Hills and Dales

I am learning to add and subtract integers (positive and negative numbers).

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

and negative numbers asFor this lesson think of positive numbers as hillsdales (holes in the ground).

Let’s make 4 + -3 (4 hills and 3 dales).

We can use 3 of the hills to fill in 3 of the dales.

That leaves us with 1 hill so 4 + -3 = 1

Examples that contain only dales are even easier.

- 3 + - 2 = ?

Step 1: Imagine the first 3 dales.

5, so -3 + -2 = -5

Step 2: Imagine the next 2 dales.

Step 3: How many dales are there in total?

Now lets look at some subtraction examples. Remember that subtraction means to take away or remove.

Step 1: Imagine the 5 dales.

-5 - -2 = ?

Step 2: The question now says we must remove 2 dales.

5 dales

remove2 dales

Step 3: How many dales are left? 3, so -5 - -2 = -3

Let’s look at 4 - -1 = ?

Step 1: Imagine the 4 hills.

4 hillsremove

1 dales

Step 2: The question says we must remove 1 dale but there aren’t any dales there.

Lets’ think about how a dale is removed. It is filled with dirt. The question says that the dirt will still be delivered. Since there is no dale to fill in it actually makes another hill.

Step 2: How many hills are there? 5, so 4 - -1 = 5

4 - -1 = ? Step 1: Imagine the 4 hills.

4 hills remove

1 dale

Sometimes it’s easier to think about the previous question as an addition question.

Step 2 : Now just look at this bit.

We have to remove a dale that’s not there. We have seen that that’s just the same as adding.

So 4 - -1 =? is the same as 4 + 1 = ?

Step 3 : Add the 1 dale. 4 + 1 = 5

Important: Subtracting a negative e.g. 6 - -4 = 10 is the same as adding e.g. 6 + 4 = 10

Now try these questions on your own..

Need some more practise? Try Pg66 of Teacher Tools Addition and Subtraction Book Numeracy resources

1) -4 + -7 = ?

2) 5 + -8 = ?

3) 7 - -2 = ?

4) -8 - -2 = ?

5) 9 + -6 = ?

Click again when you have completed each question and the answer will be displayed.

-11

-3

9

-6

3