structured curriculum lesson plan day: 010 subject: mathematics grade level:

8/14/2019 Structured Curriculum Lesson Plan Day: 010 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 010 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6C1

ITBS/TAP:Solve single step problems using subtraction or

addition with whole numbers

ISAT:

Unit Focus/Foci

Addition and Subtraction

Instructional Focus/Foci

Understanding vocabulary terms: addition, subtraction, and inverse operations

Materials

Six-Group Activity: Subtraction: Think ZeroSmall box

Several markersCalculators

Educational Strategies/Instructional Procedures

Warm-up Activity:

Read the following problem for the class and have each student respond by raising his/her hand

to volunteer to answer.

Two numbers have a sum of 1700 and a difference of 500. What are the numbers? 1100 and600.

Next, have the students use number wheels or they may play the thumbs up, thumbs down gameto indicate a correct or incorrect response. If the answer is more than 40, have the students place

their thumbs up. If the answer is less than 40, have the students will place their thumbs down. Ifthe answer is exactly 40, have the students stand.


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25+30 =

20+14 =

80-40 = Stand

59-4 =

26+15 =

32-12 =

46-6 = Stand

50-10 = Stand

40-14 =

30+12 =

Lesson:

Have the students use the calculators to show how the following activity works. Give severalstudents markers. Have students get in two lines. Call one line In, and the other line +.Have a student from the In line place his/her markers in the box. Next, call out the number of

markers to be added and ask someone from line + to place them in the box then a person fromthe + line by calling out the number that should be added. Example: 13

Example: A person from the In line pus in seven markers, then the teacher will say (-4, + 4).The person holding markers in the (-, + plus line) steps forward and counts out the four markers

to be put in the box. Ask the designated, or volunteering, student what will come out of the box.The reply should be 11. Speedy reply is one way to measure mastery of a given skill. A speedy

recall response is one which takes only about 1 seconds from the statement/problem deliverytime.. Continue for about 3 or 4 turns. (Note examples used for addition facts use the sameexample for subtraction.)


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Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in todayslesson

1) Word problems are another way to use addition and subtraction skills.(yes)2) Speedy recall is a way to measure mastery of skills.(yes)3) Missing addends are represented by the letter n.(no)4) Functions are a way to add and subtract.(yes)5) Place value is the value of a digit in a number.(no)6) Plus or minus are functions that a function machine can perform.(yes)7) When one adds with a function machine, the numbers coming out are larger than what

actually went in.(yes)8) When using the function machine, operations on top of the machine dictate the function to be

performed.(yes)

9)

When we add with the function machine, we get a sum as our answer.(yes)10)On a number line, positive numbers are to the right of the zero.(no)Free-Choice Lesson

Have the students choose a lesson from the Free Choice Activity Sheet (one box per day).

Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activity

sheet. (Subtraction: Zeros in the Ones.)

Math Workshop

Have the students go into theMath Workshop after completing their Free Choice Lesson.

Integration with Core Subject(s)

LA: Understanding explicit, factual informationUnderstanding the meaning of words in context

SC: Apply scientific method to solve problemsAnalyze and interpret data


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SS: Read and interpret maps, charts, tables, graphs, and cartoons

Sequence information, especially using timelinesSelect appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet: Subtraction: Zero in the Ones

Technology: T.I. Explorer Plus, Cruncher CD-ROM (optional)

Assessment

Consider students responses to Ten Statements lesson review and performance on worksheet asinformal assessment tools.

Homework

Have each student write one problem of his/her own and solve it. Have each student then writeout the steps necessary to solve it.

Teacher Notes


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Six Group Activity

Subtraction: Think Zero

Materials:

10 (5 x 7) index cards1 pencil1 black marker

9 x 6 envelope

Prepare the following cards using the black marker to write the problems on the front of the card

and the pencil to write the answers on the back. Write one problem on each card.

47 78 27 58 66 39 86 24 99 87- 5 - 6 - 3 - 2 - 4 - 8 - 5 - 4 -58 -67

Answers:

47 78 27 58 66 39 86 24 99 87- 5 - 6 - 3 - 2 - 4 - 8 - 5 - 4 -58 -6742 72 24 56 62 31 81 20 41 20

Think Zero

Say: Sometimes you will need to think zero when subtracting.Subtract the ones.

Subtract the tens.

56 38- 3 - 5

Use this study board to teach the students how to think about zeros in a problem. Use thisproblem as an example. 47

- 3

Ask these questions: What is the first step in solving these problems? (subtracting the ones)

When would you think about a zero in the problem? (4-0) What is the answer? (44)

Tell students that they are going to do an activity that involves subtracting and thinking of zeros.Lay a card with one subtraction problem (listed above) on it on the table and give the studentstime to write the answer to the question. As you reveal the answer say: The answer is.

Store the activity in a 9 x 6 envelope.

ThinkZero

ThinkZero


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Correlations (SG,CAS,CFS): 10D4; 6C1

ITBS/TAP:Solve single-step problems using addition or

subtraction with whole numbers

ISAT:

Unit Focus/Foci

Addition and subtraction

Instructional Focus/FociMastering addition facts

Materials

Six-Group Activity: Addition: Adding More NumbersCraft sticksBase ten blocks

CoinsT.I. Explorer Plus, CD ROM Cruncher

CalculatorsMath journals


Warm-up Activity:

Write the following vocabulary on the chalkboard , along with the examples.

1. Addend: A number that is added to another to make a total.2. 1 regrouping

Ex: 35 addends + 48 addends Base ten blocks, craft sticks, or coins may be 83 = sum used to demonstrate this example.3. Sum: When two addends are combined, the total is called the sum.4. n: n represents the unknown number in a mathematics problem.

