Multi-step Conversion Problems: Customary Lengths

10 min

Narrative

This Number Talk helps students develop strategies to find multiples of 12 mentally, using place value and the distributive property. This work prepares students for converting measurements in feet to measurements in inches.

Launch

  • Display the first 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 students’ answers and strategies.
  • Keep the expressions and the work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 45×245 \times 2
  • 45×1045 \times 10
  • 45×1245 \times 12
  • 46×1246 \times 12

Sample Response

  • 90: I doubled 40 and added 10.
  • 450: Every digit shifts one place to the left because I multiplied by 10.
  • 540: I added the previous two products.
  • 552: I just added another 12.
Activity Synthesis (Teacher Notes)
  • “How are the values of the products 45×1245 \times 12 and 46×1246 \times 12 related?” (There is one more 12 in 46×1246 \times 12.)
Standards
Building Toward
  • 5.MD.1·Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
  • 5.MD.A.1·Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

15 min

20 min