Roots of Reason
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Lines & Angles · Grade 4 · 4.G.A.1
Compare It and Sort It
Name
Date
Correct / 22
1
Which angle is bigger?
The rays can be drawn any length. Compare how wide the angle opens, not how long the rays are drawn.
left
right
1. the bigger angle is
leftrightthe same
left
right
2. the bigger angle is
leftrightthe same
left
right
3. the bigger angle is
leftrightthe same
left
right
4. the bigger angle 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
Compare It and Sort It · 4.G.A.1
Name
Date
2
Put them in order.
Each of the six angles is tilted a different way. The tilt does not change the size.
(a)
(b)
(c)
(d)
(e)
(f)
6. Write the six letters from the smallest angle to the largest.
7. Exactly one of the six is a right angle. Which letter?
8. Nothing stands open in (e). Is it still an angle?
yesno
9. What is that one called?
Roots of Reason
Compare It and Sort It · 4.G.A.1
Name
Date
3
Three rays, three angles.
The vertex letter always goes in the middle.
Three rays leave point B. That makes three different angles. 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
14. The line from P to R cuts corner P into two angles. 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?
Roots of Reason
Compare It and Sort It · 4.G.A.1
Name
Date
4
The straight angle.
A straight angle looks like a line, and it is still an angle.
One straight line passes through three points. Two rays 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?
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.
Roots of Reason
rootsofreason.org
Lines & Angles · Grade 4 · 4.G.A.1
Compare It and Sort It
Which angle is bigger
1. the same. Both open 55 degrees, and the right one has rays twice as long.
· 2. right, 75 against 40, and it is the one with the shorter rays.
3. left, 120 against 100. Both are obtuse, so the tester goes on both. · 4. the same. Two right angles, one turned 41 degrees on the page.
5. Lay one on the other, corners together and one ray on top. The second rays land together.
3. left, 120 against 100. Both are obtuse, so the tester goes on both. · 4. the same. Two right angles, one turned 41 degrees on the page.
5. Lay one on the other, corners together and one ray on top. The second rays 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 rays leave the corner running opposite ways, so it is the widest angle there is.
8. yes · 9. a straight angle. Two rays leave the corner running opposite ways, so it is the widest angle there is.
Three rays, 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 angle at R, not the one at P.
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 angle at R, not the one at P.
The straight angle
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.
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 rays, and every later comparison goes wrong the same way. Item 7 is the same habit at a tilt. Hand them the folded tester.