Understand Angle Measure as Additive

Students learn that when an angle is divided into non-overlapping parts, the measure of the whole angle equals the sum of the measures of the parts. Students connect this to the idea that angle measure is additive, similar to length and area.

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Grade 4 · Angle Addition and Unknown Angles · question 1 of 3

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20 rungs. A star at the top.

Pia waves a baton while she marches in the parade. The drawing shows its path in parts. How many degrees is the whole angle?

Your answer:

How it is taught

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A whole angle is the sum of its non-overlapping parts.

The interior ray splits the whole without changing that sum.

Read it: Parts add up to the whole

Angle ABC is 45° and angle CBD is 70°. They sit side by side with no overlap, so angle ABD is 45° + 70° = 115°.

Find the parts that sit side by side, with no overlap.
To find the whole, add the parts: 45 + 70 = 115.
To find a missing part, take the known part from the whole: 115 − 45 = 70.

The parts fill the whole angle exactly, so their measures add up to it.

A missing part is what is left of the whole after the known part.

A straight line makes a straight angle: 180°, so 2 parts of a straight angle add up to 180°.

Parts that do not overlap add up to the whole angle.

Adding the whole and a part: 115 + 45 = 160.

The whole is already the biggest. Take the part away: 115 − 45 = 70.

Two angles of 65° and 40° sit side by side, with no overlap. How many degrees is the whole angle? — 105. The parts add up to the whole: 65 + 40 = 105.

30° + 40° = 70°

When you push a door open a little, then a bit more, the total turn is just the small turns added together. Angles work the same way.

Here's an angle. Two rays meeting at a point called the vertex.

This whole angle measures seventy degrees.

Watch — we'll draw a new ray right inside the angle, splitting it into two smaller angles.

The bottom part measures thirty degrees.

Look — the top part measures forty degrees.

Grade 4 · Parts of an angle add to the whole

If we add the two parts — thirty degrees plus forty degrees…

…we get seventy degrees, the same as the whole angle!

When an angle is split into parts, the parts always add up to the whole. That's what it means to say angle measure is additive.

Now you try. Find the missing part of this angle. How many degrees left?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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