Angle Measurement and Perpendicular Lines

10 min

Narrative

The purpose of this Number Talk is to encourage students to make use of structure to perform division involving increasingly greater dividends and divisors (MP7). The reasoning here helps students to develop fluency in finding quotients of multi-digit numbers. It also reinforces students’ familiarity with factors of 180 and 360, which will be helpful as they continue to work with angle measurements.

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.

  • 180÷2180 \div 2
  • 180÷ 4180 \div  4
  • 360÷ 8360 \div  8
  • 360÷16360 \div 16

Sample Response

  • 90: 2×902 \times 90 is 180.
  • 45: 180÷4180 \div 4 is (180÷2)÷2(180 \div 2) \div 2 or 90÷290 \div 2.
  • 45: 360÷4360 \div 4 is 90, and 90÷290 \div 2 is 45.
  • 221222 \frac{1}{2}: if the divisor is doubled (from 360÷8360 \div 8 to 360÷16360 \div 16), then the quotient is halved.
Activity Synthesis (Teacher Notes)
  • “How are the expressions related?”
  • “How did finding the value of one expression help you find the value of the next expression?”
  • 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 expression in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

15 min

20 min