If the nearest space with their product has an opponent’s chip on it – they send their opponent back to start and they take that space.

2. Players continue spinning, multiplying, and moving their chip until one player lands on the last space (0). The

first person to reach the last block on the board wins.



Zero and One Product Trail

0

6

3

1

5

2

0

4

3

0

6

1

4 0 5

2

1

0

6

0

4

1

0

5

6

1

2 0 1

0

3

0

6

2

4

5

1

0

0

3

5 2 0

0

2

3

6

5

4

6

0

1

3

2

6 4 3

4

5

2

4

0

6

0

3

0

2

5

0 4 0

3

0

5

1

0

6

5

0

3

0

1

0

Start

End

Short Cut

Short Cut



Zero and One Product Trail Spinners



00

Zeros Facts

10

Zeros Facts

20

Zeros Facts

30

Zeros Facts

40

Zeros Facts

50

Zeros Facts

60

Zeros Facts

70

Zeros Facts

80

Zeros Facts

90

Zeros Facts

01

Zeros Facts

02

Zeros Facts



03

Zeros Facts

04

Zeros Facts

05

Zeros Facts

06

Zeros Facts

07

Zeros Facts

08

Zeros Facts

09

Zeros Facts



Nines Facts

Facts with a factor of 9 include the largest products but can be the easiest to learn. There are many patterns that are fun to discover. Here are three patterns:

The tens digit of the product is always one less than the “other factor (the one other than 9). The sum of the 2 digits in the product is always 9.

The sum of the 3 digits in the product is always nine.

Use your 10 fingers as a tool. For single digit multiplication we always mark the Number by folding the finger down as a marker (referred to as the “space” between the digits). In this example 3 x 9, the third finger was bent. So the answer to the first digit is the # of fingers before the bend which is 2 and the second digit is the # of fingers after the bend which is 7, therefore the answer for 3 x 9 is 27.

0 1 2 3 4 5 6 7 8 9

0 0

1 9

2 18

3 27

4 36

5 45

6 54

7 63

8 72

9 0 9 18 27 36 45 54 63 72 81



Nines Facts

Nine is faster to compute, if at first you overshoot. Here’s a very clever tack,

do 10 times and then subtract!




x9 Dot Cards

Objective: Students will use arrays to connect the tens facts to the nines fact. Activity Type: Whole Class, Small Groups, or Individuals Materials: Dot cards (cut out and laminated) Directions: Note on card assembly: After the cards are cut out and laminated, fold the cards as indicated by the pictures below (and the dotted line on the pattern) to show the relationship between x10 and x9. x10 fact x9 fact

1. Hold the card with both flaps folded out (so that both x10 and x9 show at the same time). Ask, what do you see?

How can you figure out the total number of dots?

2. Fold the flaps to show the x10 fact (as shown in the picture to the left, above). Discuss the number sentences that describe the array.

3. Fold the flaps to show the x9 fact (as shown in the picture to the right, above). Encourage the idea of using the

known tens fact to figure out the nines fact (find x10 and subtract 9).

4. Draw attention to the two expressions (9 x 7 and 7 x 9) and ask, how do we describe the dots when they positioned this way? (9 rows of 7). Rotate the card 90 degrees and repeat the question. This time they should respond “7 rows of 9”. Ask, what fact would you use to figure out the number of dots? Answers will vary.



x9 Dot Cards

10 x 1 = _____ = 1 x 10

9 x 1 = _____ = 1 x 9



x9 Dot Cards

10 x 2 = _____ = 2 x 10

9 x 2 = _____ = 2 x 9



x9 Dot Cards

10 x 3 = _____ = 3 x 10

9 x 3 = _____ = 3 x 9



x9 Dot Cards

10 x 4 = _____ = 4 x 10

9 x 4 = _____ = 4 x 9



x9 Dot Cards

10 x 5 = _____ = 5 x 10

9 x 5 = _____ = 5 x 9



x9 Dot Cards

10 x 6 = _____ = 6 x 10

9 x 6 = _____ = 6 x 9



x9 Dot Cards

10 x 7 = _____ = 7 x 10

9 x 7 = _____ = 7 x 9



x9 Dot Cards

10 x 8 = _____ = 8 x 10

9 x 8 = _____ = 8 x 9



x9 Dot Cards

10 x 9 = _____ = 9 x 10

9 x 9 = _____ = 9 x 9



x9 Dot Cards – Finding the Patterns

Use this activity if students are struggling to make the connection between x9 and x10.

Objective: Students will use arrays to connect the tens facts to the nines facts. Activity Type: Whole Class, Small Groups, or Individuals Materials: Dot cards (cut out and laminated) Directions:

1. Write the number sentences shown on the next page on the board/projector. Work with the class/group to complete the first three sentences then ask, what patterns do you notice? The students should be able to see how the amount to subtract is the same as the factor other then 10.

2. Direct each student to copy and complete all of the number sentences and write their own rule to describe the

pattern.



x9/x10 Pattern

9 = ___ x 10 ‐ ___

18 = ___ x 10 ‐ ___

27 = ___ x 10 ‐ ___

36 = ___ x 10 ‐ ___

45 = ___ x 10 ‐ ___

54 = ___ x 10 ‐ ___

63 = ___ x 10 ‐ ___

72 = ___ x 10 ‐ ___

81 = ___ x 10 ‐ ___



Three for All x9

Objective: Students will use strategies to multiply by nine. Activity Type: Groups of 2 students Materials: (Each group will need)











81

10 9 6 9 9 5 3 6

9 4 9 9 2 9 9 9

6 9 7 1 9 9 8 2

9 2 9 9 9 4 9 9

2 9 9 4 7 9 6 10



Once Around x9 Game



Game board




Variation:

On each turn have students draw a picture of the multiplication problem they have to solve on their turn in addition to finding the answer.



09

Nines Facts

19

Nines Facts

29

Nines Facts

39

Nines Facts

49

Nines Facts

59

Nines Facts

69

Nines Facts

79

Nines Facts

89

Nines Facts

99

Nines Facts

90

Nines Facts

91

Nines Facts



92

Nines Facts

93

Nines Facts

94

Nines Facts

95

Nines Facts

96

Nines Facts

97

Nines Facts

98

Nines Facts



Helping Facts

The Helping Facts are the remaining 25 multiplication facts. It is worth pointing out that there are only 15 facts remaining to master because 20 of them consist of 10 pairs of turnarounds. These facts can be learned by relating each to an already known fact or a helping fact. For example, 6 x 7 can be found by 5 x 7 and adding 7 more. There are many ways for children to use a helping fact to find a fact they do not know. Encourage students to explain their thinking and talk about the facts they believe can help them.

0 1 2 3 4 5 6 7 8 9

0

1

2

3 9 12 18 21 24

4 12 16 24 28 32

5

6 18 24 36 42 48

7 21 28 42 49 56

8 24 32 42 56 64

9



If You Didn’t Know

Objective: Students will be able to identify strategies to find the 25 remaining helping facts. Activity Type: Whole Class Materials:

Problem

Array Model Directions:

1. On the overhead/projector pose the following questions: If you didn’t know the answer to 6 x 8 (or any fact that you want students to think about), how could you figure it out by using something that you do know?

2. Let students know that their strategy should be something that they can do in their head and should not rely on

counting.

3. Provide students with copies of the ten‐by‐ten dot dot array. The lines in the array make counting the dots easier and often suggest the use of fives facts as helpers.

Extension:

Use this problem or a problem similar to this one to prompt a strategy (Even thought you are looking for students to half‐then‐double, accept any reasonable thinking strategy.)

“Carlos and Jose kept their baseball cards in albums with 6 cards on each page. Carlos had 4 pages filled, and Jose had 8 pages filled. How many cards did each boy have? “



If you didn’t know the answer to 6 x 8, how could you figure it out by using something that you do know?



Ten‐by‐Ten Dot Array



Carlos and Jose kept their baseball cards in albums with 6 cards on each page. Carlos had 4 pages filled, and Jose had 8 pages filled. How many cards did each boy have? Be sure to explain how you know your answer is correct.



Threes Facts

Three is as easy as can be, if you triple what you see.

In other words just add it thrice, this simply is one more than twice.




Once Around x3 Game



Game board




Variation:

On each turn have students draw a picture or use manipulatives to show their problem.



Fours Facts

Four is very fast to do, When you multiply by 2. Here’s a little good advice‐

Please just always double twice!




Fours Facts Introduction

Objective: Students will be able to use the double and double again strategy to find fours facts. Activity Type: Whole Group Materials: (each group will need)

1 sheet of white paper for each student

Paint brush and paint or Bingo Dobbers Directions:

1. Give each student a sheet of white paper, paint brush/sponge, and paint.

2. Have students fold the paper in half, long ways, and then in half again.

3. Tell students that by folding the paper we are making equal groups. Ask them how many equal groups we have made by folding the paper 2 times (4).

4. Ask them to choose a number between 3 and 9 and paint that many dots down the left‐hand side of the sheet.

5. Next, before the paint dries, fold the paper over immediately to the right of the dots. Ask the student to unfold

the paper and tell you how many groups of dots they have now. Ask students what number sentence they could use to represent the first fold – (x2 or double the original number).

6. Have them fold the paper again, this time in half, and ask the students how many dots they have now.

7. Create the chart below on large paper, the board, or put it on your document camera (template on the next

page). Have several students come up and fill in the results of their paper folding/painting. Have students examine the chart for patterns. Ask questions to help students see that multiplying by 4 can be solved by doubling the number in each group two times.

# Dots in 1 Group

# of Dots in 2 Groups

(x2)

# of Dots in 4 Groups

(x4)

Multiplication Sentence

Product

3 6 12 4 x 3 12



Multiply by 4 Pattern Chart

# of Dots in 1 Group

# of Dots in 2 Groups (x 2)

# of Dots in 4 Groups (x 4)

Multiplication Sentence

Product

What patterns do you notice in the chart that could help you multiply by 4?



