Slice 01
Equal Means Equal
Do the parts of a fraction have to be equal?
Why four pieces are not always fourths: a fraction needs equal shares of the whole. · About 3 minutes
All 20 slices
Pick a slice
Twenty short lessons, each about one idea that trips people up. Start with whatever’s bugging you, or answer a few questions and we’ll suggest where to begin.
Family I
Parts & Wholes
Equal shares of a whole, and what each number in a fraction is counting. Start here if fractions feel shaky: every other idea rests on these.
Slice 02
What’s the Whole?
Is half of a large pizza the same amount as half of a small pizza?
Why half of a big pizza is more than half of a small one: a fraction depends on its whole. · About 3 minutes
Slice 03
The Bottom Number
What does the bottom number of a fraction mean?
What the bottom number of a fraction counts: all the equal parts that make one whole. · About 3 minutes
Slice 04
The Top Number
What does the top number of a fraction mean?
What the top number of a fraction counts: how many of the equal parts you have. · About 3 minutes
Slice 05
Fractions of Collections
What is (one fourth) of 12?
How to find a fraction of a group, and why 1/4 of 12 counters is 3, not 1 or 4. · About 3 minutes
Family II
Fractions Have Size
Why 1/8 is smaller than 1/6, why 3/8 is less than 2/3, and how fractions live on the number line, including fractions greater than one.
Slice 06
The Bigger Denominator Trap
Is (one sixth) bigger than (one eighth)?
Why 1/8 is smaller than 1/6, even though 8 is bigger than 6. · About 3 minutes
Slice 07
The Bigger Numerator Trap
Which is bigger, (three eighths) or (two thirds)?
Why 2/3 is bigger than 3/8, even though 3 is bigger than 2. · About 3 minutes
Slice 08
More Than One Whole
Can a fraction be bigger than 1?
Why 6/4 makes sense: a fraction can equal one whole or go beyond it. · About 3 minutes
Slice 09
Counting Spaces, Not Ticks
How do you find (three fourths) on a number line?
Why we count equal spaces from 0, not tick marks, to find 3/4 on a number line. · About 3 minutes
Slice 10
One Number, Not Two
Where is (two fifths) on a number line?
Why 2/5 is one number between 0 and 1, not a 2 and a 5. · About 3 minutes
Family III
Same Value, Different Forms
How 1/2 and 2/4 can be the same number, why simplifying never shrinks a fraction, and how to compare fractions by reasoning instead of guessing.
Slice 11
Different Numbers, Same Amount
Is (one half) the same as (two fourths)?
Why 1/2, 2/4 and 4/8 are exactly the same amount, even though the numbers are different. · About 3 minutes
Slice 12
Simplifying Doesn’t Shrink
Does simplifying a fraction make it smaller?
Why 6/8 and 3/4 are the same amount, and why simplifying a fraction never makes it smaller. · About 3 minutes
Slice 13
Same Bottom, Compare the Top
How do you compare fractions with the same denominator?
Why 5/7 is bigger than 2/7: the pieces are the same size, so the one with more pieces is bigger. · About 3 minutes
Slice 14
Same Top, Compare the Pieces
How do you compare fractions with the same numerator?
Why 3/5 is bigger than 3/8: the same number of pieces, but fifths are bigger pieces than eighths. · About 3 minutes
Slice 15
Compare Without Guessing
Which is bigger, (three eighths) or (four sevenths)?
How to compare fractions like 3/8 and 4/7 by asking which side of one half each one is on. · About 4 minutes
Family IV
Working With Fractions
Why we need common units to add and subtract, why multiplying can make a number smaller, and why dividing can make it bigger.
Slice 16
Adding Different Pieces
Is (one half) + (one fourth) equal to (two sixths)?
Why 1/2 + 1/4 is 3/4, not 2/6: make the pieces the same size before you count them. · About 3 minutes
Slice 17
Keep the Unit When Adding
Is (one fifth) + (two fifths) equal to (three tenths)?
Why 1/5 + 2/5 is 3/5, not 3/10: joining fifths gives more fifths, not smaller pieces. · About 3 minutes
Slice 18
Taking Pieces Away
Is (three fourths) − (one half) equal to (two halves)?
Why 3/4 − 1/2 is 1/4, not 2/2: take away an amount using same-size pieces. · About 3 minutes
Slice 19
Multiplication Can Make Smaller
Why does multiplying by a fraction make a number smaller?
Why 1/2 × 1/2 is 1/4: multiplying by a fraction less than one takes part of an amount. · About 4 minutes
Slice 20
Division Can Make Bigger
Why does dividing by a fraction give a bigger answer?
Why 1/2 ÷ 1/4 is 2: dividing by a fraction asks how many of those pieces fit. · About 3 minutes