Ex: 35 + 48 = n35 + 48 = 83n = 83 n = unknown


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Lesson:

Write the vocabulary terms and how to solve the problems on the chalkboard. Have the students

write them in their math journals.Vocabulary: addend-a number being added to one or more numbers

Example: 6 + 3 = 9

addend addend

Problems written horizontally are in equation form. Example: 6+3=

Problems written vertically are in working form. Example: 6+3

sum- the answer that comes from adding numbers. Example: 6+3=9 sum = 0

inverse operation- an operation that undoes the results of another operation. Addition andsubtraction are inverse operations. (Example: -6 is the inverse of +6)

Have the students solve the following problems. Set the timer for 5 minutes. When timeexpires, have the students put their pencils down. The teacher will give the answers and students

will put a correct symbol next to the problems that they got right ..

1.5

+6(A: 11) 2.

7

+9(A: 16) 3.

8

+6(A: 14) 4.

7

+7(A: 14)

5.8

+3(A: 11) 6.

6

+9(A: 15) 7.

9

+6(A: 15) 8.

8

+7(A: 15)

Have the students solve the problems and label the parts of one problem from above using thevocabulary introduced in the first addition lesson.

Example {

7 addend

+2 addend(7 + 2 = 9)

9 sum

9. Christy has 5 ponytail clips. Her mother buys a new pack that has twelve (12) clips, and heraunt gave her a pack with two (2) clips. How many clips does Cristy have in all?

Example (5+12+2 = 19) Cristy has nineteen in all. How many does she need to make 20?(19+1 = 20).


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Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in todayslesson.

1) Clue words can be used to help you know that you should subtract. (no)2) Sum is the total of two addends when added. (yes)3) When we solve subtraction problems, the answer is called the difference. (no)4) Regrouping and carrying refer to the same process. (yes)5) There are two at least addends in addition. (yes)6) Digits are any of the numbers 0 through 9.(yes)7) When you combine addends that total ten or more in the ones place, you must regroup them

and put them in the tens place. (yes)8) Ones and tens places refer to place value.(yes)9) Never put more than 9 ones in the ones place.(yes)10)

n is the unknown number in a problem.(yes)

Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet. (Addition: Adding More Numbers)

Math Workshop




SC: Apply scientific method to solve problems

Analyze and interpret dataSS: Read and interpret maps, charts, tables, graphs, and cartoons



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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet: Addition: Adding More Numbers

Technology: T.I. Explorer Plus, CD ROM Cruncher (optional)

Assessment

Assess students classroom participation and ability to solve assigned problems.

Homework

Teacher Notes


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Six-Group Activity

Addition (Adding more numbers)

Materials:

5 index cards (5 x 7)1 black marker1 pencil

1 envelope (9 x 6 )

Prepare the following index cards using the black marker to write the problems on the front of

the cards and the pencil to write the answers on the back of the cards.

869

113

+496

283

554

+351

314

256

+233

195

264

+112

935

235

+125

Copy this study board and use it to reteach this lesson.

Adding More Numbers

Say: Regroup one hundred from the tens placeRegroup 2 tens from the ones place

Add 4+8+9 = 21

6 94

+ 968429

2091

1 2

Always start at the ones place and work left.

Use the study board to show the students how to solve an addition problem.

252

343

+264


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Ask these questions:

How many numbers are in the ones place? (3)What number belongs in the ones place in the sum? (9)

Say: Add up digits in the tens column.

What is the answer? (15)

What do we do with 15? (regroup)How do we write the 15 in the sum? (Write 5 in the tens place and 1 above the 2 in the hundredsplace.)

What are the numbers being added in the hundreds place? (1+2+3+2)What is the answer in the hundreds place? (8)What is the answer to the problem? (859)

Tell the students that they are going to do an activity just like the one they have just completed.

(You want them to solve the problem and regroup if necessary). Lay a card on the table andhave the students write the answer. As you reveal the answer say, The answer is Store the

activity cards and study board in the 9 x 6 envelope.


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ITBS/TAP:Solve single-step problems using addition or


ISAT:

Unit Focus/Foci

Addition and subtraction


Mastering subtraction facts

Materials

Six-Group Activity: Subtraction: (Zero In The Tens)Math journals

Base ten blocksMath cubes

Numbers cubes


Lesson:

Write clue words and vocabulary on chalkboard. Explain to the students that there are certainclue words that they should look for when deciding how to solve a problem. Examples: 1. How

many more, 2. Which has less, 3. Which is greater, 4. Which is larger 5. Which is smaller,6. What is the difference, 7. How many remain, 8. Which is fewer, 9. How many are left.

Explain that these words are used to compare or to find missing parts when solving problems.

Have the students write these terms and clue words in their math journals. Explain the

vocabulary words and examples.


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1. Fact family: A group of related facts based on one fact (locate the commonalties)

Ex: 7 + 8 = 15 __; 15 - 7 = 8; 8 + 7 =15__; 15 - 8 = 7All of the problems are different, but they all have the same digits in common.

2. Difference: The answer that comes from subtracting one number from another.

Ex: 8 - 4 = 4; 4 = the difference

3. Digit: A number symbol from 0 through 9.

Ex: 0,1,2,3,4,5,6,7,8, or 9.

4. Minuend: The digit from which another is to be subtracted.

Ex: 53 minuend

-15

5. Subtrahend : A digit that is subtracted from another to give a difference.

Ex: 53

-15

subtrahend

6. Regrouping: To rename a group that makes adding and subtracting easier. 4 (13)

Ex: 53-18

35

7. Sum: When adding numbers, the answer is the sum.

Ex: 53+18

68

sum

Show the students place value and regrouping using base ten blocks and sticks.

Have the students solve the problems above. When the students, have solved the problems, have

them select one problem and label the parts, using the vocabulary introduced in lesson one (1).

1.8

- 5(A: 3) 2.

9

- 4(A: 5) 3.

7

- 2(A: 5) 4.

8

- 6(A: 2)

5.9

- 3(A: 6) 6.

17

- 8(A: 9) 7.

14

- 6(A: 8) 8.

15

- 9(A: 6)


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9.14

- 5(A: 9) 10.

13

- 9(A: 4) 11.

96

- 24(A: 72) 12.

54

- 31(A: 23)

13.78

- 43(A: 35) 14.

