Build Multiplication Fluency

10 min

Narrative

The purpose of this Warm-up is to elicit the idea that there are different ways to calculate a product, using the standard algorithm, which will be useful when students find the products of a three-digit number and a two-digit number in a way that makes sense to them.

Launch

  • Groups of 2
  • Display the image.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

multiply. four hundred seventeen times 28.
multiply. four hundred seventeen times 28. 5 rows. First row: four hundred seventeen. Second row: multiplication symbol, 28. Horizontal line. Third row: three thousand three hundred thirty six. Fourth row: plus eight thousand three hundred forty. Horizontal line. Fifth row: eleven thousand six hundred seventy six

multiply. 28 times four hundred seventeen.
multiply. 28 times four hundred seventeen. 6 rows. First row: 28. Second row: multiplication symbol, four hundred seventeen. Horizontal line. Third row: one hundred ninety six. Fourth row: two hundred eighty. Fifth row: plus eleven thousand two hundred. Horizontal line. Sixth row: eleven thousand six hundred seventy six

Sample Response

Students may notice:

  • The numbers in the products are the same.
  • The results of the calculations are the same.
  • All the partial products are different.
  • One product has 2 partial products, and the other one has 3 partial products.

Students may wonder:

  • Why are the totals the same?
  • Will the totals always be the same if I calculate in these ways?
  • Which way of finding these products is faster?
Activity Synthesis (Teacher Notes)
  • “Why do you think the results of the two calculations are the same?” (The factors are the same, just in a different order. The order of the factors does not change the result of the multiplication.)
  • "Which way would you prefer to find the value of 417×28417 \times 28?" (I like the one with two partial products because there is less adding up to do.)
  • "Today you will get to choose how to find the products of a three-digit number and a two-digit number."
Standards
Addressing
  • 5.NBT.5·Fluently multiply multi-digit whole numbers using the standard algorithm.
  • 5.NBT.B.5·Fluently multiply multi-digit whole numbers using the standard algorithm.

15 min

15 min