Math Background

Lesson: Modeling Subtraction
Developing the Concept

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Once children have had practice subtracting from numbers to 6, you can introduce the concepts of zero in subtraction, subtracting from numbers to 8, and writing subtraction sentences vertically. Finally, provide children with exercises for which they must choose the operation.

Materials: overhead projector, 8 overhead counters, blank overhead transparency; Workmat 1, 8 counters, number and symbol cards and Subtract From (PDF file) worksheet for each child; 2 spinners (0–8) for every 2 children

Preparation: During the lesson, be prepared to give each child a set of number and symbol cards and later 8 counters and a copy of Workmat 1. Prepare Subtract From (PDF file) worksheets for each child. Make spinners with numbers 0 to 8 for each pair of children.

Prerequisite Skills and Concepts: Children should be proficient in counting and recognizing numbers to 10. Children should demonstrate an understanding of finding sums to 8 and subtracting from numbers to 6.

  • Say: We have learned how to subtract from a group and how to write subtraction sentences.
    Place 4 counters on the overhead and have the children count them. Remove 3 counters.
  • Ask: What subtraction sentence can we write?
    Elicit from children the subtraction sentence 4 − 3 = 1.
    Write this on the overhead.
  • Ask: Which number shows you how many are left?
    Children should say “one.”
  • Say: Another word for how many are left is difference. In 4 − 3, the difference is 1.
    Place 4 counters on the overhead.
  • Ask: How many counters are there?
    Children should say “four.” Remove two counters.
  • Ask: How many counters did I take away?
    Children should say “two.”
  • Ask: How many counters are left?
    Children should say “two.”
  • Say: Four minus two equals two.
    Write 4 − 2 = 2 below 4 − 3 = 1. Make sure the numbers and symbols are lined up.
    Place 4 counters on the overhead.
  • Ask: How many counters are there? (4) How many should I take away so that there are four left?
    Elicit zero.
  • Say: When you subtract zero from a number, the difference is that number.
    Write 4 − 0 = 4 below 4 − 2 = 2. Leave a space in between for one more number sentence and make sure that the numbers and symbols are lined up.
  • Ask: How many counters should I take away to get a difference of zero?
    Elicit four.
  • Say: When you subtract a number from itself, the difference is zero.
    Write 4 − 4 = 0 above 4 − 3 = 1.
    Place 4 counters on the overhead.
  • Say: Look at the pattern. We have four minus four, four minus three, four minus two and four minus zero. What number sentence should go here? (Point to the blank area between 4 − 2 = 2 and 4 − 0 = 4.) Using your number cards, show me the subtraction sentence that belongs here.
    Once children have had a chance to arrange their own number cards, have several children come up to the front of the class to hold up the cards for 4 − 1 = 3.
  • Say: Think about how we wrote number sentences for addition. What is another way that we could show this subtraction fact?
    Give children time to rearrange their own number cards into vertical form. Then have a second set of children come up and hold number cards to show the problem.
    4 - 1 = 3
  • Ask: Are the numbers in both subtraction facts the same? (yes) What do both facts show?
    The children should say that both sentences show that 4 − 1 = 3.
  • Say: When you subtract like this, you are subtracting vertically.
    On the board, have children rewrite in vertical form the other number sentences from the overhead.
  • Say: So far, the greatest number we have subtracted from is 6. Now let's use your counters to subtract from 7.
    Place seven counters on the overhead. Have the children follow along with counters and Workmat 1.
  • Ask: How many counters are there? (7)
    How many did I take away? (0)
    How many are left? (7)
    Write the number sentence 7 − 0 = 7 on the overhead.
    Repeat, putting 7 counters on the overhead and removing one more each time. On the board, write the subtraction sentences as shown below.
    7 − 0 = 7
    7 − 1 = 6
    7 − 2 = 5
    7 − 3 = 4
    7 − 4 = 3
    7 − 5 = 2
    7 − 6 = 1
    7 − 7 = 0

  • Say: Let's look at all the sentences in which we subtracted from seven. Say the numbers as I point to them.
    Have children count down each column from top to bottom: “0, 1, 2, 3, 4, 5, 6, 7” 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: Do you think the pattern will be the same if we subtract from 8 instead of from 7?
    Allow time for children to suggest answers. Place 8 counters on the overhead. Do not remove any and ask children what number sentence you can record. Repeat, placing 8 counters on the overhead, removing one more each time and then recording the number sentence. Review the pattern of the number sentences as before.
  • Say: Now let's use our counters to act out a story. Eight birds are sitting in a tree. Three fly away. How many are left?
    Give the children time to find the answer with their counters. Children should then say “five.”
  • Ask: Did we add or subtract?
    Children should answer “subtract.”
  • Ask: How do you know?
    Elicit from children that three were taken away or there are fewer counters on the mat.
  • Say: Now there are five birds in the tree. Another bird joins them. How many birds are in the tree now?
    Children should say “six.”
  • Ask: Did we add or subtract?
    Children should answer “add.”
  • Ask: How do you know?
    Elicit from children that one more was put on the mat or there are more counters on the mat. Repeat with other problems, finding sums to or differences from 8 and asking the children what operation they used. You may wish to have volunteers tell addition and subtraction stories for the others to model with counters.

    Distribute Subtract From (PDF file) worksheets. Assign children a number up to 8 as the minuend. Have them use counters to model and write all the possible subtraction sentences for this number. Have children repeat with different numbers up to 8 as time allows.

Wrap-Up and Assessment Hints
You can assess children's understanding of addition and subtraction as well as their ability to choose the correct operation by providing them with two spinners (0–8). Have the children spin the first spinner and record the number. Then have them spin the second spinner and decide whether they need to add to or subtract from the first number to get the second number. Have children record their number sentences.


Houghton Mifflin Math Grade 1