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Year 7

Generalised algebraic statements

I can use relationships that have been generalised using algebraic statements.

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New
New
Year 7

Generalised algebraic statements

I can use relationships that have been generalised using algebraic statements.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Relationships in context can be expressed using letters to represent the unknown values.
  2. Formulae in context can be expressed using letters to represent the unknown values.
  3. Number patterns can be expressed using letters to represent the unknown values.

Common misconception

Pupils may thing that letters represent an item e.g a week equals 7 days so w=7d

Get pupils to identify what value the letter represents e.g the number of days then say a number sentence that describes the relationship.

Keywords

  • Equation - An equation is used to show that one number or calculation is equal to another.

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

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

You may wish to put the formula for the cost to stay in a hotel on the board without defining the variables and get students to think about what the variables could represent, what the 100 and 80 might represent.
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.
Here is a pattern using lines to make triangles. How many lines are needed to make the fourth pattern?
An image in a quiz
Correct Answer: 9, nine
Q2.
Here is a pattern using lines to make triangles. Which statement below is the correct relationship between the pattern number and number of triangles?
An image in a quiz
Correct answer: The pattern number is the same as the number of triangles.
The number of triangles is one more than the pattern number.
The number of triangles is 3 times the pattern number.
Q3.
A shows the relationship between multiple physical variables in context.
Correct Answer: formula
Q4.
Match the expression with the statement.
Correct Answer:$$7a-4$$,a number multiplied by 7 then minus 4

a number multiplied by 7 then minus 4

Correct Answer:$$7(a-4)$$,a number minus 4 then multiplied by 7

a number minus 4 then multiplied by 7

Correct Answer:$$a+7-4$$,a number add 7 then minus 4

a number add 7 then minus 4

Correct Answer:$$a(7-4)$$,7 minus 4 then multiplied by a number

7 minus 4 then multiplied by a number

Correct Answer:$$4-7a$$,a number multiplied by 7 then subtracted from 4

a number multiplied by 7 then subtracted from 4

Q5.
Lucas walks 2 miles to school and 2 miles back each day. He can write an expression for the distance walked each day he goes to school as $$4n$$. Which statements are true?
Correct answer: $$n$$ is a variable.
$$n$$ is an unknown.
$$n$$ is the time it takes to get to school.
$$n$$ is the distance to and from school.
Correct answer: $$n$$ is the number of days he goes to school.
Q6.
The cost of a pay as you go phone is £24 plus £0.04 per text. A formula for the overall cost to use the phone is given as $$0.04\times \text{texts} + 24$$. What is the variable in this formula?
The price to buy the phone
The overall cost of using the phone
Correct answer: The number of texts sent
The texts plus the handset cost

Exit quiz

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6 Questions

Q1.
$$s=60m$$ is a formula showing the relationship between number of seconds and number of minutes. Which of these are true?
Correct answer: The number of seconds is $$60\times $$ the number of minutes.
The number of minutes is $$60\times$$ the number of seconds.
The number of minutes is 60 times bigger than the number of seconds.
Correct answer: The number of seconds is 60 times bigger than the number of minutes.
Q2.
There are 6 eggs in a box of eggs. Which of these shows the correct relationship where $$a$$ is the number of eggs and $$b$$ is the number of boxes?
Correct answer: $$a=6b$$
$$b=6a$$
$$b=a+6$$
$$a=b$$
Q3.
The cost of a taxi is £3.50 plus £1.50 per mile driven. Which is the correct formula for the cost of getting a taxi?
$$c=3.5m+1.5$$
$$c=5m$$
$$c=(3.5+1.5)$$
Correct answer: $$c=3.5+1.5m$$
Q4.
The membership fees for a rugby team are £80 for the year, £3 match fees for every game you play and £2 for each item of kit. For the formula $$c=3a+2b+80$$ match each value to its description.
Correct Answer:a,number of games played

number of games played

Correct Answer:b,number of items of kit bought

number of items of kit bought

Correct Answer:c,cost for a year

cost for a year

Correct Answer:3a,cost of match fees

cost of match fees

Correct Answer:2b,cost of kit

cost of kit

Q5.
Here is a pattern using lines to make triangles. Which of these is a formula showing the relationship between number of triangles $$(t)$$ and number of lines $$(l)$$ ?
An image in a quiz
Correct answer: $$l=2t+1$$
$$l=3t$$
$$l=t+2$$
$$l=3t+2$$
$$l=2t$$
Q6.
Here is a pattern using lines to make triangles. How many lines would be needed to make this pattern with 10 triangles?
An image in a quiz
Correct Answer: 21, twenty one