1.oa at the park - common core web viewstandard use addition and subtraction within 20 to solve word...

www.illustrativemathematics.org 1st Grade Tasks 12/2/2012

1.OA At the ParkAlignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. There were 7 children at the park. Then 4 more showed up. How many children were at the park all together?

b. There were 7 children at the park. Some more showed up. Then there were 11 children in all. How many more children came?

c. There were some children at the park. Four more children showed up. Then there were 11 children at the park. How many children were at the park to start with?

Commentary:

This task includes three different problem types using the "Add To" context with a discrete quantity; see "1.OA The Pet Snake" for an "Add To" problem with a continuous quantity. Table 1 in the glossary of the CCSSM offers a succinct overview of all addition and subtraction problem types.

Although students should experience and practice with all three problem types, they would not necessarily be introduced at the same time. Please see the K, Counting and Cardinality; K–5, Operations and Algebraic Thinking Progressions Document for in-depth information about issues related to students’ learning of these kinds of problems.

While students are expected to add and subtract fluently within 10 in first grade (1.OA.6), they are not expected to add and subtract fluently within 20 until second grade (2.OA.2).

Solution:Classifications included

Students may use objects, pictures, or equations to represent their solutions. The solutions show equations with a question mark representing the unknown value, but other symbols are often used. For example, 4 + ? = 11 might also be written 4 + ____ = 11 or 4 + ☐ = 11.

a. Total Unknown: There were 11 children in all. Possible equation: 7+4= ?

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b. Addend Unknown: 4 more children came. Possible equation: 7+ ? =11

c. Start Unknown: There were 7 children in the park to start with.Possible equation: ? +4=11

1.OA Boys and Girls, Variation 1Alignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. 9 boys and 8 girls were in the class. How many children were in the class in all?

b. 17 children were in the class. 9 were boys and the rest were girls. How many girls were in the class?

c. 17 children were in the class. There were some boys and 8 girls. How many boys were in the class?

Commentary:

These tasks types represent the Put Together/Take Apart contexts for addition and subtraction (see Table 1 in the glossary of the CCSSM for all all addition and subtraction problem types). Students may use either addition or subtraction to solve these types of word problems, with addition related to the action of putting together and subtraction related to the action of taking apart. Depending on how students think about these word problems, either is appropriate for the “addend unknown” problems. Seeing it both ways emphasizes the relationship between addition and subtraction.

The use of “in all” or “altogether” makes result unknown problems significantly easier for students, since these words are such strong cues to put sets together. Students need experiences with problems both with and without such cues. When working with categories like boys-girls-children, it is important to be sure that students understand the contexts. Please see page 10 of the K, Counting and Cardinality; K–5, Operations and Algebraic Thinking Progressions Document for in-depth information about issues related to students’ learning of these kinds of problems.

Note that while students are expected to add and subtract fluently within 10 in first grade (1.OA.6), they are not expected to add and subtract fluently within 20 until second grade (2.OA.2).


Please note that students may use objects, pictures, or equations to represent their solutions. Furthermore, the solutions show equations with a question mark representing the unknown value, but other symbols are often

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used. For example, 9+ ? =17 might also be written 9+ ____ =17 or 9+ ☐ =17 . Note that it is important to include examples with the total written on both sides of the equation.

a. Total Unknown: 17 children were in the class. Possible equations:

o 9+8= ?

o 8+9= ?

o ? = 9+8

o ? = 8+9

b. Addend Unknown: There were 8 girls. Possible equations:

o 17=9+ ?

o 17= ? + 9

o 9+ ? =17

o ? +9=17

o 17–9= ?

c. Addend Unknown: There were 9 boys. Possible equations:

o 17=8+ ?

o 17= ? + 8

o 8+ ? =17

o ? +8=17

o 17–8= ?

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1.OA Boys and Girls, Variation 2Alignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

9 children were in the class. How many boys and how many girls could have been in the class?

Solve the problem. Write an equation. Draw a picture and use it to explain your answer.

Commentary:

This task represents the Put Together/Take Apart with both addends unknown context for addition and subtraction (see Table 1 in the glossary of the CCSSM for all addition and subtraction problem types). Once a student finds one correct answer, he/she can be encouraged to find another. Ask the student to use objects, pictures, or equations to represent each answer.

Please see the K, Counting and Cardinality; K–5, Operations and Algebraic Thinking Progressions Document for in-depth information about issues related to students’ learning of these kinds of problems.

Solution:Answers

Listing the possible pairings of boys and girls in a systematic way might help the student show that s/he has found all of the possible pairings.

There are 10 possible solutions. Students can select a number between 0 and 9 to represent the number of boys (or girls) and then find the number of girls (or boys, resp).

Possible equations:

9=0+9

9=1+8

9=2+7

9=3+6

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9=4+5

9=5+4

9=6+3

9=7+2

9=8+1

9=9+0

Note that students may write the total on either side of the equation.

1.OA Finding a ChairAlignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. There are 8 children and 6 chairs. A child sits in each chair. How many children won’t have a chair?

b. There are 8 children and some chairs. A child sits in each chair. 2 children don’t have a chair. How many chairs are there?

c. There are some children and 6 chairs. A child sits in each chair. 2 children don’t have a chair. How many children are there?

d. There are 8 children and 10 chairs. A child sits in each chair. How many empty chairs are there?

e. There are 8 children and some chairs. A child sits in each chair. Two chairs are empty. How many chairs are there?

f. There are some children and 10 chairs. A child sits in each chair. Two chairs are empty. How many children are there?

Commentary:

These tasks types represent Compare contexts for addition and subtraction (see Table 1 in the glossary of the CCSSM for all addition and subtraction problem types).

