The Size of An Angle, in Degrees

10 min

Narrative

The purpose of this Warm-up is to invite students to think about 360 in terms of related numbers—as a result of addition, subtraction, multiplication, or division. The reasoning done here will be helpful when students compose angles into a sum of 360∘360^\circ or decompose a 360∘360^\circ angle into smaller angles, particularly benchmark angles such as 30∘30^\circ, 60∘60^\circ, 90∘90^\circ, and 180∘180^\circ.

Launch

  • Display the number.
  • “What do you know about 360?”
Teacher Instructions
  • 1 minute: quiet think time
  • Record responses.
  • If no students mentioned different ways to express 360, ask: “How could we express the number 360?” and “What do you know about the factors of 360?”

Student Task

What do you know about 360?

Sample Response

Sample responses:
  • It is 40 less than 400, and 60 more than 300.
  • It is 10 times 36, twice 180, and half of 720.
  • It is a multiple of 10, 20, 30, 40, 60, 90, 120, 180.
  • It is 2×1802 \times 180, 3×1203 \times 120, 4×904 \times 90, 6×606 \times 60, 9×409 \times 40, 10×3610 \times 36, 12×3012 \times 30, 15×2415 \times 24, 18×2018 \times 20.
Activity Synthesis (Teacher Notes)
  • Draw students’ attention to the factors of 360. “What are the factors of 360? How many are there?”
  • “The number 360 and its factors are important when describing angles. Let’s find out why they show up again and again as we look at a new way to describe and measure the size of an angle.”
Standards
Building On
  • 4.NBT.1·Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. <em>For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.</em>
  • 4.NBT.A.1·Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. <span>For example, recognize that <span class="math">\(700 \div 70 = 10\)</span> by applying concepts of place value and division.</span>
Building Toward
  • 4.MD.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
  • 4.MD.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
  • 4.MD.C.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
  • 4.MD.C.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

15 min

20 min