More Numerical Patterns

10 min

Narrative

This Number Talk encourages students to rely on what they know about their place value and properties of operations to find the value of products mentally. The reasoning elicited in this routine will be helpful as students use their understanding of multiplication to generate patterns and explain features of patterns that aren’t explicit in their given rules.

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.

  • 20×320 \times 3
  • 21×321 \times 3
  • 40×340 \times 3
  • 42×342 \times 3

Sample Response

  • 60: 20 is 2×102 \times 10 and 3×2×103 \times 2 \times 10 is 6×106 \times 10 or 60.
  • 63: 21×321 \times 3 is one more group of 3 than 20×320 \times 3, or is (20×3)+(1×3)(20 \times 3) + (1 \times 3).
  • 120:
    • (4×3)×10=12×10=120(4 \times 3) \times 10 = 12 \times 10 = 120
    • 40×340 \times 3 is twice 20×320 \times 3, so it is twice 60, which is 120.
  • 126:
    • 42×342 \times 3 is 2 more groups of 3 (or 6 more) than 40×340 \times 3.
    • 42 is twice 21, so 42×342 \times 3 is two times as much as 21×321 \times 3 or two times 63, which is 126.
Activity Synthesis (Teacher Notes)
  • “How can one of the previous expressions help us find the value of 42×342\times3?” (We can take 21×321\times3 and double it to get 42×342\times3. We can take 40×340\times3 and add 2 threes.)
Standards
Building On
  • 4.NBT.1·Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. <em>For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.</em>
  • 4.NBT.A.1·Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. <span>For example, recognize that <span class="math">\(700 \div 70 = 10\)</span> by applying concepts of place value and division.</span>
Building Toward
  • 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

20 min

20 min