Math Background

Lesson: Modeling and Recording Subtraction
Developing the Concept

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Once children have had practice subtracting 1 from numbers 1 through 10, you can introduce the concept of subtracting 2 from a number. Then you can move on to vertical subtraction, subtraction facts to 10, and subtracting pennies. Once children have practiced various subtraction facts, provide them with problems where they must choose the operation.

Materials: overhead projector, 10 counters, 10 pennies; Workmat 1, 10 counters, 10 pennies, number cards 1−10 and symbol cards from Learning Tools 8 and 9, for each pair of children; Subtract (PDF file) worksheets for each child

Preparation: Prepare a copy of Workmat 1 for each pair of children. Prepare a Subtract (PDF file) worksheet for each child.

Prerequisite Skills and Concepts: Children should be proficient in counting and recognizing numbers to 10. Children should have experience finding sums to 10.

  • Say: We have learned how to subtract 1 from a number and how to write subtraction sentences.
    Place 5 counters on the overhead and have the children count them. Remove 1 counter.
  • Ask: What did I just do?
    Children should say that you subtracted or took away 1.
  • Ask: What subtraction sentence can we write?
    Elicit from children the sentence 5 − 1 = 4.
    Write 5 − 1 = 4 on the overhead.
  • Ask: When you subtract 1 from 5, how many are left?
    Children should say “4.”
  • Say: The number you have left when you subtract is called the difference. In 5 minus 1, the difference is 4. Now let's start again.
    Replace the counter you removed and have children count to see there are 5 counters on the overhead again. Then remove 2 counters.
  • Ask: How many counters did we start with?
    Children should say “5.”
  • Ask: How many counters did we take away?
    Children should say “2.”
  • Say: Now let's count to find the difference.
    Children should count aloud to 3.
  • Ask: How do we write this number sentence?
    Elicit 5 − 2 = 3.
  • Say: Five minus two equals three.
    Write 5 − 2 = 3 under 5 − 1 = 4. Make sure the numbers and symbols are lined up.
  • Practice subtracting 2 from various numbers from 2 to 10. Give each pair of children 10 counters, a copy of Workmat 1, and a set of number and symbol cards. Have them follow along by having one child show the subtraction with the counters while the other child makes the corresponding subtraction sentence with the cards. Have children change roles periodically. When children show an understanding of this, put 8 counters on the overhead.
  • Ask: How many counters are there?
    Children should say “8.”
  • Say: Now let's take away 2.
    Remove 2 counters.
    Help me count how many are left.
    Children should count aloud to 6.
  • Say: Show me this subtraction sentence with your number cards and symbol cards.
    Once children have had a chance to arrange their own number cards, have several children come to the front of the class to hold up the cards for 8 − 2 = 6.
  • Ask: Think about how we wrote number sentences for addition. What is another way we could show this number sentence?
    Give children time to rearrange their own number cards into vertical form. Then write the vertical subtraction on the chalkboard.
    stacked equation: eight minus two equals six
  • Ask: Are the numbers in both sentences the same?
    Children should say “yes.”
  • Ask: What do both number sentences show?
    Children should say that the sentences show 8 − 2 = 6.
  • Say: Just as with addition, you can show a subtraction sentence this way (point to the children showing the horizontal subtraction) or this way (point to the chalkboard showing the vertical subtraction).
  • Say: Now let's use pennies instead of counters to subtract other numbers from 8.
    Have children trade their 10 counters for 10 pennies.
    Put 8 pennies on the overhead.
  • Ask: Put 8 pennies on your mat and pretend you are at the store. You see something you want to buy for 1 penny. (Remove 1 penny from the overhead.) How many pennies are left?
    Children should say “7.”
    Write 8 − 1 = 7 on the board. Put one penny back on the overhead.
  • Ask: We already found the difference of 8 minus 2. Can anyone tell me what it is?
    Children should say “6.”
    Repeat, putting 8 pennies on the overhead and then spending one more each time. Write the subtraction sentences on the board, as shown below.
    equations: eight minus one equals seven; eight minus two equals six; eight minus three equals five; eight minus four equals four; eight minus five equals three; eight minus six equals two; eight minus seven equals one; eight minus eight equals zero;
  • Say: Let's look at all the sentences where we subtracted from 8. Say the numbers as I point to them.
    Have children count down each column from top to bottom saying “1, 2, 3, 4, 5, 6, 7, 8” and then “7, 6, 5, 4, 3, 2, 1, 0.”
  • Ask: Do you see a pattern?
    Children should say that each number in the second column is 1 more than the number above it. Children should say that each number in the third column is 1 less than the number above it.
  • Ask: Everyone put 5 pennies on your workmat. Pretend you found 3 more pennies. Put them on your workmat. How many pennies do you have now?
    Children should say “8.”
  • Ask: Did we add or subtract?
    Children should say “add.”
  • Ask: How do you know?
    Children should say it is because we put 3 more on the mat (or added 3), or because the number of pennies on the mat increased.
  • Ask: Now let's pretend to spend 6 of the pennies on our mat. How many do you have now?
    Children should say “2.”
  • Ask: Did you add or subtract?
    Children should say “subtract.”
  • Ask: How do you know?
    Children should say it is because we took 6 away from the mat (or subtracted 6), or because the number of pennies on the mat decreased.

    Distribute “Subtract blank (PDF file) worksheets. Have children use the counters or pennies to subtract 3 from numbers 3 to 10.

Wrap-Up and Assessment Hints:
You can assign each child or pair of children a number or set of numbers. Have them model and write subtraction sentences with minuends up to 10 and the number that you have assigned as the subtrahend. Have children use the “Subtract blank (PDF file) worksheet to record their subtraction sentences.

Houghton Mifflin Math Grade K