Year 7

Year 7

# Axioms and negative numbers

## Lesson details

### Key learning points

1. In this lesson, we will practise negative number calculations, linking them to axioms like commutativity and associativity.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

## Video

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## Worksheet

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## Starter quiz

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### 6 Questions

Q1.
Choose the words that best fill in the gaps in order: We can use a known __________ to _________ other related facts.
commutativity, distribute
derive, product
distributive, derive
product, commutative
Q2.
Fill in the gap: Using the fact that (-7) x (-2) = 14 we can use the _____________ of multiplication to deduce that (-2) x (-7) = 14
derive
distributive
produce
Q3.
Calculate the following: (-80) ÷ (-5)
-16
-75
75
Q4.
Given that (-23) x (-14) = 322. Work out 322 ÷ (-14).
-322
14
23
Q5.
Given that (-23) x (-14) = 322. Work out (-322) ÷ 14.
-322
14
23
Q6.
Substitute n=-10 into n ÷ (-2)
-12
-5
12

## Exit quiz

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### 5 Questions

Q1.
Fill in the gap: The axioms for positive numbers, that helped us to manipulate calculations, are also true for __________________ numbers.
associative
commutative
distributive
Q2.
Which description best matches the definition of commutativity?
It doesn't matter how we group the numbers (i.e. which we calculate first)
Correct answer: The operation can be applied to the numbers in any order.
We get the same answer when we: multiply a number by a group of numbers added together, or do each multiplication separately then add them.
Q3.
What word do we use to describe the relationship: 6 x 7 = 3 x 7 + 2 x 7?
Associativity
Commutativity
Integers
Q4.
Work out (-5) x 3 + 205 x 3
-600
1800
570
Q5.
Which calculation is equal to -5?
Correct answer: -40 - (-5) + 30
(-30) ÷ (-2)
(-5) x (-5) + 5
30 ÷ 3 x (-5)