Use a Protractor to Measure Angles

10 min

Narrative

The purpose of this Warm-up is to draw students’ attention to the first few multiples of 45, which will be helpful as students continue to work with benchmark angles and use a protractor to measure angles. Students have the skills to perform the multiplication in each equation, but computing each product may be time-consuming. Students can more efficiently tell if the equations are true or false if they consider properties of operations and look for and make use of structure.

Launch

  • Display one equation.
  • “Give me a signal when you know whether the equation is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategies.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Explain your reasoning.

  • 2×45=6×152 \times 45 = 6 \times 15
  • 4×45=2×904 \times 45 = 2 \times 90
  • 3×45=180−903 \times 45 = 180 - 90
  • 6×45=45+90+1356 \times 45 = 45 + 90 + 135

Sample Response

  • True: the 45 on the left side is 3×153 \times 15, and the 6 on the right is 2×32 \times 3. Both sides are 2×3×152 \times 3 \times 15.
  • True: 2×902 \times 90 is 2×2×452 \times 2 \times 45, which is equal to 4×454 \times 45.
  • False: the right side is 90, which is 2×452 \times 45, so the 3×453 \times 45 on the left side cannot also be 90.
  • True: the right side is (1×45)+(2×45)+(3×45)(1 \times 45) + (2 \times 45) + (3 \times 45), which is equal to 6×456 \times 45.

Synthesis

  • Some students may notice that it is handy to think in terms of 2×452 \times 45 because it would mean dealing with multiples of 90 rather than with multiples of 45. Highlight their explanations.
  • If no students decomposed expressions such as 3×453 \times 45, 4×454 \times 45, and 6×456 \times 45 into sums of 1×451 \times 45 and 2×452 \times 45, discuss how this could be done. (See Sample Responses.)
Standards
Addressing
  • 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

15 min

20 min