Model and Record 2-digit Subtraction

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Everyday Math Connection

summary materials

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Model and Record

2-Digit SubtractionOBJECTIVES:

To make connections between blocks, drawings,and numerical representations of 2-digit subtractionproblems

To model subtraction with blocks and to represent theprocess with a drawing

Students model 2-digit subtractionwith blocks.

They articulate the process anddevelop a pictorial recording

technique.

Each pair of students needs:

1 block-of-100 (Students canunpack to get the blocks theyneed for particular problems.)

1 place value mat with digit cards 2-3 copies ofRecording

Subtraction activity sheet

This activity uses Digi-Blocks to model subtraction with and without regrouping. Whenstudents see that a quantity needs to be regrouped in order to subtract, they need onlyunpack a block-of-10, rather than make a trade. The structure of the blocks makesregrouping easy and obvious to students.

A sequel to this activity, Recording Subtraction Part II, can be found online in theWeekly Pack-It at www.digi-block.com. In that activity, students begin to develop analgorithm as they record the process numerically.

Unit 6Activity A Model and Record 2-Digit Subtraction

6A

UNITFull Digi-Block

Activity


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Class Introduction 20 min

Display a 2-digit subtraction problem, such as:82 38

Have students read the problem aloud and describe

to you what it means. Ask,What is the problem telling you to do?

Have students think about what the problem willlook like before they build it with blocks. Ask,

How can I begin this problem using blocks on the mat?

Have students model the minuend (beginning number)on a place value mat.

Next, have them suggest how to separate, ortake away the 38 blocks from the 82 blocks.

Allow students to realize they must unpack 1

block-of-10 before they can subtract. It is helpful to have students move the blocksto another mat, possibly on a second studentsdesk. (See figure 1.)

Have students set the digit cards to show theamount remaining (44).

Pass out copies of the activity sheet and havestudents write the problem. Ask,

How can we record what weve done with the blocks?

Have volunteers demonstrate how they can sketch

blocks to show the number 82.

Remind students that drawings do not needto be works of art. It is only important thatthey can distinguish among the different-sizedblocks.

Encourage students to show how theysubtracted 38 from 82 in their drawing. Letthem invent their own notation (i.e. arrows,loops, etc.) and have them share their drawing.

Students may cross off the block-of-10 theyunpacked and draw ten single blocks.(See figure 2.)

To show the blocks they removed or separated,

students may circle the blocks and draw arrowsto where they place the blocks. (See figure 3.)

Present another subtraction problem:73-56

This time I am going to ask you to solve this problem without

using the blocks! Draw a picture to show how you would use

the blocks to solve this problem.

Be sure that they somehow represent theregrouping idea. If students get stuck and are


tens ones

4

8 2 - 3 8 = 4 4

82

- 38

tens one s

8

leaves

44

Tens Ones

Figure 1

Figure 2


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not sure how to proceed, have them use theblocks to help them.

Share drawings of the blocks and have studentsexplain how they determined the solution to theproblem.

Include a problem that does not requireregrouping, such as 38 25. Discuss why this

problem doesnt require any unpacking.

Group Activity 20 min

Have students work individually or in pairs.

Distribute more copies of the activity sheet. List avariety of problems on the board or chart paper from

which students will choose one or two to solve:

43 26 62 37 56- 24 74-38

As students are working, have them describe whatthey are doing. Ask:

Can you show me the ____ (larger number/total) in your drawing?

How did you show that you took away (subtracted, separated)

this number, or part?

What does this (point to a part of the picture) show?

Where is your answer?

Closure 20 min

Display a problem that several students have chosento solve. Have volunteers share and compare theirdrawings. Encourage students to ask questionsof one another in order to help them clarify theirexplanations.

Continue until all problems are discussed. If time permits, it may be helpful to make

transparencies of several drawings, so studentscan see their classmates work more easily.

Assessment

As students are solving problems observe

and note, do they:

Rely solely on the blocks to solve the

problem?

Solve the problem from a drawing of the

block model?

Represent the blocks and describe the

procedures they use accurately and

clearly?

Distinguish between problems that need

regrouping and those that do not?


Tens Ones

Figure 3


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ACTIVITY

SH

EET

DB-48

Name______________

Problem:

2.Write about what you did:

1. Draw the blocks to model the problem:

Tens Ones


Recording Subtraction

Student Book pp. 20-21

Documents

Model and Record 2-digit Subtraction