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Year 10
Higher

Further algebraic terminology

I can appreciate the difference between an equation, an identity, an expression, a term and a formula.

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Year 10
Higher

Further algebraic terminology

I can appreciate the difference between an equation, an identity, an expression, a term and a formula.

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Lesson details

Key learning points

  1. A single number or letter, or the product of numbers and/or variables.
  2. An expression contains one or more terms, where each term is separated by an operator.
  3. An equation is a statement that two expressions are equal, indicated by =
  4. An identity is an equation which is always true, regardless of the values substituted in.
  5. A formula is a mathematical rule or relationship connecting two or more variables.

Keywords

  • Term - A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

  • Expression - Expressions contain one or more terms, where each term is separated by an operator.

  • Equation - An equation is used to show 2 expressions that are equal to each other.

  • Identity - An identity is an equation that holds true for all values of the variables. The symbol ≡ is used to show two expressions are equivalent and form an identity.

  • Formula - A formula is a rule linking sets of physical variables in context.

Common misconception

Pupils can think the formula for the number of days in a week is w=7d because a week has seven days.

Pupils should always write down exactly what the letter is representing. E.g. 'the number of days' and 'the number of weeks'. Then think about what calculation they are doing. 'To find the number of days I multiply the number of weeks by 7'. d=7w.


To help you plan your year 10 maths lesson on: Further algebraic terminology, download all teaching resources for free and adapt to suit your pupils' needs...

In the second learning cycle, give the pupils the opportunity to think about what formula they know and use. This can be in mathematics, other subjects in the school curriculum and other areas of their lives.
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This content is © Oak National Academy Limited (2025), 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 $$2x - 3$$ for $$x = 5$$
Correct Answer: 7
Q2.
Evaluate the expression $$x^2 + 2x + 1$$ for $$x = 3$$
Correct Answer: 16
Q3.
Evaluate the expression $$x^3 - 2x^2 + x - 1$$ for $$x = 2$$
Correct Answer: 1
Q4.
Evaluate the expression $$\frac{x^2}{2} - 3x + 2$$ for $$x = 4$$
Correct Answer: -2
Q5.
Collect the following like terms $$ 5a + 7a - 2a^2 $$
$$10a$$
$$10a^2$$
Correct answer: $$12a - 2a^2$$
Q6.
Collect the following like terms $$ 5ab + 7a - 2ab + b $$
Correct answer: $$3ab + 7a + b$$
$$12ab + b$$
$$13abb$$

Exit quiz

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6 Questions

Q1.
A car travels at a constant speed of 60 miles per hour. Which of the following shows the correct relationship between the number of hours driven, $$h$$, and the total distance traveled, $$d$$?
Correct answer: d = 60h
60d = h
d = 60h + 60
Q2.
A worker earns £15 per hour. Which of the following shows the correct relationship between the number of hours worked, $$h$$, and the total earnings, $$e$$?
Correct answer: $$e = 15h$$
$$e = 15 + h$$
$$e = \frac{15}{h}$$
$$e = 15 - h$$
Q3.
If a tree grows 2 feet each year, which of the following shows the correct relationship between the number of years, $$y$$, and the total growth, $$g$$, of the tree?
Correct answer: $$g = 2y$$
$$g = y + 2$$
$$g = \frac{2} {y}$$
Q4.
A savings account earns 5% interest per year on a deposit of £100. Which of the following shows the correct relationship between the number of years, $$y$$, and the total interest earned, $$i$$
Correct answer: $$i = 5y$$
$$i = 100y$$
$$i = 5 + y$$
$$i = \frac{y}{5}$$
Q5.
A farmer harvests 200 apples from each tree every year. Which of the following shows the correct relationship between the number of trees, $$t$$, and the total number of apples harvested, $$a$$?
Correct answer: $$a = 200t$$
$$a = t + 200$$
$$a = \frac{200}{t}$$
$$a = t - 200$$
Q6.
A recipe requires 3 eggs to make a cake. Which of the following shows the correct relationship between the number of cakes, $$c$$, and the total number of eggs needed, $$e$$?
Correct answer: $$e = 3c$$
$$e = c + 3$$
$$e = c - 3$$