Roots of Reason
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Classifying Figures · Grade 4 · 4.G.A.2
Classifying Figures Check
Name
Date
Correct / 23
1
Write the closest name
- every one of them is turned, and turning changes nothing
same length
same way, never meet
square corner
1. (a)
closest
2. (b)
closest
3. (c)
closest
4. (d)
closest
5. (e)
closest
6. (f)
closest
7. every figure with a square corner
8. every figure with no pair running the same way
9. every figure that is a right triangle
10. the figure with four sides alike and no square corner
Roots of Reason
Classifying Figures Check · 4.G.A.2
Name
Date
quadrilateral four straight sides
trapezoid exactly one pair runs the same way
parallelogram two pairs run the same way
rectangle four square corners
rhombus four sides the same length
square four square corners and four sides alike
right triangle three sides, one square corner
obtuse triangle three sides, one corner past square
2
Accept it or turn it down
- the letters point back to page 1
11. Figure (d) is a rectangle, so it is not a parallelogram.
truefalse
12. Figure (a) carries a square corner, so it is not a triangle.
truefalse
13. A triangle can carry a square corner and still have no two sides the same length.
truefalse
14. Figure (f) has a pair of sides running the same way, so it cannot carry a square corner.
truefalse
15. Figures (b) and (e) both have two pairs running the same way, so they answer to the same closest name.
truefalse
16. A figure with four square corners always has two pairs of sides running the same way.
truefalse
17. A classmate sorts the six figures on page 1 by whether each one carries a square corner, and says that sorting settles which name each figure answers to. Say what is wrong, and name two figures that show it.
Roots of Reason
Classifying Figures Check · 4.G.A.2
Name
Date
3
Put JKLM in every group it belongs to
18. a pair of sides that run the same way
19. the closest name
20. one wider name it also answers to
21. One of these is true of JKLM. Mark it.
a square, so not a rectangle
a square, a rectangle and a rhombus
a rectangle only when turned square to the page
4
Draw one that answers to both at once
- count the gaps between the dots, not the dots
22. Draw a figure with a square corner and exactly one pair of sides running the same way.
closest name
23. Draw a figure with three sides, one square corner, and two sides the same length.
closest name
Roots of Reason
rootsofreason.org
Classifying Figures · Grade 4 · 4.G.A.2
Classifying Figures Check
Write the closest name
1. right triangle 2. parallelogram 3. obtuse triangle 4. rectangle 5. rhombus 6. trapezoid
Six figures, six different names, none of them sitting square to the page. Take a wider name as correct only where the reader also gave the closest one.
Six figures, six different names, none of them sitting square to the page. Take a wider name as correct only where the reader also gave the closest one.
Report the sets
7. a, d, f 8. a, c 9. a 10. e
Item 8 is the two triangles: three sides cannot hold a pair running the same way. Item 10 turns on both marks at once, since (d) also carries square corners and (b) has two pairs of sides alike rather than four.
Item 8 is the two triangles: three sides cannot hold a pair running the same way. Item 10 turns on both marks at once, since (d) also carries square corners and (b) has two pairs of sides alike rather than four.
Accept it or turn it down
11. false 12. false 13. true 14. false 15. false 16. true
11. A rectangle has two pairs running the same way, so it is a parallelogram as well. 12. A square corner and three sides sit together happily, and (a) is the proof. 13. (a) has sides of three different lengths. 14. (f) carries both, one pair and two square corners. 15. (b) and (e) both have two pairs, and (e) has four sides alike while (b) does not. 16. Four square corners force both pairs to run the same way.
11. A rectangle has two pairs running the same way, so it is a parallelogram as well. 12. A square corner and three sides sit together happily, and (a) is the proof. 13. (a) has sides of three different lengths. 14. (f) carries both, one pair and two square corners. 15. (b) and (e) both have two pairs, and (e) has four sides alike while (b) does not. 16. Four square corners force both pairs to run the same way.
Roots of Reason
Classifying Figures Check · Answer Key · 4.G.A.2
Say what is wrong
17. Sorting on one attribute reports that attribute and nothing else. (a) and (d) both carry a square corner and answer to different names. (b) and (e) carry none and also answer to different names. The name needs the sides and the corners together.
Put JKLM in every group it belongs to
18. JK and LM, or KL and MJ 19. square 20. rectangle, or rhombus, parallelogram or quadrilateral 21. a square, a rectangle and a rhombus
Draw one that answers to both at once
22. Any four sided figure with one pair running the same way and at least one square corner. Figure (f) on page 1 is one, and so is any four sided figure with two dots along one side, a square corner turned up from it, and the opposite side shorter and running the same way. Closest name trapezoid.
23. A triangle with a square corner and the two sides that meet at it drawn the same length. Closest name right triangle, and isosceles right triangle is also correct. Turn down any drawing where the equal sides are the two that do not meet at the square corner, because the longest side of a right triangle cannot be matched by another.
23. A triangle with a square corner and the two sides that meet at it drawn the same length. Closest name right triangle, and isosceles right triangle is also correct. Turn down any drawing where the equal sides are the two that do not meet at the square corner, because the longest side of a right triangle cannot be matched by another.
Mark 11, 15, 19 and 20 together. A reader who turns down every wider name holds that a figure answers to one name only, and no single item shows that as clearly as the four of them side by side. Mark 12, 14 and 21 together for the other habit, sorting once and calling the classification settled.