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Lines of Symmetry · Grade 4 · 4.G.A.3
When the Dots Are Gone
Name
Date
Correct / 25
1
Draw every line of symmetry, then count.
There are no dots this time, and the page does not say how many to look for.
Draw every line of symmetry each picture has, then write the count. Turn the page around if it helps you see a slanted one.
1. (a)
lines it holds
2. (b)
lines it holds
3. (c)
lines it holds
4. (d)
lines it holds
5. (e)
lines it holds
6. (f)
lines it holds
7. (g)
lines it holds
8. (h)
lines it holds
9. (i)
lines it holds
10. Pictures (h) and (i) are one arrow, turned. Say why one is far easier to draw.
Roots of Reason
When the Dots Are Gone · 4.G.A.3
Name
Date
2
Use both parts of the test.
Equal distances are only the first part. The line joining the two points must also cross the fold at a right angle.
Measure from the dashed line to B and to D. Then lay a ruler along the join from B to D and look at the corner it makes with the dashed line.
11. (j)
distancessamenot the same
crossesat a right angleat a slant
so itfoldsdoes not
12. (k)
distancessamenot the same
crossesat a right angleat a slant
so itfoldsdoes not
13. (l)
distancessamenot the same
crossesat a right angleat a slant
so itfoldsdoes not
14. (m)
distancessamenot the same
crossesat a right angleat a slant
so itfoldsdoes not
Roots of Reason
When the Dots Are Gone · 4.G.A.3
Name
Date
2
Use both parts of the test.
Equal distances are only the first part. The line joining the two points must also cross the fold at a right angle.
15. In picture (k) the two distances came out the same and the line cuts the figure into two equal parts, and it still does not fold. Name the one measurement that settled it.
Roots of Reason
When the Dots Are Gone · 4.G.A.3
Name
Date
3
The round piece and the missing half.
For one of these, the lines of symmetry cannot be counted.
16. A round piece folds onto itself along every line through its middle. A classmate says that is because it has no straight sides. The oval beside it has no straight sides either.
Lines the oval holds
So the classmate is wrong. Say what decides it for the round piece.
17. Draw the missing half so the whole picture folds onto itself along the dashed line. There is nothing to count along, so measure each corner across.
corners on the whole picture
corners you had to add
times as wide as the half
18. A picture is printed on a page you may not cut or fold. Write the test you would use to be certain it holds a line of symmetry, and say what you would measure to run it.
Roots of Reason
rootsofreason.org
Lines of Symmetry · Grade 4 · 4.G.A.3
When the Dots Are Gone
Draw every line of symmetry, then count
1. (a) 1 upright 2. (b) 2 3. (c) 0 4. (d) 1 across 5. (e) 6 6. (f) 0 7. (g) 5 8. (h) 1 across 9. (i) 1 slanted
Picture (c) turns onto itself halfway round and never folds, which is the one most often called symmetric. In (e) three lines run corner to corner and three side to side. In (g) every line runs from a corner to the middle of the facing side.
10. One arrow, so both hold one line. In (h) it runs straight across the page and the directions tried first find it. In (i) the same line leans, so both fail and the picture reads as holding none.
Picture (c) turns onto itself halfway round and never folds, which is the one most often called symmetric. In (e) three lines run corner to corner and three side to side. In (g) every line runs from a corner to the middle of the facing side.
10. One arrow, so both hold one line. In (h) it runs straight across the page and the directions tried first find it. In (i) the same line leans, so both fail and the picture reads as holding none.
Measure both halves of the test
Distances are read in the student's own units, so mark the comparison rather than the number.
11. (j) same, square, folds 12. (k) same, at a slant, does not 13. (l) same, square, folds 14. (m) not the same, does not
15. The corner the join from B to D makes with the dashed line. In (k) it is not a right angle, so B does not land on D when the picture is folded. Equal distance says the corners are as far out as each other and nothing about the direction they lie in. Folding checks the direction without anyone naming it, which is why a student can fold correctly and still believe equal distance is enough.
11. (j) same, square, folds 12. (k) same, at a slant, does not 13. (l) same, square, folds 14. (m) not the same, does not
15. The corner the join from B to D makes with the dashed line. In (k) it is not a right angle, so B does not land on D when the picture is folded. Equal distance says the corners are as far out as each other and nothing about the direction they lie in. Folding checks the direction without anyone naming it, which is why a student can fold correctly and still believe equal distance is enough.
The round piece and the missing half
16. The oval holds 2, one along its length and one across it, so having no straight sides is not what does it. What decides it for the round piece is that every point on its edge is the same distance from one middle point, so every line through that point leaves the same edge either side.
17. Whole picture: 8 corners, 3 added, and 2 times as wide as the half given. Each added corner sits as far out from the line as its match, on the square across from it.
18. Accept any test measuring two things: that a pair of matching points sit the same distance from the line, and that the join between them crosses it square. A student naming only distance has written half the test.
17. Whole picture: 8 corners, 3 added, and 2 times as wide as the half given. Each added corner sits as far out from the line as its match, on the square across from it.
18. Accept any test measuring two things: that a pair of matching points sit the same distance from the line, and that the join between them crosses it square. A student naming only distance has written half the test.
Mark 1 to 9 as one answer, not nine. A student who wrote 1, 2, 0, 1, 2, 0, 1, 1, 0 stopped at the lines running straight up and across the page, which is one habit, not nine separate errors. The lines missed are three in (e), four in (g), and the only one in (i).