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These problems explicitly describe one-to-one correspondences without using comparison language. Such problems are easier for students to solve than problems that use comparison language such as “How many more?” or “How many fewer.” Please see the K, Counting and Cardinality; K–5, Operations and Algebraic Thinking Progressions Document for in-depth information about issues related to students’ learning of these kinds of problems.

Solution:Answers

a. 2 children will not have a chair.

b. There are 6 chairs.

c. There are 8 children.

d. There are 2 empty chairs.

e. There are 10 chairs.

f. There are 8 children.

1.OA Maria’s MoneyAlignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. Ali had $9. Maria had $5. How many more dollars did Ali have than Maria?Ali had $9. Maria had $5. How many fewer dollars did Maria have than Ali?

b. Ali had $4 more than Maria. Maria had $5. How many dollars did Ali have?Maria had $4 less than Ali. Maria had $5. How many dollars did Ali have?

c. Ali had $4 more than Maria. Ali had $9. How many dollars did Maria have?Maria had $4 less than Ali. Ali had $9. How many dollars did Maria have?

Commentary:

This task includes problem types that represent the Compare contexts for addition and subtraction (see Table 1 in the glossary of the CCSSM for all all addition and subtraction problem types). There are three types of comparison problems – those with an unknown difference and two known numbers; those with a known difference and a bigger unknown number; and those with a known difference and smaller unknown number.

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Each of these problem types can be solved using addition or subtraction, although the language in specific problems tends to favor one approach over another.


Students benefit from encountering one problem type limited to small numbers and to develop strategies for that type of problem before encountering mixed sets of problems and larger numbers that distract the student from the problem itself. Over time they will be able to distinguish between types of problems in mixed sets and apply the appropriate strategy to solve each.

Solution:Classifications included (need solutions written for other three Qs)

This solution is written in teacher language. Students may use objects, pictures, or equations to represent their solutions. While students are expected to add and subtract fluently within 10 at grade 1 (1.OA.6), they are not expected to add and subtract fluently within 20 until second grade; see 2.OA.2.

The solutions show equations with a question mark representing the unknown value, but other symbols are often used. For example, 4 + ? = 9 might also be written 4 + ____ = 9 or 4 + ☐ = 9.

a. Difference Unknown:Ali had $4 more than Maria. (or)Maria had $4 less than Ali.Possible equations: 5 + ? = 9; 9 – 5 = ?

b. Bigger Unknown: Ali had $9.Possible equations: 5 + 4 = ?; ? - 4 = 5

c. Smaller Unknown: Maria had $5.Possible equations: ? + 4 = 9; 9 – 4 = ?

1.OA Measuring BlocksAlignment 1: 1.OA.A.1

Domain OA: Operations and Algebraic Thinking

Cluster Represent and solve problems involving addition and subtraction.

Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and

equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1.

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Have two or more blocks of different lengths on hand and paper clips to use to measure them. The blocks need to measure a whole number of paper clips whose combined length is less than or equal to 20 paper clips.

Have students work in pairs. Give each pair a block to measure using paper clips. After they have measured their block, say,

Find someone who measured the other block. Ask them how many paper clips long it is. How long will the two different blocks be together if they are laid end-to-end? First try to figure this out. Then put the blocks end-to-end and measure it to check your answer.

Ask students to explain how they solved the problem and whether their answer checked out correctly. Even if students added correctly, they may not have lined up the paperclips very carefully and could get different lengths. This is a good opportunity to talk about how important it is to be careful when measuring.

Next, ask the students,

Imagine you put another block end-to-end with the first one you measured. Together, they measure 18 paper clips. How long is the new block? Draw a picture to explain how you know.

Ask students to explain how they solved the problem and whether their answer checked out correctly. Finally, ask the students to write equations to represent their work.

Commentary:

This task is a kernel for an instructional task that could be elaborated with commentary about teaching strategies and examples of student work. When this website is fully functional, teachers will be able to submit tasks and related materials for review. The Illustrative Mathematics Project invites teachers to begin this work.

1.OA School SuppliesAlignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and

equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1.

Pia takes some money to the store to buy school supplies. She buys some paper for $3 and a pen for $2. After she buys these supplies, she has $7 left. How much money did Pia bring to the store?

Commentary:

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This task could be used for either instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them. The solution shown is very terse; students' solution strategies are likely to be much more varied.

Solution:Tape diagram

Students who are familiar with tape diagrams might use them to solve the problem by first drawing a picture:

and then reasoning, "If she spent $2 + $3 dollars and had $7 left over, then she had $2+$3+$7=$12 to start."

There are many more strategies that students might use.

Solution:Using Addition with Objects

Students could use objects to add

2+3=5 5+7=12

Students who have mastered fluent addition for numbers up to 12 could also add these two quantities in their head.

1.OA Sharing MarkersAlignment 1: 1.OA.A.1Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. Char had 10 markers. She gave 3 to a friend. How many did she have left?

b. Char had 10 markers. She gave some to a friend. Now she has 7 left. How many markers did she give to her friend?

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c. Char had some markers. She gave 3 to a friend. Then she had 7 left. How many markers did she have to start with?

Commentary:

These tasks types represent the Take From contexts for addition and subtraction (see Table 1 in the glossary of the CCSSM for all all addition and subtraction problem types). This task includes the three different problem types using the Take From context: result unknown, change unknown, and start unknown. Students need experience and practice with all three types.

Result unknown problems (a) and change unknown problems (b) are both fairly easy for most students, since they can be acted out directly. Start unknown problems (c) are the most difficult of the three for most children because they involve thinking about a situation in reverse (“undoing” the action in a situation). Guessing an initial amount then trying it out to see if it works is another possible strategy.


The solutions below are written in teacher language. Students may use objects, pictures, or equations to represent their solutions. While students are expect to add and subtract fluently within 10 at grade 1 (1.OA.6), they are not expected to add and subtract fluently within 20 until second grade; see 2.OA.2.

