Quadratic equations can model real-life situations.
Solutions would need to be interpreted in context.
The difference of two squares is not only used in algebra, but can be used to quickly calculate numerical expressions.
Where there is a choice of method, you will decide the most efficient method to use.

Keywords

Partial product - A partial product refers to any of the multiplication results that lead up to an overall multiplication result.
Binomial - A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.
Factorise - To factorise is to express a term as the product of its factors.
Solution (equality) - A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.

Common misconception

Including solutions which are not valid in the context of the question.

Pupils should finish every problem by substituting their solutions back into the original problem. This will help them check their answers but also make them think about whether their solutions are valid in context.

Question 3 of Task A can be extended further. Direct pupils to consider what types of numbers lead to integer solutions. 15 and 21 are both shown to work but what other numbers will also work?

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.

What expression represents the following: I start with a number ($$n$$), subtract 3, and then double the result.

Correct Answer: 2(n-3), 2(n - 3)

Q2.

What expression represents the following: I take a number ($$n$$), multiply it by 5, and then add 10 to the product.

Correct Answer: 5n + 10, 5n+10

Q3.

What expression represents the following: I triple a number ($$n$$) and then subtract 4 from it.

Correct Answer: 3n - 4, 3n-4

Q4.

Which expression represents the following: I square a number ($$n$$), then subtract twice the number from the square.

$$n^2 - n$$

Correct answer: $$n^2 - 2n$$

$$n^2 - 2n^2$$

Q5.

Which expression represents the following: I take a number ($$n$$), halve it, and then add the square of the number to this result.

$$(\frac{n}{2})^2 + n$$

Correct answer: $$\frac{n}{2} + n^2$$

$$\frac{n^2}{2} + n$$

Q6.

A rectangle has side lengths of $$3x + 5$$ and $$4x - 3$$. Write an expression for the perimeter of the shape.

Correct Answer: 14x + 4, 2(7x + 2), 14x+4, 2(7x+2)

Exit quiz

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6 Questions

Q1.

The sum of two consecutive even integers is 506. What is the value of the smallest integer?

Correct Answer: 252

Q2.

I take a number, add 6, and multiply the result by 9. My new number is 900. What was the original number?

Correct Answer: 94

Q3.

The sum of three consecutive integers is 72. What is the largest integer?

Correct Answer: 25

Q4.

If the square of a positive number is decreased by 5, the result is 139. What is the number?

Correct Answer: 12

Q5.

The area of a square is $$49 cm^2$$. What is the perimeter?

Correct Answer: 28 cm , 28

Q6.

The sum of a negative number and half its square is equal to 40. What is the number?

Correct Answer: -10