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
- every shape is turned, so nothing 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 square. Use a folded paper corner. Do not guess from how it looks.
1. (a)
parallel pairs
square corners
2. (b)
parallel pairs
square corners
3. (c)
parallel pairs
square corners
4. (d)
parallel pairs
square corners
5. (e)
parallel pairs
square corners
6. (f)
parallel pairs
square corners
7. Two of the six have two pairs of parallel sides and no square corner at all. Which two letters?
and
Roots of Reason
Sorting Shapes by Their Lines · 4.G.A.2
Name
Date
2
Every name it answers to
- a shape can carry more than one
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 square corners
rhombus four sides equal
square four square corners 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
- test every corner, not the one that looks likeliest
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 a corner that is close to square but is not. Which letter, and how did you settle it?
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 square corners.
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 square corners 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 square corners with them, which is the whole of what separates a parallelogram from a rectangle.
Every name it answers to
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 square corners 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 square corners 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, and the folded corner settles it: laid into that corner it leaves a sliver of daylight, so the corner is under square.
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, and the folded corner settles it: laid into that corner it leaves a sliver of daylight, so the corner is under square.
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 reader 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 rather than as one belief. Shape e carries 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.