Double, Double Four in a Row

Objective: Students will be able to use the double and double again strategy to find fours facts. Activity Type: Groups of 2 Materials: (each group will need)

1 Game Board

2 colors of counters (1 color for each student)

1 number spinner

1 double, double spinner

Recording sheet for each student Directions:

1. Players take turns spinning both spinners. If they spin 3 double they need to first fill in their spin on their recording sheet, and then cover the space on the board which answers their spin. (Note: the recording sheet is important so that students can see that when they double this is a x2 fact and when they double, double it is a x4 fact.)

2. If the space is already covered by another player, that player can choose to remove their opponents chip and place their chip in that spot or they can choose another space on board to cover, as long as they can state the multiplication fact to claim that space.

3. The first player to cover 4 spaces in a row wins.



Double, Double Four in a Row

2 14 20 8

24 6 18 4

8 20 36 10

32 40 12 28

16 4 16 12



Double, Double Four in a Row Spinners



Double, Double Four in a Row Student Recording Sheet

Number on Spinner

Fill inD for Double

DD for Double, Double

Multiplication Expression

Product



Triple Tac Toe

Objective: Students will be able to use helping facts to multiply. Activity Type: Groups of 2 Materials: (each group will need)

Triple Tac Toe Board in a clear sheet protector or laminated

Dry Erase Markers (1 color for each player) Directions:

1. Players take turns choosing a square and solving the problem. If that answer is on any other triple‐tac‐toe boards, the player puts an x/o through the squares with the same answer.

2. The first player to get three x/o’s on a board wins and receives 1 point.

Continue as many games as desired or until time runs out. The winner is the player who has the most points when time has run out.



Sixes Facts

Six is pretty quick to do, just multiply by 3 then 2.

If this sounds like too much trouble, triple first before you double.




Using Fives Facts to Find the Sixes Facts

Objective: Students will explore the relationship between the fives and sixes multiplication facts. Activity Type: Whole group or cooperative groups of 4. Materials:

Snap cubes

X5 and x6 word problems sheets in plastic sheet protectors

Dry erase marker and eraser

Recording Sheet Directions: Introduction to the exploration:

1. Talk to students about the fact that sometimes our facts for one multiplication fact can help us find others. For example, x5 and x10. If you taught the lesson on the relationship between x5 and x10 bring the chart of patterns back out so that students can see how finding the relationships between facts can help you learn other facts.

2. Tell students that today they are going to look for patterns between x5 and x6. Pose the following question to them: What are the patterns that you notice when you multiply one number by 5 and then the same number by 6?

3. Show students an example. Ask them to pick a number to fill in on both the x5 and x6 sheet. Model using the

cubes to build the groups. Fill in the corresponding chart.

4. Have student in small groups fill in as many numbers as they can (suggest using less than 11 objects in each bag).

5. When they finish the exploration, ask students to look at their recording sheet and talk about the patterns of 5 answers, the patterns of 6’s, and the relationship between the 2 facts.

6. At the end of the exploration, put one of the group’s recording sheets up on the document camera. Talk about

the patterns. The goal is to have students see that the x6 fact is just the number in the group more than the 5’s fact. For example 6 x 7 is just 5 x 7 + 7. Other helping fact suggestion: This lesson can be done with any of the helping facts by modifying the word problem sheet. For example change the x6 page to be x4 and look at the relationship between x5 and x4.



You have 5 bags of candy to give to your friends. You put _____ pieces of candy in each bag. How many pieces of candy do you have all

together?

______ x ______ = ______



You have 6 bags of candy to give to your friends. You put _____ pieces of candy in each bag. How many pieces of candy do you have all

together?

______ x ______ = ______



Fives and Six Fact Recording Sheet

Number in each bag

x5 Fact x5

Productx6 Fact

x6 Product

What do you add to the fives fact to equal

the sixes fact?

What patterns do you see in the fives and sixes facts? How does the fives fact help you find the sixes fact?



Multiply by Six Rummy

Objective: Students will use multiplication strategies to multiply by 6. Activity Type: Groups of 2‐4 students Materials:

Copy each page of cards several times (at least 3 times) Directions:

1. Shuffle cards and deal 8 cards to each player. All remaining cards will be played face down, in a pile, in the middle of the table. Turn the top card of the face down pile up beside the pile. This is the discard pile.

2. The object of the game is to make as many six facts as you can and be the first player to get rid of all of their cards.

3. On each turn a player can either draw a card from the face down pile or take a card(s) from the discard pile. If the player takes a card(s) from the discard pile they must use them in a “run of cards” (3 or 4 in a run).

4. The player then can lay down a run of 3 or 4 if they have one (on the table in front of them so all players can see it). If they don’t have a run of 3 or 4 they have to discard one of their cards. The player’s turn ends when they discard a card.

5. Players continue pulling cards, trying to lay a run of 3 or 4, playing on another student’s run of 3, and discarding until a player discards his/her last card.

6. After one of the players discards their last card players get 1 point for each card they have in a run of 3 or 4 or played another student’s run. If students still have cards in their hand, they lose 1 point for each card they have.

7. Play as many rounds as time allows or until someone has 25 points. Clarifications A run of 3 cards = 3 representations of a sixes fact.

Examples of a run of 3 cards: dot card (that shows 3 rows of 6), 3 x 5 and 3 x 6 dot card (that shows 3 rows of 6), 3 x 6 and 18 dot card (that shows 3 row or 6), 3 x 5 and 18 3 x 5, 3 x 6, and 18

A run of 4 cards = all the cards to represent a sixes fact.

Examples of a run of 4 cards: Dot card (that show 4 rows of 6), 4 x 5, 4 x 6, and 24

Playing on another student’s run of 3 = If a student has the final card in another student’s run of 3, they may declare they run it belongs with and then keep the card in front of them. Pulling from the discard pile = If a student decides to take a card from the discard pile, they have to take all the cards in front of the card they want and must use the last card in a run. For example, if the 4th card back in the discard pile is 4 x 5 and a student needs this to make a run, they would pull the 4 x 5 and the 3 cards in front of it. They would then play this card with the other 2 or 3 cards to make a run. Students still must discard a card to end their turn.



9 x 5

related fact

8 x 5

related fact

7 x 5

related fact

6 x 5

related fact

5 x 5

related fact

4 x 5

related fact

3 x 5

related fact



9 x 6 sixes fact

8 x 6 sixes fact

7 x 6 sixes fact

6 x 6 sixes fact

5 x 6 sixes fact

4 x 6 sixes fact

3 x 6 Sixes fact



54

48

42

36

30

24

18



Cover Up Multiply by Six

Objective: Students will use multiplication strategies to multiply by 6. Activity Type: Groups of 2 Materials:


Game board


1. On their turn, players spin the spinner . Then they multiply the number on the spinner by number six and then cover one space on the board that matches that product.

2. Players continue taking turns spinning and marking their quotient until all the spaces are filled. If there are no

more spaces for a student’s product, they lose their turn.

3. At the end the student with the most chips, wins.

Variations: The first player to get six in a row wins. If a player spins a product that is already covered, they may choose to

remove their opponents chip or they may state another problem (of their choice) and cover the product.



30 6 0 36 42 54 12

48 24 54 18 24 12 6

0 30 12 48 36 42 48

42 18 0 6 18 24 36

18 36 30 42 54 0 18

12 30 6 54 48 12 30

42 48 24 36 6 24 54Adapted from Basic Games by Marcy Cook



Helping Facts: Be Productive Game x6

Objective: Students will use the helping facts to multiply by 6. Activity Type: Groups of 2 students Materials: (each group will need the following)

Game board inside a clear plastic sheet protector (by placing the game board into a plastic sheet the student can write on it with a dry erase marker allowing the game to be player many times on 1 board).


Paper Clip for spinner

Directions:

1. The first player spins the spinner (with a paper clip and pencil) and multiples the number on the spinner by 6. The student then states the multiplication fact and the product. The student then crosses off that product.

2. Play continues until a player has crossed off all the numbers. The player that crosses off all the numbers on their

side of the board first, is the winner.



Be Productive x6

24

42

6

36

54

18

60

48

30

12 12 24 48

60

6 42

30

18

54

36



Eights Facts

Eight is very much like four, simply double but once more. Since 2 times 2 times 2 is 8,

double three times works out great!




Once Around x8 Game



Game board


1. On their turn, students spin the spinner and state the problem and product. They then move their marker to the next square on the game board with that product.


Variation:

On each turn have students draw a picture or use manipulatives to show their problem.



Helping Facts: Be Productive Game x8

Objective: Students will use the helping facts to multiply by 8. Activity Type: Groups of 2 students Materials: (each group will need the following)




Directions:

1. The first player spins the spinner (with a paper clip and pencil) and multiples the number on the spinner by 8. The student states the multiplication fact and the product. The student then crosses off that product.


side of the board, first, is the winner.



Be Productive x8

80

72

64

56

48

40

32

24

16

8 8 16 24

32

40

48

54

64

72

80



Helping Facts: Be Productive Game x6 and x8

Objective: Students will use the helping facts to multiply by 6 and 8. Activity Type: Groups of 2 students Materials: each group will need the following




Blank Number cube labeled: 6, 6, 6, 8, 8, 8

Directions:

1. The first player spins the spinner (with a paper clip and pencil) and rolls the number cube. The student states the multiplication fact and the product. The student then crosses off that product.





Be Productive x6 and x8

48

36

24

18

42

32

48

64

56

24 48 18 32

64

56

24

42

24

48

36



Cube for Being Productive Helping Facts

6

8

8

8 6 6



Sevens Facts

Seven doesn’t take much time, even though it is a prime. Here is all you have to do,

first times 5 then add times 2.




Order, Order

Objective: Students will use helping facts to multiply numbers. Activity Type: Groups of 2 students Materials: (each group will need the following)



Spinner

Directions: Object of the game: To be the first player to have all the boxes filled with products from least to greatest.

1. The first player spins the spinner. They then multiply the number by 2 (doubles the number). 2. The player then chooses a box in which to put their product. Once a number is written in a box it may not be

moved.