67

- 24(A: 43)

Example: Subtrahend, minuend, difference

4 minuend

- 3 subtrahend

1 difference

15. Joey has fifteen trading cards. He gives his friend (four) cards. How many cards does hehave left? (15-4 = 11) He trades two cards for a yo-yo. How many cards are left now?(11-2 = 9; there are nine left.)

Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in todayslesson.

1) Clue words can be used to help know when you should subtract. (yes)2) Difference is the answer when one subtracts. (yes)3) How many left is a clue word phrase. (yes)4) Minuend is a digit in a subtraction problem. (yes)5) Remainder is the amount left over when dividing. (no)6) Place value refers to the amount that each digit in a number stands for. (yes)7) Mile is a unit for measuring distance. (no)8) A pattern is numbers or items in a regular or repeating order. (no)9) When we add digits, the answer is called sum. (yes)10) Borrowing and regrouping/carrying make addition and subtracting easier. (yes)Free-Choice Lesson



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Assessment

Use students responses and participation in class discussion as an assessment tool.

Homework

Write the following on the chalkboard. Have students copy it and complete it for homework.Label parts of problems. Demonstrate regrouping and borrowing with explanations for three of

the problems.

36

12

19

12

75

32

675

317

465

76

Teacher Notes

Check to make sure that students have copied clue words and vocabulary in their math journals.


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ITBS/TAP:Solve single-step problems using subtraction or


ISAT:

Unit Focus/Foci

Solving addition and subtraction


Practicing addition and subtraction using function machines (inverse operation)

Materials

Six-Group Activity: Subtraction (Regrouping the tens)

Small boxSeveral markers

CalculatorsWorksheet (Functions)


Warm-up Activity:

Read the following problems and have each student respond by raising his/her hand to volunteer

to answer.

Examples: 7+7 = (14) 8-7 = (1)14-7 = (7) 10+6 = (16)


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Lesson:

Have students use calculators to complete the activity. Give markers to the students. Have

students form two lines. Call one lineIn, and the other lineplus. Have a student from theIn lineplace his/her markers in the box, then have a student from theplus line call out the number that

should be added. Example: 13

Example: Have a person from theIn line place 7 markers in the box. Next, say: (-4, +4).

Instruct student holding the markers in the (-, + line) step forward and count out four markers toplace in the box. Ask the designated (or volunteering) student to give the number of markers to

be withdrawn from the box if the reply is 11. (Speedy reply, about 11

2seconds to answer.)

Allow time for several students to have a chance. (Note: Use the same example for additionfacts as the one used for subtraction.)

Give the students a copy of the worksheet and explain that the same principle needs to be

followed to complete the functions in the six drawings, using the number at the top to add orsubtract.

-5

In out

10 5

7 2

8 3

5 0

12 7

+2in out

4 6

6 8

5 7

16 18

9 11


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-3

in out

4 1

9 6

7 4

5 23 0

8 5

+7

in out

4 11

6 13

8 15

9 16

5 12

3 10

+9

2 11

0 9

1 10

4 13

5 14

6 15

-10in out

12 2

14 4

18 8

16 6

11 1

10 0


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Functions Worksheet

1). -3 2). +4

IN OUT IN OUT

18 15 0 4

15 12 1

12 9 2

9 3

6 4

3 5

3). -8 4). +6

IN OUT IN OUT

18 3

16 5

14 7

12 9

10 11

8 13

5). -10 6). -2

IN OUT IN OUT

90 19

80 16

70 13

60 10

50 7

40 4


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Explain: Function machines are machines similar to a calculator, except that they always add

or subtract the same amount from whatever digits are put into the machine. Example: We havea (+5) function machine. Any digits put into the machine will automatically have 5 added to

them to give a sum.

Example: You put the digit 8 into the in slot on the machine; when the number comes out, it willbe (8+5), therefore 13 will come out of the out function. For subtraction, 5 would be taken awayfrom any number put into the machine.

+5

In out

8 13

Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in todays

lesson.

1) Word problems are another way to use addition and subtraction skills. (yes)2) Speedy recall is a way to measure mastery of skills. (yes)3) Missing addends are represented by the letter n. (no)4) Function machines are a way to add and subtract. (yes)5) Place value is the value of a digit in a number. (no)6) Plus or minus are functions that a function machine can perform. (yes)7) When one adds with a function machine, the numbers coming out are larger than what

actually went in. (yes)8) When using the function machine, numbers and operational signs on top of the machinedictate the function to be performed. (yes)

9) When we add with the function machine, we get a sum as our answer. (yes)10)On a number line, positive numbers are to the right of the zero. (yes)Free-Choice Lesson

Have the students choose a lesson from the Free-Choice Activity sheet, (one box per day).


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Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activity

sheet: Subtraction (Regrouping the tens).

Math Workshop

Have the students go into theMath Workshop after completing their Free-Choice Lesson.






Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Subtraction (Zeros in the tens and ones).

Technology:

Assessment

Informally assess students responses to Ten Statements and students performance onworksheets.


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Homework

Instruct students to solve each problem and write explanations for each answer given. Have the

students write a problem of their own to share.

1.

Andy has four cents. He wants nine cents for milk money. How much more moneydoes he need? (5)

2. Last night Trina had five apples, but she ate two. How many does she have now? (3)

3. During band practice, Quentin broke three clarinet reeds. Now he has four reeds.How many reeds did he have at the beginning of band practice? (7)

4.

Olga has to do ten math problems. She has done six problems. How many problemsare left to do? (4)

Teacher Notes


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3 km

Westerville

Puerto

Blanco

Colby

Riverdale

4 km6 km

2 km

Sea Cliff

Lesson:

Explain to the students that the lesson for today has a geography connection. Before getting into

the activity, introduce and explain the following vocabulary words:

Vocabulary: 1. Kilometers 2. Metric 3. Distance1. Kilometer: a unit of distance in the metric system equal to one thousand (1,000) meters.2. Metric: having to do with the meter or the system of measurement based on it3. Distance: space in between. (Example: from one city to another)After going over the vocabulary, ask the students to look at the map in the lesson. Display thesame map on the overhead projector. Explain that each of the little red dots represents a

beginning or ending point. Trace along the overhead drawing and have the students follow alongwith their fingers in the lesson.

