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Fraction Foundations · Set 2 of 4 · Grade 3
What a Fraction Says
A fraction is not two numbers. It is one number that tells a tiny story:
the bottom cuts, the top counts.
the bottom cuts, the top counts.
1
The bottom number cuts
cut by 2
cut by 4
cut by 8
Same whole every time. More cuts means smaller pieces.
2
The top number counts
count 1
count 2
count 3
The cuts never change. Only the counting changes.
3
Write it: top over bottom
=
3
4
count 3 on top, cut by 4 on the bottom, one line in between. One number.
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What a Fraction Says · The bottom number
Name
Date
The Bottom Number Cuts
2 big pieces
The bottom number tells how many equal pieces
the whole is cut into.
the whole is cut into.
8 small pieces
1.Three chocolate bars, all the same size. Color one piece of each bar. Then circle the bar where your piece is biggest.
cut 2
cut 4
cut 8
The biggest piece came from the bar cut into pieces.
2.Think about it. If you cut the same bar into more and more pieces, what happens to the size of each piece? Circle one, then say why to a partner.
each piece gets bigger
each piece gets smaller
each piece stays the same
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What a Fraction Says · The bottom number, part two
Name
Date
Bigger Bottom, Smaller Piece
one piece of 3
A bigger bottom number does not mean more.
It means the whole was cut into smaller pieces.
It means the whole was cut into smaller pieces.
one piece of 10
1.Two granola bars, same size. One is shared by 3 hikers, one by 10 hikers. Color one hiker's piece in each bar. Then answer.
3 hikers
10 hikers
Who gets the bigger piece: a group of hikers.
2.A true burger story. A restaurant sold a third-pound burger. Customers thought it was less meat than a quarter-pound burger, because 4 is bigger than 3. Draw two same-size burgers: cut one into 3 equal parts, one into 4 equal parts. Color one part of each. Who was right?
The bigger piece is one part of
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What a Fraction Says · The top number
Name
Date
The Top Number Counts
count 1
The top number counts pieces, just like counting apples.
It only makes sense once you know the size of the piece.
It only makes sense once you know the size of the piece.
count 3
1.Every pie is cut into 4 equal parts. Color exactly the number of pieces written under each pie.
color 1
color 2
color 3
color 4
When you color all 4, you have the whole pie again.
2.Now read the pictures. Write how many pieces are colored, out of how many pieces in all.
out of
out of
out of
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What a Fraction Says · Putting it together
Name
Date
Writing It Down
Top counts, bottom cuts, one line in between.
Together they make one number.
Together they make one number.
3
4
1.Read each picture. Write its fraction: colored pieces on top, total pieces on the bottom.
2.Now go the other way. Cut and color each shape to match its fraction.
12
23
Recipes, road signs, and gas pumps all speak fraction.
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Fraction Foundations · Set 2 of 4 · Grade 3
Answer Key and Teacher Notes
The bottom number cuts (page 2)
1. The biggest piece comes from the bar cut into 2 pieces 2. Each piece gets smaller
Bigger bottom, smaller piece (page 3)
1. The group of 3 hikers gets the bigger piece 2. The bigger piece is one part of 3. The customers were wrong: a third of a pound is more than a quarter of a pound.
The top number counts (page 4)
1. Any 1, 2, 3, then all 4 quarters colored 2. 2 out of 3 · 1 out of 4 · 5 out of 6
Writing it down (page 5)
1. 3/4 · 1/3 · 5/6 2. Circle: 2 equal parts, 1 colored. Bar: 3 equal parts, 2 colored.
Concepts before tricks: this set never mentions a comparison rule, and that is deliberate. Pages 2 and 3 let students discover that a bigger bottom number makes smaller pieces by coloring same-size wholes, so nobody needs "bigger denominator means smaller fraction" as a memorized fact. Notation waits until page 5, after both numbers mean something. If a student writes 4/3 for three colored quarters, they are counting the whole, not the pieces: go back to page 4, task 2, and ask "how many are colored?" before "how many in all?"