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Fraction Equivalence · Set 4 of 4 · Grade 3
Same Number, New Name
One half and two fourths are not two answers.
They are one number wearing two names.
They are one number wearing two names.
1
Cut every piece again and nothing is lost
1 of 2 shaded
2 of 4 shaded
4 of 8 shaded
The shading never moved. Only the number of cuts changed.
2
Equal fractions land on the same place
The top line takes 2 jumps to reach 1. The bottom line takes 4. One half and two fourths stop at the same spot.
3
Whole numbers have fraction names too
44
= 1
3 =
31
Three wholes, each one cut into a single piece. The bottom number can be 1.
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Fraction Equivalence · Making a new name
Name
Date
Find the Twins
1 of 3
Cut every piece in two and the picture keeps
the same shading with twice as many names.
the same shading with twice as many names.
2 of 6
1.The top strip is already shaded. Cut the bottom strip along the dotted marks, then shade the same amount and write what you shaded.
12
=
of
13
=
of
34
=
of
2.Look at your three answers. Every time you cut each piece in two, what happened to the two numbers in the fraction?
both numbers doubled
only the bottom doubled
both numbers stayed the same
The amount of the strip that is shaded
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Fraction Equivalence · On the number line
Name
Date
Same Point, Two Names
If two fractions are the same number,
the line has nowhere else to put them.
the line has nowhere else to put them.
12
=
24
1.Both lines are the same length. Put a dot at 1/2 on the top line and a dot at 2/4 on the bottom line. Then draw a straight line between your two dots.
0cut into 2 equal jumps1
0cut into 4 equal jumps1
Your line between the dots goes straight down sideways
2.This line is cut into 6 equal jumps. Put a dot at 4/6. Then write the name that same point has on a line cut into thirds.
46
=
of
How many sixths make one third?
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Fraction Equivalence · Whole numbers
Name
Date
Whole Numbers Wear Fractions
4 of 4
Shade every piece and you are back to one whole.
Count wholes and the bottom number is 1.
Count wholes and the bottom number is 1.
44
= 1 =
11
1.Shade every piece, then write the fraction you shaded and what it equals.
of =
of =
of =
2.Draw the wholes, then finish the fraction. Each whole stays in one piece.
2 wholes
=
2
5 wholes
=
3.Read it backward. Write the whole number each fraction is hiding.
81
=
66
=
One of these is a pile of wholes. The other is a whole cut up and put back together.
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Fraction Equivalence · Comparing
Name
Date
Which One Is Bigger
same size pieces
Compare the count when the pieces match.
Compare the piece when the count matches.
Compare the piece when the count matches.
same count
1.Same bottom number. Shade each strip, then circle the bigger fraction.
3/8
5/8
3/85/8
Same size pieces, so just count them.
2.Same top number. Shade each strip, then circle the bigger fraction.
2/3
2/6
2/32/6
Same count, so the bigger piece wins.
3.The trap. Ada ate half of a small pizza. Ben ate a third of a giant pizza. Ben ate more food. Did Ada break the rule that one half is bigger than one third?
yes, the rule brokeno, the wholes were different
Comparing fractions only works when both come from the
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Fraction Equivalence · Set 4 of 4 · Grade 3
Answer Key and Teacher Notes
Find the twins (page 2)
1. 2 of 4 · 2 of 6 · 6 of 8 2. both numbers doubled; the shaded amount did not change. Shading must line up with the strip above it, not just count correctly.
Same point, two names (page 3)
1. Both dots land on the middle tick, so the line between them goes straight down 2. Dot on the 4th tick; 2 of 3; 2 sixths make one third.
Whole numbers wear fractions (page 4)
1. 3 of 3 = 1 · 4 of 4 = 1 · 6 of 6 = 1 2. Two whole shapes, 2/1; five whole shapes, 5/1 3. 8 and 1
Which one is bigger (page 5)
1. 5/8 2. 2/3 3. No, the wholes were different. One half is bigger than one third only when both come from the same whole.
Set 4 closes the strand, so nothing here is a shortcut. Equivalence is taught as re-cutting rather than as multiplying the top and bottom by the same number, because a student who only knows the rule cannot tell whether 2/4 got bigger. Page 3 is the check that matters: if the two dots do not land together, the jumps were not equal, and the fix is on Set 3 page 4, not here. Page 5 deliberately never compares two fractions with different tops and different bottoms, which is Grade 4 work. Task 3 is the one to talk through out loud, because the same-whole condition is the part students drop first and the part every later comparison depends on.