Decompose Area

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for multiplying a mixed number by a whole number. These understandings help students develop fluency and will be helpful later in this lesson when students decompose rectangles with fractional side lengths to find the area.

Launch

  • Display one problem.
  • “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 strategy.
  • Keep problems and work displayed.
  • Repeat with each problem.

Student Task

Find the value of each expression mentally.

  • 3×203 \times 20
  • 3×243 \times 24
  • 5×25 \times 2
  • 5×2125 \times 2\frac{1}{2}

Sample Response

  • 60: I know 3×2=63 \times 2 = 6, so 3×20=603 \times 20 = 60.
  • 72: I know 3×20=603 \times 20 = 60, 3×4=123 \times 4 = 12, so 60+12=7260+12=72.
  • 10: I just know it.
  • 121212\frac{1}{2}: I added half of 5 to 10 from the previous problem.
Activity Synthesis (Teacher Notes)
  • “How does breaking apart the numbers help us find the product?” (It is easier to find the product of big numbers when we decompose the numbers and add the smaller partial products.)
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