3. The next player spins, multiplies, and places a number.

4. On each player’s turn they must place the product so that all of their numbers are in order from least to greatest. If they cannot place a number, they lose a turn.

5. The first player to fill all the boxes with their numbers from least to greatest wins.



Player 1 Player 2



Three for All Helping Facts

Objective: Students will use helping facts to multiply by 3, 4, 6, 7, and 8. Activity Type: Groups of 2 students Materials: (each group will need the following)











33

Helping Facts

43

Helping Facts

34

Helping Facts

63

Helping Facts

36

Helping Facts

73

Helping Facts

37

Helping Facts

83

Helping Facts

38

Helping Facts

44

Helping Facts

64

Helping Facts

46

Helping Facts



74

Helping Facts

47

Helping Facts

84

Helping Facts

48

Helping Facts

66

Helping Facts

76

Helping Facts

67

Helping Facts

86

Helping Facts

68

Helping Facts

77

Helping Facts

87

Helping Facts

78

Helping Facts



88

Helping Facts



Websites to Practice Multiplication/Division Facts

Arithmetic Four (Shodor)- http://www.shodor.org/interactivate/activities/ArithmeticFour/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc. The game is like “Connect Four.” Players must answer an arithmetic fact to be able to enter a piece of their color on the board. Operations can be selected and timer set for answering each fact. Number Invaders - http://www.mathplayground.com/balloon_invaders.html This game is like “Space Invaders.” Players choose an operation and a factor, and use the space bar and arrow keys to launch the “number (product) popper.” This game can be customized to practice specific facts (e.g. multiply by 6). Arademic Skillbuilders - http://www.arcademicskillbuilders.com/ This website includes many games to practice multiplication and division. These games contain mixed fact practice. Multiplication Hidden Picture - http://www.aplusmath.com/games/picture/MultPicture.html This game requires students to match basic facts to the answer to uncover a hidden picture. The facts in this game are mixed. Helping with Math - http://www.helpingwithmath.com/by_subject/multiplication/mul_games.htm - There are several games here for students. This game can be customized to practice specific facts (e.g. multiply by 6). Apples in the Basket - http://www.kidsnumbers.com/apple-baskets-multiplication.php This game uses baskets of apples to how the concrete basis of multiplication. This game can be customized to practice specific facts (e.g. multiply by 6). Fruitshoot Multiplication - http://www.sheppardsoftware.com/mathgames/fruitshoot/fruitshoot_multiplication.htm Students have to shoot fruit that answer the shown multiplication problem. This game can be customized to practice specific facts (e.g. multiply by 6). Aquatic Speedway - http://www.multiplication.com/flashgames/aquaticspeedway.htm In this game students race sea animals by answering multiplication problems. This game can be customized to practice specific facts (e.g. multiply by 6). Product Game - http://illuminations.nctm.org/ActivityDetail.aspx?id=29 This game is a computerized version of the original “Four in a Row” game. This game can be customized to practice specific facts (e.g. multiply by 6).



Mixed Strategies Multiplication Activities



Multiplication Fact Sorts Objective: Students will be able to identify the strategy given a multiplication sentence. Activity Type: Whole Group Note: These are various ways for students to sort multiplication facts. Strategy Groups: Twos Facts (Doubles), Fives Facts, Nines Facts, Zeros and Ones Facts, and Helping Facts Sort and Stand – Distribute a basic fact to each student. Then call out a strategy and have the students stand if their fact can be solved using that strategy. Have each student say the fact and the answer. Sort and Find – Post the basic fact strategies around the room. Distribute a basic fact to each student. On the count of three have the students find the basic fact strategy that matches their basic fact and stand under the sign. Have students begin trading cards while the teacher plays music. When the music stops, the students take the new card they have and go stand under the fact strategy they would use to solve their problem. Graffiti Sort – Hang up one large sheet of chart paper for each of the fact strategies. Put students into 5 groups. Each group will begin at one of the posters with every student using a different color marker. When music begins students, without talking, each write down 1 fact (and the product) that could be solved with that strategy. When the music stops, students switch to the next poster. The teacher continues rotating groups until each group has been to each poster. When finished, have a whole group discussion to determine if each of the number sentences fit the strategy.



Spinning Fact Sort Objective: Students will be able to identify the strategy given a multiplication sentence. Activity Type: Group of 2‐4 students Materials:

Spinners

Each student needs a Spinning Fact Sort Game Board in a clear sheet protector or laminated

Dry erase marker Directions:

1. Spin the two spinners to find the fact. 2. Write the fact under the strategy needed to solve the problem.

3. The first student to have 3 facts in each box wins.



Spinning Fact Multiplication Sort

Twos Facts ~ Doubles

Fives Facts

Nines Facts

Zeros and Ones Facts

Helping Facts



Multiplication Four in a Row Objective: Students will be able to use multiplication strategies to solve problems. Activity Type: Group of 2‐3 students Materials: (each group will need)

2 paper clips

Game board

Counters/Chips – different color for each student Directions:

1. The first player covers two numbers below the board with the paper clips and then covers the product with one of his/her markers.

2. At each succeeding turn, each player may move only one paper clip, and then the player covers the

corresponding product with his/her marker. Students may stack the 2 clips on 1 number to form a problem like 2 x 2, 3 x 3, etc….

3. The first player to get four in a row wins.



Product Four in a Row

1 2 3 4 5 6

7 8 9 10 12 14

16 18 15 21 24 27

20 28 32 36 25 30

35 40 45 42 48 54

49 56 63 64 72 81



Buzz, Buzz Objective: Students will be able to identify multiples of a given number. Activity Type: Group of 4‐10 students Materials: none Directions:

1. Students will need to sit in a circle. 2. The teacher states a number (e.g. 4) and students begin to count off, each saying one number; however, they

cannot say any number that is a multiple of 4. Then there is a multiple of 4, that student must say “buzz” (e.g. 1, 2, 3, buzz, 5, 6, 7, buzz, etc..) Students continue until the teacher says “stop”.

Variation:

When students are proficient with “buzz”, the teacher might add another multiple and students must say “beep” for that one. If a number is a multiple of both, the student would need to say “buzz‐beep”.

Double Dice Multiplication Objective: Students will be able to use strategies to multiply numbers. Activity Type: Groups of 2 students Materials:

4 Number cubes (1‐6 for facts up to 6 or 0‐9 cubes for facts up to 9)

Chips/counters Directions:

1. Students each roll 2 cubes. They multiply the numbers they roll. The students compare the products and the player with the largest product receives a chip.

2. Each round continues the same way (students roll dice, multiply, and award a chip to the player with the

greatest product). At the end of the allotted time, the player with the most chips wins.



Multiplication Yahtzee Objective: Students will be able to use strategies to multiply numbers. Activity Type: Groups of 2 students Materials: (each group will need)

Two 9‐sided Number Cubes or 2 spinners labeled 0‐9

Game board in a clear sheet protector or laminated

Dry erase makers Directions:

1. Player 1 rolls the 2 dice and multiplies the two numbers together. Next, the player writes the problem and the product on the appropriate line on their game board (i.e. 4 x 7 = 28 would be written beside 20‐29).

2. Player 2 rolls the 2 dice and continues as in step one. If the student rolls something they already have

filled in, they lose their turn. The first player to fill up all their spaces wins.



Multiplication Yahtzee

Player 1 Player 2

0‐9

10‐19

20‐29

30‐39

40‐49

50‐59

60‐69

70‐79

80‐89

90‐99



Multiplication Mania Objective: Students will be able to use strategies to multiply numbers. Activity Type: Groups of 2 students Materials: (each group will need)

Multiplication Mania Game Board

Digit cards

Chips/counters – one color for each player Directions:

1. The cards are shuffled and five cards are dealt to each player. The remaining cards are placed face down in a center stack.

2. The first player multiplies the numbers on their cards and claims the answer on the game board by covering it

with a counter/chip. If, during the game, all possible answers are unavailable, the player misses a turn.

3. The player must show the cards used to make the answer. These cards are then discarded to one side. These are reshuffled and used again if needed.

4. The player then draws two new cards. If a student draws a wild card they may use this card for any number.

When a player uses the wild card, they say, “The Wild Card will be a 5” (or any number).

5. Each of the other players has a turn.

6. The first player to make a 2 x 2 square or a line of four counters in a row is the winner.



Multiplication Mania

1 2 3 4 5 6

7 8 9 10 11 12

15 16 18 20 21 24

25 27 28 30 32 35

36 40 42 45 48 49

54 56 63 64 72 81

6 12 24 36 48 56



Double Doom

Objective: Students will be able to use strategies to multiply numbers (1‐6 facts). Activity Type: Groups of 2 students Materials: (each group will need)

Hundreds Board

2 number cubes (1‐6) Directions:

1. Each player starts at 0. On your turn, you roll two dice and multiply the numbers together. You move forward

that number of spaces on the hundreds chart. If you roll doubles, you have to go back to zero!

2. Players take turns rolling, multiply, and then adding that product to their total until a student reaches or passes

100. The first student to reach to pass 100 wins.



Double Doom Hundreds Board

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100



BingTac Objective: Students will be able to use strategies to multiply numbers. Activity Type: Groups of 2 students Materials: (each group will need)

Multiplication board (1 copy needed for each game)

2 spinners

1 colored pencil for each player Directions:

1. Each player chooses one colored pencil/marker. The first player spins the spinners. Using the colored pencil, the player records this product in one of the appropriate boxes on the game sheet. For example if the player rolls 5 and 7, the player may record the product (35) in the box designated by 5 x 7 or 7 x 5.

2. If all the appropriate products boxes have been used, the player loses that turn. If a player records a product incorrectly, the player must erase the incorrect product and then they lose that turn.

3. When doubles are thrown, the player records the product and rolls again. 4. Players take turns rolling the dice (spinners) and recording products. The first player with six recorded products

in a row, column, or diagonal is the winner. Variation

1. The numbers on the dice and on the board may be varied. 2. Bingtac may be played as an addition game in which the sum of two dice are recorded.



