Ways to Divide Greater Numbers

10 min

Narrative

The purpose of this True or False? is to reinforce the relationship between tens and ones (that 1 ten is equal to 10 ones, or 1 group of 10 is 10 groups of 1). This will be helpful when students use base-ten blocks to represent division and decompose tens into ones to facilitate the process of dividing. It also allows students to practice finding the product of a one-digit whole number and a multiple of 10.

Launch

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

Student Task

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

  • 4×10=40×14 \times 10 = 40 \times 1
  • 4×20=4×2×104 \times 20 = 4 \times 2 \times 10
  • 8×20=8×2×18 \times 20 = 8 \times 2 \times 1
  • 8×20=16×108 \times 20 = 16 \times 10
Solution Steps (4)
  1. 1
    Evaluate 4×10 = 40×1
    →True: 4×10=40 and 40×1=40, both equal 40
  2. 2
    Evaluate 4×20 = 4×2×10
    →True: 4×20=80, and 4×2×10=8×10=80, associative property
  3. 3
    Evaluate 8×20 = 8×2×1
    →False: 8×20=160, but 8×2×1=16, not equivalent
  4. 4
    Evaluate 8×20 = 16×10
    →True: 8×20=160 and 16×10=160, using 8×2=16

Sample Response

  • True: 4 tens is 40 ones. Both sides are equal to 40.
  • True: The 2×102 \times 10 is 20, so both sides show 4 groups of 20.
  • False: On the left is 8 groups of 20. On the right is 8 groups of 2, since 2×12 \times 1 is 2.
  • True: 20 is 2×102 \times 10, so 8×208 \times 20 is the same as 8×2×108 \times 2 \times 10, which is 16×1016 \times 10. 
Activity Synthesis (Teacher Notes)
  • “How can you justify your answer without finding the value of both sides?”
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Does anyone want to add on to _____’s reasoning?”
Standards
Addressing
  • 3.NBT.3·Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
  • 3.NBT.A.3·Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., <span class="math">\(9 \times 80\)</span>, <span class="math">\(5 \times 60\)</span>) using strategies based on place value and properties of operations.

20 min

15 min