Sensim Math · Depth 한국어

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

Mia is 5 cm5\ \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 m 25 cm1\ \text{m}\ 25\ \text{cm}, find Liam's height in meters and centimeters.

5 cm Mia Liam
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.
Liam=Mia−5 cm\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 m 25 cm=100+25=125 cm1\,\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 cm=1 m 20 cm125 - 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!
Variant 2 answer: Liam = Mia - 10 cm; Liam's height is 1 m 30 cm

Mia is 10 cm10\ \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 m 40 cm1\ \text{m}\ 40\ \text{cm}, find Liam's height in meters and centimeters.

10 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 10 cm taller than Liam, so Liam is 10 cm shorter than Mia.
Liam=Mia−10 cm\text{Liam} = \text{Mia} - 10 \text{ cm}
'Taller by 10' run backwards means the shorter person is the taller minus 10.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 40 cm to centimeters: 1 m is 100 cm, plus 40 cm.
1 m 40 cm=100+40=140 cm1\,\text{m}\ 40\,\text{cm} = 100 + 40 = 140 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 10 cm difference from Mia's 140 cm.
140−10=130 cm=1 m 30 cm140 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 10 cm, the other is just 10 cm less -- simple Grade 2 take-away with lengths!
Variant 3 answer: Liam = Mia - 7 cm; Liam's height is 1 m 53 cm

Mia is 7 cm7\ \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 m 60 cm1\ \text{m}\ 60\ \text{cm}, find Liam's height in meters and centimeters.

7 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 7 cm taller than Liam, so Liam is 7 cm shorter than Mia.
Liam=Mia−7 cm\text{Liam} = \text{Mia} - 7 \text{ cm}
'Taller by 7' run backwards means the shorter person is the taller minus 7.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 60 cm to centimeters: 1 m is 100 cm, plus 60 cm.
1 m 60 cm=100+60=160 cm1\,\text{m}\ 60\,\text{cm} = 100 + 60 = 160 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 7 cm difference from Mia's 160 cm.
160−7=153 cm=1 m 53 cm160 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 7 cm, the other is just 7 cm less -- simple Grade 2 take-away with lengths!
Variant 4 answer: Liam = Mia - 25 cm; Liam's height is 1 m 30 cm

Mia is 25 cm25\ \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 m 55 cm1\ \text{m}\ 55\ \text{cm}, find Liam's height in meters and centimeters.

25 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 25 cm taller than Liam, so Liam is 25 cm shorter than Mia.
Liam=Mia−25 cm\text{Liam} = \text{Mia} - 25 \text{ cm}
'Taller by 25' run backwards means the shorter person is the taller minus 25.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 55 cm to centimeters: 1 m is 100 cm, plus 55 cm.
1 m 55 cm=100+55=155 cm1\,\text{m}\ 55\,\text{cm} = 100 + 55 = 155 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 25 cm difference from Mia's 155 cm.
155−25=130 cm=1 m 30 cm155 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 25 cm, the other is just 25 cm less -- simple Grade 2 take-away with lengths!
Variant 5 answer: Liam = Mia - 12 cm; Liam's height is 1 m 16 cm

Mia is 12 cm12\ \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 m 28 cm1\ \text{m}\ 28\ \text{cm}, find Liam's height in meters and centimeters.

12 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 12 cm taller than Liam, so Liam is 12 cm shorter than Mia.
Liam=Mia−12 cm\text{Liam} = \text{Mia} - 12 \text{ cm}
'Taller by 12' run backwards means the shorter person is the taller minus 12.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 28 cm to centimeters: 1 m is 100 cm, plus 28 cm.
1 m 28 cm=100+28=128 cm1\,\text{m}\ 28\,\text{cm} = 100 + 28 = 128 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 12 cm difference from Mia's 128 cm.
128−12=116 cm=1 m 16 cm128 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 12 cm, the other is just 12 cm less -- simple Grade 2 take-away with lengths!
Variant 6 answer: Liam = Mia - 15 cm; Liam's height is 1 m 35 cm

Mia is 15 cm15\ \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 m 50 cm1\ \text{m}\ 50\ \text{cm}, find Liam's height in meters and centimeters.

