**National curriculum content**

- Use simple formulae
- Generate and describe linear number sequences
- Express missing number problems algebraically
- Find pairs of numbers that satisfy an equation with two unknowns
- Enumerate possibilities of combinations of two variables

**Lesson objectives**

- 1-step function machines
- 2-step function machines
- Form expressions
- Substitution
- Formulae
- Form equations
- Solve 1-step equations
- Solve 2-step equations
- Find pairs of values
- Solve problems with two unknowns

**What we want children to know**

Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

- Missing numbers, lengths, coordinates and angles
- Formulae in mathematics and science
- Equivalent expressions (for example,
*a*+*b*=*b*+*a*) - Generalisations of number patterns
- Number puzzles (for example, what two numbers can add up to).

- For each number they put into a function machine, there is an output.
- Use simple algebraic inputs e.g. y. Using these inputs in a function machine leads them to forming expressions e.g. y + 4.
- Children are introduced to conventions that we use when writing algebraic expressions. e.g. y × 4 as 4𝑦.
- Children substitute into simple expressions to find a particular value.
- Understand that the same expression can have different values depending on what has been substituted.
- Use simple formulae to work out values of everyday activities such as the cost of a taxi or the amount of medicine to take given a person’s age.
- Use algebraic notation to form one-step equations.
- Solve simple one step equations involving the four operations.
- Progress from solving equations that require one-step to equations that require two steps.
- Use their understanding of substitution to consider what possible values a pair of variables can take.
- Find possible solutions to equations which involve multiples of one or more unknown.

**What skills we want children to develop**

Use knowledge to solve reasoning and problem solving questions such as:

**True or false?**

ab + b = 18

Mo says, ‘a and b must both be odd numbers’.

Is this true or false? Explain your decision.

**Connected calculations**

p and q each stand for whole numbers.

p + q = 1000 and p is 150 greater than q.

Work out the values of p and q.

**Generalising**

Write a formula for the 10th, 100th and nth terms of the sequences below.

4, 8, 12, 16 ………

0.4, 0.8, 1.2, 1.6, …….

**Possible answers**

a, b and c are integers between 0 and 5.

a + b = 6

b + c = 4

Find the values of a, b and c.

How many different possibilities can you find?

**Vocabulary/Mathematical Talk**

- What do you think “one-step function” means?
- Do some functions have more than one name?
- What is the output/input if ….?
- How many sets of inputs and outputs do you need to be able to work out the function? Explain how you know.
- How can you write + 5 followed by – 2 as a one-step function?
- If I change the order of the functions, is the output the same?
- If you add 3 to a number and then add 5 to the result, how much have you added on altogether?
- How can you write 𝑥 × 3 + 6 differently?
- Are 2𝑎 + 6 and 6 + 2𝑎 the same? Explain your answer.
- What does it mean when a number is next to a letter?
- Is 𝑎 + 𝑏 + 𝑏 the same as 𝑎 + 2𝑏?
- What’s the difference between an expression and an equation?
- What’s the difference between a formula and an equation?
- Why do you think the equation is set up on a balance? What does the balance represent? How does this help you solve the equation?
- Why do you have to do the same to each side of the equation?
- Does the order the equation is written in matter?

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