Represent Problems on the Coordinate Grid

10 min

Narrative

The purpose of this True or False is for students to demonstrate understandings they have of the properties of operations. These understandings will be helpful later when students use addition and multiplication to solve problems involving money. Each expression here is chosen to represent the total value of a set of coins (nickels, dimes, and quarters).

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.

  • (2×10)+(3×5)=(3×10)+(1×5)(2 \times 10) + (3 \times 5) = (3 \times 10) + (1 \times 5)
  • (3×25)+(5×5)=8×25(3 \times 25) + (5 \times 5) = 8 \times 25
  • (4×25)+(10×5)=(2×25)+(10×10)(4 \times 25) + (10 \times 5) = (2 \times 25) + (10 \times 10)

Sample Response

  • True: 2 groups of 10 and 3 groups of 5 is the same as 3 groups of 10 and 1 group of 5, or 20+15=30+520 + 15 = 30 + 5.
  • False: (3×25)+(5×5)=4×25(3 \times 25) + (5 \times 5) = 4 \times 25
  • True: 100+50=50+100100 + 50 = 50 + 100

Synthesis

  • “Which statement was your favorite to think about and why?” (I liked the first one because I could calculate all the values mentally.)
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

15 min