← Undo more/less to find original length · Work Backwards to Recover a Start Value

Undo more/less to find original length · 10 practice problems

2.MD.B.5

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: Liam = Mia - 3 cm; Liam's height is 1 m 17 cm

Mia is $3\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 20\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 3 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 20 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 3 cm taller than Liam (the figure shows the 3 cm head-height difference).
Mia's height is 1 m 20 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 3 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 3 cm, undo that difference: Liam's height is Mia's height minus 3 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 3 cm taller than Liam, so Liam is 3 cm shorter than Mia.

\text{Liam} = \text{Mia} - 3 \text{ cm}

'Taller by 3' run backwards means the shorter person is the taller minus 3.

2Write Mia's height in centimeters

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

Convert 1 m 20 cm to centimeters: 1 m is 100 cm, plus 20 cm.

1\,\text{m}\ 20\,\text{cm} = 100 + 20 = 120 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 3 cm difference from Mia's 120 cm.

120 - 3 = 117 \text{ cm} = 1\,\text{m}\ 17\,\text{cm}

117 cm regroups into 1 m (100 cm) and 17 cm left over.

Answer: Liam = Mia - 3 cm; Liam's height is 1 m 17 cm

4 · Reviewdoes it hold up?

Liam (1 m 17 cm) is exactly 3 cm shorter than Mia (1 m 20 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 3 cm taller, then cut 3 cm off Mia's 120 cm bar to read 117 cm = 1 m 17 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 3 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 3 cm, the other is just 3 cm less -- simple Grade 2 take-away with lengths!

Variant 2 easy answer: Liam = Mia - 5 cm; Liam's height is 1 m 20 cm

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

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#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.

2Write Mia's height in centimeters

#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.

3Subtract to find Liam's height

#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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

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

Variant 3 easy answer: Liam = Mia - 12 cm; Liam's height is 1 m 16 cm

Mia is $12\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 28\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 12 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 28 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 12 cm taller than Liam (the figure shows the 12 cm head-height difference).
Mia's height is 1 m 28 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 12 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 12 cm, undo that difference: Liam's height is Mia's height minus 12 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 12 cm taller than Liam, so Liam is 12 cm shorter than Mia.

\text{Liam} = \text{Mia} - 12 \text{ cm}

'Taller by 12' run backwards means the shorter person is the taller minus 12.

2Write Mia's height in centimeters

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

Convert 1 m 28 cm to centimeters: 1 m is 100 cm, plus 28 cm.

1\,\text{m}\ 28\,\text{cm} = 100 + 28 = 128 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 12 cm difference from Mia's 128 cm.

128 - 12 = 116 \text{ cm} = 1\,\text{m}\ 16\,\text{cm}

116 cm regroups into 1 m (100 cm) and 16 cm left over.

Answer: Liam = Mia - 12 cm; Liam's height is 1 m 16 cm

4 · Reviewdoes it hold up?

Liam (1 m 16 cm) is exactly 12 cm shorter than Mia (1 m 28 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 12 cm taller, then cut 12 cm off Mia's 128 cm bar to read 116 cm = 1 m 16 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 12 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 12 cm, the other is just 12 cm less -- simple Grade 2 take-away with lengths!

Variant 4 medium answer: Liam = Mia - 5 cm; Liam's height is 1 m 25 cm

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 $1\ \text{m}\ 30\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 5 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 30 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 30 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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#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.

2Write Mia's height in centimeters

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

Convert 1 m 30 cm to centimeters: 1 m is 100 cm, plus 30 cm.

1\,\text{m}\ 30\,\text{cm} = 100 + 30 = 130 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 5 cm difference from Mia's 130 cm.

130 - 5 = 125 \text{ cm} = 1\,\text{m}\ 25\,\text{cm}

125 cm regroups into 1 m (100 cm) and 25 cm left over.

Answer: Liam = Mia - 5 cm; Liam's height is 1 m 25 cm

4 · Reviewdoes it hold up?

Liam (1 m 25 cm) is exactly 5 cm shorter than Mia (1 m 30 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 5 cm taller, then cut 5 cm off Mia's 130 cm bar to read 125 cm = 1 m 25 cm.

Standardsmin 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.

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

Variant 5 medium answer: Liam = Mia - 8 cm; Liam's height is 1 m 25 cm

Mia is $8\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 33\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 8 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 33 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 8 cm taller than Liam (the figure shows the 8 cm head-height difference).
Mia's height is 1 m 33 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 8 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 8 cm, undo that difference: Liam's height is Mia's height minus 8 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 8 cm taller than Liam, so Liam is 8 cm shorter than Mia.

