Math Background

Lesson: Inverse Relationship Between Addition and Subtraction
Developing the Concept

Once children are proficient in finding related facts, they are ready to discover fact families.

Materials: per child: 10 red cubes and 10 blue cubes

Preparation: none

Prerequisite Skills and Concepts: Children should understand addition and subtraction. They should also understand sums through 12 and subtracting from 12 or less, the numbers they are working on. They should also understand related facts.

Remind children about the related facts that you covered. Take time to review several pairs of related addition and subtraction facts.

  • Say: Today we are going to learn something new. Remember, we talked about related facts. Well, today we are going to talk about a fact family. All the facts in a fact family are related.

    Pick up 4 red cubes and 2 blue cubes.

  • Say: I will put the red cubes together and the blue cubes together. Now I will place the blue cubes on the end of the red cubes to make a train.
  • Ask: What fact can you make from this train?
    (4 + 2 = 6)

    Write each of the facts on the board as you introduce them.

  • Say: Watch as I turn the train end to end.
  • Ask: What fact do you see now? What is the same about the two facts?
    (2 + 4 = 6; they use the same 3 numbers.)
  • Ask: Can we show a subtraction fact using this train? How?
    Elicit from children that you can break one of the colors of cubes off the train.

    Break the blue cubes off the train.

  • Ask: What subtraction fact have I made?
    (6 − 2 = 4)

    Put the train back together. This time break off the red cubes.

  • Ask: What subtraction fact have I made this time?
    (6 − 4 = 2)
  • Say: What do you notice about the four facts that we just made?
    Children should say that there are two addition and two subtraction facts and that all four facts have the same 3 numbers.
  • Ask: How are the numbers related?
    The same numbers are used in all four facts.

    Repeat with other fact families that have four facts. Then use 3 red and 3 blue cubes to make a train.

  • Ask: What is the addition fact? What will happen when I turn this train end to end?
    (3 + 3 = 6; it is the same.)

    Break 3 red cubes off the train.

  • Ask: What is the subtraction fact? Will the fact change if I break off the blue cubes?
    (6 − 3 = 3; no.)
  • Ask: What can you tell me about a doubles fact family?
    Children should say that it has only 2 facts in it—one addition and one subtraction.

    Have children work with the cubes to make fact families. Then write a fact on the board and invite children to write the complete family. Be sure to include some doubles facts.

  • Finally, give children 3 numbers such as 3, 6, and 9.
  • Ask: What fact family can you make from these 3 numbers?
    (3 + 6 = 9, 6 + 3 = 9, 9 − 3 = 6, 9 − 6 = 3)

    Repeat with other numbers, including doubles.

Wrap-Up and Assessment Hints
Children need lots of practice with related facts. As you assess, give one fact and have the children write the fact family. Or ask questions such as, Can you write a related addition fact for 12 − 5 = 7? As you observe, check to see that children are using the correct sign and are doing the correct operation for the sign that is in the exercise.

Houghton Mifflin Math Grade 1