BingTac

x 0 1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

8

9



BingTac Spinners



Children’s Literature Multiplication

P = K‐2 I = 3‐5

Title Author Year Level

Amanda Bean’s Amazing Dream Cindy Neuschwander 1998 P/I

Anno’s Magic Seeds Anna 1995 I

Anno’s Mysterious Multiplying Jar Anno 1983 I

Bunches & Bunches of Bunnies Louise Mathews 1978 P/I

Each Orange Had 8 Slices Paul Giganti, Jr. 1992 P/I

A Grain of Rice Helena Clare Pittman 1986 I

The King’s Chessboard David Birch 1998 I

Minnie’s Diner Doyle Ann Dodds 2004 I

One Hundred Hungry Ants Elinor J. Pinczes 1993 P/I

One Hundred Seagulls Makes a Racket Betsy Franco 2003 P/I

One Riddle, One Answer Lauren Thompson 2001 I

Pigs Go to Market Amy Acelrod 1997 I

Stacks of Trouble Martha F. Brenner 200 P/I

Too Many Cooks! Andrea Buckless 2002 P/I

Too Many Kangaroo Things to Do! Stuart J. Murphy 1996 P/I

Twins Betsy Franco 2003 P/I

Two of Everything Lily Toy Hong 1993 P/I

2 x 2 = Boo Loreen Leedy 1995 I

What Comes in 2’s, 3’s, and 4’s? Suzanne Aker 1990 P/I



Division Basic Fact Strategies

Office of Elementary Education Draft 2

2009‐2010



Division Fact Acquisition

It is important that students have a mastery of multiplication facts before beginning division facts. Additionally, an understanding of the connections between multiplication and division is key to the acquisition of division facts. One such vehicle to making these connections are word problems. It is important to note that in “real world” settings, division often involves remainders. Early exposure to the concept of remainders or “left over” is important to building a foundation for more complex division. On the following pages you will find several lessons to help begin to connect multiplication and division. Additionally you will find assessments for each of the types of division facts (twos, fives, ones, etc….) to help diagnose which facts students need to work on. If you find that a student is struggling with a particular set of division facts go back to that particular multiplication strategy to determine if they are fluent with the multiplication facts for that strategy before working on the division facts. The layout of this section parallels the multiplication section: assessment, introductory lessons, and activities to support each division strategy.



Types of Division Problems

Researchers have separated division problems into categories based on the kinds of relationships involved. These structures represent different types of thinking about division. Students do not need to be taught this vocabulary (partition and measurement) but it is beneficial to teachers to understand the different thought processes associated with these structures.

Partition/Partitive (fairsharing) ‐ The number of groups is known, the number in each group is unknown. Mark has 24 apples. He wants to divide them equally into 4 bags (to give to his 4 friends). How many apples will be in each bag? Jake has 36 pieces of candy. He wants to divide them equally between 6 of his friends. How many pieces of candy will each friend receive? Richard has 40 matchbox cars. He wants to put the same number of cars on each of his 4 shelves. How many cars will he put on each shelf?

Measurement (repeated subtraction) ‐ The number in each group is known, the number of groups is unknown. Mark has 24 oranges. He put them into bags containing 6 oranges each. How many bags did Mark use? Jake has 36 pieces of candy. He is going to give each friend 6 pieces of candy. How many friends will receive candy? Richard has 40 matchbox cars. He wants to display them on shelves. If he puts 4 cars on each shelf, how many shelves will he need?

