Start and move on a number line

Where do you arrive when moving right from a negative position?

From −2, three steps right pass −1, 0, 1. Starting at −2 and adding the move +3 ends at 1.

Start at −2 and walk three units right. The steps land on −1, 0 and 1. Do not count the starting point as the first step.

Write a rightward move as a positive change and a leftward move as a negative change. Three steps right is +3; three left is −3. Moving right increases the value even from a negative start.

Starting at −2 and adding +3 gives −2+3=1. Starting at 2 and adding −3 gives 2+(−3)=−1. The parentheses show that the whole negative number −3 is being added.

The endpoint alone does not tell you the distance walked. From −2 to 1, the three rightward steps have distance 3. Endpoint 1 and movement distance 3 are different.

Each move in this activity keeps one direction. Zero steps leave the endpoint at the start. A round trip’s total path length is a different question from its final position.

One line needed a reference, direction and unit. Coordinates in a plane will require horizontal and vertical directions and an ordered pair. For ratios, first revisit common units and multiplier rules. Use the links below to review only the preparation you need.

Listen one paragraph at a time

1 / 6

2 / 6

3 / 6

4 / 6

5 / 6

6 / 6

Hold on to this distinction

Mark the start and count intervals. Three steps right from −2 land on −1, 0, 1; do not count −2 as a step.

Change it and check

Change the start, direction and step count. Move one step at a time, then check the expression. Changing a control returns you to the new start.

Starting positionMove directionNumber of steps

Number line with one-unit intervals. A: −2, B: −2. Values increase to the right. On narrow screens, scroll the diagram horizontally.

Start −2; Move +0; Current position B −2. 0/2
Move one step at a time and predict the endpoint.

Starts range from −3 to 3, and moves from zero to three steps in one direction. The activity stays within −6 to 6. Multiplying negatives and subtracting a negative are not yet covered.

Try with paper and objects

Lay equally spaced labels −3 through 3 on the floor. Start at −1, step twice right, and name start, move and endpoint separately.

Check and explain another example

Check your idea 1

Starting at −3, where do two steps right end?

Check your idea 2

Which expression represents three steps left from 2?

Apply it in a new setting

A robot at position −1 makes no move. Where does it end?

Write an answer yourself

Return to the explanation

Compare with a solution

2 · number only

The steps land on 0, 1, 2, so −1+3=2.

Does your explanation include these ideas?

Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.

Count intervals rather than the starting point.Name start, change and endpoint separately.Explain the signs of right and left moves.