The solutions show equations with a question mark representing the unknown value, but other symbols are often used. For example, 10 - ? = 7 might also be written 10 - ____ = 10 or 10 - ☐ = 7.


a. Result Unknown: Char had 7 markers left. Possible equation: 10 – 3 = ?

b. Change Unknown: Char gave 3 markers to her friend.Possible equation: 10 – ? = 7

c. Start Unknown: Char had 10 markers to start with.Possible equation: ? – 3 = 7

1.OA The Pet Snake Alignment 1: 1.OA.A.1DomainOA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

a. The class had a pet snake. It was 14 inches long. It grew 3 more inches. How long is it now?

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b. The class had a pet snake. It was 14 inches long. It grew a few more inches. Now it is 17 inches long. How many inches did it grow?

c. The class had a pet snake. It grew 3 more inches. Now it is 17 inches long. How long was it to start?

Commentary:

These tasks types represent the Add To contexts for addition and subtraction (see Table 1 in the glossary of the CCSSM for all all addition and subtraction problem types). This task uses a continuous quantity; see "1.OA At the Park" for an Add to problem with a discrete quantity. These problem types wouldn't necessarily be given to students at the same time although students will need experience and practice with all three types. Please see the K, Counting and Cardinality; K–5, Operations and Algebraic Thinking Progressions Document for in-depth information about issues related to students’ learning of these kinds of problems.

While students are expected to add and subtract fluently within 10 in first grade (1.OA.6), they are not expected to add and subtract fluently within 20 until second grade (2.OA.2).

Solution:Classifications Included

Students may use objects, pictures, or equations to represent their solutions. The solutions show equations with a question mark representing the unknown value, but other symbols are often used. For example, 14 + ? = 17 might also be written 14 + ____ = 17 or 14 + ☐ = 17.

a. Total Unknown: The snake was 17 inches long. Possible equation: 14+3= ?

b. Addend Unknown: The snake grew 3 more inches. Possible equation: 14+ ? =17

c. Start Unknown: The snake was 14 inches long to start.Possible equation: ? +3=17

1.OA Daisies in vasesAlignment 1: 1.OA.A.2Domain OA: Operations and Algebraic ThinkingCluster Represent and solve problems involving addition and subtraction.Standard Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Jasmine has eight daisies and three vases - one large, one medium-sized and one small.



She puts 5 daisies in the large vase, 2 in the medium vase and 1 in the small vase.

Can you find another way to put daisies so that there are the most in the large vase and least in the small vase?

Try to find as many ways as you can put the daisies in the vases with the most in the large vase and the least in the smallest vase. If you think you have found them all, explain how you know those are all the possibilities.

Commentary:

This instructional task can be thought of as a sequel to K.OA.3, which asks students to consider all the decompositions of a number into two addends.

Because first grade students may have trouble reading this task even thought they are intellectual capable of working on this problem, it will help if the teacher reads the prompt to the students and then has them work together in pairs or small groups. Some students will interpret "most" to mean "strictly greater than" and some will allow for the possibility that "most" and "second most" are actually equal. Either interpretation of "most" is fine as long as the students are consistent with this interpretation throughout. Similarly, whether a vase can remain empty can be left to students and teachers.

Solution:List, and decomposition strategy.

The full list is:

8 in the large, and none in the others, which we abbreviate as 8,0,0 .

7 in large, 1 in medium, 0 in small, which we abbreviate as 7,1,0 .

6,2,0

6,1,1

5,3,0

5,2,1

4,4,0

4,3,1

4,2,2

3,3,2



If students and the teacher decide to not allow empty vases or equal numbers, there are only two possibilities, the other being 4,3,1 . It is likely that at least equal amounts will be allowed, in which case there are five possibilities.

One full solution strategy is to first decide how many are in the first vase, and then decide from there how many in the second and third vases.

1.OA $20 Dot MapAlignment 1: 1.OA.C.6Domain OA: Operations and Algebraic ThinkingCluster Add and subtract within 20.Standard Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8+6=8+2+4=10+4=14 ); decomposing a number leading to a ten (e.g.,

13−4=13−3−1=10−1=9 ); using the relationship between addition and subtraction (e.g., knowing that

8+4=12 , one knows 12−8=4 ); and creating equivalent but easier or known sums (e.g., adding 6+7 by

creating the known equivalent 6+6+1=12+1=13 ).

The attached graphic shows a map. You must get from start to finish by visiting three of the dots, at each dot you have to pay the specified number of dollars. If you have $20 can you get from start to finish and visit three dots?



Bonus Question #1: Can you find a way to get from start to finish and spend all $20? Can you find a way to get from start to finish and spend less then $20?

Bonus Question #2: How many different routes can you find from start to finish that go to three dots and cost $20 or less?

Commentary:

The language for this task is written above a 1st grade reading level, so it will need to be introduced verbally by the teacher. This problem helps students to practice adding three numbers whose sum are 20 or less. It is an open-ended problem with many solutions. This problem would work well either as a whole group or students could work on it as individuals or pairs. If this problem is presented whole group, the teacher needs to blow the graphic up using an Elmo, Smart Board or overhead projector. If students are going to work on it in pairs they will need to be given print-outs of the graphic.

Solution:Solutions

1 + 9 + 9 = 19

1 + 9 + 10 = 20



1+ 10 + 9 = 20

7 + 10 + 3 = 20

8 + 6 + 3 = 17



1.OA Using lengths to represent equality Alignment 1: 1.OA.D.7Domain OA: Operations and Algebraic ThinkingCluster Work with addition and subtraction equations.Standard Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6=6 , 7=8−1 , 5+2=2+5 , 4+1=5+2 .

