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Year 7

Priority of operations with positive integers

I can calculate using priority of operations, including brackets, powers and exponents with positive integers

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New
New
Year 7

Priority of operations with positive integers

I can calculate using priority of operations, including brackets, powers and exponents with positive integers

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Division and multiplication have the same priority.
  2. With addition and subtraction, subtractions can all be re-written as additions of the additive inverse.
  3. Brackets can make the priority much clearer and avoid ambiguity.
  4. Sometimes brackets can be implicit.

Common misconception

Students do not see the implicit brackets eg Sqrt(49 + 36) is not sqrt (49)+square root of (36)

Look for extended lines or operations which indicate an implicit brackets.

Keywords

  • Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

  • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Ask students to write the calculation in their books, 2 + 3 x 4 x 5 + 6. Ask each student to put in a pair of brackets and then work out the answer. Go around the class and ask what is their answer so the class try to discover where the brackets are.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Complete the statement. The additive inverse of a number is a number that, __________
Correct answer: when added to the original number, gives the sum of 0
when added to the original number, gives the sum of 1
when multiplied by the reciprocal the product is 1
when multiplied by the reciprocal the product is (-1)
Q2.
Match each number with its additive inverse.
Correct Answer:4,(-4)

(-4)

Correct Answer:(-40),40

40

Correct Answer:0.4,(-0.4)

(-0.4)

Correct Answer:(-400),400

400

Q3.
Select all the fractions that are equivalent to $${2} \over {3}$$.
$${1} \over {3}$$
$${1} \over {2}$$
Correct answer: $${4} \over {6}$$
Correct answer: $${20} \over {30}$$
$${3} \over {2}$$
Q4.
Match each calculation with an equivalent commutative calculation.
Correct Answer:$$A + B $$,$$B + A$$

$$B + A$$

Correct Answer:$$A\times B$$,$$B\times A$$

$$B\times A$$

Correct Answer:$$A + B + C$$,$$B + C + A$$

$$B + C + A$$

Q5.
Work out the missing number: $$9.8 \times 0.5 + 9.8 \times$$ $$= 9.8$$
Correct Answer: 0.5, 1/2
Q6.
Work out the missing number: $$34 \times 0.8 + 34 \times$$ $$= 68$$
Correct Answer: 1.2, 12/10, 6/5

Exit quiz

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6 Questions

Q1.
This image is a help guide to the priority of operations. Which set of operations must you always apply first when they are in a calculation?
An image in a quiz
Addition and subtraction
Multiplication and division
Roots and exponents
Correct answer: Brackets
Q2.
How would you complete a calculation when an operation is repeated?
Correct answer: Do them both at the same time
Go left to right
Ignore them and do those operations last
Q3.
Without using a calculator, work out: $$4\times5 + 6\times7$$ =
Correct Answer: 62
Q4.
Without using a calculator, work out: $$200\;-(12\;–\;8)\times5\times3^2$$ =
Correct Answer: 20
Q5.
The answer to this calculation is 54. Match the triangle, star, square and arrow to the correct operation or numerical value.
An image in a quiz
Correct Answer:$$\star$$ ,+

+

Correct Answer:$$\triangle$$,$$\times$$

$$\times$$

Correct Answer:$$\square$$,$$-$$

$$-$$

Correct Answer:$$\uparrow$$,2

2

Q6.
Without using a calculator, work out: $$90 + \sqrt{40\times10}-12\times5$$ =
Correct Answer: 50