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
- somebody already measured these for you
same length
same way, never meet
square corner
Sides marked alike carry the mark that was measured. Write the closest name each figure answers to, 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 answer to one name only. Which two letters?
and
Roots of Reason
What the Marks Tell You · 4.G.A.2
Name
Date
2
Accept it or turn it down
- the letters point back to page 1
quadrilateral four straight sides
parallelogram two pairs parallel
rectangle four square corners
rhombus four sides equal
square four square corners and four sides equal
8. Figure (b) has four square corners, so it cannot be a parallelogram. The rule for parallelogram says nothing about square corners.
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 which names it answers to.
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 square corner on (f) is not really square, because neither of its sides runs straight across the page. Say what is wrong with that.
15. Figure (a) answers to all five names. Figure (e) answers to one. Both have four straight sides. Say what (a) carries that (e) does not.
Roots of Reason
What the Marks Tell You · 4.G.A.2
Name
Date
3
Draw it, then name it
- corners on the dots, and put your own marks on
16. Draw a figure with two pairs of sides that run the same way, and no square corner.
closest name
17. Draw a figure with four square corners, with the sides not all the same length.
closest name
18. Draw a figure with four sides the same length, and no square corner.
closest name
19. Draw a figure with four square corners 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 square corners 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 carries 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 carries a parallel pair, so no wider name is reached at all.
Accept it or turn it down
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 square corner 12. false 13. true
14. The folded corner fits the corner on (f) whichever way the page is turned, so square is about the two sides and not about the page.
15. Figure (a) carries two pairs of parallel sides, four equal sides and four square corners. Figure (e) carries none of the three.
10. true 11. false, four equal sides is half of the rule for square and (c) has no square corner 12. false 13. true
14. The folded corner fits the corner on (f) whichever way the page is turned, so square is about the two sides and not about the page.
15. Figure (a) carries two pairs of parallel sides, four equal sides and four square corners. Figure (e) carries none of the three.
Draw it, then name it
Drawings vary. Mark a drawing correct when the marks the reader added agree with the figure they drew.
16. parallelogram 17. rectangle
18. rhombus 19. square
20. Two sides that are both square to the same third side run the same way, so they never meet however far they go. Four square corners give that twice over.
20. Two sides that are both square to the same third side run the same way, so they never meet however far they go. Four square corners give that twice over.
Four of the six claims are false, so marking by pattern shows as a run and not as one slip. Read 8 and 11 together: 8 refuses a name because the rule never mentions a property the figure carries, and 11 grants a name on half a rule. No figure is called a trapezoid here, because the two definitions in use disagree about (c) and (d).