Van de Walle K‐3 pg. 78



Alternate Set of Division Assessments

Timing: 3 seconds per question



Student Tracking Chart ‐ Division

Students

Twos Facts

Fives Facts

Zero and Ones Facts

Nines Facts

Helping Facts

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25



Name: __________________________________


6 ÷ 2 = ___ 18 ÷ 2 = ___

16 ÷ 8 = ___ 12 ÷ 6 = ___

2 ÷ 1 = ___ 6 ÷ 3 = ___

4 ÷ 2 = ___ 8 ÷ 2 = ___

14 ÷ 2 = ___ 16 ÷ 2 = ___

18 ÷ 9 =___ 12 ÷ 2 = ___

8 ÷ 4 = ___ 14 ÷ 7 = ___

2 ÷ 2 = ___

Name: __________________________________


6 ÷ 2 = ___ 18 ÷ 2 = ___

16 ÷ 8 = ___ 12 ÷ 6 = ___

2 ÷ 1 = ___ 6 ÷ 3 = ___

4 ÷ 2 = ___ 8 ÷ 2 = ___

14 ÷ 2 = ___ 16 ÷ 2 = ___

18 ÷ 9 =___ 12 ÷ 2 = ___

8 ÷ 4 = ___ 14 ÷ 7 = ___

2 ÷ 2 = ___

Name: __________________________________


6 ÷ 2 = ___ 18 ÷ 2 = ___

16 ÷ 8 = ___ 12 ÷ 6 = ___

2 ÷ 1 = ___ 6 ÷ 3 = ___

4 ÷ 2 = ___ 8 ÷ 2 = ___

14 ÷ 2 = ___ 16 ÷ 2 = ___

18 ÷ 9 =___ 12 ÷ 2 = ___

8 ÷ 4 = ___ 14 ÷ 7 = ___

2 ÷ 2 = ___

Name: __________________________________


6 ÷ 2 = ___ 18 ÷ 2 = ___

16 ÷ 8 = ___ 12 ÷ 6 = ___

2 ÷ 1 = ___ 6 ÷ 3 = ___

4 ÷ 2 = ___ 8 ÷ 2 = ___

14 ÷ 2 = ___ 16 ÷ 2 = ___

18 ÷ 9 =___ 12 ÷ 2 = ___

8 ÷ 4 = ___ 14 ÷ 7 = ___

2 ÷ 2 = ___



Name: __________________________________


20 ÷ 5 =____ 5 ÷ 1 =____

10 ÷ 2 =____ 30 ÷ 5 =____

45 ÷ 5 =____ 40 ÷ 5 =____

25 ÷ 5 =____ 35 ÷ 7 =____

5 ÷ 5 = ____ 15 ÷ 5 =____

40 ÷ 8 =____ 45 ÷ 9 =____

35 ÷ 5 =____ 10 ÷ 5 =____

15 ÷ 3 =____ 30 ÷ 6 =____

20 ÷ 4 =____

Name: __________________________________


20 ÷ 5 = ____ 5 ÷ 1 =____

10 ÷ 2 = ____ 30 ÷ 5 =____

45 ÷ 5 =____ 40 ÷ 5 =____

25 ÷ 5 =____ 35 ÷ 7 =____

5 ÷ 5 = ____ 15 ÷ 5 =____

40 ÷ 8 =____ 45 ÷ 9 =____

35 ÷ 5 =____ 10 ÷ 5 =____

15 ÷ 3 =____ 30 ÷ 6 =____

20 ÷ 4 =____

Name: __________________________________


20 ÷ 5 =____ 5 ÷ 1 =____

10 ÷ 2 =____ 30 ÷ 5 =____

45 ÷ 5 =____ 40 ÷ 5 =____

25 ÷ 5 =____ 35 ÷ 7 =____

5 ÷ 5 = ____ 15 ÷ 5 =____

40 ÷ 8 =____ 45 ÷ 9 =____

35 ÷ 5 =____ 10 ÷ 5 =____

15 ÷ 3 =____ 30 ÷ 6 =____

20 ÷ 4 =____

Name: __________________________________


20 ÷ 5 =____ 5 ÷ 1 =____

10 ÷ 2 =____ 30 ÷ 5 =____

45 ÷ 5 =____ 40 ÷ 5 =____

25 ÷ 5 =____ 35 ÷ 7 =____

5 ÷ 5 = ____ 15 ÷ 5 =____

40 ÷ 8 =____ 45 ÷ 9 =____

35 ÷ 5 =____ 10 ÷ 5 =____

15 ÷ 3 =____ 30 ÷ 6 =____

20 ÷ 4 =____



Name: __________________________________


3 ÷ 1 = ____ 6 ÷ 6 = ____

0 ÷ 7 = ____ 7 ÷ 7 = ____

0 ÷ 3 = ____ 0 ÷ 6 = ____

0 ÷ 5 = ____ 1 ÷ 1 = ____

7 ÷ 1 = ____ 9÷ 1 = ____

0 ÷ 4 = ____ 0 ÷ 1 = ____

0 ÷ 2 = ____ 0 ÷ 8 = ____

9 ÷ 9 = ____ 0 ÷ 9 = ____

6 ÷ 1 = ____ 3 ÷ 3 = ____

Name: __________________________________


3 ÷ 1 = ____ 6 ÷ 6 = ____

0 ÷ 7 = ____ 7 ÷ 7 = ____

0 ÷ 3 = ____ 0 ÷ 6 = ____

0 ÷ 5 = ____ 1 ÷ 1 = ____

7 ÷ 1 = ____ 9÷ 1 = ____

0 ÷ 4 = ____ 0 ÷ 1 = ____

0 ÷ 2 = ____ 0 ÷ 8 = ____

9 ÷ 9 = ____ 0 ÷ 9 = ____

6 ÷ 1 = ____ 3 ÷ 3 = ____

Name: __________________________________


3 ÷ 1 = ____ 6 ÷ 6 = ____

0 ÷ 7 = ____ 7 ÷ 7 = ____

0 ÷ 3 = ____ 0 ÷ 6 = ____

0 ÷ 5 = ____ 1 ÷ 1 = ____

7 ÷ 1 = ____ 9 ÷ 1 = ____

0 ÷ 4 = ____ 0 ÷ 1 = ____

0 ÷ 2 = ____ 0 ÷ 8 = ____

9 ÷ 9 = ____ 0 ÷ 9 = ____

6 ÷ 1 = ____ 3 ÷ 3 = ____

Name: __________________________________


3 ÷ 1 = ____ 6 ÷ 6 = ____

0 ÷ 7 = ____ 7 ÷ 7 = ____

0 ÷ 3 = ____ 0 ÷ 6 = ____

0 ÷ 5 = ____ 1 ÷ 1 = ____

7 ÷ 1 = ____ 9÷ 1 = ____

0 ÷ 4 = ____ 0 ÷ 1 = ____

0 ÷ 2 = ____ 0 ÷ 8 = ____

9 ÷ 9 = ____ 0 ÷ 9 = ____

6 ÷ 1 = ____ 3 ÷ 3 = ____



Name: __________________________________


45 ÷ 9 =____ 63 ÷ 7 =____

18 ÷ 2 =____ 36 ÷ 9 =____

54 ÷ 6 =____ 9 ÷ 9 = ____

72 ÷ 9 =____ 27 ÷ 3 =____

54 ÷ 9 =____ 81 ÷ 9 =____

63 ÷ 9 =____ 45 ÷ 5 =____

36 ÷ 4 =____ 27 ÷ 9 =____

72 ÷ 8 =____ 18 ÷ 9 =____

Name: __________________________________


45 ÷ 9 =____ 63 ÷ 7 =____

18 ÷ 2 =____ 36 ÷ 9 =____

54 ÷ 6 =____ 9 ÷ 9 = ____

72 ÷ 9 =____ 27 ÷ 3 =____

54 ÷ 9 =____ 81 ÷ 9 =____

63 ÷ 9 =____ 45 ÷ 5 =____

36 ÷ 4 =____ 27 ÷ 9 =____

72 ÷ 8 =____ 18 ÷ 9 =____

Name: __________________________________


45 ÷ 9 =____ 63 ÷ 7 =____

18 ÷ 2 =____ 36 ÷ 9 =____

54 ÷ 6 =____ 9 ÷ 9 = ____

72 ÷ 9 =____ 27 ÷ 3 =____

54 ÷ 9 =____ 81 ÷ 9 =____

63 ÷ 9 =____ 45 ÷ 5 =____

36 ÷ 4 =____ 27 ÷ 9 =____

72 ÷ 8 =____ 18 ÷ 9 =____

Name: __________________________________


45 ÷ 9 =____ 63 ÷ 7 =____

18 ÷ 2 =____ 36 ÷ 9 =____

54 ÷ 6 =____ 9 ÷ 9 = ____

72 ÷ 9 =____ 27 ÷ 3 =____

54 ÷ 9 =____ 81 ÷ 9 =____

63 ÷ 9 =____ 45 ÷ 5 =____

36 ÷ 4 =____ 27 ÷ 9 =____

72 ÷ 8 =____ 18 ÷ 9 =____



Name: __________________________________


12 ÷ 3 =____ 16 ÷ 4 =____

49 ÷ 7 =____ 48 ÷ 6 =____

32 ÷ 4 =____ 24 ÷ 3 =____

12 ÷ 4 =____ 64 ÷ 8 =____

21 ÷ 7 =____ 28 ÷ 4 =____

18 ÷ 3 =____ 32 ÷ 8 =____

42 ÷ 6 =____ 48 ÷ 8 =____

28 ÷73 =____ 21 ÷ 3 =____

24 ÷ 4 =____ 56 ÷ 7 =____

Name: __________________________________


12 ÷ 3 =____ 16 ÷ 4 =____

49 ÷ 7 =____ 48 ÷ 6 =____

32 ÷ 4 =____ 24 ÷ 3 =____

12 ÷ 4 =____ 64 ÷ 8 =____

21 ÷ 7 =____ 28 ÷ 4 =____

18 ÷ 3 =____ 32 ÷ 8 =____

42 ÷ 6 =____ 48 ÷ 8 =____

28 ÷73 =____ 21 ÷ 3 =____

24 ÷ 4 =____ 56 ÷ 7 =____

Name: __________________________________


12 ÷ 3 =____ 16 ÷ 4 =____

49 ÷ 7 =____ 48 ÷ 6 =____

32 ÷ 4 =____ 24 ÷ 3 =____

12 ÷ 4 =____ 64 ÷ 8 =____

21 ÷ 7 =____ 28 ÷ 4 =____

18 ÷ 3 =____ 32 ÷ 8 =____

42 ÷ 6 =____ 48 ÷ 8 =____

28 ÷73 =____ 21 ÷ 3 =____

24 ÷ 4 =____ 56 ÷ 7 =____

Name: __________________________________


12 ÷ 3 =____ 16 ÷ 4 =____

49 ÷ 7 =____ 48 ÷ 6 =____

32 ÷ 4 =____ 24 ÷ 3 =____

12 ÷ 4 =____ 64 ÷ 8 =____

21 ÷ 7 =____ 28 ÷ 4 =____

18 ÷ 3 =____ 32 ÷ 8 =____

42 ÷ 6 =____ 48 ÷ 8 =____

28 ÷ 7 =____ 21 ÷ 3 =____

24 ÷ 4 =____ 56 ÷ 7 =____



Introducing Division: The Doorbell Rang

Objective: Students will be able to represent division with manipulatives.

Students will be able to represent division with a number sentence. Students will be able to connect division facts to multiplication facts.

Activity Type: Whole class Materials: (each group will need)

The Doorbell Rang Hutchins

Counters

Activity Sheet Warm‐up: Ask students, “What does it mean if we divide something”. Share student responses. Ask students to “turn and talk” to their neighbor about reasons we would need to divide something. Let students know that you will call on students to share their partner’s response so they will need to listen carefully to what their partner says. Record some of the student responses on chart paper to post. Whole Group:

1. Read The Doorbell Rang to the class. Begin by selecting 13 volunteers to “act” as you are reading the story. Tell each of the students the name of the character that he or she will be. One student will be the doorbell ringer. (Instruct the doorbell ringer to ring the bell each time you read “as the doorbell rings.”) Instruct the actors/actresses to come up front when they hear their name in the book.

2. Read The Doorbell Rang by Pat Hutchins. Have two students start up at the front. These two students will have

to divide the 12 cookies up between themselves. Each time the doorbell rings, more students come up. Each time students need to divide the cookies among themselves. As students divide these cookies up, ask student how we could record the division with a number sentence.

3. You may want to read the book the second time and have different students “act” this time so that everyone

has the opportunity.

4. Ask students questions like, “What happened when we had to divide by more people?” , “How would you complete this sentence? “The more groups/people you have to divide by the ______” etc…

5. Have students’ complete “The Doorbell Rang” sheet. Students will use this sheet to model division as they are

showing how many cookies each of the children got in the story each time that the doorbell rang. Have students use chips to represent the cookies and then record their drawings and number sentences on their sheets. Ask students if there is a multiplication sentence that we could use to also represent our situation (to make the connection between multiplication and division).

Closure/Assessment: Pose a new question to students: “I have 48 cookies and 8 students. How many cookies will each group receive?” Ask students to model and solve using their chips. Have students check their response by using multiplication. (continued next page)



Homework: Bring in a small bag of items from home that we can divide tomorrow. Tomorrow follow up by having students bring up their items and choose students to divide the items between. After they have divided the items, then have a students use their white boards to model the situation with a division sentence.

Extend: Increase the number of cookies given to gifted children and, during independent practice, give them a more difficult problem to work.

Remediation: Allow children to use larger objects to answer simpler problems. These students may need paper plates or cups to represent each child (when they are dividing out groups).



The Doorbell Rang

People at the Table Draw a Picture to Represent the Number of Cookies

each will receive Division Sentence

Victoria and Sam

Victoria, Sam, Tom, and Hannah

Victoria, Sam, Tom, Hannah, Peter, and his

little brother

Victoria, Sam, Tom, Hannah, Peter, little

brother, Joy, Simon, and 4 cousins



How Close Can You Get? Objective: Students will be able to “think multiplication” to problems involving division.

Students will be able to connect “near facts” to “remainders”. Activity Type: Whole class Materials:

Fact Family House

Division Houses for each student

Chart paper for each small group

Markers

Cubes (the base ten units cubes work well)

Warm‐up: 1. Have students generate a list of ideas about things that we “divide” and why we might divide them. Post this list

on large chart paper (later on children can use this list to generate their own math division problems). 2. Discuss how we are not always able to divide equally; sometimes we have “left over” or a “remainder”.

Whole Group:

1. Say to the class “Suppose I have 3 boys and I will give each boy 4 pieces of candy. What multiplication sentence can I write to represent how many pieces of candy I have altogether?” (3 x 4 = 12).

2. Ask the class, “Suppose, now, I have 12 pieces of candy and I want 2 boys to share that

candy equally. Could I write a multiplication sentence for this? Is there missing information?” (Yes –> 2 x ___ = 12). Use this problem to discuss how we can also write this as a division sentence.

3. Use the fact family house to show them that the division facts can be turned around

into multiplication to help them solve division problems. Explain that Multiplication and Division are related like Addition and Subtraction. When students create the division sentences be sure to ask questions like “Why does the 12 have to be in the first box? Why doesn’t 3 divided by 12 work? Can you model that with chips?”

4. Explain to the class that today they will solve problems where things have to be divided. Sometimes these things can be divided equally and sometimes they cannot. It is their job to use their multiplication skills and strategies to help them solve these problems.

Group Work:

5. Show students the Division House and read the problem – “There are _______ toys in the attic. If we divide these toys equally among all the rooms, how many toys will be in each room?” Ask students to give you a number of toys that they want in our attic. Fill that number in and have students use their cubes to figure out how many toys would be in each room.



6. Pose the following question to each group, “When I divide the toys equally between 2 rooms, is there a pattern with the numbers that divide equally with no remainders?” Ask students to try out different numbers, record them on their chart paper, and try to find a pattern.

7. As students work, ask students questions to help find the pattern (that all even numbers divide equally).

Closure:

8. Have each group share a number that divided equally. Discuss the patterns they found and how multiplying by 2 helps them when they are dividing by 2.

Extension:

1. For groups that find the pattern, have them use a house with a different number of rooms.

2. In another lesson each group could be assigned a different house (with different numbers of rooms) to find the pattern of the answers with no remainders.



÷ =

÷ =

× =

× =



There are _______ toys in the attic. If we divide these toys equally between all the rooms, how many toys will be in each room?

