Lesson 4

Subtraction with Base-Ten Pieces

Est. Class Sessions: 2

Summarizing the Lesson

Challenge students by presenting the following problem that involves two trades:

152
− 78

Ask:

X
  • Show or tell how you estimate the answer to this problem. (Possible response: I use the 200 Chart. I start at 152 and then go back 8 rows because that is 80 and 78 is close to 80. I estimate the difference to be about 72.)

Tell student pairs to represent 152 with base-ten pieces and then take 78 away. Make sure they are placing pieces to represent the number 152 and then removing the pieces that represent 78. Give students some time to work through the problem and then share their answers. Remember that students can choose whether they subtract the ones first or the tens first. Circulate as the students work to witness their various approaches.

After students have had time to find a solution, ask:

X
  • What was different about this problem? (There were two trades.)
  • If 152 is more than 78, you should be able to subtract 78. Who has an idea for how to do that? (Trade the flat for skinnies and a skinny for bits.)
  • If you trade one flat for skinnies, how many skinnies do you get? (10)
  • If you trade one skinny for bits, how many bits do you get? (10)

Have students leave their piles on their desks as you ask a volunteer to model his or her solution strategy using display base-ten pieces. Make sure he or she clearly explains the trades. To see if the student’s answer seems reasonable, ask the class to compare it to their estimate.

Students may solve this problem in a variety of ways. Some students may begin on the right by trying to subtract 8 ones from 2 ones, or take 8 bits from 2 bits. However, some students may begin the problem from the left instead. Others might find it easier to do all the trading first and then subtract. Select other students to demonstrate their various approaches.

Ask:

X
  • Show us how you solved 152 − 78.
  • Who can show us another way to solve it?
  • Which method is easier? Which is more efficient? Why?
  • What happens when you are subtracting and you don’t have enough bits? (You take one of the skinnies away and trade it for 10 bits. Then you can take away as many bits as you need.)
  • What if you don't have enough skinnies? (You can do the same thing—you trade. You can trade 1 flat for
    10 skinnies.)
  • Does trading change your number? (No. 10 bits is the same as 1 skinny, and 10 skinnies is the same as
    1 flat, so the value of the number stays the same.)

Next ask students to check their subtraction with addition.

To assist them, ask:

X
  • What number is shown by the pieces in your take-away pile? (78)
  • What number is shown by the pieces in your answer pile? (74)
  • What number is shown when you put the piles back together? (152)
  • What does this tell you? (78 + 74 = 152, so I know my answer is correct.)

Ask students to solve the problem a second way to check the calculations. Remind them that they can use strategies from the Subtraction Strategies Chart.

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