Have students trace the remaining distances and record theiranswers in math journals.

Circulate around the room to give assistance to students who are

having difficulty.

Junctioncity


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Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in todayslesson.

1) In the number 754, the digit 5 has the value of 50. (no)2) A kilometer is a unit of distance in the metric system. (yes)3) Todays lesson was based on speedy recall of addition and subtraction facts. (yes)4) Tracing the distance on the map is also geography. (yes)5) Distance is the space between points. (yes)6) A kilometer is equal to 1,000 meters. (yes)7) A kilometer is equal to 3,280.8 feet or 5

8of a mile. (no)

8) Metric: having to do with the meter or the system of measurement based on it (yes)9) Clue words can be used to let you know you should subtract. (no)10)Problem solving can be used when money is part of the problem. (yes)Free Choice Lesson


Six-Group Activity


sheet. (Subtraction: Regrouping and Thinking Zero)

Math Workshop








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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet: (Subtraction: Regrouping and ThinkingZero.)

Technology:

Assessment

Use students responses during lesson, Warm-up Activity and, completion of classroom tasks as

means for informal assessment.

Homework

Teacher Notes


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3 km

Westerville

Puerto

Blanco

Colby

Riverdale

4 km6 km

2 km

Sea Cliff

WORKSHEET

Along the roads shown, how many kilometers is it between.

1. Westerville and Junction city?2. Junction City and Colby?3. Riverdale and Colby?4. Westerville and Riverdale?5. Riverdale and Sea Cliff?6. Puerto Blanco and Riverdale?7. Puerto Blanco and Westerville?8. Sea Cliff and Colby?9. Westerville and Sea Cliff?10.Westerville and Colby?11.From Westerville, is it a shorter trip to Puerto Blanco or to Sea Cliff? How much shorter?12.From Colby, is it a longer trip to Sea Cliff or to Riverdale? How much longer?13.Which is farther, Junction City to Sea Cliff or Junction City to Riverdale? How much

farther?14.If you drove from Westerville to Sea Cliff to Riverdale, how many kilometers would you

drive in all?

Junction

city


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Six Group Activity

Addition: Regrouping and Think Zero

Materials:

10 (5 x 7) index cards1 black marker1 pencil

1 (9 x 6 ) envelope


the card and the pencil to write the answers on the back. Write one problem on each index card.

36

+ 6

42

1 79

+ 9

88

1 25

+ 6

31

1 66

+ 9

75

1 92

+ 8

100

141

+ 9

50

1

74

7

671

+

38

+ 3

41

1 13

+ 7

20

1 54

+ 7

61

1


Regrouping and Think Zero

Say: Sometimes you will need to think zero when adding.

29

+ 9

38

1

Step 1: Add the digits in the ones place. 9+9 = 18 (regroup 18; 1 ten and 8 ones)

Step 2: Add the digits in the tens place. 1+2 = 3 (Think of zero when there is no number to

add.)

Review the study board with the students and show them how to think of zero when there is nonumber.

Tell the students that they are going to do an activity that calls for them to think of zero whenthere is no number. Lay one of the ten cards given above on the table and have the students

write the answer. As you reveal the answer say: The answer is Store the activity cards andstudy board in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C1; 10D4

ITBS/TAP:Solve single step problems using addition or


ISAT:

Unit Focus/Foci



Assessing unit concepts formally

Materials


Warm-up Activity:

Remind the students that they were instructed to review the previous. Help them to start todayslesson by instructing them to follow the Thumbs Up game rules: (up if a response is yes/correctand thumbs down if the response is no/incorrect).

7 + 9 = (16) 6 + 6 = (12) 14 - 2 = (9)

12 + 12 = (20) 9 + 4 = (19) 16 - 4 = (12)

(6 + 5 = 11) (11 - 5 = 6) is an example of inverse operation .

(6 + 9 = 15) (15 - 9 = 6) example of a function machine .

n - 7 = 5 example of missing addend.

n = 1212 - 7 = 5

5 + 4 = (9) 6 - 3 = (3) 4 + 9 = (13) 9 + 9 = (18) 5 - 1 = (4)

14 - 6 = (8) 10 - 3 = (7) 8 - 1 = (7)

The arrow direction represent the thumbs position.


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10. Define the following: multi-digit, addend, regrouping, borrowing, difference

11. 5 + 7 = n n = 10 3 7 + 4 = n

12. 5 + 11 = 17 - 7 = 4 + 20 =

13. a. 14 b. 17 c. 26 d. 32 e. 12+ 3 + 2 - 3 -12 + 35

14. n + 11 = 35 10 + 2 = n n - 2 = 10

15. Jerry bought five marbles for 25 /c . His friend gave him three marbles for a baseball tradingcard. He lost two marbles out of a hole in his pocket. How many marbles does Jerry have

now? _________________

16. Alexis won a paper doll kit that had 20 dolls and 10 outfits to dress the dolls. She shared herdolls with her two best friends. She gave each one (2) two dolls and one outfit which

consisted of shoes, dress, hat, and purse. How many dolls does Alexis have left?________________ How many doll outfits does Alexis have now? ___________________


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Ten Statements


No Ten Statements today.

Free-Choice Lesson


Six-Group Activity

No Six-GroupActivity today.

Math Workshop



LA: Understanding explicit, factual information

Understanding the meaning of words in contextSC: Apply scientific method to solve problems

Analyze and interpret data

SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelines

Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:


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Technology:

Assessment

See attached formal assessment. Check for 80% mastery.

Homework

Teacher Notes


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Key

1. Addition2. Minuend 47

Subtrahend - 29Difference 18

3. Sum

4. Inverse operations

5. *The ones place in the minuend is smaller than the ones place in the subtrahend; therefore,

you have to borrow a ten from the tens place and convert it to ones before subtracting.

