Roots of Reason
Roots of Reason
rootsofreason.org
bring a ruler and the folded corner
Lines & Angles · Grade 4 · 4.G.A.1 with 4.G.A.2 and 4.G.A.3

Sort It Every Way

Name Date Correct / 23
1 Two names each - one for the sides, one for the angles, and both rows get filled
(a)
(b)
(c)
(d)
(e)
(f)
figure by side length by angle size 1. (a)  2. (b)  3. (c)  4. (d)  5. (e)  6. (f)  
Roots of Reason CA CCSS 4.G.A.1 rootsofreason.org · Page 1 of 5
Roots of Reason
Sort It Every Way · 4.G.A.2
Name Date
2 Measure before you name - the numbers on the sides decide it, not how the drawing looks
6.06.56.0
(g) centimeters
5.25.25.2
(h) centimeters
5.46.25.7
(i) centimeters
Name each one by its side lengths.
7. (g) 8. (h) 9. (i)
10. One of the three carries a second true name as well, because every triangle of its kind is also of the other kind. Which letter, and what is the second name?
11. Two of these look like they have equal sides and only one of them has. Say what you would check to be sure, and where you would look for it.
Roots of Reason CA CCSS 4.G.A.2 rootsofreason.org · Page 2 of 5
Roots of Reason
Sort It Every Way · 4.G.A.3
Name Date
3 Fold it, do not just halve it - one part has to land on the other, not just match it in size
12. Is the drawn line a fold line?
yesno
13. Is the drawn line a fold line?
yesno
14. Draw every fold line. How many?
15. Draw every fold line. How many?
16. The line in question 12 cuts the shape into two pieces of exactly the same size, and it is still not a fold line. Say how you can tell the difference.
Roots of Reason CA CCSS 4.G.A.3 rootsofreason.org · Page 3 of 5
Roots of Reason
Sort It Every Way · 4.G.A.1
Name Date
4 One figure, everything at once - the tick marks say the two long sides are equal
PRQS
17. Name the angle at the top in three letters: angle
18. QS meets PR square on. Draw a small square at each of the two corners that makes.
19. Name triangle PQR by its side lengths:
20. By its angles it isacuterightobtuse
21. Is QS a fold line?yesnoHow many does PQR have?
22. Now take the smaller triangle PQS on its own. By sides it is and by angles it is
23. Triangle PQR has no square corner, but QS cuts it into two triangles that do. Say how that can happen.
Roots of Reason CA CCSS 4.G.A.1 rootsofreason.org · Page 4 of 5
Roots of Reason
Roots of Reason
rootsofreason.org
Answer Key
Lines & Angles · Grade 4 · 4.G.A.1 with 4.G.A.2 and 4.G.A.3

Sort It Every Way

Two names each
1. (a) equilateral, acute  ·  2. (b) isosceles, right  ·  3. (c) scalene, obtuse
4. (d) isosceles, obtuse  ·  5. (e) scalene, right  ·  6. (f) isosceles, acute
Measure before you name
7. (g) isosceles, 6.0, 6.0 and 6.5  ·  8. (h) equilateral  ·  9. (i) scalene, 5.4, 5.7 and 6.2
10. h, also isosceles. Three equal sides means at least two are.
11. Read the two side lengths and compare the numbers. On (g) they are 6.0 and 6.5, which is a difference the eye lets past at this size.
Fold it
12. no. Folded on it, the pieces do not land on one another.  ·  13. yes, and so is the other diagonal.
14. 4, two through the side middles and two corner to corner.  ·  15. 2.
16. Fold it, or turn the tracing over on the line. Equal size is not the test. The test is whether one piece lands exactly on the other.
One figure, everything
17. angle PQR or angle RQP  ·  18. squares at angle PSQ and angle QSR
19. isosceles  ·  20. acute, the widest angle sits at Q  ·  21. yes, and PQR has 1
22. PQS is scalene and right. All three of its sides differ.
23. QS makes a new angle at S that neither P, Q nor R had. The corners of the small triangles are not the corners of the big one.
Mark page 1 by columns, not by figures. A page with the left column full and the right one blank is the whole finding: the student is treating the two sortings as a choice. Item 12 is the second one to check, and item 10 the third.