Fraction Games

10 min

Narrative

The purpose of this Estimation Exploration is for students to develop strategies for finding the product of a fraction and a mixed number. Since 2892 \frac{8}{9} is so close to 3, a good estimate is 3×283 \times 28 or 84. Students may refine this estimate using the distributive property 

\begin{array} 28 \times 2\frac{8}{9} &=& 28 \times \left(3 - \frac{1}{9}\right)\\ &=& 28 \times 3 - 28 \times \frac{1}{9} \end{array}

Since 289\frac{28}{9} is about 3, 84−384 - 3 or 81 is a good estimate. Students will use these ideas in the lesson when they find products of fractions, whole numbers, and mixed numbers.

Launch

  • Groups of 2
  • Display the image.
  • “What is an estimate that’s too high? Too low? About right?”
Teacher Instructions
  • 1 minute: quiet think time
  • 1 minute: partner discussion
  • Record responses.

Student Task

28×28928 \times 2 \frac{8}{9}

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • too low: 56 or less
  • about right: 80–83
  • too high: 84 or more
Activity Synthesis (Teacher Notes)
  • “How does 28×28928 \times 2\frac{8}{9} compare to 28×228 \times 2? How do you know?” (It’s larger because 2892 \frac{8}{9} is greater than 2.)
  • “Why is 28×328 \times 3 a good estimate?” (2892\frac{8}{9} is really close to 3.)
  • “Is 28×28928 \times 2\frac{8}{9} greater or less than 28×328 \times 3? How do you know?” (Less, because 2892\frac{8}{9} is less than 3.)
Optional: Reveal the actual value, 808980\frac{8}{9}, and add it to the display.
Standards
Addressing
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

20 min

15 min