Roots of Reason
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Reading the Marks · Grade 4 · 4.G.A.2
What the Marks Tell You
Name
Date
Correct / 20
1
Name it from the marks.
The marks show measurements someone already made.
same length
same way, never meet
right angle
Sides marked alike have the mark that was measured. Write the closest name for each figure, then one wider name that is also true of it. Write none where there is no wider name.
1. (a)
closest
also true
2. (b)
closest
also true
3. (c)
closest
also true
4. (d)
closest
also true
5. (e)
closest
also true
6. (f)
closest
also true
7. Two of the six have only one name. Which two letters?
and
Roots of Reason
What the Marks Tell You · 4.G.A.2
Name
Date
2
Agree or disagree.
The letters name the figures on page 1.
quadrilateral four straight sides
parallelogram two pairs parallel
rectangle four right angles
rhombus four sides equal
square four right angles and four sides equal
8. Figure (b) has four right angles, so it cannot be a parallelogram. The rule for parallelogram says nothing about right angles.
truefalse
9. Two sides that do not cross anywhere inside a figure must be running the same way.
truefalse
10. Figure (d) is turned on the page. Turning it does not change its names.
truefalse
11. Figure (c) has four sides the same length, so it is a square.
truefalse
12. Figure (a) is a square, so it is not a rhombus.
truefalse
13. Every rhombus is a parallelogram.
truefalse
14. A classmate says the right angle on (f) is not really a right angle, because neither of its sides runs straight across the page. Say what is wrong with that.
15. All five names fit figure (a). One fits figure (e). Both have four straight sides. Say what (a) has that (e) does not.
Roots of Reason
What the Marks Tell You · 4.G.A.2
Name
Date
3
Draw it, then name it.
Put the corners on dots, then add your own marks.
16. Draw a figure with two pairs of sides that run the same way, and no right angle.
closest name
17. Draw a figure with four right angles, with the sides not all the same length.
closest name
18. Draw a figure with four sides the same length, and no right angle.
closest name
19. Draw a figure with four right angles and four sides the same length.
closest name
20. Conditions 17 and 19 never mention parallel sides, yet both of your figures have two pairs. Say how four right angles force that.
Roots of Reason
rootsofreason.org
Reading the Marks · Grade 4 · 4.G.A.2
What the Marks Tell You
Name it from the marks
Closest name first, then any one wider name that is also true.
1. (a) square, then rectangle, rhombus, parallelogram or quadrilateral 2. (b) rectangle, then parallelogram or quadrilateral
3. (c) rhombus, then parallelogram or quadrilateral 4. (d) parallelogram, then quadrilateral
5. (e) quadrilateral, none 6. (f) quadrilateral, none
7. e and f. Neither has a parallel pair, so no wider name is reached at all.
1. (a) square, then rectangle, rhombus, parallelogram or quadrilateral 2. (b) rectangle, then parallelogram or quadrilateral
3. (c) rhombus, then parallelogram or quadrilateral 4. (d) parallelogram, then quadrilateral
5. (e) quadrilateral, none 6. (f) quadrilateral, none
7. e and f. Neither has a parallel pair, so no wider name is reached at all.
Agree or disagree
8. false, the rule for parallelogram asks for two parallel pairs and stays silent about corners, and silence is not a bar
9. false, sides can lean toward each other and meet past the edge of the drawing
10. true 11. false, four equal sides is half of the rule for square and (c) has no right angle 12. false 13. true
14. The folded corner fits the corner on (f) whichever way the page is turned, so a right angle is about the two sides and not about the page.
15. Figure (a) has two pairs of parallel sides, four equal sides and four right angles. Figure (e) has none of the three.
10. true 11. false, four equal sides is half of the rule for square and (c) has no right angle 12. false 13. true
14. The folded corner fits the corner on (f) whichever way the page is turned, so a right angle is about the two sides and not about the page.
15. Figure (a) has two pairs of parallel sides, four equal sides and four right angles. Figure (e) has none of the three.
Draw it, then name it
Drawings vary. Mark a drawing correct when the marks the student added agree with the figure they drew.
16. parallelogram 17. rectangle
18. rhombus 19. square
20. Two sides that are both at right angles to the same third side run the same way, so they never meet however far they go. Four right angles give that twice over.
20. Two sides that are both at right angles to the same third side run the same way, so they never meet however far they go. Four right angles give that twice over.
Four of the six claims are false, so marking by pattern shows up as several wrong answers in a row, not as one careless error. Read 8 and 11 together: 8 rejects a name because the rule leaves out a property the figure has, and 11 accepts a name when only half the rule is met. No figure is called a trapezoid here, because the two definitions in use disagree about (c) and (d).