Attributes of Other Quadrilaterals

10 min

Narrative

This Number Talk prompts students to rely on properties of operations and the relationship between multiplication and division to divide within 100. The reasoning helps students develop fluency in division.

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.

  • 70÷770\div7
  • 77÷777\div7
  • 63÷763\div7
  • 56÷756\div7

Sample Response

  • 10: I know 7×10=707\times10=70, so 70 divided by 7 is 10. I just know it.
  • 11: Because 70÷770\div7 is 10, then it is just one more group of 7, so 77÷777\div7 is 11.
  • 9: 63 is 7 less than 70, so it is 1 fewer group of 7, which is 9 groups.
  • 8: It is 1 fewer group of 7 than the previous problem since 63−56=763-56=7. I know that 8×7=568\times7=56, so 56 divided by 7 is 8.

Synthesis

  • “What pattern do you see as you look at the expressions and their values? Why is that happening?” (I noticed that the first number in the first expression increased by 7 for the second expression, so there would be 1 more group of 7. The first number in the third expression is 7 less than 70, so there’s 1 less group of 7. The first number in the last expression is 7 less than 63, so there’s 1 less group of 7.)
  • As needed, record student thinking with expressions or equations. Consider using smaller numbers to help test any generalizations students make about the pattern.
  • Consider asking:
    • “Did anyone notice a different pattern”?
    • “Did anyone notice the same pattern but would explain it differently?”
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.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <em>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</em>
  • 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.
  • 3.OA.D.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <span>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</span>

20 min

15 min