Undo more/less to find original length

2.MD.B.5 · adapt · grade 2

Archetype: Work Backwards to Recover a Start Value · step in a 9-type progression

Mia is $5\ \text{cm}$ taller than Liam.

Use this relationship to express Liam's height in terms of Mia's height.

If Mia's height is $1\ \text{m}\ 25\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

Understand

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.

Givens

Mia is 5 cm taller than Liam (the figure shows the 5 cm head-height difference).
Mia's height is 1 m 25 cm.

Unknowns

Liam's height expressed in terms of Mia's height.
Liam's actual height in meters and centimeters.

Constraints

1 m = 100 cm.
Liam is shorter than Mia, so we subtract the 5 cm difference.

Plan

#11 Work Backwards · also uses: #1 Draw a Diagram

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.

Execute

#11 Work Backwards 2.MD.B.5

Mia is 5 cm taller than Liam, so Liam is 5 cm shorter than Mia.

\text{Liam} = \text{Mia} - 5 \text{ cm}

'Taller by 5' run backwards means the shorter person is the taller minus 5.

#1 Draw a Diagram 2.MD.B.5

Convert 1 m 25 cm to centimeters: 1 m is 100 cm, plus 25 cm.

1\,\text{m}\ 25\,\text{cm} = 100 + 25 = 125 \text{ cm}

Same-unit lengths can be subtracted once both are in centimeters.

#11 Work Backwards 2.MD.B.5

Take away the 5 cm difference from Mia's 125 cm.

125 - 5 = 120 \text{ cm} = 1\,\text{m}\ 20\,\text{cm}

120 cm regroups into 1 m (100 cm) and 20 cm left over.

Answer: Liam = Mia - 5 cm; Liam's height is 1 m 20 cm

Review

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.

Draw a Diagram (tool 1): draw two height bars with Mia's 5 cm taller, then cut 5 cm off Mia's 125 cm bar to read 120 cm = 1 m 20 cm.

Standards · min grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 5 cm height difference to find Liam's height in m and cm.

💡 If someone is taller by 5 cm, the other is just 5 cm less — simple Grade 2 take-away with lengths!