\text{Liam} = \text{Mia} - 8 \text{ cm}

'Taller by 8' run backwards means the shorter person is the taller minus 8.

2Write Mia's height in centimeters

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

Convert 1 m 33 cm to centimeters: 1 m is 100 cm, plus 33 cm.

1\,\text{m}\ 33\,\text{cm} = 100 + 33 = 133 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 8 cm difference from Mia's 133 cm.

133 - 8 = 125 \text{ cm} = 1\,\text{m}\ 25\,\text{cm}

125 cm regroups into 1 m (100 cm) and 25 cm left over.

Answer: Liam = Mia - 8 cm; Liam's height is 1 m 25 cm

4 · Reviewdoes it hold up?

Liam (1 m 25 cm) is exactly 8 cm shorter than Mia (1 m 33 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 8 cm taller, then cut 8 cm off Mia's 133 cm bar to read 125 cm = 1 m 25 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 8 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 8 cm, the other is just 8 cm less -- simple Grade 2 take-away with lengths!

Variant 6 medium answer: Liam = Mia - 10 cm; Liam's height is 1 m 30 cm

Mia is $10\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 40\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 10 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 40 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 10 cm taller than Liam (the figure shows the 10 cm head-height difference).
Mia's height is 1 m 40 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 10 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 10 cm, undo that difference: Liam's height is Mia's height minus 10 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 10 cm taller than Liam, so Liam is 10 cm shorter than Mia.

\text{Liam} = \text{Mia} - 10 \text{ cm}

'Taller by 10' run backwards means the shorter person is the taller minus 10.

2Write Mia's height in centimeters

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

Convert 1 m 40 cm to centimeters: 1 m is 100 cm, plus 40 cm.

1\,\text{m}\ 40\,\text{cm} = 100 + 40 = 140 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 10 cm difference from Mia's 140 cm.

140 - 10 = 130 \text{ cm} = 1\,\text{m}\ 30\,\text{cm}

130 cm regroups into 1 m (100 cm) and 30 cm left over.

Answer: Liam = Mia - 10 cm; Liam's height is 1 m 30 cm

4 · Reviewdoes it hold up?

Liam (1 m 30 cm) is exactly 10 cm shorter than Mia (1 m 40 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 10 cm taller, then cut 10 cm off Mia's 140 cm bar to read 130 cm = 1 m 30 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 10 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 10 cm, the other is just 10 cm less -- simple Grade 2 take-away with lengths!

Variant 7 medium answer: Liam = Mia - 20 cm; Liam's height is 1 m 25 cm

Mia is $20\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 45\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 20 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 45 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 20 cm taller than Liam (the figure shows the 20 cm head-height difference).
Mia's height is 1 m 45 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 20 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 20 cm, undo that difference: Liam's height is Mia's height minus 20 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 20 cm taller than Liam, so Liam is 20 cm shorter than Mia.

\text{Liam} = \text{Mia} - 20 \text{ cm}

'Taller by 20' run backwards means the shorter person is the taller minus 20.

2Write Mia's height in centimeters

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

Convert 1 m 45 cm to centimeters: 1 m is 100 cm, plus 45 cm.

1\,\text{m}\ 45\,\text{cm} = 100 + 45 = 145 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 20 cm difference from Mia's 145 cm.

145 - 20 = 125 \text{ cm} = 1\,\text{m}\ 25\,\text{cm}

125 cm regroups into 1 m (100 cm) and 25 cm left over.

Answer: Liam = Mia - 20 cm; Liam's height is 1 m 25 cm

4 · Reviewdoes it hold up?

Liam (1 m 25 cm) is exactly 20 cm shorter than Mia (1 m 45 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 20 cm taller, then cut 20 cm off Mia's 145 cm bar to read 125 cm = 1 m 25 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 20 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 20 cm, the other is just 20 cm less -- simple Grade 2 take-away with lengths!

Variant 8 hard answer: Liam = Mia - 15 cm; Liam's height is 1 m 35 cm

Mia is $15\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 50\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 15 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 50 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 15 cm taller than Liam (the figure shows the 15 cm head-height difference).
Mia's height is 1 m 50 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 15 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 15 cm, undo that difference: Liam's height is Mia's height minus 15 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 15 cm taller than Liam, so Liam is 15 cm shorter than Mia.

\text{Liam} = \text{Mia} - 15 \text{ cm}

'Taller by 15' run backwards means the shorter person is the taller minus 15.

2Write Mia's height in centimeters

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

Convert 1 m 50 cm to centimeters: 1 m is 100 cm, plus 50 cm.