3 126. 42

-3408

1

63 *In this problem when the two addends in the ones place are added, the sum is 10+18 or more, the ten ones move them to the tens place, then proceed to solve the

81 problem.

H T OU E N

N N ED S S

RED

S

T OE NN E

S S


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Difference: When you subtract, the answer is the difference.

11. A. 12 B. 7 C. 11

12. A. 16 B. 10 C. 2413. A. 17 B. 19 C. 23 D. 20 E. 47

14. A. 24 B. 12 C. 1215. 616. A. 16 B. 8


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ISAT:

Unit Focus/Foci



Computing multi-digit addition with regrouping

Materials

Six-Group Activity: Addition: Regrouping the Ones

Base ten blocksGameDont Go Over 1000

Math journalsPencilPaper


Warm-up Activity:

Draw the puzzle below on the chalkboard. Explain to the students that the object of the puzzle isto have numbers totaling 10, along all sides of the puzzle, using digits 1 to 6, and no digit may be

used more than once.3

2 6

5 4 1Answers will vary.


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Encourage students to try to find more than one solution to the puzzle.

Allow approximately ten minutes for students to solve the puzzle, move around the classroom

adding and checking their students papers. Ask the students how they were able to solve thepuzzle.

Lesson:

Conduct have a short oral review, asking students to define the following vocabulary terms.

1. Algorithm: step by step way to solve certain kinds of problems

2. Place value: the value of a digit based on its position in a number (Ask for anexample.) Regrouping may be used.

3. Multi-digit: having more than one digit4. Regrouping: To rename a number to make adding and subtracting easier

If available, use base ten cubes to demonstrate the strategy. Ask for student input as youdemonstrate the example.

Next, group students in groups of no more than (five) per group and assign each group (five)problems. Assign problems in addition to the 5 original problems.

If the text is not available, any text with math problems with more than one digit may be used.

Allow the students to complete the assignment, then ask for two volunteers from each group (ordelegate students) to explain a problem selected by the teacher.

Ten Statements


1) Place value is based on the position a digit appears in a number. (yes)2) To rename a number to make adding and subtracting easier. (yes)3) In the number 489, there are nine ones, eight tens and four hundreds. (yes)4) The perimeter of a figure is the distance around it. (no)5) Multi-digit means having more than one digit. (yes)


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Technology:

Assessment

Informally assess students ability to solve the Warm-up Activity puzzle and class participation.

Homework

Write these problems on the chalkboard. Have students copy them and complete them forhomework.

1. 267+159

2. 956+356

3. 250+169

4. 685+39

5. 867+97

6. Explain in writing how to solve this problem:156

259

+

Teacher Notes

Introduce the Dont Go Over 1000 Game.


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Six Group Activity

Addition: Regrouping the Ones

Materials:


9 x 6 envelope


the card and the pencil to write the answers on the back. Write only one problem on each card.

16

+37

74

+49

35

+99

98

+87

27

+68

58

+95

84

+77

33

+59

62

+58

69

+62

Answers:

16

+37

53

1 74

+49

123

1 35

+99

134

1 98

+87

185

1 27

+68

95

1 58

+95

153

1 84

+77

161

1 33

+59

92

1 62

+58

120

1 69

+62

131

1


Regrouping the Ones

Discuss the following with the students:

Step 1: Add the ones and regroup.

48

+258 +5 = 13 ones (1 ten + 3 ones)

3

1

Step 2: Add the tens.

48

+25

73

1


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Use the regrouping chart to review these sample problems and ask questions such as these:

93

+58

65

37

+

Tell the students to look at the ones place and add the numbers (8+3 = 11).

Should we rename the answer? (yes)Tell me where the numbers go? (1 in the ones place and 1 regrouped over the tens place)Whats the next step? (add the tens)

Whats the answer? (15)What is the total answer? (151)

Tell the students that they are going to do an activity just like the one they just did. You wantthem to regroup and write the answer. Lay one of the ten index cards on the table and have the

students write the answer. As you reveal the answer say: The answer is Store theactivity cards and study board in the 9 by 6 envelope.


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ISAT:

Unit Focus/Foci



Multidigits addition with regrouping - mental math

Materials

Six-Group Activity: Addition (regrouping the ones)

Math cubesCoins

Math journalsPaperPencil

Two 0-5 cubes (red) and two 5-10 cubes (blue)


Warm-up Activity:

Dont Go Over 1000 Game. Allow approximately 10 minutes for this game. After going over

the rules, and demonstrating how the game is played, circulate among the groups to observeparticipation of students.

Warm-up: Dont Go Over 1000 GamePlayers: Two or more

Object: To get the sum closest to, but not over 1000.Math Focus: Place value, multidigit addition and mathematical reasoning.


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Example1: 26 + 43 = (69) Allow students to give a response before giving them the correct

reply. (69) If a student gives the correct response, ask how he/she got the answer.

Example 2: 84 + 54 = 118108 Follow same procedure as example 1.

138

After going through the examples, use random selection from your text book, and call upon

students to give the answer. Ask a student what strategy was used to arrive at his/her answer.

As a final learning enhancement strategy, have the students role play after all the responses have

been given. Those students who were struggling may be paired with another student and given aproblem: Example: 492 + 759 = 1251. Ask one student to play the part of the teacher and

explain the addition algorithm. Once he/she is finished have the students exchange roles andrepeat the process.

Ten Statements


1) Missing digits in the addend are replaced by the letter n. (yes)2) Algorithms may be used to explain the steps use to solve the following example: 492 + 759

= 1251. (yes)3) The game, Dont Go Over 1000, is designed to help students understand multi-digit addition

and math reasoning. (yes)4) Place value is one of the steps when one explains the algorithms in multi-digit addition.

