More Practice to Represent and Solve

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies students have for multiplying single-digit factors and then adding two-digit numbers. The expressions involve two operations. They encourage students to look for and make use of structure as they use their understanding of equal-size groups and properties of operations to find products and sums (MP7). The reasoning here will be helpful later when students solve two-step word problems.

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 strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 20+(2×3)20 + (2 \times 3)
  • 30+(4×3)30 + (4 \times 3)
  • 50+(8×3)50 + (8 \times 3)
  • 99+(8×3)99 + (8 \times 3)
Solution Steps (4)
  1. 1
    Calculate 20+(2×3)
    →2×3=6, then 20+6=26
  2. 2
    Calculate 30+(4×3)
    →4×3=12, then 30+12=42
  3. 3
    Calculate 50+(8×3)
    →8×3=24, then 50+24=74
  4. 4
    Calculate 99+(8×3)
    →8×3=24, then 99+24=123 (use 100+24=124, minus 1)

Sample Response

  • 26: Two groups of 3 is 6, and 20+6=2620+6=26.
  • 42: I know that 4×34 \times 3 is 2 times 2×32 \times 3 or 2×62 \times 6, which is 12, and 30+12=4230 + 12 = 42.
  • 74: I know 8×38 \times 3  is twice 4×34\times 3, so it is 12+1212+12, which is 24. Adding 50 and 24 gives 74.
  • 123: It's like the problem right before it, but you have to add 99 and 24 instead of 50 and 24. Adding 24 to 100 gives 124, so adding 24 to 99 gives 123.
Activity Synthesis (Teacher Notes)
  • “How did the first two expressions help you find the values of the last two expressions?”
  • Consider asking:
    • “Who can restate ___ 's reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that <span class="math">\(8 \times 5 = 40\)</span>, one knows <span class="math">\(40 \div 5 = 8\)</span>) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

15 min

20 min