Addition & Subtraction Length Word Problems - Second Grade Mathematics

Measurement does not exist in isolation on a ruler; in the real world, lengths are constantly being combined, trimmed, cut, joined, and compared. You might need to know how much fabric is required to sew two curtains, how much yarn remains after knitting a scarf, or how much taller a sunflower grew over the summer. Addition and subtraction length word problems apply all of your operational strategies within 100 to physical distances. In this chapter, you will master joining lengths (addition), cutting or reducing lengths (subtraction), and solving two-step measurement challenges with units clearly attached.

Joining Lengths (Addition Problems)

When two or more physical objects are connected end to end, their combined total length is found by adding their individual lengths together.

Connecting Two Wooden Boards:
Board A: [=========================] 35 cm
Board B:                            [====================] 28 cm
Total:   [===============================================] [ ? ] cm

Equation: 35 cm + 28 cm = [ ? ] cm
Calculate: 35 + 28 = 63 cm.
Combined Total Length: 63 centimeters.

Always Include the Measurement Unit!

In measurement word problems, a bare number is incomplete! If you calculate 63, you must ask: 63 what? 63 inches? 63 feet? 63 meters? Always attach the correct unit label: 63 cm. An answer without a unit is like a person without a name.

Cutting and Removing Lengths (Subtraction Problems)

When a piece is cut away from a longer material, or when an object is shortened, you use subtraction to find the remaining length.

Cutting a Ribbon:
Original Spool: [==================================================] 75 inches
Cut Piece:      [=======================] 38 inches
Remaining:                              [--------------------------] [ ? ] inches

Equation: 75 inches - 38 inches = [ ? ] inches
Calculate: 75 - 38 = 37 inches.
Remaining Ribbon: 37 inches.

The Take-Away Action

In the ribbon story above, the starting whole is 75 inches. A 38-inch piece is cut off and removed. Subtracting 75 - 38 leaves 37 inches of ribbon on the spool.

Growth and Distance Over Time

Many measurement stories involve objects growing taller or animals traveling distances over time.

Sunflower Growth Story:
In June, a sunflower was 42 inches tall.
By August, the sunflower had grown to 68 inches tall.
How many inches did the sunflower grow over the summer?

Model: 42 in (Start) + [ ? ] in (Growth) = 68 in (End)
Inversion: 68 - 42 = 26 inches.
The sunflower grew 26 inches over the summer.

Missing Growth Addends

Notice how growth problems are often unknown addend problems: Start Height + Growth = Final Height. You solve them by subtracting the initial height from the final height.

Two-Step Length Word Problems

Advanced measurement problems require two operations to reach the final answer.

Two-Step Example:
Story: A carpenter has a wooden plank that is 90 inches long.
He cuts off one piece that is 24 inches long for a shelf.
He cuts off a second piece that is 35 inches long for a bench.
How many inches of the wooden plank are left?

Step 1: Find total length cut off:
        24 in + 35 in = 59 inches cut.

Step 2: Subtract from original plank:
        90 in - 59 in = 31 inches left.
The carpenter has 31 inches of plank left.

Practice Exercises

Exercise 1: A tailor joins two strips of fabric together. The blue strip is 47 inches long and the white strip is 38 inches long. What is the total length of the joined fabric?

Exercise 2: A roll of craft paper was 80 feet long. Art students used 46 feet of paper to create a mural. How many feet of craft paper remained on the roll?

Exercise 3: In spring, a young tree was 54 centimeters tall. By autumn, it was 82 centimeters tall. How many centimeters did the tree grow between spring and autumn?

Exercise 4: Liam had a 100-inch roll of electrical wire. He used 28 inches for a lamp and 45 inches for a radio. How many inches of wire did Liam have left on the roll?

Solutions and Explanations

Solution to Exercise 1: To find the total length, add the two strips: 47 inches + 38 inches. Add tens: 40 + 30 = 70. Add ones: 7 + 8 = 15. Combine: 70 + 15 = 85 inches. The joined fabric is 85 inches long.

Solution to Exercise 2: To find the remaining paper, subtract: 80 feet - 46 feet. Regroup 1 ten: 10 - 6 = 4 ones, and 7 tens - 4 tens = 3 tens. Exactly 34 feet of craft paper remained on the roll.

Solution to Exercise 3: To find the tree's growth, find the difference between final height and starting height: 82 cm - 54 cm. Regroup 1 ten: 12 - 4 = 8 ones, and 7 tens - 5 tens = 2 tens. The tree grew 28 centimeters.

Solution to Exercise 4: Step 1: Find total wire used: 28 inches + 45 inches = 73 inches. Step 2: Subtract total wire used from the 100-inch roll: 100 - 73 = 27 inches. Liam had 27 inches of wire left on the roll.