SME
Grade 5 Math · Problem type
Solve multi-step problems with units
Use this for “2 gallons of juice poured into 8-ounce cups. How many cups can be filled?”
Diagram
32 full shares of 8 make 256 in the smaller unit, with 0 left over.
This is an example. Type your own values to start a new problem.
Amount in bigger unit
example
Smaller units in 1 bigger unit
example
Amount in smaller unit
worked out (not typed)
Size of one share
example
Full shares
worked out (not typed)
Left over
worked out (not typed)
Formulas
2 × 128 = 256
Amount in bigger unit × smaller units in 1 bigger unit = amount in smaller unit
whole groups of 8 in 256 = 32
Amount in smaller unit ÷ size of one share = full shares, with some left over
256 − 32 × 8 = 0
Amount in smaller unit − full shares × size of one share = left over
Assumptions
•
First change the big amount to the small unit: 1 gallon = 128 fluid ounces, 1 pound = 16 ounces, 1 yard = 36 inches.
•
Then divide by the size of one share. The whole number is the full shares; the rest is left over.
•
Also 1 gallon = 4 quarts, 1 foot = 12 inches, 1 hour = 60 minutes, 1 kilogram = 1,000 grams, 1 ton = 2,000 pounds.
Step-by-step
WE KNOW
Amount in bigger unit: 2
Smaller units in 1 bigger unit: 128
Size of one share: 8
FIND
amount in smaller unit, full shares, left over
Step 1 · Find amount in smaller unit
2 × 128 = ?
Amount in bigger unit × smaller units in 1 bigger unit = amount in smaller unit
Change to the smaller unit first: each bigger unit is that many smaller units.
1
1
2
8
×
2
2
5
6
Amount in smaller unit = 256
Step 2 · Find full shares
whole groups of 8 in 256 = ?
Amount in smaller unit ÷ size of one share = full shares, with some left over
Divide by the size of one share. Keep the whole number: the full shares.
256 ÷ 8 = 32, remainder 0
Full shares = 32
Step 3 · Find left over
256 − 32 × 8 = ?
Amount in smaller unit − full shares × size of one share = left over
What the full shares don’t use is left over: less than one share.
Left over = 0 (nothing is left over)
Check
Put the numbers back in. Both sides should match.
2 × 128 = 256 ✓
whole groups of 8 in 256 = 32 ✓
256 − 32 × 8 = 0 ✓
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Compare measurements in different units
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Graph points on the coordinate plane
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