SME
Grade 4 Math · Problem type
Understand angles as parts of a turn
Use this for “a quarter turn is how many degrees?” or “how many 20° angles make a full turn?”
Diagram
270° and 90° make 360°: a full turn.
This is an example. Type your own values to start a new problem.
Equal parts of the turn
example
Parts in the angle
example
One part
calculated · °
Angle
calculated · °
Rest of the turn
worked out (not typed) · °
Formulas
360 ÷ 4 = 90
360 ÷ equal parts of the turn = one part
3 × 90 = 270
Parts in the angle × one part = angle
270 + 90 = 360
Angle + rest of the turn = 360
Assumptions
•
A full turn is 360°. Cut the turn into equal parts: a quarter turn is 360 ÷ 4 = 90°.
•
An angle that is some of those parts is that many times the part: 3 quarter turns is 270°.
•
The turn is cut into 2, 3, 4, 5, 6, 8, 9, 10, 12, 18 or 36 equal parts.
Step-by-step
WE KNOW
Equal parts of the turn: 4
Parts in the angle: 3
FIND
one part, angle, rest of the turn
Step 1 · Find one part
360 ÷ 4 = ?
360 ÷ equal parts of the turn = one part
Share the full turn into equal parts.
Think: ? × 4 = 360
360 ÷ 4 = 90 because 90 × 4 = 360
One part = 90°
Step 2 · Find angle
3 × 90 = ?
Parts in the angle × one part = angle
That many parts, each the same size.
3 × 9 = 27, so 3 × 90 = 270
Angle = 270°
Step 3 · Find rest of the turn
270 + ? = 360
Angle + rest of the turn = 360
What is left of the full turn of 360°.
Rest of the turn = 360 − 270
2
16
3
6
0
−
2
7
0
9
0
Rest of the turn = 90°
Check
Put the numbers back in. Both sides should match.
360 ÷ 4 = 90 ✓
270°
is
3
4
of
a
turn
✓
270 + 90 = 360 ✓
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