Multiply Numbers Greater than 20

10 min

Narrative

This Number Talk encourages students to think about the multiplication of one-digit numbers and multiples of 10 and to rely on place value to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students multiply one-digit numbers by greater two-digit numbers.

Launch

  • Display the first 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.

  • 3×103 \times 10
  • 3×203 \times 20
  • 3×503 \times 50
  • 3×253 \times 25
Solution Steps (4)
  1. 1
    Calculate 3×10
    →3×10 = 30 (basic fact)
  2. 2
    Calculate 3×20 using place value
    →3×20 = 3×2×10 = 6×10 = 60
  3. 3
    Calculate 3×50 using place value
    →3×50 = 3×5×10 = 15×10 = 150
  4. 4
    Calculate 3×25 using decomposition
    →3×25 = 3×20 + 3×5 = 60 + 15 = 75

Sample Response

  • 30: Three groups of 10 is 30. I just knew it.
  • 60: Twenty is twice 10, so the product is twice 30, which is 60. Twenty is 2×102 \times 10, and 3×2×103 \times 2 \times 10 is 6×106 \times 10 or 6 groups of 10, which is 60.
  • 150: Fifty is 10+20+2010 + 20 + 20, so 3×503 \times 50 is (3×10)+(3×20)+(3×20)(3 \times 10) + (3 \times 20) + (3 \times 20) or 30+60+6030 + 60 + 60, which is 150. Fifty is 5×105 \times 10, so 3×503 \times 50 is 3×5×103 \times 5 \times 10 or 15×1015 \times 10, which is 150.
  • 75: Twenty-five is half of 50, so 3×253 \times 25 is half of 3×503 \times 50 or half of 150, which is 75. It’s 3×53 \times 5 more than 3×203 \times 20, so it’s 15 more than 60, or 60+1560 + 15, which is 75.
Activity Synthesis (Teacher Notes)
  • “How did the first three problems help you solve the last problem?” (Since I knew 3×203 \times 20 was 60, I just added 3×53 \times 5, or 15, to 60. I broke 3×253 \times 25 into 3×103 \times 10, 3×103 \times 10, and 3×53 \times 5 to make it easier to multiply. Since 25 is half of 50, I took half of  3×503 \times 50 to find 3×253 \times 25, and half of 150 is 75.)
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.
  • 3.OA.5·Apply properties of operations as strategies to multiply and divide.
  • 3.OA.B.5·Apply properties of operations as strategies to multiply and divide.<span>Students need not use formal terms for these properties.</span> <span>Examples: If <span class="math">\(6 \times 4 = 24\)</span> is known, then <span class="math">\(4 \times 6 = 24\)</span> is also known. (Commutative property of multiplication.) <span class="math">\(3 \times 5 \times 2\)</span> can be found by <span class="math">\(3 \times 5 = 15\)</span>, then <span class="math">\(15 \times 2 = 30\)</span>, or by <span class="math">\(5 \times 2 = 10\)</span>, then <span class="math">\(3 \times 10 = 30\)</span>. (Associative property of multiplication.) Knowing that <span class="math">\(8 \times 5 = 40\)</span> and <span class="math">\(8 \times 2 = 16\)</span>, one can find <span class="math">\(8 \times 7\)</span> as <span class="math">\(8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56\)</span>. (Distributive property.)</span>

15 min

15 min