Problem
Undo more/less to find original length
Mia is 5 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 25 cm tall, find Liam's height in meters and centimeters.
Measurement & data
Your answer
Watch out Mia is the one who is taller by 5 cm, so Liam must be shorter — take 5 cm away, do not add it.
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. Then plug in Mia's known height and subtract, converting to m and cm.
1STEP 1
Express Liam in terms of Mia
Mia is 5 cm taller than Liam, so Liam is 5 cm shorter than Mia.
Liam = Mia - 5 cm
'Taller by 5' run backwards means the shorter person is the taller minus 5.
2.MD.B.5Work BackwardsBecause 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
Change 1 m 25 cm into centimeters: 100 + 25 = 125 cm.
1 m 25 cm = 100 + 25 = 125 cm
Same-unit lengths can be subtracted once both are in centimeters.
2.MD.B.5Draw A Diagram3STEP 3
Subtract to find Liam's height
Take 5 cm off Mia's 125 cm: 125 - 5 = 120 cm, which is 1 m 20 cm.
125 - 5 = 120 cm = 1 m 20 cm
120 cm regroups into 1 m (100 cm) and 20 cm left over.
2.MD.B.5Work BackwardsAnswer
Liam = Mia - 5 cm; Liam's height is 1 m 20 cm
125 - 5 = 120 cm = 1 m 20 cm
Liam (1 m 20 cm) is exactly 5 cm shorter than Mia (1 m 25 cm), matching the figure's labeled difference; both are sensible child heights.
Takeaway
If someone is taller by 5 cm, the other is just 5 cm less — simple Grade 2 take-away with lengths!
- Express Liam in terms of Mia
- Write Mia's height in centimeters
- Subtract to find Liam's height
Where next?
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