÷ =Remainder or

Number of “Left Over” Toys




÷ =Remainder or




Remainder or Number of “Left

Over” Toys

There are _______ toys in the attic. If we divide these toys equally between all the rooms, how many toys will be in each

÷ =





Over” Toys ÷ =



A Remainder of One Lesson Objective: Students will be able to “think multiplication” to problems involving division. Students will be able to connect “near facts” to “remainders”. Activity Type: Whole class and small group Materials:

A Remainder of One by Elinor J. Pinczes

Counters ‐ 25 per group for the Introduction to the lesson

Counters – between 20 and 50 for the group problem solving portion of the lesson

Chart paper – for recording group work Note: 3D counters work best so that students can stand them in rows like the ants. Suggestions include bears counters, bug counters, cm cubes, or informal manipulatives such a gummy bears. But

Warm‐up/Whole Group:

1. Show the students the book A Remainder of One and ask students to predict what the title means and how it might apply to the story.

2. Read the story to students. Ask them to look for the math they see in the story. Throughout the reading, the

teacher will pause allowing for students to comment. Also, the teacher will ask the students for alternative solutions that they believe may be possible for “Joe’s” problem.

Small Group Work:

3. Give each group 25 counters. Reread the story and this time have each group model the division in the book. Ask students probing questions such as, “What patterns do you notice in the division?”, etc… Variation: If your class has 25 students, model the bug squadrons with students. Be sure to check the student’s work for understanding as they work.

4. Collect counters and put students into groups of 4. Distribute a new set of counters – 20‐50 per group or you

may want to let students choose their own manipulative.

5. After all members agree on a number of manipulatives to work with, students in the group are to find ways to create marching groups just as Joe had to do within A Remainder of One. All answers/strategies must be recorded on chart paper to share with the class.

6. The students may group in any way they wish, with any number of manipulatives they wish ranging again,

between twenty and fifty. If, when grouping the manipulatives, students have any remainders, they must state so within their recordings.

7. Throughout the problem‐solving activity, walk around the room, observing the students to make sure that all

students are staying on task and participating with their group members. Be sure to spend time with each group, asking for students reasoning, along with encouraging new strategies.

(continued on the next page)



Closure: Each group will have an opportunity to share up to five strategies that they found when working with their manipulatives. During this time, students are to also specify how many manipulatives they chose to work with. Be sure to ask those students who are not sharing their findings if they may think of a strategy that the group presenting had not thought of. Variation: If you believe your students need more structure to their problem solving feel free to use the Remainder One Variation Sheet to help guide their exploration.



Remainder One Variation

1. Figure out what would happen if 20 bugs tried to group themselves into 1 line, 2 lines, 3 lines, and so on up to 10 lines. How many bugs could be in each line? Will there be any bugs left over?

Record your answer like this: 1 line of _____ with a remainder of ____ 2 lines of _____ with a remainder of ____ 3 lines of _____ with a remainder of ____ 4 lines of _____ with a remainder of ____ 5 lines of _____ with a remainder of ____ 6 lines of _____ with a remainder of ____ 7 lines of _____ with a remainder of ____ 8 lines of _____ with a remainder of ____ 9 lines of _____ with a remainder of ____ 10 lines of _____ with a remainder of ____

2. Choose another number of bugs and do the activity again.



Remainder Race Objective: Students will be able to “think multiplication” to problems involving division.

Students will be able to connect “near facts” to “remainders”. Activity Type: Groups of 2‐4 players Materials:

1 different color counter for each player

Game board

Paperclip for spinner

Directions:

1. Each player begins by placing a marker on START (43). Numbers on the path are dividends. The number spun becomes the divisor.

2. The first player spins to determine a divisor for 43. The player then completes the division, states the resulting

division problem with the answer, and moves ahead the number of spaces equal to the remainder. Example: If 7 is spun, the player says, “43 divided by 7 equals 6 with a remainder of 1” and moves one space.

3. Players alternate turns until one player reaches or goes beyond FINISH.

Questions for discussion after the game:

Which numbers did you prefer to spin? Explain why.

Why numbers did you prefer to land on? Explain why.

What strategies did you use to find your answer?



Remainder Race

Star

t 43

30

22

47

29

15

46

31

20

37

18

24

35

44

41

27

51

23

31

42

19

28

49

38

45

57

21

50

34

48

16

29

44

32

25

40

37

43

17

23

33

51

39

35

41

26

19

47

End

36



Twos (Doubles) Facts The main strategy that will be used with division facts is division as “think multiplication”. When used in this think‐multiplication manner, the child uses known multiplication facts to find the answer. In this case students should think half when dividing by 2. If children are struggling with these facts be sure they have mastered these multiplication facts first.

÷ 0 1 2 3 4 5 6 7 8 9

0 0

1 2

2 0 2 4 6 8 10 12 14 16 18

3 6

4 8

5 10

6 12

7 14

8 16

9 18



Two’s Division Fact Lesson

Objective: Students will be able to divide numbers involving 2. Activity Type: Whole class, groups Materials:

Bags – with various even numbers of items in each bag (each group should have a different bag)

Paper plates (optional) Directions:

1. Arrange students into pairs. Distribute a bag of counters to each pair. Have a different number of counters in each bag but make sure they all have an even number.

2. Ask each pair to find out how many counters are in the bag and then divide them equally between themselves.

If desired, distribute two paper plates for students to use when dividing and organizing their counters. Allow time for students to complete this activity.

3. Select one pair of students to share what they discovered about their bag of counters. Have them share, how

many counters they had altogether and how many each person received when they divided them.

4. Ask the class if there is a number sentence that could be written to describe what happened with this pair’s bag of counters. As they share record the information on the “Pair Sharing Overhead” or chart paper. Continue allowing pairs to share and having the class give the division number sentence that fits each pairs’ set of counter.

5. Once everyone has had an opportunity to share their results, ask what pattern they see in the number sentence.

Ask what pattern students see when they divide by 2 (when dividing by 2 you are finding half). Ask students if there is a multiplication strategy that we have learned that is related to this strategy. Discuss how they can use what they know from multiplication to help them with division. You may want to use the Fact Family House here.

Closure: Ask each pair of students to make a poster for dividing by 2 to help others learn their division facts. Discuss possible illustrations they could use. Allow time for students to complete their posters and to share some.



Pairs Sharing Number of Counters

Number of People

Number of Counters each

received Number Sentence



Two Pairs Array Game

Objective: Students will be able to divide numbers involving 2. Activity Type: Groups of 2‐3 Materials:

Set of Double Array Cards

Set of Double Array Fact Directions:

1. Shuffle or mix up the cards. Spread them out on the table face down. 2. First player turns over two cards. If one is a “basic fact” and the other one the “array” that matches it, it’s a

match and the player keeps the cards if they can correctly state the quotient.

3. If it is not a match or he/she gives the wrong answer, the player puts them back face down on the table.

4. Each player takes turns trying to match the “fact” to the “array”, keeping the matches and replacing the unmatched.

5. The game ends when there are no more matches to be made.

6. The player with the most matches wins.



Two Pairs Game Fact Cards

2 ÷ 2 12 ÷ 24 ÷ 2 14 ÷ 26 ÷ 2 16 ÷ 28 ÷ 2 18 ÷ 210 ÷ 2 20 ÷ 2



Fives Facts The main strategy that will be used with division facts is division as “think multiplication”. When done in this think‐multiplication manner, the child uses known multiplication facts to find the answer. If children are struggling with these facts be sure they have mastered these multiplication facts first.

÷ 0 1 2 3 4 5 6 7 8 9

0 0

1 5

2 10

3 15

4 20

5 0 5 10 15 20 25 30 35 40 45

6 30

7 35

8 40

9 45



Nickel Fives Game

Objective: Students will be able to use multiplication strategies to help them solve division problems involving 5. Activity Type: Groups of 2 Materials:

Nickel Five Game Cards

1 Nickel Directions:

1. Flip the nickel calling “heads” or “tails”. The winner of the flip goes first. 2. Shuffle or mix up the cards. Lay face‐down on the table in six rows with five in each row.

3. Winner of the “flip” turns over three cards. If they make a Nickel Five division sentence (one that has “5” as the

divisor), the player keeps the cards. If not, he/she returns them to their places. For example, if a student picks up 15, 5, and 3 they could keep the cards by showing that 15 divided by 5 equals 3.

4. Players rotate turns trying to pick up three cards that will make fives fact.

5. The game is over when no more facts can be made. The player with the most cards wins the game.



Nickel Fives Game

1 2 3 4 5

6 7 8 9 10

5 5 5 5 5

5 5 5 5 5

5 10 15 20 25

30 35 40 45 50



Zeros and Ones Facts Students need to see the connection between multiplication and division. If students have trouble dividing by one, they do not understand the Identity Property in Multiplication (any number multiplied by 1 equals itself). Before tackling division, make sure students have a solid understanding of multiplication and the patterns it creates.

÷ 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2

3 0 3

4 0 4

5 0 5

6 0 6

7 0 7

8 0 8

9 0 9



Snap Cube Dividing Lesson

Objective: Students will be able to model division by 1 using manipulatives. Activity Type: Whole class, groups Materials:

Snap Cubes (for pairs of students)

.75 inch grid paper Directions:

1. Distribute 10 snap cubes and a piece of grid paper to each pair of students. 2. Using a document camera/overhead make a train of cubes that is 6 cubes long. Ask students to describe the

train. Student responses my include: it is 6 cubes long, it is six cubes long and one cube wide, it uses only one row of cubes, it is one by six or one row of six cubes, etc….

3. Instruct students to work with their partners and make as many different trains as possible using only one row

or one column. Explain that no train should have more than 10 cubes in it. Allow time for students to create all possible trains.

4. Instruct students to organize the trains on their desk from smallest to largest. Then ask them to look for any

patterns they might see. Students should share that they all have only one row or column of cubes; they increase by one as they get bigger.

