Length Problems and the Number Line

Quick answer

A number line works like a long ruler: every number is a length measured from 0. Adding is a jump forward — 25 + 15 starts at 25 and jumps 15 to land on 40 — and subtracting is a jump back. Word problems about lengths, such as a ribbon cut shorter or two strings compared, can be drawn this way and written as number sentences, as long as every length is in the same unit.

What you'll learn

Show whole numbers as lengths from 0 on a number line
Show sums and differences within 100 as jumps on a number line
Solve word problems about lengths in the same unit

Numbers are lengths from 0

A number line is like a long ruler. The marks are the same distance apart, and each number tells how far it is from $0$ .

Twenty-five as a length

The bar shows $25$ as a length: $25$ units from $0$ .

Add with a jump forward

To add $25 + 15$ , start at $25$ . Then jump forward $15$ .

Twenty-five and fifteen more

You land on $40$ . So $25 + 15 = 40$ .

Subtract with a jump back

To find $60 - 35$ , start at $60$ and jump back $35$ .

Sixty take away thirty-five

You land on $25$ . So $60 - 35 = 25$ .

Why a jump is a length

The jump from $25$ to $40$ covers $15$ units. It is a length of $15$ , laid down end to end after the first $25$ .

That is what adding lengths means: put one length after the other and find the total. Subtracting takes a length away from the end. Every jump is a length, so the number line turns adding and subtracting into measuring.

Length word problems

Draw the lengths on a number line or a ruler, then write a number sentence. Every length must be in the same unit.

A ribbon is $45$ centimeters long. Ana cuts off $18$ centimeters. How long is it now?

$45 - 18 = \square$ . Jump back $15$ to $30$ , then $3$ more to $27$ . The ribbon is $27$ centimeters long.

Worked examples

Common mistakes

Practice problems

Find $35 + 20$ on a number line.

Answer

$55$

Full solution

Start at $35$ and jump forward $20$ : $45$ , then $55$ .
What number sentence does this number line show?

What does it show?

Answer

$70 - 30 = 40$

Full solution

The jump starts at $70$ and goes back to $40$ . That is a jump back of $30$ .
A board is $72$ centimeters long. A piece $25$ centimeters long is cut off. How long is the board now?

Answer

$47$ centimeters

Full solution

$72 - 25 = 47$ . Jump back $20$ to $52$ , then $5$ to $47$ .
A worm is $9$ centimeters long. A snake is $85$ centimeters long. How much longer is the snake?

Answer

$76$ centimeters

Full solution

$85 - 9 = 76$ . Jump back $5$ to $80$ , then $4$ to $76$ .
Two sticks are $38$ inches and $27$ inches long. How long are they end to end?

Answer

$65$ inches

Full solution

End to end means add: $38 + 27 = 65$ .
Show $40$ as a length on a number line. Where does it start and end?

Answer

It starts at $0$ and ends at $40$ .

Full solution

Every length on a number line is measured from $0$ . So $40$ runs from $0$ to $40$ .
A plant was $18$ centimeters tall. It grew $15$ centimeters. How tall is it now?

Answer

$33$ centimeters

Full solution

$18 + 15 = 33$ . Jump $2$ to $20$ , then $13$ more to $33$ .
Kim’s scarf is $54$ inches long. It is $19$ inches longer than Lee’s. How long is Lee’s scarf?

Answer

$35$ inches

Full solution

Lee’s is shorter by $19$ . $54 - 19 = 35$ .
Fill in the box: $46 + \square = 80$ . Use jumps.

Answer

$34$

Full solution

From $46$ , jump $4$ to $50$ , then $30$ to $80$ . The jumps add to $4 + 30 = 34$ .
Ann counts the marks from $30$ to $35$ on a number line marked by ones and says the length is $6$ . What went wrong?

Hint

Count the spaces, not the marks.

Answer

She counted the mark at $30$ too. The length is $5$ .

Full solution

From $30$ to $35$ there are $5$ spaces, one for each unit. There are $6$ marks, because the marks sit at both ends.

$35 - 30 = 5$ .

Frequently asked questions

How is a number line like a ruler?

Both have equally spaced marks starting at 0, and each number tells how far it is from 0.

How do I add on a number line?

Start at the first number and jump forward by the second. For 25 + 15, start at 25 and jump 15 to land on 40.

How do I subtract on a number line?

Start at the first number and jump back. For 60 − 35, start at 60 and jump back 35 to land on 25.

Can I add 5 feet and 3 inches to get 8?

No. Lengths can only be added or subtracted when they are in the same unit.

How do I find how much longer one thing is?

Subtract the shorter length from the longer one. On a number line, it is the jump from the shorter length to the longer one.

What to learn next

Counting Money: Coins, Dollars and CentsGrade 2 money: know pennies, nickels, dimes, quarters and dollar bills, count mixed coins by skip-counting, use the ¢ and dollar signs, and solve money word problems.

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

CCSS.MATH.CONTENT.2.MD.B.5Measurement and DataUse addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
CCSS.MATH.CONTENT.2.MD.B.6Measurement and DataRepresent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

For teachersPrint problems onlyTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.

Quick answer

What you'll learn

Frequently asked questions

How is a number line like a ruler?

How do I add on a number line?

How do I subtract on a number line?

Can I add 5 feet and 3 inches to get 8?

How do I find how much longer one thing is?

What to learn next

Standards alignment

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