Joining Equal Groups of Tens and Ones

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In this section children model an example that includes a two-digit number,such as 3 x 15, by showing 15 on three separate Place mats and thencombining the blocks in each place. Through this model, the children learn

that the basic meaning of multiplication applies to the larger blocks as well.

Exploring Multiplication of Tens and OnesRemind the children that they have been using the single blocks to model

multiplication, and explain that now they are going to use the larger blocksas well. Present a story problem with a two-digit number. For example:

Three children each have 23 blocks.

How many blocks do they have altogether?

For demonstration, find a place where youcan spread out three Place mats, one abovethe other. Arrange the mats and have singleblocks, blocks-of-10, and empty holders

available. Ask for three volunteers to arrange23 blocks on each of the mats.

To emphasize the importance of finding thetotal number of blocks in each place, ask,

How many groups of 20 do you see? How many

groups of 3 do you see?

Then have children push together the blocks in each column, tell the total num-ber of blocks-of-10 and ones (the order doesnt matter), set the Digit Flip Cardsto show the number, and write the related multiplication sentence (3 23 = 69).

Have children follow a similar procedure for two or three more examples thatdo not require regrouping, such as 4 21, 2 42, and 3 32. For the lastexample, show children how they can work with just one mat, placing theseparate groups one above the other. This will save space when children areworking independently or in small groups.

Whether using several mats or a single mat, make sure children always clearlyidentify the separate groups. It is important that they see the image of therepeated addition model because this reinforces the idea that they are multi-

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Focus Exploring multiplication with the blocks and

the Place mat

You can use several Place mats to model multiplication of two-digit numbers. Shown here is the model for 3 23.


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plying the whole number, not separatedigits. Given the limited space, it is bestto keep the number of groups to 5 or lessat this stage.

Next present a problem with regrouping,asking three children to model 3 16.As with the previous examples, childrenfirst form the 3 separate groups, thencombine the blocks and find the totalnumber in each place. Note that childrencan either count the blocks or add tofind the total in each place.

This time, children must pack the blocksin order to set the Digit Flip Cardscorrectly. This should not be difficultbecause it is the same process they have used throughout these units.

Have children work in pairs or smallgroups to find the answers to 4 13and 3 26. Provide time for childrento record their work on paper. They canuse drawings, words, and numbers todepict their steps. This recording

process provides another way for chil-dren to make multiplication meaningfuland is a vital component of their learning.Invite children to share their recordingswith one another, perhaps in relation toparticular story problems. Over time,such work gives you important insightinto childrens growth of understanding.At this stage, however, the main focus ison performing the tasks with the blocksand communicating the process.

Children should have many opportunities to combine equal groups consistingof blocks-of-10 and single blocks. Connect the process to multiplicationexamples presented in both vertical and horizontal forms, as well as to avariety of story problems. To encourage children to ref lect on the process, askquestions like these:

How many single blocks will there be when you put them together?

Why are you packing those single blocks?

How many new blocks-of-10 will there be? Why?

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To save space,children can model 3 32 on a single mat.Just be sure they clearly show 3 groups of 32.

This child found a way to show on paper the regrouping that wasneeded for 4 13.


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4-34-3For a greater challenge, you can extend these ideas to three-digit numbers.Children will discover that they can use exactly the same procedures as formultiplication of two-digit numbers.

Practicing Key IdeasRoll a Product

Children work in pairs. One child places blocks to show a two-digit number on the

Place mat.The other child rolls a die.The number rolled tells how many groups to make

of the number on the mat.Together, children form the groups.Then they find the

product and record their work using drawings,stamps, words, or a number sentence.

Assessing Learning

1. Have the child make 3 groups of 32 on the Place mat and set the DigitFlip Cards to show the total number. Does the child make the groups correctly? find the correct answer?

2. Present 5 23 in vertical or horizontal form. Ask the child to show youhow to use the blocks to find the product and explain what he or she isthinking. Does the child model the example correctly? find the correct answer?

clearly explain his or her thinking?

3. Have the child use the blocks and Place mat to model a story problem.For example:

You made 3 buildings with blocks.

Each building had 24 blocks.

How many blocks did you use in all?Does the child model the problem correctly using single blocks or blocks-of-10 and

singles? (either is appropriate)

find the correct answer? clearly explain his or her thinking?

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Joining Equal Groups of Tens and Ones