Lesson 5

Subtract Mixed Numbers

Est. Class Sessions: 2–3

Summarizing the Lesson

To summarize the lesson, ask students to solve the following problem using any strategy they choose:

X

John wants to make instant soup. He has to add 11/4 cups of water per serving. His bowl fits 22/3 cups. Can he make 2 servings in his bowl?

  • Does this problem need an exact answer or can you estimate? How did you decide? (estimate; Possible response: As long as 11/4 + 11/4 cups is less than 22/3 cups, he can make 2 servings in his bowl. The question doesn't say how many more cups are left after filling the bowl with 2 servings.)
  • Who would like to show how they solved the problem? (Possible response: I used mental math. 11/4 + 11/4 is 21/2 . I know 21/2 is less than 22/3 because 1/2 is less than 2/3 , so he has enough room to make 2 servings in the bowl.)

Present this problem to the students:

X

According to the directions on the packet, John needs to add 31/3 cups of water to his lemonade mix. He has 11/9 cups of water in his water bottle. How much more water does he need to make the lemonade?

  • Does this problem ask for an exact answer or can you estimate? How did you decide? (exact answer; Possible response: The question asks, “How much more water does he need?” Recipes usually call for exact measurements.)
  • What number sentence describes this situation? (Possible response: 31/3 − 11/9 )
  • How can estimation help before you find the exact answer? (Estimating can help you know if your exact answer is reasonable.)
  • Do you think the answer will be closer to 0, 1, 2, or 3? (Possible response: 2)
  • Who would like to show how they solved the problem? (Possible response: I used mental math with a few notes and counted up. 8/9 cup more water makes 2 cups. 9/9 cup more water makes 3 cups. I know 1/3 is equivalent to 3/9 . 8/9 + 9/9 + 3/9 = 20/9 . I wrote down 20/9 and changed it to 22/9 . He needs 22/9 more cups of water.)
  • Did someone solve the problem using a paper and pencil method? Show us. (Possible response: I know 3 × 3 = 9, so I used 9 as a common denominator: 33/9 − 11/9 . I subtracted the fractions 3/9 − 1/9 = 2/9 , and then subtracted the wholes 3 − 1 = 2. He needs 22/9 more cups of water.)
  • How do these answers compare with your estimate?
  • Do you have a favorite subtraction strategy? Why is it your favorite?
  • Do you like to use a variety of subtraction strategies? How do you decide which strategy to use? (Possible responses: Some strategies work better for different subtraction situations. For example, I might use mental math and count up when there is a “How many more” problem. I can think of a ruler as a number line when there are halves, fourths, and eighths involved. I might use fraction circle pieces if the denominators are 2, 3, 4, 5, 6, 8, 10, or 12. I can use paper-and-pencil to solve any fraction problem, especially ones with unlike denominators.)
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