Use Properties to Multiply Decimals

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for place value relationships and the properties of operations as they find the value of different products (MP7). The products all have the same value, 6, and also all have a decimal factor of 0.1 or 0.01. The whole number factors are organized differently and this encourages students to think flexibly about how to find products of a whole number and a decimal.

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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 40×2×0.140 \times 2 \times 0.1
  • 20×0.1×420 \times 0.1 \times 4
  • 0.1×800.1\times 80
  • 0.01× 20× 400.01 \times 20 \times 40

Sample Response

  • 8: 40×2=8040 \times 2 = 80 and 80×0.1=8.080 \times 0.1 = 8.0
  • 8: 20×420 \times 4 is the same as 40×240 \times 2 so the value of the expression is the same as the first one.
  • 8: 80 tenths is equal to 8 ones.
  • 8: It is the same as 800×0.01800 \times 0.01.
Activity Synthesis (Teacher Notes)
  • “How is the last expression different from the others?” (It has a hundredth in the product instead of a tenth.)
  • “How did you find the value of this expression?” (I knew 40×20=80040 \times 20 = 800 and then 800 hundredths is 8.)
Standards
Addressing
  • 5.NBT.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 5.NBT.B.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

20 min

15 min