(yes)5) Graphs may be used to show comparisons. (no)6) Mental math is math solved in ones head, not with paper and pencil. (yes)7) Factors are numbers multiplied by another number. (no)8) The game Dont Go Over 1000, provides practice with approximating answers and place

value. (yes)9) When you approximate an answer the object is to get as close as possible to an answer

without actually solving the problem with paper and pencil. (yes)

10)In Muddle at the Bat, Mr. Muddle wanted to know how well the bat did what it was supposedto do. (no)


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Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Addition (2-digit to 1-digit regrouping)

Math Workshop





Analyze and interpret dataSS: Read and interpret maps, charts, tables, graphs, and cartoons

Sequence information, especially using timelines


Connection(s)

Enrichment: Complete Enrichment Lesson 12.

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet Addition: 2-digit to 1-digit regrouping

Technology:

Assessment

Class participation and response during oral class instruction and warm-up.


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Homework

Write the numbers in standard form.

1. 700 + 30 + 5 6. 900,000 + 6,000 + 5002.

50 + 2 7. 500,000 + 6 + 7,0003. 600 + 20 + 7 8. 40 + 9 + 90,000

4. 1,000 + 400 + 8 9. 9 + 100 + 2,0005. 400,000 + 50 + 7 10. 50,000,000 + 30,000

Teacher Notes

Bring pennies for the next lesson. (Game Mat Money) Review Transaction Game Mat and Roll

a Problem Games for introduction in chapter 13. Remember that yesterday, the studentsperformed problems 4 and 13 from todays homework.

Answers to homework:

1.) 735, 2.) 52, 3.) 627, 4.) 1,408, 5.) 400,057, 6.) 906,500, 7.) 507,006, 8.) 90,049,9.) 2,109, 10.) 50,030,000


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Six Group Activity

Addition: Regrouping the Ones

Materials:


9 x 6 envelope


the card and the pencil to write the answers on the back. Write only one problem on each card.

16

+37

74

+49

35

+99

98

+87

27

+68

58

+95

84

+77

33

+59

62

+58

69

+62

Answers:

16

+37

53

1 74

+49

123

1 35

+99

134

1 98

+87

185

1 27

+68

95

1 58

+95

153

1 84

+77

161

1 33

+59

92

1 62

+58

120

1 69

+62

131

1


Regrouping the Ones

Discuss the following with the students:

Step 1: Add the ones and regroup.

48

+258 +5 = 13 ones (1 ten + 3 ones)

3

1

Step 2: Add the tens.

48

+25

73

1


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ITBS/TAP:Solve single step problems using subtraction or

addition with whole numbers.

ISAT:

Unit Focus/Foci



Multi-digit subtraction with regrouping

Materials

Six-Group Activity: Subtraction: One-Digit by Two-Digit Regrouping)

Play moneyNumber cubes


Warm-up Activity:

(Problem of the day): Present the problem. Allow the students to solve the problem, label theparts, and write out the steps used to solve the problem.

89102 Minuend-321 Subtrahend

581 Difference


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Lesson:

Next, write the example from466

905

. on the chalkboard. Write and explain each step. Ask the

students to recall place values and ask them to give the place values in the number 594. Ask the

student to provide another name for the steps used to explain the sample. (Algorithms) Stepsneeded to solve some problems. Ask the students what should be done when no tens are

available for regrouping. Allow students to respond. Write the example below the chalkboard.

1.905

4662.

9

905

466

39

15 3.

15

439

905

46615

Explanation:

9 hundreds = 90 tens

Regrouped 90 tens & 5 from addend = 89 tens & 15 ones, now subtract.

Circulate throughout the classroom providing assistance to students as they complete tenproblems as an in class assignment. Any multi-digit and subtraction problems may be used.

Each student may be able to solve at least one problem on this particular assignment.

Collect papers: check, return. (next class meeting)

Divide the students into groups: assign word-problems from your text. Any word problems

from any text may be substituted for the multi-digit and subtraction.

Word problems were introduced in lesson 7. Therefore, students are expected to complete thisassignment based on prior knowledge.

Allow a spokesperson from each group to explain the steps used to solve one of the problems.(Five groups of six students). Each student in the group should be able to solve a problem.

Another grouping could be six groups of students where each group solves one problem.


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Ten Statements


1) Algorithms are steps used to solve some problems. (yes)2) In the number 594 there are place values representing the ones, tens, and hundreds places.

(yes)3) Regrouping is to rename to make adding and subtracting easier. (yes)4) If a zero appears in the tens place in the minuend, and the digit in the subtrahend in the ones

place in the minuend, then borrow from the hundreds place and convert them to tens. (yes)5) There can be up to three digits in a period. (yes)6) Place value is the value of a digit in a number. (yes)7) Multi-digits refers to more than one digit. (no)8) An addend is a number that is added to another number to make a sum. (yes)9)

The number 4,725 is written in standard form. (yes)10)The words four thousand, seven hundred, thirty nine is an example of expanded form. (yes)

Free-Choice Lesson

Have the students choose a lesson from the Free Choice Activity sheet (one box per day).

Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher directed activity

sheet: Subtraction: One-Digit by Two-Digit Regrouping

Math Workshop






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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet.

Technology: T.I. Explorer Plus, Cruncher CD-ROM (optional)

Assessment

Successful completion of classroom assignments and 80% class participation can be used asassessment guidelines. *Note: Must be at least three digits. One of the digits must be a zero inthe tens place in the minuend.

Homework

Have students create a word problem and explain the algorithms used to solve the problem.Teacher Notes


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Six Group Activity

Subtraction: 1-digit by 2-digit regrouping

Materials:

6 index cards (5 x 7)1 black marker1 pencil

1 unlined sheet of paper9 x 6 envelope

Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the backs.

32

70

36

15

39

881

27

406

7

443

27

74

Answers:

23

0716

/

3 8

63

1514

/

1 5

93

88117

/

1 4 9

72

04613

/

6 1 3

7

44313

/

3 3 7

72

476

/

4 7

Copy this study board on the unlined paper and explain the steps to solving a subtraction

problem.

Example:

77

61

39 18

/

Step 1. Since you cannot subtract 6 from 3, rename 1 ten in the tens column. (10+3=13) Put a

small 1 next to the 3 in the top number to show that it is now 13.

