Problem
Undo more/less to find original length
Mia is 5 cm taller than Liam. If Mia's height is 1 m 25 cm, find Liam's height in meters and centimeters.
Measurement & data
Your answer
Watch out Don't just see taller and add 5 cm to find Liam's height — Liam is shorter, so you must subtract.
How to solve
Strategy Work Backwards — Since Mia is taller by 5 cm, undo that difference: Liam's height is Mia's height minus 5 cm. Convert Mia's height to cm, subtract, then express the result in m and cm.
1STEP 1
Express Liam's height in terms of Mia's
Since Mia is 5 cm taller, Liam must be 5 cm shorter than Mia.
Liam = Mia − 5 cm
Saying Mia is 5 cm taller than Liam means her height is Liam's height with an extra 5 cm stacked on top. So taking that same 5 cm back off Mia's height returns Liam's height.
Work Backwards2.MD.B.5Because Mia is 5 cm taller than Liam, Liam's height is Mia's height minus 5 cm.
Why?
Saying Mia is 5 cm taller than Liam means her height is Liam's whole height with an extra 5 cm stacked on top, so Mia's height equals Liam's height plus 5 cm.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Once Liam's height plus 5 cm makes Mia's height, taking that same 5 cm back off Mia's height gives Liam's height again.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Write Mia's height in centimeters
1 m 25 cm equals 100 cm plus 25 cm, which is 125 cm.
1 m 25 cm = 100 + 25 = 125 cm
To subtract lengths, both must share the same unit. Converting m to cm just counts how many 100 cm bundles there are, so 1 m becomes 100 cm, plus the leftover 25 cm makes 125 cm.
Draw A DiagramMeasuring Length3STEP 3
Subtract to find Liam's height
125 − 5 = 120 cm, which is 1 m 20 cm.
125 − 5 = 120 cm = 1 m 20 cm
Taking away the 5 cm difference from Mia's 125 cm leaves Liam's actual height. 120 cm splits into one bundle of 100 cm (1 m) with 20 cm left over, giving 1 m 20 cm.
Work Backwards2.MD.B.5Measuring LengthAnswer
1 m 20 cm
125 − 5 = 120 cm = 1 m 20 cm
Check — Liam (1 m 20 cm) is exactly 5 cm shorter than Mia (1 m 25 cm), matching the original condition.
Takeaway
A 'taller by' relationship reverses into subtraction. Subtracting 5 cm from Mia's height gives Liam's height, 1 m 20 cm.
- Flip the relationship: Liam = Mia − 5 cm
- Mia's height in cm: 125 cm
- Subtract to get: 1 m 20 cm
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