5. Ask if anyone can think of any easy way to describe the trains using numbers and division. If necessary, ask for a

number sentence. Students should come up with “Number ÷ 1 = Number”. They may give specific examples.

6. Discuss how the train models dividing a number by one. Return to the train you made on the overhead or with cubes.

7. Ask what number sentence we would write for this train (6 ÷ 1 = 6). Repeat with several trains made by students to make sure that students see the connection between the physical model and the number sentence. The number sentence simply describes the model in numbers and symbols.

8. Instruct students to record all of their trains on the grid paper and write a number sentence for each.

Closure: Have students play Divide by 1 concentration.



Divide by 1 Concentration Cards

9 ÷ 1

8 ÷ 1

7 ÷ 1

6 ÷ 1

5 ÷ 1

4 ÷ 1

3 ÷ 1

2 ÷ 1

1 ÷ 1

9 ÷ 1

8 ÷ 1

7 ÷ 1

6 ÷ 1

5 ÷ 1

4 ÷ 1

3 ÷ 1




2 ÷ 1

1 ÷ 1

9

8

7

6

5

4

3

2

1

9

8

7

6

5




4

3

2

1



Zeros Math Mysteries

Objective: Students will be able to use multiplication strategies to help them solve division problems involving 0. Activity Type: Whole Group or Small Groups Materials:

Zeros Division Fact Stories

Directions:

1. Model the following problem with the whole group: a. There is no soda in the fridge. How many cans of soda can 3 friends each have?

2. Ask students:

a. What information do we know in this story? b. What could we draw to represent this situation? c. What number sentence could we write to solve this problem?

3. Have students read the stories and choose 3 to solve. They will draw a picture, write a number sentence, and then try to determine the pattern when dividing by 0.



Name: ________________________ Math Mysteries

Directions: Choose three number stories. On the next page, draw a picture of the story and write a number sentence. When you are finished determine what is the same about these problems.

After 5 days, Ben’s plant grew 10 cm taller while the height of Jack’s plant did not change. How much did Jack’s plant grow each day?

Matthew has no money. If three friends ask to borrow the same amount from him, how much can he give each friend?

Emma and Ashley see an empty chocolate box on the table. How many chocolates can they each have?

There are no bottles of water in the refrigerator. How many bottles of water can 5 friends each have?

The rollercoaster at Hershey Park has 6 cars. Each car was empty. How many people, in total, were on the rollercoaster?

Natasha likes to make omelets using 3 eggs each time. She has no eggs. How many omelets can she make?



Draw a picture of your story here.

What number sentence would you write to solve this problem?

What is the same about all of these number stories? What patterns do you see between the problems?







Race to 100

Objective: Students will be able to use multiplication strategies to help them solve division problems involving 0, 1 and 2. Activity Type: Small Groups of 2‐4 players Materials:

1 blank cube labeled: 2, 4, 8, 10, 16, 24 (Cube A)

1 blank cube labeled: 0, 0, 1, 1, 2, 2 (Cube B)

Each player needs a blank piece of paper to keep score. Directions:

1. The first player rolls both cubes. 2. The player divides the number rolled on Cube A by the number of Cube B. The player then adds the resulting

quotient to zero and records the total on their sheet of paper.

3. Each of the other players has a turn.

4. For each new round, the player adds the new total to their previous total so that they keep a cumulative total.

5. The first player to reach a total of 100 or more is the winner.



Cube A for Race to 100

2

10

16

4 24 8



Cube B for Race to 100

0

1

1

0 2 2



Nines Facts The main strategy that will be used with division facts is division as “think multiplication”. When used in this think‐multiplication manner, the child uses known multiplication facts to find the answer. If children are struggling with these facts be sure they have mastered these multiplication facts first.

÷ 0 1 2 3 4 5 6 7 8 9

0 0

1 9

2 18

3 27

4 36

5 45

6 54

7 63

8 72

9 0 9 18 27 36 45 54 63 72 81



Nines Division Fact Introduction Lesson

Objective: Students will be able to develop strategies to divide numbers involving 9. Activity Type: Whole Class, Groups of 2‐3 Materials:

hundreds chart for each student

patterns with Nifty Nines Warm‐up:

1. Distribute hundreds charts. Instruct students to skip‐count by nines and color each dividend of nine. Once finished, ask students to study the chart for patterns and record their ideas in their journals.

2. Display a hundreds chart on the overhead/document camera. Allow students to share the patterns they found

and discuss how they might help students remember nines facts. Record their ideas on chart paper. Some of the patterns may include:

a. Diagonal line on the chart b. Sum of the digits of each dividend equals 9 c. You can count up 1‐2‐3‐4‐5‐6‐7‐8‐9 on the tens digit of the dividends and then count up 1‐2‐3‐4‐5‐6‐7‐8‐

9 on the ones digit of the dividends. Pairs Work:

3. Distribute a copy of “Patterns with Nifty Nines” to each student. In pairs have students complete this activity. Closure: (Whole Group)

4. Gather together again. Discuss what they noticed from the chart. Record their ideas on chart paper. One new pattern they may have seen is that the first digit of each dividend is one less than the quotient. (54 ÷ 9 = 6).



Hundreds Board

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100



Patterns with Nifty Nines In the box below, complete the “Patterns with Nines” facts by filling in each product. Use manipulatives or your hundreds chart if you need to.

Directions

Describe the patterns you find in the list of Nifty Nines on the lines below.

Explain how these patterns can help you remember the facts.

Use the list of patterns you recorded about the Nines patterns you found on the Hundreds Chart. Compare them to the ones you found here.

0 ÷ 9 = _____

9 ÷ 9 = _____

18 ÷ 9 = _____

27 ÷ 9 = _____

36 ÷ 9 = _____

45 ÷ 9 = _____

54 ÷ 9 = _____

63 ÷ 9 = _____

72 ÷ 9 = _____

81 ÷ 9 = _____

90 ÷ 9 = _____



Nifty Nines Game

Objective: Students will be able to use strategies to divide numbers involving 9. Activity Type: Groups of 2 Materials:

Game board laminated or in a clear plastic sheet protector

Dry erase marker

Spinners for each group

2 Paper clips for each group (for the spinner)

Counter Directions:

1. Player one spins both spinners. He/she divides the dividend by the divisor and records the quotient on the sheet of paper. If the player‘s quotient has a remainder or they give an incorrect answer, the record a zero for the round.

2. Player 2 spins each spinner. He/she divides the dividend by the divisor and records the quotient on the sheet of

paper. If the player‘s quotient has a remainder or they give an incorrect answer, they record a zero for the round.

3. The player with the largest quotient wins the round and gets a counter.

4. Players repeat the spinning and writing 9 more times.

5. The winner is the player with the most counters.



Nifty Nines Game 1. Players spin both spinners. They divide the dividend by the divisor and record the quotient on the sheet of

paper. If the player‘s quotient has a remainder or they give an incorrect answer, they record a zero for the round.

2. The player with the largest quotient wins the round and gets a counter.

3. Players repeat the spinning and writing 9 more times.

4. The winner is the player with the most counters.

Round Player 1 Problem Quotient Player 2 Problem Quotient

1

2

3

4

5

6

7

8

9

10



Nifty Nines Game Spinner

Dividend Spinner

Divisor Spinner



Helping Facts The main strategy that will be used with division facts is division as “think multiplication”. When used in this think‐multiplication manner, the child uses known multiplication facts to find the answer. If children are struggling with these facts be sure they have mastered these multiplication facts first.

0 1 2 3 4 5 6 7 8 9

0

1

2

3 9 12 18 21 24

4 12 16 24 28 32

5

6 18 24 36 42 48

7 21 28 42 49 56

8 24 32 42 56 64

9



Double Pairs Poster Activity

Objective: Students will be able to use arrays and the double/half strategy to find solutions to fours facts. Activity Type: Groups of 2 Materials:

Grid paper

Scissors

Glue or Tape

Markers or crayons

Chart or Construction paper Directions:

1. Each pair of students will create a poster for the Fours as “Double Pairs” facts. Be sure that there is a group to make a poster for each of the Fours Facts.

2. Shade or color in a rectangular array on the grid paper for a division fact whose divisor is four. (12 ÷ 4 would

have a rectangle with four rows of three squares colored or shaded.) Cut it out and glue it on a piece of blank paper.

3. Shade or color in a second array that is exactly the same as the first one. Use a different color marker or crayon, if desired. Cut it in half so that you have two equal groups of rows in each half. Discard one half of the new array. Glue the remaining half to the same paper that has the first array.

4. Write a division fact for each array.

5. Make displays for all the Fours as “Double Pairs” facts for a class bulletin board. 6. When students finish, have them fill in their pattern in the Patterns in a Table. Closure: Have a whole group discussion about the patterns discovered in Fours.

6 ÷ 2 = 3 12 ÷ 4 = 3



Patterns in a Table

What patterns can you discover when you compare the quotients of a number when it’s divided by 2 (half) and it’s divided by 4(half, half)? Fill in the facts that your group discovered while creating your Fours as “Double Pairs” facts.

Dividend ÷ 2 ÷ 4

0

4

8

12

16

20

24

28

32

36

40



Look at Arrays for Fours as “Double Pairs” HELP WANTED: We need talented artists to create posters to help students learn their Fours as “Double Pairs” facts. YOUR TASK: Create posters for the Fours as “Double Pairs” facts.

1. Each pair of students will create a poster for the Fours as “Double Pairs” facts. 2. Shade or color in a rectangular array on the grid paper for a division fact whose divisor is

four (12 ÷ 4 would have a rectangle with four rows of three squares colored or shaded). Cut it out and glue it on a piece of blank paper.

3. Shade or color in a second array that is exactly the same as the first one. Use a different color marker or crayon, if desired. Cut it in half so that you have two equal groups of rows in each half. Discard one half of the new array. Glue the remaining half to the same paper that has the first array.

