Use Whole Number Facts

10 min

Narrative

The purpose of this True or False is for students to demonstrate strategies and understandings they have for using the associative property of multiplication. The numbers in this Warm-up are whole numbers. In this lesson, students will use whole number products to find the value of the product of a whole number and a decimal and this requires using the associative property of multiplication.

Launch

  • Display one equation.
  • “Give me a signal when you know whether the equation is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategy.
  • Repeat with each equation.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 30×2×10=6×1030 \times 2 \times 10 = 6 \times 10
  • 30×2×10=20×3×1030 \times 2 \times 10 = 20 \times 3 \times 10
  • 60×10=30×2060 \times 10 = 30 \times 20

Sample Response

  • False: 30×230 \times 2 doesn't equal 6.
  • True: 30×2=20×330 \times 2 = 20 \times 3
  • True: They both equal 600.

Synthesis

  • Display the first equation.
  • “How can you show this is false without finding the value of both sides?” (I know 30×230 \times 2 is not 6 and multiplying both sides by 10 will not make them equal.)
  • Display second equation.
  • “How can you show this is true without finding the value of both sides?” (I know 30×230 \times 2 and 20×320 \times 3 are equal and then they are both multiplied by 10.)
Standards
Addressing
  • 5.OA.2·Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. <em>For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.</em>
  • 5.OA.A.2·Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. <span>For example, express the calculation “add <span class="math">\(8\)</span> and <span class="math">\(7\)</span>, then multiply by <span class="math">\(2\)</span>” as <span class="math">\(2 \times (8 + 7)\)</span>. Recognize that <span class="math">\(3 \times (18932 + 921)\)</span> is three times as large as <span class="math">\(18932 + 921\)</span>, without having to calculate the indicated sum or product.</span>

15 min

20 min