Roots of Reason
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Sorting Shapes · Grade 4 · 4.G.A.2
Sorting Shapes by Their Lines
Name
Date
Correct / 24
1
Mark what you measure.
Each shape is turned, so no side lines up with the edge of the page.
For each shape, count the pairs of sides that run the same way and never meet, then count the corners that are right angles. Use a folded paper corner. Do not guess from how it looks.
1. (a)
parallel pairs
right angles
2. (b)
parallel pairs
right angles
3. (c)
parallel pairs
right angles
4. (d)
parallel pairs
right angles
5. (e)
parallel pairs
right angles
6. (f)
parallel pairs
right angles
7. Two of the six have two pairs of parallel sides and no right angle at all. Which two letters?
and
Roots of Reason
Sorting Shapes by Their Lines · 4.G.A.2
Name
Date
2
Every name that fits.
A shape can have more than one name.
Use the marks you made on page 1, not the pictures. A shape belongs to a name whenever it meets that name's rule, even if a closer name also fits.
quadrilateral four straight sides
parallelogram two pairs parallel
rectangle four right angles
rhombus four sides equal
square four right angles and four sides equal
shape
quadrilateral
parallelogram
rectangle
rhombus
square
8. (a)
9. (b)
10. (c)
11. (d)
12. (e)
13. (f)
14. Every square is a rectangle.
truefalse
15. Every rectangle is a square.
truefalse
16. One of the two statements above is true and the other is false. Use a shape from page 1 to show why the false one is false.
Roots of Reason
Sorting Shapes by Their Lines · 4.G.A.2
Name
Date
3
Which ones are right triangles?
Check every angle, not only the one that looks like a right angle.
17. (g) right triangle?
yesno
18. (h) right triangle?
yesno
19. (i) right triangle?
yesno
20. (j) right triangle?
yesno
21. (k) right triangle?
yesno
22. (l) right triangle?
yesno
23. One of the six has an angle that is close to a right angle but is not one. Which letter, and how did you check?
24. A classmate says (k) is the only right triangle because it is the only one sitting flat. Say what is wrong with that.
Roots of Reason
rootsofreason.org
Sorting Shapes · Grade 4 · 4.G.A.2
Sorting Shapes by Their Lines
Mark what you measure
Written as parallel pairs, then right angles.
1. 2, 4 2. 2, 4 3. 2, 0 4. 2, 0 5. 1, 0 6. 0, 0
7. c and d. Two pairs of parallel sides do not bring right angles with them, which is the whole of what separates a parallelogram from a rectangle.
7. c and d. Two pairs of parallel sides do not bring right angles with them, which is the whole of what separates a parallelogram from a rectangle.
Every name that fits
8. (a) all five names 9. (b) quadrilateral, parallelogram, rectangle
10. (c) quadrilateral, parallelogram, rhombus 11. (d) quadrilateral, parallelogram
12. (e) quadrilateral 13. (f) quadrilateral. Shape a is the only one that fills every column.
14. true 15. false 16. Shape b has four right angles and its sides are not all equal, so it is a rectangle and not a square.
10. (c) quadrilateral, parallelogram, rhombus 11. (d) quadrilateral, parallelogram
12. (e) quadrilateral 13. (f) quadrilateral. Shape a is the only one that fills every column.
14. true 15. false 16. Shape b has four right angles and its sides are not all equal, so it is a rectangle and not a square.
Which ones are right triangles
17. (g) yes, 90, 36.6, 53.4 18. (h) no, 85, 45.3, 49.7 19. (i) yes, 90, 54, 36
20. (j) no, 60, 60, 60 21. (k) yes, 90, 45, 45 22. (l) no, 122, 25.2, 32.8
23. h. The folded corner shows it: laid into that corner it leaves a small gap, so the angle is less than a right angle.
24. Three of the six are right, and (g) and (i) are turned. Sitting flat is a fact about the page, not about the corner.
20. (j) no, 60, 60, 60 21. (k) yes, 90, 45, 45 22. (l) no, 122, 25.2, 32.8
23. h. The folded corner shows it: laid into that corner it leaves a small gap, so the angle is less than a right angle.
24. Three of the six are right, and (g) and (i) are turned. Sitting flat is a fact about the page, not about the corner.
Mark page 2 by rows, not by names. A student who has ticked exactly one box per shape has answered every row wrongly in the same way, and it will read as five near misses when the cause is one wrong idea. Shape e has one pair of parallel sides and no name beyond quadrilateral is asked for it, because the two definitions of trapezoid in circulation disagree about shapes c and d.