4. Write a division fact for each array.

5. Make displays for all the Fours as “Double Pairs” facts for a class bulletin board.

6 ÷ 2 = 3 12 ÷ 4 = 3



Half, Half Four in a Row

Objective: Students will be able to use the half and half again strategy to find fours facts. Activity Type: Groups of 2 Materials: (each group will need)

1 Game Board


1 number spinner

1 half, half Four in a Row Spinner

Recording sheet for each student Directions:

1. Players take turns spinning both spinners. If they spin 32 half they need to first fill in their spin on their recording sheet, and then cover the space on the board which answers their spin. Note: the recording sheet is

important so that students can see that when they half this is a 2 fact and when they half, half, it is a 4 fact.

2. If the space is already covered by another player, that player can choose to remove their opponents chip and place their chip in that spot or they can choose another space on the board to cover, as long as they can state the division fact to claim that space.

3. The first player to cover 4 spaces in a row wins.



Half, Half Four in a Row

1 3 10 7

7 2 9 6

8 10 3 1

4 9 8 6

5 2 4 5



Half, Half Four in a Row Spinners



Half, Half Four in a Row Student Recording Sheet

Number on Spinner

Fill inH = Half

HH = Half, Half

Division Expression

Quotient



DIVISION GAMES THAT CAN BE USED TO PRACTICE ANY

FACTS STRATEGY



Cover Up – Division All Facts

This game can be used for any specific division fact. For example, if you want students to practice dividing by 5, use

this game board and the 5 spinner. Objective: Students will use division strategies to divide basic facts. Activity Type: Groups of 2 Materials:


Game board

Paper clip for spinner

Spinner for the division facts students are working on Directions:

1. On their turn, players choose the spinner that they want to use for this turn. They spin the spinner. They divide the number on the spinner by the number beside their spinner and then cover one space on the board that matches that quotient.

2. Players continue taking turns spinning and marking their quotient until all the spaces are filled. If there are no

more spaces for a student’s quotient, they lose their turn. 3. At the end, the student with the most chips wins.

Differentiation:

If students need to work on different facts, each student can use the spinner for the facts they need to work

on. For example, (using the same game board) one student may have a 3 spinner, another player might be

using a 6 spinner, etc… This works because the quotients of all the facts (0‐9) are the numbers (0‐10).



Cover Up ‐ Division Game Board

7 2 0

five 4 seven 8

two 3

six zero nine

9 one

three 1 four

5 eight 6



Cover Up ‐ Division Game Board

one 3 seven 7

0 zero 6 three

six 2 nine

9 two 8

5 4

eight five

four 1



TigerLand All Facts

This game can be used for any specific division fact. For example, if you want students to practice dividing by 5, use

this game board and the 5 spinner. Objective: Students will use division strategies to divide basic facts. Activity Type: Groups of 2 ‐ 4 Materials:

Pawn (different color pawn for each player)

Game board

Paper clip for spinner

Spinner for facts that you want students to practice Directions:

1. On their turn each player spins their spinner. They divide the number they spin by the number written beside the spinner. They move their pawn to the closest space with their quotient.

2. Players continue taking turns spinning, dividing, and moving to the next closest quotient until one player lands on the last space.

3. To get to the last spinner, the player must have a quotient which is even.

Differentiation:






Four in a Row All Facts

Objective: Students will be able the double and double again strategy to find fours facts. Activity Type: Groups of 2 Materials: (each group will need)

1 Three in a Row Game Board


1 number spinner Directions:

1. On their turn, players spin the division spinner (for the facts they need to work on). They then divide the number on the spinner by the number beside their spinner. The player covers a space on the board with this quotient with one of their chips. If there are no more spaces with their quotient the player loses their turn.

2. Players continue taking turns spinning, dividing, and covering the quotient until one player has 4 counters in a row on the board.

Variation:

3. If the space is already covered by another player, that player can choose to remove their opponent’s chip and place their chip in that spot or they can choose another space on board to cover, as long as they can state the multiplication fact to claim that space.

Differentiation:






Four in a Row

0 9 4 8 5 9

3 4 0 2 4 3

7 2 1 8 10 0

6 10 9 1 5 6

6 8 3 5 2 0

5 1 7 8 10 7



Be Productive Game All Division Facts

Objective: Students will use the helping facts to multiply by 6 and 8. Activity Type: Groups of 2 students Materials: (each group will need the following)




Spinner with the facts students need to practice

Directions:

1. The first player spins the spinner (with a paper clip and pencil) and divides by the number beside the spinner. The student then states the division fact and the quotient. The student then crosses off that quotient.





Be Productive

9

8

7

6

5

4

3

2

1

0 0

1

2

3

4

5

6

7

8

9



Three for All All Division Facts

Objective: Students will use strategies to divide by 2. Activity Type: Groups of 2 students Materials: (Each group will need)





1. Players take turns choosing 2 numbers in the box (crossing them off with a dry erase marker) to make a division fact.






Three for All 1

1 2 1 8 1 9 1 5 1 0

4 1 5 1 1 1 3 1 7 1

1 6 1 9 1 4 1 1 1 6

3 1 0 1 7 1 8 1 2 1



Three for All 2

2 2 2 12 2 18 2 0 2 6

6 2 4 2 14 2 8 2 16 2

2 10 2 16 2 0 2 18 2 10

8 2 14 2 12 2 4 2 2 2



Three for All 3

3 3 3 15 3 24 3 0 3 9

9 3 6 3 18 3 27 3 18 3

3 12 3 21 3 6 3 27 3 24

15 3 0 3 21 3 12 3 3 3



Three for All 4

4 4 4 20 4 24 4 28 4 12

12 4 28 4 8 4 32 4 0 4

4 16 4 36 4 0 4 32 4 16

8 4 20 4 24 4 36 4 4 4



Three for All 5

5 5 5 40 5 35 5 20 5 10

15 5 20 5 30 5 45 5 0 5

5 35 5 10 5 40 5 0 5 30

25 5 15 5 45 5 25 5 5 5



Three for All 6

6 6 6 30 6 24 6 36 6 12

18 6 42 6 54 6 48 6 0 6

6 12 6 36 6 24 6 54 6 42

18 6 30 6 48 6 0 6 6 6



Three for All 7

7 7 7 35 7 28 7 56 7 21

21 7 49 7 63 7 0 7 0 7

7 56 7 42 7 14 7 63 7 42

35 7 14 7 49 7 28 7 7 7



Three for All 8

8 8 8 48 8 64 8 48 8 32

40 8 24 8 16 8 0 8 0 8

8 56 8 64 8 40 8 16 8 72

32 8 72 8 56 8 24 8 8 8



Three for All 9

9 27 9 54 9 18 9 45 9 9

45 9 72 9 81 9 72 9 63 9

9 36 9 18 9 0 9 27 9 36

9 9 63 9 0 9 81 9 54 9



MIXED STRATEGY GAMES

These games combine all 0‐9 facts together in the same game.

These games are appropriate after students have gained strategies

for finding facts.



Star Struck Division

Objective: Students will use division strategies find quotients. Activity Type: Groups of 2‐3 Materials:


Game board

Game Cards Directions:

1. On their turn, players draw a card. They then solve the division problem. The quotient is the number of spaces the player moves forward.

2. Players continue pulling a card, solving the problem, and moving forward the quotient until one player reaches

the end of the game board. If a student is incorrect, they lose their turn.



Star Struck Division Cards

12 ÷ 2 12 ÷ 6 12 ÷ 4

14 ÷ 2 15 ÷ 3 16 ÷ 4

18 ÷ 9 20 ÷ 10 20 ÷ 5

24 ÷ 6 24 ÷ 8 27 ÷ 9

30 ÷ 10 32 ÷ 4 36 ÷ 6

36 ÷ 9 40 ÷ 10 42 ÷ 6

45 ÷ 9 48 ÷ 6 49 ÷ 7

54 ÷ 6 56 ÷ 8 63 ÷ 9



Children’s Literature Division

P = K‐2 I = 3‐5

Title Author Year Level

Clean – Sweep Campers Lucille Recht Penner 2000 P/I

Divide and Ride Stuart J. Murphy 1997 P/I

The Doorbell Rang Pat Hutchins 1986 P/I

Eating Fractions Bruce McMillan 1991 P

Everybody Wins! Shiela Bruce 2001 P/I

Gator Pie Louise Mathews 1995 P/I

How Hungry Are You? Donna Jo Napoli 2001 P/I

Jump, Kangaroo, Jump! Stuart J. Murphy 1999 P/I

One Hundred Seagulls Make a Racket Betsy Franco 2003 P/I

One Hungry Cat Joanne Rocklin 1997 P/I

Remainder of One, A Elino J. Pinczes 1995 P/I

17 Kings and 42 Elephants Margaret Mahy 1987 P/I



Old Maid Game

To change a concentration/memory game into Old Maid, just add an “old maid” card to each set of cards.

Directions: 1. Put students into groups of 3 or 4. 2. Instruct students to deal out the cards. (One student in the group will have 1

more card that all the other players. 3. The players put all of the cards into their hand. 4. The dealer begins. The dealer draws one card from the person on their right.

If they have a pair of cards in their hand that matches they announce the problem card and the solution card and places the matched pair on the table.

5. The next player goes and draws a card from the person on his right. If they have a pair of cards in their hand that matches they announce the problem card and the solution card and places the matched pair on the table.

6. If a player draws a card and does not have a match in their hand they do not lay any cards down and the next player continues.

7. The match does not have to be made from the card they pulled from the other player.

8. The loser is the person left with the “old maid” card. The winner is the person with the most matches.

Added Card to turn this concentration into Old Maid

Old Maid



Go Fish Game

To change a concentration game into Go Fish, follow the directions below.

1. Put students into groups of 2, 3 or 4. 2. Instruct students to deal out seven cards to each player.

3. Place the remaining cards in the center face down.

4. The dealer begins. The dealer asks another player if they have a card to

match a card in their hand. If the player does have the card he/she surrenders it to the requester. The requester makes the match and lays the two cards to the side. If the player does not have the card, he/she says “go fish” and the requester draws a card from the center of the table.

5. The next player follows the same procedure.

6. The winner is the person with the most matches at the end of the game.



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multiplication and division basic math packet july 2010

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