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Year 10
Foundation

Problem solving with algebraic manipulation

I can use my knowledge of algebraic manipulation to solve problems.

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New
New
Year 10
Foundation

Problem solving with algebraic manipulation

I can use my knowledge of algebraic manipulation to solve problems.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Quadratic equations can model real-life situations.
  2. Solutions would need to be interpreted in context.
  3. The difference of two squares is not only used in algebra, but can be used to quickly calculate numerical expressions.

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.

Forming equations skills are essential for this lesson. This may be something you wish to revisit first. Clear steps of working will allow pupils to make a start on a problem even if they are unclear how to reach the final answer.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Evaluate the expression $$\frac{3x}{2x + 5}$$ for $$x = 5$$.
Correct Answer: 1
Q2.
Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 19$$. Give your answer as a decimal.
Correct Answer: 0.95
Q3.
A book store sells a book for £25, which is 25% more than its cost price. Which of these calculates cost price, $$p$$, of the book?
$$p = 25 - 0.25 \times 30$$
Correct answer: $$p = \frac{25}{1.25}$$
$$p = 25 + 0.25 \times 100$$
Q4.
Expand and simplify $$4(x - 2) - 2(3x + 4)$$
$$2x - 16$$
Correct answer: $$-2x - 16$$
$$x - 16$$
Q5.
Simplify the expression $$\frac{x^2 - 9}{x - 3}$$
Correct answer: $$x + 3$$
$$x - 3$$
$$x^2 + 3x$$
Q6.
Fully factorise the expression $$2x^2 + 12x$$
Correct Answer: 2x(x+6), 2x(x + 6)

Exit quiz

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6 Questions

Q1.
A right triangle has area $$24 cm^2$$ and side lengths $$x$$ and $$x + 2$$. What is the value of $$x$$?
Correct Answer: 6, 6cm, 6 cm
Q2.
The sum of two consecutive odd integers is 156. What are the two integers?
Correct Answer: 77, 79, 79, 77
Q3.
What is the positive value of $$x$$ where $$(x + 4)(x - 2) = 0$$?
Correct Answer: 2
Q4.
The difference between the square of a positive integer and the integer itself is 110. What is the integer?
Correct Answer: 11
Q5.
The sum of the squares of two consecutive positive integers is 365. What is the smallest integer?
Correct Answer: 13
Q6.
The product of two consecutive integers is 272. What are the two integers?
Correct answer: 16 and 17
14 and 15
17 and 18