Step 2. Cross out the 9 in the tens column and make it an 8 to show that you have renamed 1 ten.


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4

Step 3. Subtract: 13-6=7

Step 4. Subtract: 8-1=7

Check:

39

77

61

3918

/

+

Step 5. Check: 16+77=93

Explain to the students that they are going to do an activity just like the one they just finished.Lay a card on the table and have the students write the answer. As you reveal the answer say:The answer is Store the activity cards and study board in the 9 x 6 envelope.


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ITBS/TAP:Solve single-step problems using subtraction or


ISAT:

Unit Focus/Foci



Subtracting multi-digit numbers with regrouping

Materials

Six-Group Activity: Subtraction (Regrouping the tens )

Play moneyNumber cubes

Math journalsEducational Strategies/Instructional Procedures

Warm-up Activity:

Write these quiz problems on the chalkboard. Allow students five minutes to complete them.

65

203

57

200

96

634

195

048

165

542

Lesson:

Ask the students if they remember place value. Ask them what place values are in the number

594. Ask the students to suggest another name for the steps used to explain the example.(Algorithms: steps needed to solve some problems.) Ask the students what one should do when

there are no tens to regroup. Allow students to respond. Explain the steps to solving 905 466.


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Say: Step 1. Write the problem 905

-466

Step 2. Look at the tens place and ask yourself if you need to regroup. (yes) 905

-466

Step 3. Regroup89

90 5

-4 6 6

Step 4. Subtract89

90 5

-4 6 64 3 9

The answer is 439

Explanation:

9 hundred = 90 tensRegrouped 90 tens & 5 ones from addend = 89 tens & 15 ones. Now subtract.

Assign some similar problems. Circulate around the room and give assistance where needed.

Observe the procedures students use to solve several problems. Have several students put theproblem on chalkboard and explain.

Collect students papers. Check the papers and return them during the next math class.

Assemble students into five groups of six students. Each student in the group should be able tosolve the problem(s) independently. Allow a spokesperson from each group to explain the steps

used to solve one of the problems

Explain the following problem at the chalkboard. Have students write each step in the solution

to the problem in their math journals.

Problem: Tim sold 594 tickets for the spring music festival. He sold 378 adult tickets. The restwere childrens tickets. How many childrens tickets did Tim sell? Find the difference.


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594

- 378

Start at the right. Subtract the ones. You cant subtract 8 from 4.Regroup the 9 tens and 4 ones. 9 tens and 4 ones = 8 tens and 14 ones.

5 9 4

- 3 7 8

8 14

Subtract the ones. 14 - 8 = 6

5 9 4

- 3 7 8

6

8 14

Subtract the tens

8-7 = 1There is one ten.

5 9 4

- 3 7 8

1 6

8 14

Subtract the hundreds.5-3 = 2

There are 2 hundreds.Tim sold 216 childrens tickets.

5 9 4- 3 7 8

2 1 6

8 14

Roll a Problem Game

Players: Two or MoreObject: To get the greatest sumMath Focus: Multi-digit arithmetic, place value, and mathematical reasoning


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Rules:

1. Use blanks to outline an addition problem on your paper like this:

+

2. The first player rolls the cube four times.3. Each time the cube is rolled, write that number in one of the blanks in the problem outline.

4. When all the blanks have been filled in, find the sum of the 2 two-digit numbers.5. The player with the greatest sum is the winner.

There are variations: Consult Game Mat

Consult Game Mat for Rules for the: Transaction Game

Ten Statements

Review the ten statements and have the students writeyes if they heard it in todays lesson and

no if they did not. If the answer is no, say: The statement is true, but it was not heard in todayslesson.

1) Algorithms are steps used to solve some problems. (yes)2) In the number 594, there are place values representing the ones, tens, and hundreds places.

(yes)3) In the problem 506 258, regrouping needs to take place. (yes)4) In the problem 594 378 you cant subtract 8 from 4 so, you must regroup. (yes)5) There can be up to three digits in a period. (no)6) Subtrahend is a number that is subtracted from another number. (yes)7) Multi-digit refers to more than one digit. (yes)8) Any number to the zero power is always one. (no)9) The number 4,725 is written in standard form. (no)10)Four thousand, seven hundred, thirty nine is an example of expanded form. (no)Free-Choice Lesson

Have the students choose a lesson from the Free-Choice Activity sheet (one box per day).


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Six-Group Activity


sheet: Subtraction (Regrouping the tens ).

Math Workshop

Have the students go into theMath Workshop after completing their Free-Choice Lesson.






Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Subtraction (Regrouping tens to ones).

Technology:


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Assessment

Informally assess students ability to successfully complete classroom assignment. Check for

80% class participation.

Homework

Have students create a word problem and explain the algorithms used to solve the problem. The

problem must contain a minimum of three digits; one of the digits must be a zero in the tensplace of the minuend.

Teacher Notes

Have students make an entry in their math journals.


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As opposed to the correct way: $5.97

+ $3.00$8.97

Decimals can be the most damaging aspect of a mathematics problem if improperly placed.

Misplaced decimals in solving money problems can represent the difference between dollars andcents. Dollar amounts are to the left of a decimal. Cents are to the right of the decimal. Whenyou add or subtract numbers like 294 minus 101 you align them like this: 294

- 101

Subtract ones from ones, tens from tens and so on. The same is true with adding. Only addition

is used.

Use the chalkboard or the overhead to explain examples.

When adding or subtracting dollar amounts like $4.96 plus or minus $2.23, list them according

to the decimal point. Decimal point: A dot that separates the ones place from the tenth place.$4.96 $4.96

- $2.23 or + $2.23$2.73 $7.19

When adding or subtracting dollar amounts, subtract or add dollars to or from dollars, andcents to or from cents.

Examples: $35.14 $26 $14.07 $26.00+ $14.26 -$10 +$5.65 -$ 14.07

When writing $26 you can add the decimal point and the two zeros to help line the digits

correctly.

Allow students to ask questions.


