Hills and Dales

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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
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For this lesson think of positive numbers as hills
and negative numbers as
dales (holes in the ground).
Lets 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
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Examples that contain only dales are even easier.
- 3 - 2 ?
Step 1 Imagine the first 3 dales.
Step 2 Imagine the next 2 dales.
5, so -3 -2 -5
Step 3 How many dales are there in total?
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Now lets look at some subtraction examples.
Remember that subtraction means to take away or
remove.
-5 - -2 ?
5 dales
2 dales
Step 1 Imagine the 5 dales.
remove
Step 2 The question now says we must remove 2
dales.
Step 3 How many dales are left?
3, so -5 - -2 -3
5
Lets look at 4 - -1 ?
4 hills
1 dales
remove
Step 1 Imagine the 4 hills.
Step 2 The question says we must remove 1 dale
but there arent 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.
5, so 4 - -1 5
Step 2 How many hills are there?
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Sometimes its easier to think about the previous
question as an addition question.
4 - -1 ?
Step 1 Imagine the 4 hills.
1 dale
Step 2 Now just look at this bit.
remove
4 hills
We have to remove a dale thats not there. We
have seen that thats just the same as adding.
Important Subtracting a negative e.g. 6 - -4
10 is the same as adding e.g. 6 4 10
So 4 - -1 ? is the same as 4 1 ?
Step 3 Add the 1 dale.
4 1 5
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Now try these questions on your own..

1. -4 -7 ?
2. 5 -8 ?
3. 7 - -2 ?
4. -8 - -2 ?
5. 9 -6 ?

-11
Click again when you have completed each question
and the answer will be displayed.
-3
9
-6
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Need some more practise? Try Pg66 of Teacher
Tools Addition and Subtraction Book Numeracy
resources