MATERIALS

Cuisenaire rods or paper strips cut to whole centimeter lengths

ACTIONS

Students work in pairs.

One student puts a few rods (or strips) end-to-end. The other student matches that length with a different combination of rods (or strips). When two different ways of making the same length are found, the students write a number sentence

reflecting the equality.

For example, if the first student uses a rod of length 4, a rod of length 2 and a rod of length 1 and the second student uses three rods of length 2 and a rod of length 1 (as shown below), they should write 4+2+1=2+2+2+1.

4+2+1=2+2+2+1 Commentary:



The act of trying to find equal lengths with the rods helps students develop a physical understanding for the meaning of equality. Students are more likely to generate and understand complex equalities than they would be able to do only abstractly.

A variation that would help scaffold students from physical objects to drawings would be to have them draw a color-matched picture of their Cuisenaire rods on graph paper in addition to writing the equation. For example, a student might draw the following picture for the example given in the task statement:

One variation may include having the teacher choose one (larger) Cuisenaire rod. Then each student in each pair would match that length. From there, the students write a number sentence describing an equality based on the rods they chose. This variation connects to 1.MD.1 and 1.MD.2 as well as 1.OA.7. Some students may need a small white board or paper to record how they made their long rod as they create it; otherwise some students might forget which rods they chose.

Solution:Sample Solution

For example, if the first student arranges Cuisenaire end to end like this (in this example there are 3 rods)

then the second student could use Cuisenaire rods to match the total length like this

The two students then write a number sentence to describe the relationship.

3+2+2=4+1+1+1

1.OA Valid Equalities?Alignment 1: 1.OA.D.7Domain OA: Operations and Algebraic ThinkingCluster Work with addition and subtraction equations.



Standard Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6=6 , 7=8−1 , 5+2=2+5 , 4+1=5+2 .

Decide if the equations are "true" or "false." Make sure you can explain your answer.

a. 2+5=6

b. 3+4=2+5

c. 8=4+4

d. 3+4+2=4+5

e. 5+3=8+1

f. 1+2=12

g. 12=10+2

h. 3+2=2+3

i. 32=23

Commentary:

The purpose of this task is to help broaden and deepen students understanding of the equals sign and equality. For some students, an equals sign means "compute" because they have so often seen expressions of the form

4+3=

In this task, students have to explicitly attend to the meaning of the equal sign by determining whether or not the left-hand expression and the right hand expression are actually equal. This task helps students attend to precision (as in Standard for Mathematical Practice 6) by helping them explicitly attend to the meaning of mathematical notation and carefully analyze whether it is being used correctly.

While the written answers are simple "true" or "false" responses, students need to be working in a setting where they have opportunities to elaborate with verbal explanations.

Many of these problems naturally lead to discussions of topics such as place value and properties of addition.

Solution:Some possible explanations.



While the question asks for simple "true" or "false" answers, complete solutions include some valid explanation. There are many possible explanations, so we give a variety of kinds of explanations in these solutions.

a. False. 2+5 equals 7 and not 6 .

b. True. Both sides equal 7 .

c. True. Since 4+4=8 , 8=4+4 .

d. True. We can combine the three and the two on the left to get 5 , and then after reordering both sides are 4+5 .

e. False. 3+5 is 8 but 8+1 is 9.

f. False. 1+2=3 , which is less than 12 .

g. True. If you count up two from 10 you get 12 . (Alternately, 12 means one ten and two ones.)

h. True. You can always change the order of numbers being added.

i. False. 32 is 3 tens and 2 ones. 23 is 2 tens and 3 ones.

1.NBT Counting Circles IIAlignment 1: 1.NBT.ADomain NBT: Number and Operations in Base TenCluster Extend the counting sequence.

Setup

Have students stand and form a circle facing in toward each other. Select a counting sequence to be practiced with no more than 6-10 numbers in the sequence, for example 97-104.

Actions

Have the students start counting around the circle one by one until the last number in the sequence is reached. When the last number is reached all students clap and that student is out and sits down on the floor in the middle of the circle. Start the counting sequence over again until another student reaches the number at the end of the sequence, everyone claps and that student sits in the center with the first student. Continue repeating the sequence until only one child is left standing and the rest are seated in the center of the circle. For example: for the counting sequence 97-104; the first child says “ninety-seven”, the next child says “ninety-eight” and so on until the 8th student gets to “one hundred four” at this point everyone claps and the eighth child sits in the center of the circle, the ninth child starts over with “ninety-seven” and so on.



With a larger class this activity can be modified by splitting into two groups and practicing different counting sequences or by stopping after 5-10 students are sitting down. It can also be modified to allow students who have sat down to come back in when another student misses a number in the sequence if they can state the correct number, in which case, the teacher can just stop the activity after about 10 minutes.

Commentary:

This activity is designed to target trouble spots that children have with counting so it is important to keep the sequence short and focused. If the majority of the class is struggling with the getting past 30 into the next family, or the "teen" numbers, or crossing the century from 99 to 100 this activity can be used to target a specific area and then move on to the next trouble spot. This activity is also effective for skip counting sequences.

It is important to keep the counting moving quickly and smoothly thus keeping the sequence to no more than ten numbers is key, as well as, offering support to the students either with the teacher giving the number name to a student if they are struggling or by having a written record that students can refer to. The idea is not for the student to figure out the counting sequence but to hear it and practice it repeatedly in a facile manner. Supporting students in this way keeps the activity moving quickly, allows students to "hear" the sequence repeatedly and keeps it from taking too long.

If you are practicing in the “teen” range or with counting by ten, English Language Learners often have trouble with the articulation of these numbers saying 50 for fifteen, 60 for sixteen, 70 for seventeen or visa versa so practice within this specific range is useful to emphasize the proper articulation of these number names.

