Roots of Reason
Roots of Reason
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no protractor, no ruler
Lines & Angles · Grade 4 · 4.G.A.1

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Name Date Correct / 22
1 Which opening is bigger? - the arms can be any length, so read the gap, not the arms
left
right
1. the bigger opening is
leftrightthe same
left
right
2. the bigger opening is
leftrightthe same
left
right
3. the bigger opening is
leftrightthe same
left
right
4. the bigger opening is
leftrightthe same
5. In question 1 the two angles are the same size. Say how you can tell that without measuring either one.
Roots of Reason CA CCSS 4.G.A.1 rootsofreason.org · Page 1 of 5
Roots of Reason
Compare It and Sort It · 4.G.A.1
Name Date
2 Put them in order - six openings, six tilts, and the tilt tells you nothing
(a)
(b)
(c)
(d)
(e)
(f)
6. Write the six letters from the smallest opening to the largest.
7. Exactly one of the six is a square corner. Which letter?
8. Nothing stands open in (e). Is it still an angle?
yesno
9. What is that one called?
Roots of Reason CA CCSS 4.G.A.1 rootsofreason.org · Page 2 of 5
Roots of Reason
Compare It and Sort It · 4.G.A.1
Name Date
3 Three arms, three angles - the corner letter goes in the middle every time
ACDB
Three rays leave point B. That makes three different openings. Name each one in three letters.
10. between ray BA and ray BC   angle 11. between ray BC and ray BD   angle 12. the widest one on the figure   angle
13. Which two fit together to make the widest one? and
PQRS
14. The line from P to R cuts corner P into two openings. Name the two pieces, then the whole corner.
piece: angle piece: angle whole corner: angle
15. Jonah named a piece angle QRP. That name points at a corner somewhere else. Which one?
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Roots of Reason
Compare It and Sort It · 4.G.A.1
Name Date
4 The flat one - an angle with no gap in it is still an angle
PQR
One straight mark carries three points. Two arms leave Q, running opposite ways.
16. Is there an angle at Q?yesno
17. Name it in three letters: angle
18. What is that kind called?
MNOK
Ray OK leaves the straight mark at O and cuts the flat angle in two.
19. angle MOK isacuterightobtuse
20. angle KON isacuterightobtuse
21. Put together, the two make one angle.
22. A ray cuts a straight angle in two and one piece is acute. What must the other piece be? Say how you know.
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Roots of Reason
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Answer Key
Lines & Angles · Grade 4 · 4.G.A.1

Compare It and Sort It

Which opening is bigger
1. the same. Both open 55 degrees, and the right one has arms twice as long.  ·  2. right, 75 against 40, and it is the one with the shorter arms.
3. left, 120 against 100. Both are obtuse, so the tester goes on both.  ·  4. the same. Two square corners, one turned 41 degrees on the page.
5. Lay one on the other, corners together and one arm on top. The second arms land together.
Put them in order
6. a, d, b, f, c, e   25, 62, 90, 108, 145, 180 degrees.  ·  7. b, and it sits at a tilt so it does not look like one.
8. yes  ·  9. a straight angle. Two arms leave the corner running opposite ways, so it is the widest opening there is.
Three arms, three angles
10. angle ABC   11. angle CBD   12. angle ABD. Reverse the outer letters if you like. B stays in the middle.
13. ABC and CBD, 52 and 66, which is the 118 of angle ABD.  ·  14. angle QPR, angle RPS, angle QPS
15. corner R. QRP puts R in the middle, so it names the opening at R, not the one at P.
The flat one
16. yes   17. angle PQR or angle RQP   18. a straight angle
19. acute, 55 degrees   20. obtuse, 125 degrees   21. straight, because 55 and 125 make 180.
22. obtuse. The two pieces make 180 together. An acute piece is under 90, so what is left is over 90 and under 180.
Mark item 1 first. Answering right there means reading the arms, and every later comparison goes wrong the same way. Item 7 is the same habit at a tilt. Hand them the folded tester.