Fraction Foundations · Set 1 of 4 · Grade 3
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Ready for Fractions?
Scan for the anchor chart
Before fractions, we check two things you already know.
If you can draw both, you are ready.
If you can draw both, you are ready.
1
Division makes equal groups
3 equal groups
or
groups of 3
6 ÷ 3 says both. Two pictures, one fact.
2
One whole can be cut into equal parts
one whole
→
2 equal parts
→
4 equal parts
A fraction cuts one thing, a sandwich, a pizza, an hour, into equal pieces.
The rule for this whole packet:
"If you can't draw it, you don't get it."
So we draw everything.
Roots of Reason
Ready for Fractions · Check 1
Name
Date
Division Two Ways
6 ÷ 3 has two different pictures.
Can you draw them both?
Can you draw them both?
1.Picture one: split 6 buttons into 3 equal groups. Draw the buttons inside the circles. Deal them out fairly.
Each group gets buttons.
2.Picture two: take 6 buttons and make groups of 3. Draw a loop around every group of 3.
I made groups. Both pictures say 6 ÷ 3 =
Roots of Reason
Ready for Fractions · Check 2
Name
Date
Cutting One Whole
fair
Now there is only one brownie. Your knife must be fair:
every piece exactly the same size.
every piece exactly the same size.
not fair
1.Draw straight lines to cut each brownie. Use a ruler if you like.
2 equal parts
4 equal parts
3 equal parts
Check yourself: would every friend be happy with any piece?
2.Cut the pancake into 2 equal parts. Then cut the second pancake into 4 equal parts.
4 equal parts means each part is called one
Roots of Reason
Ready for Fractions · Check 2, part two
Name
Date
Equal Parts Detective
equal
Some of these cuts are fair. Some only look fair.
Circle equal or not equal under each one.
Circle equal or not equal under each one.
not equal
1.Look closely at the sizes of the pieces, not just how many pieces there are.
equalnot equal
equalnot equal
equalnot equal
equalnot equal
equalnot equal
equalnot equal
2.Fix the trick. Shape C above is a circle cut into 3 pieces, but the pieces are not equal. Draw your own circle cut into 3 truly equal parts. Hint: it looks like a peace sign, not a T.
Roots of Reason
Ready for Fractions · Putting it together
Name
Date
Sharing One Thing
equal groups
Here is the bridge: sharing 12 cookies makes equal groups.
Sharing 1 sandwich makes equal parts. Both are division.
Sharing 1 sandwich makes equal parts. Both are division.
equal parts
1.Draw the fair cuts. 2 friends share 1 sandwich. 4 friends share 1 pizza. 3 friends share 1 granola bar.
sandwich · 2 friends
pizza · 4 friends
granola bar · 3 friends
Each friend's piece of pizza is one of the whole pizza.
2.Think about it. Finish the sentence in your own words: "A fraction is what you get when you divide one whole into..."
Fractions live in every kitchen.
Roots of Reason
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Fraction Foundations · Set 1 of 4 · Grade 3
Answer Key and Teacher Notes
Division two ways (page 2)
1. Each group gets 2 2. 2 groups; 6 ÷ 3 = 2. Task 1 is sharing into a known number of groups (partitive); task 2 is measuring out groups of a known size (quotative). Students should draw both without prompting.
Cutting one whole (page 3)
1. Any straight fair cuts count: 2 parts (1 line), 4 parts (2 lines), 3 parts (2 lines, evenly spaced) 2. Each part of the 4-cut pancake is one fourth (quarter)
Equal parts detective (page 4)
1. A equal · B not equal (a half and two quarters) · C not equal · D not equal · E equal (4 matching triangles) · F equal 2. Three cuts from the center, evenly spaced, like a peace sign or pie chart. Reading order: A B C on the top row, D E F on the bottom.
Sharing one thing (page 5)
1. Fair cuts as above; each pizza piece is one fourth (quarter) 2. Accept any version of "equal parts"
This set is a formative assessment, not a lesson. A student who draws both division pictures on page 2 and cuts fairly on pages 3 and 4 is ready for numerators and denominators. Watch shape C on page 4: many students, even middle schoolers, accept a circle cut into a half and two quarters as "thirds" because they count 3 pieces. Piece count is not the concept; equal size is. If pages 2 or 3 wobble, review division meanings before starting fractions.