1\,\text{m}\ 50\,\text{cm} = 100 + 50 = 150 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 15 cm difference from Mia's 150 cm.

150 - 15 = 135 \text{ cm} = 1\,\text{m}\ 35\,\text{cm}

135 cm regroups into 1 m (100 cm) and 35 cm left over.

Answer: Liam = Mia - 15 cm; Liam's height is 1 m 35 cm

4 · Reviewdoes it hold up?

Liam (1 m 35 cm) is exactly 15 cm shorter than Mia (1 m 50 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 15 cm taller, then cut 15 cm off Mia's 150 cm bar to read 135 cm = 1 m 35 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 15 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 15 cm, the other is just 15 cm less -- simple Grade 2 take-away with lengths!

Variant 9 hard answer: Liam = Mia - 25 cm; Liam's height is 1 m 30 cm

Mia is $25\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 55\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 25 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 55 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 25 cm taller than Liam (the figure shows the 25 cm head-height difference).
Mia's height is 1 m 55 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 25 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 25 cm, undo that difference: Liam's height is Mia's height minus 25 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 25 cm taller than Liam, so Liam is 25 cm shorter than Mia.

\text{Liam} = \text{Mia} - 25 \text{ cm}

'Taller by 25' run backwards means the shorter person is the taller minus 25.

2Write Mia's height in centimeters

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

Convert 1 m 55 cm to centimeters: 1 m is 100 cm, plus 55 cm.

1\,\text{m}\ 55\,\text{cm} = 100 + 55 = 155 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 25 cm difference from Mia's 155 cm.

155 - 25 = 130 \text{ cm} = 1\,\text{m}\ 30\,\text{cm}

130 cm regroups into 1 m (100 cm) and 30 cm left over.

Answer: Liam = Mia - 25 cm; Liam's height is 1 m 30 cm

4 · Reviewdoes it hold up?

Liam (1 m 30 cm) is exactly 25 cm shorter than Mia (1 m 55 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 25 cm taller, then cut 25 cm off Mia's 155 cm bar to read 130 cm = 1 m 30 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 25 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 25 cm, the other is just 25 cm less -- simple Grade 2 take-away with lengths!

Variant 10 hard answer: Liam = Mia - 7 cm; Liam's height is 1 m 53 cm

Mia is $7\ \text{cm}$ taller than Liam.

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

If Mia's height is $1\ \text{m}\ 60\ \text{cm}$ , find Liam's height in meters and centimeters.

Show solution

1 · Understandwhat's really being asked

Mia is 7 cm taller than Liam. We first express Liam's height in terms of Mia's, then, given Mia is 1 m 60 cm tall, find Liam's height in meters and centimeters.

Givens

Mia is 7 cm taller than Liam (the figure shows the 7 cm head-height difference).
Mia's height is 1 m 60 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 7 cm difference.

2 · Planchoose the strategy

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

Since Mia is taller by 7 cm, undo that difference: Liam's height is Mia's height minus 7 cm. Then plug in Mia's known height and subtract, converting to m and cm.

3 · Execute3 carry out the plan

1Express Liam in terms of Mia

#11 Work Backwards 2.MD.B.5

Mia is 7 cm taller than Liam, so Liam is 7 cm shorter than Mia.

\text{Liam} = \text{Mia} - 7 \text{ cm}

'Taller by 7' run backwards means the shorter person is the taller minus 7.

2Write Mia's height in centimeters

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

Convert 1 m 60 cm to centimeters: 1 m is 100 cm, plus 60 cm.

1\,\text{m}\ 60\,\text{cm} = 100 + 60 = 160 \text{ cm}

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

3Subtract to find Liam's height

#11 Work Backwards 2.MD.B.5

Take away the 7 cm difference from Mia's 160 cm.

160 - 7 = 153 \text{ cm} = 1\,\text{m}\ 53\,\text{cm}

153 cm regroups into 1 m (100 cm) and 53 cm left over.

Answer: Liam = Mia - 7 cm; Liam's height is 1 m 53 cm

4 · Reviewdoes it hold up?

Liam (1 m 53 cm) is exactly 7 cm shorter than Mia (1 m 60 cm), matching the figure's labeled difference; both are sensible child heights.

Another way: Draw a Diagram (tool 1): draw two height bars with Mia's 7 cm taller, then cut 7 cm off Mia's 160 cm bar to read 153 cm = 1 m 53 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Subtracting the 7 cm height difference to find Liam's height in m and cm.

💡Takeaway. If someone is taller by 7 cm, the other is just 7 cm less -- simple Grade 2 take-away with lengths!