Jump, Add, Subtract: Number Lines to 100

SECTION 1

The Story of Number Lines

Long ago, people needed ways to count and keep track of numbers. They used their fingers, made marks on sticks, and even tied knots in ropes! But sometimes they needed to see numbers in order to solve problems better.

Ancient Times

Counting on Fingers

People used their 10 fingers to count and add numbers together.

1600s

First Number Lines

Smart people drew lines with numbers to help solve math problems.

1800s

School Number Lines

Teachers started using number lines to help kids learn to add and subtract.

Today

Number Lines Everywhere

We use number lines on rulers, thermometers, and in math class every day!

Number lines became popular because they help us see math instead of just thinking about it. When we jump forward on a number line, we add. When we jump backward, we subtract!

SECTION 2

What Makes Number Lines Work

A number line is like a straight road with numbers written along it. Each number has its own spot, and they go in order from small to big.

Numbers in Order

Numbers are lined up from 0 to 100, with each number in its special place.

Equal Spaces

The distance between each number is always the same, like steps on stairs.

Jump Forward to Add

When we add, we hop to the right toward bigger numbers.

Jump Backward to Subtract

When we subtract, we hop to the left toward smaller numbers.

✦ KEY TAKEAWAY

Think of a number line like a hopscotch game! You start on one number and hop forward to add or hop backward to subtract. Each hop takes you to the next number in line.

SECTION 3

See How Number Lines Work

This number line shows how to add and subtract by jumping. The green circles show where we start, the blue arrows show jumping forward to add, the yellow arrows show jumping backward to subtract, and the pink circles show our final answers.

Look at how the number line helps us solve problems! When we add 3 + 2, we start at 3 and make two jumps forward. When we subtract 7 − 2, we start at 7 and make two jumps backward. Both problems give us the same answer: 5!

SECTION 4

The Math Rules

Number lines follow simple math rules that make them work every time. These rules help us know which way to jump and how far to go.

ADDITION RULE

Start Number + Jump Size = End Number

When adding, always jump to the right toward bigger numbers.

SUBTRACTION RULE

Start Number − Jump Size = End Number

When subtracting, always jump to the left toward smaller numbers.

COUNTING RULE

Count Each Jump = 1, 2, 3, 4, 5...

Each space you jump counts as one number. Count your jumps to make sure you land on the right answer.

These rules work for any numbers from 0 to 100! The most important thing to remember is: addition goes right, subtraction goes left.

SECTION 5

Smart Jumping Strategies

There are different ways to jump on number lines. Some ways are faster and easier than others!

This diagram shows two different ways to solve the same problem. The small jumps method uses seven jumps of +1 each. The big jumps method uses one jump of +5 and one jump of +2. Both get us to 32!

Strategy	When to Use	Example
Small Jumps (+1)	Adding small numbers (1-5)	8 + 3: Jump +1, +1, +1
Big Jumps (+10)	Adding tens	30 + 20: Jump +10, +10
Mixed Jumps	Adding larger numbers	15 + 8: Jump +5, then +3

SECTION 6

Step-by-Step Solution

Let's solve a problem together using a number line! We'll find the answer to 46 + 15 step by step.

Solving 46 + 15

Step 1 — Draw the Number LineDraw a line and mark numbers around where we'll work. We need numbers from about 40 to 65.

Number line ready with tick marks

Step 2 — Find the Starting PointPut a circle or dot on the number 46. This is where we start our jumps.

Starting at 46

Step 3 — Plan Your JumpsWe need to add 15. Let's use big jumps: first jump +10, then jump +5.

Plan: +10, then +5

Step 4 — Make the First JumpFrom 46, jump 10 spaces to the right. Count: 47, 48, 49, 50, 51, 52, 53, 54, 55, 56.

Land on 56

Step 5 — Make the Second JumpFrom 56, jump 5 more spaces to the right. Count: 57, 58, 59, 60, 61.

Final answer: 61

Step 6 — Check Your WorkCount all your jumps: 10 + 5 = 15. We jumped 15 spaces from 46, so 46 + 15 = 61. ✓

Answer confirmed!

SECTION 7

Making Number Lines Easier

Here are some helpful tips to make number lines work better for you!

Helpful Tip	Why It Works
Use your finger to hop	Your finger helps you count jumps and not get lost
Jump to friendly numbers	Numbers like 10, 20, 30 are easier to work with
Count your jumps out loud	Saying numbers helps you remember where you are
Draw arrows for big jumps	Arrows help you see which direction and how far

✦ KEY TAKEAWAY

Number lines are like a sidewalk with numbers painted on it! When you want to visit a friend's house, you walk there step by step. Number lines work the same way — you "walk" from one number to another by counting your steps.

SECTION 8

Number Lines Get Even Bigger!

Right now we're learning about number lines to 100, but number lines can go much bigger! Let's see what comes next in your math journey.

What You Know Now	What You'll Learn Later
Number lines 0 to 100	Number lines to 1000 and beyond!
Adding and subtracting by jumping	Multiplying by making equal jumps
Whole numbers only	Fractions and decimals between numbers
Numbers that go up	Negative numbers that go below zero

The jumping skills you're learning now will help you with all kinds of math in the future. Number lines are used by scientists, engineers, and even video game designers!

SECTION 9

Practice Problems

Now it's your turn to try! Use number lines to solve these problems. Remember to start at the first number and jump forward for addition or backward for subtraction.

PROBLEM 1 — CONCEPTUAL

If you start at 12 on a number line and want to add 6, which direction do you jump and how many spaces?

PROBLEM 2 — BASIC CALCULATION

Use a number line to solve 8 + 5. Show your work by describing your jumps.

PROBLEM 3 — INTERMEDIATE

Solve 35 − 8 using a number line. What's the smartest way to make your jumps?

PROBLEM 4 — APPLIED

Sarah has 42 stickers. She gives away 15 stickers to friends. How many stickers does she have left? Use a number line to solve.

PROBLEM 5 — CRITICAL THINKING

Tim is at number 18 on a number line. He makes some jumps and ends up at 31. Did he add or subtract? How do you know? What numbers could he have added?

SUMMARY

Number Line Mastery

Number lines are powerful tools that help us see math problems instead of just thinking about them. When we jump forward (to the right), we add numbers together. When we jump backward (to the left), we subtract numbers. The key is to count your jumps carefully to make sure you land on the right answer.

Remember that you can make big jumps or small jumps — whatever feels easier for the problem you're solving. Use friendly numbers like 10, 20, and 30 to make your jumps faster and easier. With practice, number lines will become your favorite way to solve addition and subtraction problems up to 100!