Practicing counting sequences going backward is a particularly important skill to develop that later supports student development with subtraction and can often pose difficulty for children. It is critical to play this and other such games using backward number sequences after students have developed facility going forward.

Solution:Solution

Possible counting sequences for forward counting: crossing the decade from any one family into another, for example 26-34, 37-43 etc. or crossing the century and beyond, for example 97-104, 108-112, 115-124

Possible counting sequences for backward counting: the teens 20-11 or any crossing the decade sequences going backward.

Possible counting sequences for multiplicative or “skip” counting: by tens (10, 20, 30, 40, 50, 60, 70, 80, 90, 100) by 5s and by 2s.

1.NB Hundred Chart Digit GameAlignment 1: 1.NBT.A.1Domain NBT: Number and Operations in Base TenCluster Extend the counting sequence.Standard Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.



Materials

A 100 chart per pair of students

A set of digit cards per pair of students (four each of cards 0-9)

Two different colors of counting chips, one for each student

Action

Player One draws two cards and then makes and reads aloud both of the numbers that can be made with those digits. Player One then chooses which of the two numbers to cover on their 100 chart.

Player Two draws two cards and then makes and reads aloud both of his /her numbers and chooses which number to cover on the 100 chart.

Players cannot cover a number that has already been covered, but they may have more than one counter in each row.

If a player cannot make a number that is uncovered/available with the cards they drew, they lose their turn for that round.

Play continues until one player has at least one number covered in each row of the 100 chart.

If students run out of cards they should re-shuffle the cards and continue play.

For a shorter version, students work together to cover at least one number in each row on the 100 chart.

This can be extended by asking students to record the numbers they create.

Commentary:

Ideally, students will place counters strategically. For example, if they get they draw the cards 1 and 3 and they already have a “teen” number covered they would place the counter on “31.” Students will often end up with more than one counter in each row as they reach the point in the game that they only have a few rows left to cover a number in.

This game can be useful to help students who are having trouble with reversing numerals when reading numbers, for example, 14 as 41 or vise versa. Students often make this mistake because of the difference between reading teens which are read from right to left “Fourteen” versus “forty-one” which is read from left to right. Children will sometimes carry this over into other numbers and read 72 as 27 etc.

If you have extended the activity so that the students are recording the numbers, the opportunity may arise to discuss the role of "zero" when reading and writing numbers. For example, if a student draws a 9 and a 0 and has to decide whether to cover nine or ninety, we would not record the nine as 09 but only 9. Generally, however, issues with "zero" do not cause much confusion until students are writing three digit numbers. This can still offer a place to start this discussion with children.



A long pause when identifying a number may indicate that a student is counting in order to get a “running start” to help identify a number. You may also see some “sub-vocal” counting (sort of like counting under their breath) from another number to arrive at the correct numeral name. This is a common student strategy that should be noted when assessing a student’s facility with number identification. Make sure to note if students have to count to identify as this indicates that additional practice is needed with this numeral before they can be considered facile.

Solution:Solution

A winning game board will have one number in each row of the hundred chart covered by one color of counting chip, for example, 8, 12, 25, 34, 46, 51, 67, 78, 88, 93. If the shorter version is being played then the numbers may be covered by chips of both color.

1.NBT Choral Counting IIAlignment 1: 1.NBT.A.1Domain NBT: Number and Operations in Base TenCluster Extend the counting sequence.Standard Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Materials

100 chart or large number line, preferably one that extends beyond 100.

A pointer

Setup

Have students sit in the whole group meeting area.

Actions

Lead the students in chanting the counting sequence starting with one to one hundred; use the pointer to follow the number sequence. Then start counting at various numbers other than one that are randomly selected from 1-120. Have a student take over the job of pointing out the number sequence. Highlight the multiples of ten using a marker or a colored screen and have students chant the counting sequence by 10s, by 5s and by 2s. This should be done daily.

Commentary:

Counting the days in the month on the classroom calendar is another great place to practice the counting sequence; first count the number of days total and then count from the current date to the end of the month to get practice starting at numbers other than one.



Students should practice backward counting on a regular basis; it supports students in learning subtraction. Students should have some facility with forward counting before practicing backward counting.

It is important start from different numbers each day when counting by ones to increase student flexibility with the number sequence.

Solution:Solution

Start the counting sequence with one to one hundred, then begin picking starting numbers other than one.This will help students build the flexibility to start a count from a number other than one.

Select a number from 1-50 and count backward by ones; once students are fluent, move to numbers from 50-100 as starting points.

Count by decuple numbers — 10,20,30,40,50,60,70,80,90,100, by 5s to 50 and by 2s to 20.

1.NBT Start/Stop Counting IIAlignment 1: 1.NBT.A.1Domain NBT: Number and Operations in Base TenCluster Extend the counting sequence.Standard Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.Practice 7

Setup

Students should be seated on chairs at their tables or desks. The teacher will give a counting sequence (for example, 20-120) to the students.

Actions

Begin with the teacher walking around the room while counting aloud from a number between 1 and 20. The teacher continues to count until he/she chooses a student by patting them on the shoulder. The student and teacher switch roles, the teacher sits in the student’s chair while the student resumes the count and walks around the room. At the teacher’s signal (clap, snap, chime etc.) the student selects the nearest student and switches places with another child who continues the count. Repeat this until each child has had a turn counting. If a child reaches 120 before each child has been given a chance to count, begin the sequence over again or if the children are ready reverse the sequence.

Commentary:

It is important to keep the counting moving quickly and smoothly so offering support to the students from the teacher by giving the number name to a student if they are struggling or having the whole



group count with them until they can be independent is appropriate. The idea is not for the student to figure out the counting sequence but to hear it and practice it repeatedly in a facile manner.

