Fractions

Lesson 18

Objective

Express whole numbers greater than 1 as fractions.

Common Core Standards

Core Standards

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  • 3.NF.A.3.C — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Example: express 3 in the form 3 = 3/1; recognize that 6/1 = 6. Example: locate 4/4 and 1 at the same point of a number line diagram.

Criteria for Success

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  1. Understand that a fraction is equivalent to a whole number if they are the same size or the same point on a number line.
  2. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers (e.g., $$3=\frac{6}{2}$$).
  3. Explain the equivalence of a whole number with a fraction using an area model, number line, or other method (MP.3, MP.5).
  4. Look for and express regularity in repeated reasoning to generalize that when the numerator can be evenly divided by the denominator in a fraction, the fraction is equivalent to the quotient of that division (MP.8). (Note: this is beyond the scope of 3.NF.3 and therefore is optional, though it is likely students will deduce this pattern.)

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Anchor Tasks

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Problem 1

Yong portions milk into servings that are each $$\frac{1}{4}$$ bottle of milk. He has 8 servings altogether. Yong says he has 2 bottles of milk. Do you agree or disagree? Explain your thinking.

Guiding Questions

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Problem 2

Explain how $$ \frac{12}{3}=4$$. Use an area model or a number line to support your thinking.

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • Compare the number lines and area models in #1. What does each representation help you see?
  • In #2, what strategy did you use to find the whole number fractions without having to partition a number line again?
  • How did you use the pattern you noticed in #3 to determine the number of tenths equivalent to 2 wholes? 3 wholes? 4 wholes?
  • How did you use the pattern you noticed in #4 to determine what 6 wholes was equivalent to in terms of halves? Thirds? Fifths? Eighths?
  • How did you use the patterns you noticed in previous problems to help you solve #5?
  • Did Kevin have more orange pieces or apple pieces in #5, Part C? How do you know? Did anyone solve by reasoning about the size of each piece? Explain.

Target Task

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Determine how many sixths are in 3 wholes. Draw a model to help explain your thinking.

Mastery Response

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