15 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 15 cm taller than Liam, so Liam is 15 cm shorter than Mia.
Liam=Mia−15 cm\text{Liam} = \text{Mia} - 15 \text{ cm}
'Taller by 15' run backwards means the shorter person is the taller minus 15.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 50 cm to centimeters: 1 m is 100 cm, plus 50 cm.
1 m 50 cm=100+50=150 cm1\,\text{m}\ 50\,\text{cm} = 100 + 50 = 150 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 15 cm difference from Mia's 150 cm.
150−15=135 cm=1 m 35 cm150 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 15 cm, the other is just 15 cm less -- simple Grade 2 take-away with lengths!
Variant 7 answer: Liam = Mia - 8 cm; Liam's height is 1 m 25 cm

Mia is 8 cm8\ \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 m 33 cm1\ \text{m}\ 33\ \text{cm}, find Liam's height in meters and centimeters.

8 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 8 cm taller than Liam, so Liam is 8 cm shorter than Mia.
Liam=Mia−8 cm\text{Liam} = \text{Mia} - 8 \text{ cm}
'Taller by 8' run backwards means the shorter person is the taller minus 8.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 33 cm to centimeters: 1 m is 100 cm, plus 33 cm.
1 m 33 cm=100+33=133 cm1\,\text{m}\ 33\,\text{cm} = 100 + 33 = 133 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 8 cm difference from Mia's 133 cm.
133−8=125 cm=1 m 25 cm133 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 8 cm, the other is just 8 cm less -- simple Grade 2 take-away with lengths!
Variant 8 answer: Liam = Mia - 20 cm; Liam's height is 1 m 25 cm

Mia is 20 cm20\ \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 m 45 cm1\ \text{m}\ 45\ \text{cm}, find Liam's height in meters and centimeters.

20 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 20 cm taller than Liam, so Liam is 20 cm shorter than Mia.
Liam=Mia−20 cm\text{Liam} = \text{Mia} - 20 \text{ cm}
'Taller by 20' run backwards means the shorter person is the taller minus 20.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 45 cm to centimeters: 1 m is 100 cm, plus 45 cm.
1 m 45 cm=100+45=145 cm1\,\text{m}\ 45\,\text{cm} = 100 + 45 = 145 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 20 cm difference from Mia's 145 cm.
145−20=125 cm=1 m 25 cm145 - 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

Review

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.

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.

Standards · min 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.
💡 If someone is taller by 20 cm, the other is just 20 cm less -- simple Grade 2 take-away with lengths!
Variant 9 answer: Liam = Mia - 5 cm; Liam's height is 1 m 25 cm

Mia is 5 cm5\ \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 m 30 cm1\ \text{m}\ 30\ \text{cm}, find Liam's height in meters and centimeters.

5 cm Mia Liam
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 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.

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.
Liam=Mia−5 cm\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 30 cm to centimeters: 1 m is 100 cm, plus 30 cm.
1 m 30 cm=100+30=130 cm1\,\text{m}\ 30\,\text{cm} = 100 + 30 = 130 \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 130 cm.
130−5=125 cm=1 m 25 cm130 - 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

Review

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.

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.

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!
Variant 10 answer: Liam = Mia - 3 cm; Liam's height is 1 m 17 cm

Mia is 3 cm3\ \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 m 20 cm1\ \text{m}\ 20\ \text{cm}, find Liam's height in meters and centimeters.

3 cm Mia Liam
Show solution

Understand

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.

Plan

#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.

Execute

#11 Work Backwards 2.MD.B.5
Mia is 3 cm taller than Liam, so Liam is 3 cm shorter than Mia.
Liam=Mia−3 cm\text{Liam} = \text{Mia} - 3 \text{ cm}
'Taller by 3' run backwards means the shorter person is the taller minus 3.
#1 Draw a Diagram 2.MD.B.5
Convert 1 m 20 cm to centimeters: 1 m is 100 cm, plus 20 cm.
1 m 20 cm=100+20=120 cm1\,\text{m}\ 20\,\text{cm} = 100 + 20 = 120 \text{ cm}
Same-unit lengths can be subtracted once both are in centimeters.
#11 Work Backwards 2.MD.B.5
Take away the 3 cm difference from Mia's 120 cm.
120−3=117 cm=1 m 17 cm120 - 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

Review

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.

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.

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