English Language Learners will often have trouble with the articulation of the “teen” numbers saying 50 for fifteen, 60 for sixteen, 70 for seventeen or vise versa, so it is important to emphasize and model the proper articulation of these number names.

Practicing the counting sequence going backward is a particularly important skill to develop in children; this supports student development with subtraction and can often pose difficulty. This activity can easily be reversed after students are facile with the forward counting sequence.

Another trouble spot students may encounter when counting forward is crossing from one family into the next family, i.e. “crossing the decade” and “crossing the century” from 99 to 100,101 then often “crossing the decade” again at 109-110. Students will leave out the decade number for example, “27, 28, 29, 31” or will not be able to go past 100 or go from “99, 100, 200”. Focusing on these short sequences to help them cross the decade/century can be helpful

Any signal used in classroom routines can be helpful to indicate to students to switch off, others such as; clapping, snapping, a clicker, a maraca/shaker can be used as well. Also students often enjoy playing this game with a play microphone that magnifies the voice and can be passed off to each player.

Solution:Solution

Any counting sequence can be selected depending on student abilities. In a first grade class 1-100 might be a starting point but this can easily be extended to 1-120 or 20-120 going forward and 100-1 going backward.

1.NBT “Crossing the Decade” ConcentrationAlignment 1: 1.NBT.A.1Domain NBT: Number and Operations in Base TenCluster Extend the counting sequence.Standard Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

This game is a version of the traditional memory or concentration game.

You will need to create a set of number cards for each of the pair of numbers that cross the decade, i.e., 19 and 20, 29 and 30, 39 and 40, 49 and 50, etc.

Students place all the number cards that end with “_9” face down in an 3x3 array on the left and all the number cards that end with “_0” face down in a 3x3 array on the right. Working in pairs or trios, students take turns. The first student selects a card from the left array, stating the number name and the counting number that follows (“I have 39, I need 40”).



He or she then picks one card from the array on the right (the “_0” numbers), hoping to find the target number. If the student does not find a pair, both cards are replaced face down in their original spots. It is now the second student's turn to choose a card from the “_9” array and to try to find the appropriate “_0” card. Students should try to remember where each number is located. (The game is called "Concentration" not "Guessing.")

When a student finds a matching pair he or she keeps that pair of cards. Play continues until all cards have been matched. The student with the most matched pairs wins.

Commentary:

One of the most common areas that young children struggle with when learning to count forward is crossing from one family to the next, for example getting to 29 in the counting sequence and not knowing what comes next or stating a random decade number. This game supports student development in this area. Students should have beginning knowledge of the counting sequence beyond the “teen” numbers before playing this game.

This game can be introdåuced whole group on the board by making slightly larger cards and using a sentence pocket chart (or magnetic tape on a magnetic board) to arrange the cards in two arrays face down against the board. The teacher then plays against the rest of the class, modeling the process of picking from the left to begin, stating the number name and the number after and then picking from the right.

It is very important to train the students to draw a card from the left and state what they need before they draw from the right. This will encourage them to think about and problem solve the next decade number. When the students get in the habit of picking up two cards simultaneously the game become much more about luck (although they do have to confirm that it is a pair, so do get some practice) and students are less likely to internalize the information and use it when counting.

Students who become proficient with playing the game to support counting forward can gain experience in backward counting by picking from the right array first (the "_0" numbers) and then looking for the correct "_9" number. Changing the cards to 20-21, 30-31, 40-41, 50-51 etc with the “_0” numbers on the left and the “_1” numbers on the right is very supportive for another common error in backward counting which is to leave out the decade number when counting backward ie. “33, 32, 31, 29, 28”.

Solution:Solution

Cards will be matched 19-20, 29-30, 39-40, 49-50, 59-60, 69-70, 79-80, 89-90, 99-100. This game can be modified when playing for the first time or for a struggling student by only making cards up to 50 and making 2 of each pair.



1NBT Number of the DayAlignment 1: 1.NBT.A.1Domain NBT: Number and Operations in Base TenCluster Extend the counting sequence.Standard Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

MATERIALS

Large chart paper, markers, math journals, pencils, 100 chart.

DIRECTIONS

Students will count the "Number of the Day" beginning with 1 on the first day of school, and adding one number for each day of school. Each day the class will chorally count up to the last number added to the 100 chart (or a hand drawn chart of numbers) by 1s or 10s. The teacher will then add the next number in the counting sequence to the chart to represent the number of the current day (this way the chart grows by one for each day students are in school).

The teacher then draws a bubble map on chart paper with the number of the day in the middle bubble. The teacher models and guides students in drawing and writing the number in different ways; see the picture below.



Commentary:

This activity provides a connection between the counting sequence and an experience from students' daily lives. It helps to give the students a sense of how "many" each number is.

This task begins as a whole group activity with the teacher guiding instruction. Writing the number in different forms becomes an independent activity over time; however, the class should go over it together in order to make sure students are correctly completing the task.

Repeatable, daily activities are one of the best ways to instill the counting sequence for children. This task also reinforces many skills related to understanding and representing numbers, such as using tally marks, the word form, expanded form, and place value.

As the year progresses, the teacher can adjust the focus in response to the size of the number. For example, when the year starts and the numbers are in the single digits, this will be a relatively short activity; as the numbers get very large tally marks can be dropped from the activity, in favor of spending additional time on representing tens and ones.

The first grade standard requires students to count to 120. However, if a teacher would like to extend the activity beyond 120 there is no reason to stop once the 120th day of school passes.

Note: Many 100 charts are sold in teacher stores although it may be more difficult to find a chart that goes above 100. The teacher can make their own on a large piece of chart paper by writing each day's number as the day happens, making sure to keep each column straight.

1.NBT Ordering NumbersAlignment 1: 1.NBT.B.3Domain NBT: Number and Operations in Base TenCluster Understand place value.Standard Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of

comparisons with the symbols > , = , and < .



