SME
Grade 5 Math · Problem type
Line plots with fractions
Use this for “The line plot shows beakers holding 1/8, 1/4, 3/8 or 1/2 liter.”
Chart
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1/8
2 beakers
1/4
3 beakers
3/8
1 beaker
1/2
2 beakers
Water in liters
This is an example. Type your own values to start a new problem.
Beakers with 1/8 L
example
Beakers with 1/4 L
example
Beakers with 3/8 L
example
Beakers with 1/2 L
example
Total water
worked out (not typed) · liters
Number of beakers
worked out (not typed)
Each beaker if shared equally
worked out (not typed) · liters
Formulas
2
×
1
8
+
3
×
2
8
+
1
×
3
8
+
2
×
4
8
=
2
3
8
Beakers × liters at each mark, added = total water
2 + 3 + 1 + 2 = 8
Add the counts = number of beakers
2
3
8
÷
8
=
19
64
Total water ÷ number of beakers = each beaker if shared equally
Assumptions
•
Each X is one beaker. Write every amount in eighths: 1/4 = 2/8 and 1/2 = 4/8.
•
The total adds beakers × liters at each mark: an amount of water in liters, not a count.
•
Shared equally, each beaker gets the total ÷ the number of beakers.
Step-by-step
WE KNOW
Beakers with 1/8 L: 2
Beakers with 1/4 L: 3
Beakers with 3/8 L: 1
Beakers with 1/2 L: 2
FIND
total water, number of beakers, each beaker if shared equally
Step 1 · Find total water
2
×
1
8
+
3
×
2
8
+
1
×
3
8
+
2
×
4
8
=
?
Beakers × liters at each mark, added = total water
Write each amount in eighths of a liter. Multiply by the beakers at each mark, then add.
2
×
1
8
=
2
8
3
×
2
8
=
6
8
1
×
3
8
=
3
8
2
×
4
8
=
8
8
2
8
+
6
8
+
3
8
+
8
8
=
19
8
19
8
=
2
3
8
liters
Total
water
=
2
3
8
liters
Step 2 · Find number of beakers
2 + 3 + 1 + 2 = ?
Add the counts = number of beakers
Count every X.
Number of beakers = 8
Step 3 · Find each beaker if shared equally
2
3
8
÷
8
=
?
Total water ÷ number of beakers = each beaker if shared equally
Share the total equally: divide it by the number of beakers.
19
8
÷
8
=
19
64
liter
each
Each
beaker
if
shared
equally
=
19
64
liter
Check
Put the numbers back in. Both sides should match.
2
×
1
8
+
3
×
2
8
+
1
×
3
8
+
2
×
4
8
=
2
3
8
✓
2 + 3 + 1 + 2 = 8 ✓
2
3
8
÷
8
=
19
64
✓
Topic check
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