SME
Grade 3 Math · Fractions
Fractions as numbers
Use this for “Mark 5/4 on a number line from 0 to 2.”
Diagram
5/4: 5 jumps of 1/4 from 0.
That is 1 whole and 1/4 more.
Wholes: 1
Parts past the last whole: 1
This is an example. Type your own values to start a new problem.
Parts counted
example
Parts in one whole
example
Wholes
worked out (not typed)
Parts past the last whole
worked out (not typed)
Formulas
5
4
fills
1
whole
Full wholes in the parts counted = wholes
5
4
=
1
whole
and
1
4
Parts counted = wholes × parts in one whole + parts past the last whole
Assumptions
•
Cut 0 to 1 into equal parts. The bottom number says how many.
•
The top number counts the jumps from 0.
•
4/4 lands on 1, the same point as the whole number.
Step-by-step
WE KNOW
Parts counted: 5
Parts in one whole: 4
FIND
wholes, parts past the last whole
Step 1 · Find wholes
5
4
fills
?
wholes
Full wholes in the parts counted = wholes
Count the jumps from 0. Every full set of equal parts makes 1 whole.
Count
5
jumps
of
1
4
from
0:
1
4
,
2
4
,
3
4
,
4
4
,
5
4
1 × 4 = 4 parts make 1 whole
Wholes = 1
Step 2 · Find parts past the last whole
5
4
=
1
whole
and
?
4
Parts counted = wholes × parts in one whole + parts past the last whole
Take away the parts that make wholes. The rest are left over.
Parts past the last whole = 5 − 1 × 4
1 × 4 = 4
5 − 4 = 1
Parts past the last whole = 1
Check
Put the numbers back in. Both sides should match.
5
4
fills
1
whole
✓
5
4
=
1
whole
and
1
4
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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More problem types
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Fractions of a set
Use this for “What fraction of the umbrellas are shaded?”
Represent whole numbers as fractions
Use this for “How many fourths make a whole?” or 8/4 = 2.
Understand the whole
Use this to find the whole from one part: “This bar is 1/3. Draw the whole.”
Equal parts of an area
Use this for “Is each part one fourth of the area?”