Malik is given a list of numbers:

1 5 10 50 100

He wants to include the following numbers so all numbers will be listed in order from least (on the left) to greatest (on the right):

49,7,22,98, and 3

Where in the list should he put each of these numbers?

Commentary:

The purpose of this task is to give students an opportunity to compare numbers less than 100 to benchmark numbers. Even though a number line is not explicitly given in the task, it is useful for students to list the numbers in the order they would appear on the number line; this allows them to focus on the relative ordering without worrying about the exact placement on the number line. Students should also have a chance to do similar tasks with a number line.

1.NBT.3 asks students to record comparisons with the symbols >,= and < . While this task does not ask for this, it helps build up an understanding of the relative magnitude of numbers which is a precursor to proficiency with the more abstract symbolic comparisons.

The reading level for this task is high for first grade, so it would be a good idea for teachers to present this task to students orally.

Solution:solution

We know that 3 is the smallest number in our list of new numbers so we will find a place for 3 in the row first. 3 is greater than 1 but less than 5 so Malik should put 3 in the row between 1 and 5. The row of numbers is:

1 5 10 50 100

The next greatest number in our new list is 7. 7 is greater than 5 but less than 10 so Malik should put 7 in the row between 5 and 10. The new row of numbers is:

1 3 5 7 10 50 100


1 3 5 7 10 22 50 100 28 [email protected]



1 3 5 7 10 22 49 50 100

The greatest number in our new list is 98. 98 is greater than 50 but less than 100 so Malik should put 98 in the row between 50 and 100. The new row of numbers is:

1 3 5 7 10 22 49 50 98 100

We have added all of our new numbers to the old row in order from least (on the left) to greatest (on the right) so this is Malik’s final row of numbers.

1.MD Making a clockAlignment 1: 1.MD.BDomain MD: Measurement and DataCluster Tell and write time.

MATERIALS

12 sheets of laminated paper or tag board with the numbers 1-12 12 sheets of laminated paper or tag board with the numbers 0, 5, 10, ... 55 1 long arrow (minute hand) 1 short arrow (hour hand) White board, dry erase marker 1 large clock face with hands that can be moved to different positions Small clock faces with hands that can be moved to different positions (1 for each pair of students) A cut-out circle with the sun on one side and moon on the other.

ACTIONS

The students sit in a large arc/rainbow. The teacher explains that they are going to make a giant clock to practice telling time.

The teacher shows students a clock and asks what numbers they see on it. After students respond, the teacher has students help position the tag board sheets with the numbers 1-12 in a circle on the floor to represent a clock. Students count from 1 o'clock through 12 o'clock as the numbers are laid out.

Then the teacher says,

There are 60 minutes in an hour. When the minute hand goes from one number to the next, that means five minutes have passed. It starts on the 12; that means 0 minutes have passed.



Then the teacher has a student put the paper with the 0 below the paper with the 12 on it. Next, the teacher models counting by 5's, having a student place the corresponding number of minutes below each of the numbers 1-11.

Then the teacher says,

When the minute hand reaches 12 again, that is 60 minutes, and one hour has passed. Now the count starts over for the next hour.

The students and teacher can count by 5s together pointing to each of the numbers 1-11.

The teacher then discusses the hour and minute hands and shows how they move in a clockwise direction. The teacher models moving the hands to show time to the hour and half hour.

In pairs, the students create the same time on their mini-clocks. The teacher guides the students in telling the times to their partner and shows them how to write the times on the whiteboard in both word format (i.e. eight o'clock) and digital format (8:00).

Once students have demonstrated proficiency in identifying what time it is, the teacher uses the moon/sun icon to show that the same time can occur at night or during the day. For example, she can model 12:00 lunchtime and hold up the sun icon, and model 12:00 while the students are in bed and hold up the moon icon. This can be extended with other events that are relevant to the students' lives.

Commentary:

The purpose of this task is to introduce students to the concept of reading an analog clock.

This task can be extended by having students take turns moving the hour and minute hands on the class clock or mini-clocks, as well as figuring out the times. The teacher should use times that are on the hour and half hour (example: 12:00, 1:30, 4:00, 6:30, etc). Students can also write the times on paper or mini whiteboards. To teach the vocabulary of "clockwise," students can practice a clock dance with their partner. The partners face each other, and one gently moves the other's arm in a clockwise motion through each imaginary number on a clock, chanting one o'clock, two o'clock, etc. Or, the teacher can lead the entire class through a clock dance, with the students moving their their own arms.

Learning to tell time is a skill that will need to be practiced often in the classroom. There are many different games students can play to reinforce telling time (time bingo and time matching games are fun).

1.MD Favorite Ice Cream FlavorAlignment 1: 1.MD.C.4Domain MD: Measurement and DataCluster Represent and interpret data.Standard Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.



Materials:

Pocket chart

Sentence strip

Square pieces of paper for each student

Popsicle sticks

Setup:

Write a question that has three choices as an answer on a sentence strip. For example,

“Which flavor of ice cream do you like best?”

Put the three categories on the bottom of the pocket chart. For example,

Chocolate Vanilla Strawberry

Write interpretation questions on the popsicle sticks. For example,

“How many students answered this question?”

“Which has the most?”

“Which has the fewest?”

“Are any the same?”

“How many are in each category?”

Actions:

Begin with all students sitting together in the meeting area. Read the question aloud to the students, and ask individual students to answer the question by putting a paper square above their answer. Ensure that as each child answers, they put their paper above the previous square, not to the side of the square. When each child has answered, you will have a bar graph with three categories.

Draw a popsicle stick and model answering the question to the whole group. Divide students into five groups and have each group pick a popsicle stick. Students then read the question on the popsicle stick, discuss the question as a group, and then answer it in front of the class using the graph as a model to defend their answer.

