Compare Perimeters of Rectangles

10 min

Narrative

This Number Talk elicits the strategies and understandings students have for multiplying a whole number and a fraction mentally. The reasoning here prepares students to perform multiplication to solve problems about the perimeters of rectangles with fractional side lengths later in the lesson.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 2×322 \times \frac{3}{2}
  • 4×344 \times \frac{3}{4}
  • 4×944 \times \frac{9}{4}
  • (2×34)+(2×94)\left(2 \times \frac{3}{4}\right) + \left(2 \times\frac{9}{4}\right)

Sample Response

  • 3: Two times 32\frac{3}{2} is 62\frac{6}{2}, which is 3.
  • 3:
    • 4 groups of 34\frac{3}{4} make 124\frac{12}{4}, which is 3.
    • 2×342 \times \frac{3}{4} is 64\frac{6}{4}, which is 1241\frac{2}{4} or 1121\frac{1}{2}, so 4×344 \times \frac{3}{4} is twice 1121\frac{1}{2} or 3.
  • 9: 94=9×14\frac{9}{4} = 9 \times \frac{1}{4} so 4×94=4×9×144 \times \frac{9}{4} = 4 \times 9 \times \frac{1}{4}, which is 364\frac{36}{4} or 9.
  • 6:
    • 2×34=642 \times \frac{3}{4} = \frac{6}{4} and 2×94=1842 \times \frac{9}{4} = \frac{18}{4}, and 64+184=244\frac{6}{4} + \frac{18}{4} = \frac{24}{4}, which is 6.
    • 2×342 \times \frac{3}{4} is half of 4×344 \times \frac{3}{4} or half of 3, which is 1121\frac{1}{2}. 2×942 \times \frac{9}{4} is half of 4×944 \times \frac{9}{4}, or half of 9, which is 4124\frac{1}{2}. Adding 1121\frac{1}{2} and 4124\frac{1}{2} gives 6.
Activity Synthesis (Teacher Notes)
  • “How do the first three expressions help you find the value of the last expression?”
Standards
Addressing
  • 4.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

10 min

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10 min