Multiply More Decimals

10 min

Narrative

The purpose of this Estimation Exploration is for students to apply what they know about area and multiplication of decimals to a situation where the side lengths of the rectangle are decimals. Students will approximate the length and width to obtain a product of decimals which they can find mentally. This prepares them for work in the lesson where students will find more complex products of decimals since making an estimate is a good way to check work. 

Launch

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

Student Task

Image of map of Central Park.

Central Park is a large park in Manhattan. It is about 3.85 kilometers long and 0.79 kilometer wide. What is the approximate area of Central Park?

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • Too low: 2 to 2.5 square kilometers
  • About right: near 3 square kilometers
  • Too high: 3.5 square kilometers or more

Synthesis

  • Invite students to share their estimates.
  • “How do you know the area is greater than 2 square kilometers?” (I know that 3×0.73 \times 0.7 is 21 tenths or 2.1 and it’s more than that.)
  • “How do you know the area is less than 3.2 square kilometers?” (I know 3.85 is less than 4 and 0.79 is less than 0.8. Then 4×0.84 \times 0.8 is 32 tenths or 3.2.)
Standards
Addressing
  • 5.NBT.1·Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • 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.A.1·Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • 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