Subtract the overlap from total length

2.MD.B.52.MD.A.4 · adapt · grade 2

Archetype: Overlap Reduces the Total · step in a 4-type progression

Find the length from ㉠ to ㉣ in meters and centimeters.

(Figure) On a single straight line the four points ㉠, ㉡, ㉢, ㉣ are marked in order from left to right. The length from ㉠ to ㉢ is $2\ \mathrm{m}\ 55\ \mathrm{cm}$ , the length from ㉡ to ㉣ is $2\ \mathrm{m}\ 89\ \mathrm{cm}$ , and the overlapping part from ㉡ to ㉢ is $1\ \mathrm{m}\ 50\ \mathrm{cm}$ .

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Understand

Four points A, B, C, D lie in order on a line. The span A to C is 2 m 55 cm, the span B to D is 2 m 89 cm, and the overlapping middle span B to C is 1 m 50 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 2 m 55 cm.
B to D = 2 m 89 cm.
Overlap B to C = 1 m 50 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

Plan

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

Execute

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

Write each length in centimeters so they can be combined.

255\,\text{cm},\ 289\,\text{cm},\ 150\,\text{cm}

Same-unit lengths add and subtract cleanly.

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

255 + 289 = 544 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (150 cm) to get the true length A-D.

544 - 150 = 394 \text{ cm} = 3\,\text{m}\ 94\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 3 m 94 cm

Review

A-D should be longer than either single span (2 m 55 cm or 2 m 89 cm) but less than their sum (5 m 44 cm); 3 m 94 cm fits between, so it is reasonable.

Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 255 - 150 = 105 cm; then A-D = A-B + B-D = 105 + 289 = 394 cm = 3 m 94 cm.

Standards · min grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡 When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!