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Ten Statements


1) A dot that separates the ones place from the tenth place is called a decimal point. (yes)2) It is important to line decimal points up when solving problems with money amounts. (yes)3) When solving money problems, separate the dollars from the cents with a decimal point.

(yes)4) Difference is the answer when subtracting digits. (no)5) The cents in money problems are to the right of the decimal point. (yes)6) Cents are in the ones and tens places. (yes)7) When adding money (dollars and cents), dollars are added to dollars and cents are added to

cents. (yes)8) Clue words can be used to let you know when to subtract. (no)9)

Misplacing a decimal can cause major problems when solving money problems. (yes)10)A kilometer is equal to a thousand meters. (no)

Free-Choice Lesson


Six-Group Activity


sheet: Subtraction: 1-Digit by 2-Digit Regrouping

Math Workshop

Have the students work in theMath Workshop after completing their Free Choice Lesson.


LA: Understanding explicit factual informationUnderstanding the meaning of words in context



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Connection(s)

Enrichment:

Fine Arts:

Home: Distribute checkbook register sheets. Have students balance the checkbook using the

entries given.

Checkbook Register Sheet

Old Balance Deposit Withdrawal New Balance

Judy $94.14 $13.00 -

Shirley $104.12 - $11.00Kim $98.65 $61.00 -

Tiph $76.82 $19.00 $25.00

Joe $49.02 $70.00 -

Thad $12.45 $6.00 -

Treii $27.00 $14.00 $5.00

Remediation: See attached Six Group Activity sheet: Subtraction (1-digit by 2-digitregrouping)

Technology:

Assessment

Informally assess students ability to at least 75% of assigned work.

Assess students participation in classroom activities.

Homework

Teacher Notes

Remember to presort coins.


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Six Group Activity

Addition: Subtracting tens and ones

Materials:


9 x 6 envelope


the cards and the pencil to write the answers on the backs.

62

- 41

93

- 61

51

- 21

64

- 52

37

- 15

61

- 10

77

- 55

65

- 12

97

- 25

36

- 25

Answers:

62

- 41

21

93

- 61

32

51

- 21

30

64

- 52

12

37

- 15

22

61

- 10

51

77

- 55

22

65

- 12

53

97

- 25

72

36

- 25

11

Copy this study board to use with this lesson.

Subtracting tens and ones

Step 1: Subtract the ones.

5 - 3 = 2

75

- 23

2

Step 2: Subtract the tens: 7-2=5Step 3: To check subtraction, you must add

75

75fromsubtractedt wasnumber tha23

answer52

:Check

+


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75

- 23

52

52

+ 23

75

These numbers must be the same

Use this study board to teach the students how to check a subtraction problem using addition.

Use this example:

95

- 41


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ITBS/TAP:Perform arithmetic operations involving

integers, fractions, decimals and percents

ISAT:

Unit Focus/Foci



Formally assessing addition and subtraction

Materials


Inform the students that todays assessment will cover lessons 16 through 20. Day 19 included a

mini-review (Six Group Activity). Instruct students to remove everything except pencils andscrap paper from their desktops. Present the following assessment. (See attached.)


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Test

1. Define multi-digit.

2. Define regrouping as it is shown in the example. 411- 299

3. 471 4. 72 5. 410 6. 340 7. 242- 28 - 13 - 219 + 223 +129

8. 113 9. 100 10. 101 11. 97 12. 631+ 202 + 76 - 22 - 2 - 252

13. Susie traveled fourteen miles from her college to the nearest shopping mall, and another 2

miles to pick up fresh vegetables from the market. How many miles did Susie travel?_______________.

14. If Susie travels this same route twice a week, how many miles does she travel all together?

_______________.

15. Grace bought nine pencils for $1.09. She sold six pencils for twelve cents each. How muchmoney will Grace get if she sells all nine pencils? _______________. Will Grace make a

profit or lose money? Write and solve a problem to prove your answer.

16. $1.37 17. $2.49 18. $.98 19. $3.90- $.94 + $1.03 - $.21 -$2.29


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Mental Math. Estimate by rounding. Then solve.

20. Estimate: $1.47 21. Estimate: $2.04 22. Estimate: 134

______ - $1.04 ______ + $0.97 _______ - 20

23. Estimate: 108 24. Estimate: 215 25. Estimate: 170______ - 33 + 106 + 280

26. Bonus: (5 points) Answer for extra credit. (7 + 6 = 13) (13 - 6 = 7) This is an example of

________ ________. 6 13+ 7 - 6

13 7


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Answer Key

1. Multi-digit - a problem with three or more digits.

2. In problem #2, the digits in the ones and tens place in the minuend are smaller than the digits

in the ones and tens place in the subtrahend. Borrow one 10 from the tens place and changethem to ones. Subtract 9 from eleven (in the ones place). Now move to the tens place. 9tens cannot be subtracted from 0 tens. Borrow 10 tens from the hundreds place and subtract.

9 tens from 10 tens equal 1 ten. Finally calculate the hundreds place, 2 hundreds from 3hundreds equal 1 hundred. The difference is 12.

2 9 9

1 1 2

3 1 04 1 1

3. 443 4. 59 5. 191 6. 563 7. 371

8. 315 9. 176 10. 79 11. 95 12. 379

13. 16 miles 14. 32 miles or 64 miles (5 extra points for any student who comes upwith 64 miles).

15. $1.08 (lose money) $1.09 paid for pencils$.01 loss - 1.08 if sold for $.12 each

$ 0.01

16. $.43 17. $3.52 18. $.77 19. $1.61

20. _____ $.43 21. _____ $1.07 22. _____ 114

23. _____ 75 24. 321 25. 450

26. Inverse Operation


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Ten Statements


No Ten Statements today.

Free-Choice Lesson


Six Group Activity

No Six-Group Activity today.

Math Workshop

Have the students work in theMath Workshop after completing their Free Choice Lesson.




Analyze and interpret data

SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelines


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:


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Technology:

Assessment

Homework

Teacher Notes

structured curriculum lesson plan day: 010 subject: mathematics grade level:

Documents