Commentary:

Before students answer their question in front of the group, ensure that each group understands their question and is able to defend their answer using the graph.



This activity can become a daily math routine that can be done during calendar or as a transition to start the morning.

English language learners can benefit from sentence frames such as:o “__________ students answered this question.”o “More students answered __________.”o “Fewer students answered __________.”o “__________ and __________ have the same number of students that answered.”o “__________ students answered __________.”

As students become familiar with this activity, you may want to ask higher-level interpretation questions such as

o “How many more/less are in __________ than __________?”o “Which category did more than half of the students answer?”

The teacher can also pull popsicle sticks and ask individual students to answer the question if time does not allow for small group discussion.

Other questions to ask students as variations on this task: o “How do you get to school?” Possible categories: bus, walk, car/trucko “Which animal do you like best?” Possible categories: dog, cat, birdo “Do you have siblings?” Possible categories: brother, sister, noneo “Which food do you like best?” Possible categories: pizza, spaghetti, chicken nuggetso “Which activity do you like to do best at recess?"Possible categories: swing, slide, dig

Solution:Solution

Once students have all placed their squares in the pocket chart, you will have a bar graph with three categories. Here are some examples of student answers to two of the questions:

How many students answered this question?

“Eighteen students answered the question. I know because I counted up all the squares and there are 18 of them.”

Which has the most?

“Chocolate has the most students who prefer it. I know because the bar for chocolate is taller than the bars for the other flavors.”

1.G Counting SquaresAlignment 1: 1.G.A.2Domain G: GeometryCluster Reason with shapes and their attributes.Standard Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a



composite shape, and compose new shapes from the composite shape.Students do not need to learn formal names such as “right rectangular prism.”Not yet tagged

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How many squares are in this picture?

Commentary:

This task is intended to be a simpler form of 1.G.A.2 Overlapping Rectangles. The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares, and stimulate interest as students compete to try to find the most squares. Furthermore, older students may also benefit from such an exercise as well, which could be aligned with 2.G.1.

Solution:1

In addition to the nine small squares, there are four 2×2 squares (shown below), and one 3×3 square, for a total of 14 squares.



1.G Make Your Own PuzzleAlignment 1: 1.G.A.2

Domain G: Geometry

Cluster Reason with shapes and their attributes.

Standard Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a

composite shape, and compose new shapes from the composite shape.Students do not need to learn formal names such as “right rectangular prism.”

Give each student scissors, an envelope, and a square of colored paper (the colored paper should be of a wide spectrum to make it easier to keep puzzles apart).

Have the students cut the square into four pieces, then put those pieces in the envelope. The student can then trade puzzles as many times as they like and try to solve each others’ puzzles by reassembling the shapes into a square.

Commentary:

The purpose of this task is to give students a hands-on experience with composing and decomposing geometric figures and is meant as an instructional task. While the standard suggests particular figures, students should not be limited to the ones listed in the standard. Students will definitely benefit from this type of activity before they are asked to make more formal arguments related to composing and decomposing shapes in later grades. This task would also be appropriate for advanced kindergarten students (see K.G.6).

There are many ways to go about this task (see solution) so students should be encouraged to be creative when cutting their paper. They should also be encouraged to use language to describe each of the smaller pieces, both as they are making their own puzzle and as they are assembling each others’. This may be a mixture of informal



and formal language; for example the last puzzle in the solutions might be described as “a rectangle, a triangle and two pieces with wiggly sides.”

The count of four pieces should be considered a rough suggestion. If a limit of four pieces is not challenging enough for a group, puzzles with more pieces are possible. It is also possible a student will generate more than four pieces by accident when making their puzzle.

Solution:Possible cuts

Four of many possibilities:

1.G Overlapping RectanglesAlignment 1: 1.G.A.2Domain G: GeometryCluster Reason with shapes and their attributes.Standard Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a

composite shape, and compose new shapes from the composite shape.Students do not need to learn formal names such as “right rectangular prism.”



How many rectangles are in this picture?

Commentary:

The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing rectangles, and stimulate interest as students compete to try to find the most rectangles. Furthermore, older students may also benefit from such an exercise as well, which could be aligned with 2.G.1 or even 3.G.1.

Students could work in teams and would benefit from having lots of copies of the figure and colored pencils at hand. Then students could compare their rectangles and sort them into piles which contain the same rectangles to help them decide if two rectangles found by different students are actually the same rectangle. This will help reduce the chances that a rectangle gets counted twice.

While inappropriate for assessment purposes in elementary school, this task was adapted from problem #19 on the 2011 American Mathematics Competition (AMC) 8 Test. For older students, the focus is not so much on understanding how to compose shapes from other shapes, but on finding a systematic way of enumerating the rectangles. The most efficient way to do this is to identify the seven regions in some way that is easy to refer to and check to see that all the ways of combining them that result in a rectangle are included in the list. An example of how this approach might look is in the third solution. This task shows how concepts that students learn in elementary school can reappear in more sophisticated forms in much later grades.



Solution:1

As shown, there are 11 rectangles.



Solution:Shaded rectangles

The 11 rectangles in the first solution can be viewed as being composed of the non-overlapping regions shown here:



The rectangles shown in the first solution, color coded by region, are shown below:



Students who color the regions distinct colors are showing the decomposition called for in the standard more clearly, but as this is an exploratory challenge problem for 1st graders, it is not required that they do it this way.

Solution:3

If this task were used with significantly older students, a more abstract representation of the rectangles might be accessible to them:

Partition the figure into non-overlapping regions as shown. The list of rectangles are b , c , d , ab , bc , cd , cf , de , abcd , bcfg , and cdef .


1.oa at the park - common core web viewstandard use addition and subtraction within 20 to solve word...

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