Math Background

Lesson: Addition and Subtraction Facts to 20
Developing the Concept

Once children are comfortable with using a few different strategies to solve addition and subtraction problems, encourage children to apply them to the facts to 20. If manipulatives such as cubes are available, children may find it helpful to use them and fact cards. You will use many of the same strategies that you used in facts to 10 and add several new ones. Encourage children to share the strategies they use and tell why they used them.

Materials: snap cubes or other available items, such as paper clips, fact cards, pencils, paper

Preparation: Prepare fact cards for addition facts through 20 and for the corresponding subtraction facts. Write the strategy on each card.

Prerequisite Skills and Concepts: Children should have a good foundation in addition and subtraction facts through 10.

  • Say: There are different ways to help us learn our addition and subtraction facts. They are called strategies, and they make learning the facts easier. Today we are going to talk about some of those strategies.
  • Say: One of the ways we can learn some of our facts is to use the doubles strategy. That means that the two addends, or the two numbers we add, are the same. I am going to write two addends on the chalkboard.
  • Write 5 + 5. Point out that both numbers are the same. Have a volunteer write the equals sign and sum. Then have children write the fact on their papers. Repeat with several different double facts. You may want to point out that all doubles have sums that are even numbers.
    Now point out 5 + 5 = 10 again and beside it, write 5 + 6.
  • Say: You can use doubles to help you learn other facts. They are called doubles-plus-one facts. Look at both facts. What is the same and what is different?
    Elicit that both facts have a 5 as one addend, but in the second fact, the second addend has been changed to 6, or one more than 5.
  • Ask: What do you think the sum will be? (11) Why?
    (The second addend was 1 more so the sum should be 1 more.)
    Have a volunteer write the equals sign and sum.
  • Write 6 + 5 on the chalkboard.
  • Ask: What is the sum? (11)
  • Ask: Did the sum change? Why or why not?
    (No; the addends have been reversed, but they are the same numbers, so the sum will be the same.)
    Have children write the facts. Repeat with other doubles-plus-one facts.
  • Say: Today we will talk more about related facts. We found that addition facts that use the same three numbers, such as 9 + 4 = 13 and 4 + 9 = 13, are related. Notice that the addends and the sums in each fact are the same, but the numbers in the addends are reversed. Today we are going to write more of these related addition facts.
  • Say: I have written 7 + 8 on the chalkboard. Who can tell me the sum? (The sum is 15.)
    Invite a volunteer to write the equals sign and the answer. Have all the children then write the number sentence on their papers.
  • Say: This fact has used three numbers. I will point to the 2 addends and the sum. We know that we can make a related fact using these same three numbers.
  • Ask: Would someone like to write the related fact on the chalkboard?
    Have a volunteer write 8 + 7 = 15 under the first fact. Have all the children write the second fact under the first fact. Discuss that the addends are the same but now appear in a different order. You may want to draw lines between the numbers that are the same to show the children that this is so.
  • Ask: Has the sum changed?
    Elicit that the order of addends has changed but the sum has not changed.
  • Say: If we know these addition facts, we can use them to help us learn the subtraction facts. Look at the facts on the chalkboard. Remember, they have the same three numbers in both of them.
  • Ask: Can anyone tell me how we might make a subtraction fact from these 3 numbers?
    Elicit that the order of the numbers can be changed—that one of the smaller numbers can be taken away from the larger number. Help a volunteer write one of the subtraction facts on the chalkboard and then have children write the fact on their papers. Repeat for the other subtraction fact.
  • Say: We say these four facts are a fact family, or are related. If you know one addition fact, you can find its related facts, or fact family. You can use this strategy for many combinations of numbers. It's an important strategy for you to remember. You will use it many times.
  • Repeat with other combinations. Be sure to include the doubles for 12, 14, 16, 18, and 20. Point out that doubles only have two members in their family.
  • Say: Let's try a double fact. I will write 6 + 6 = 12 on the chalkboard.
  • Ask: Will we have a related addition fact?
    Elicit that because the two addends are the same, the other fact will be exactly the same, so there is only one addition fact. Then ask a volunteer to write the subtraction fact on the chalkboard.
  • Ask: What can you tell me about a double fact family?
    Doubles have only one addition fact and one subtraction fact in their family.
  • Review with children easy facts, such as 10 + 4. Then introduce the Make a Ten strategy.
  • Say: Sometimes when you work with larger numbers, it is easier to use the Make a Ten strategy.
  • Write 9 + 5 on the chalkboard. Point to the 9.
  • Say: First, you can make a 10 by taking 1 from the 5 and adding it to the 9 to make 10. Now you have a 10 and a 4 because you took 1 from the 5. If you add 10 and 4, you get 14, so 9 + 5 = 14.
  • Walk the children through the process as you point out each step that you take. Remind them that they must not forget what they subtracted from one number to add to the other number. Repeat with other combinations, such as 7 + 4, 8 + 3, and so on. You may want to use a ten frame and counters on the overhead for children who have difficulty with the strategy.
  • Say: The last thing that we are going to do is add three numbers. The strategies that you have learned will be very helpful.
    On the chalkboard, write an addition problem, such as
    8 + 2 + 8.
  • Ask: How would you add these numbers?
    Allow time for discussion of different strategies, such as adding the doubles, finding a fact they know, or making a ten. Repeat with other numbers, allowing time for children to explain their thinking.

Wrap-Up and Assessment Hints
Find out which facts children have mastered and which facts they need help with. If a fact has not been mastered, ask children how they might go about figuring it out. Find out what they are thinking and then select a strategy that builds on what they already know. Encourage children to use number relationships and fact families.

Houghton Mifflin Math Grade 2