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

A variable is a quantity that can take on a range of values.

Problem solving with expressions and equations

Maths

Checking understanding of expressions and equations

Securing understanding of expressions and equations

Representing a generalised number

Algebraic notation

Algebraic terminology

Representing an unknown or variable

Generalised algebraic statements

Substituting particular values

Like terms

Simplifying by collecting like terms

Multiplying an expression by a constant

Multiplying an expression by a term

Multiplying and simplifying with multiple expressions

Simplifying before multiplying with multiple expressions

Highest common factor with algebraic terms

Factorising expressions

In this unit, pupils formalise algebraic notation and terms and begin to formulate an understanding of basic algebraic manipulation. This understanding is built upon in the future unit where pupils learn how to solve linear equations

In this unit, pupils learnt how to represent the structure of a problem with two unknowns using a diagram. This understanding is built upon in this unit and formalised

In this unit, pupils learn about generalisation and formal algebraic manipulation techniques such as substitution, collecting like terms and factorising.

Expressions and equations

$$n + (n+1) + (n+2)$$ is an algebraic __________ for the sum of three consecutive numbers.

Some ink has spilled onto this addition pyramid. What would the expression in the top box of the pyramid be?

If we were working on a proof about six consecutive whole numbers, which expressions would we use?

We end up with the number we started with.

We always end up with double the number we started with.

We can express the number trick, "Pick a number. Multiply it by 6. Add 15. Divide by 3. Subtract 5" algebraically as $$(6n+15)\div3-5$$. What does it prove?

$$n+(n+1)+(n+2)$$ are not consecutive numbers.

Sam writes $$n+(n+1)+(n+2) \equiv 3n+3 \equiv 3\times n+1 $$ and says, "I have proven that the sum of three consecutive numbers is one more than a multiple of 3". Where is their error?

Which of the below algebraic expressions supports the proof that the sum of two consecutive whole numbers is always odd?

contains at least one variable or unknown.

Which of the below accurately completes the sentence? An algebraic term __________

Simplify $$a+2b+c+b+2c+d$$ by collecting like terms.

The answer is always the number you started with.

The answer is always 5 but it only works for whole numbers.

Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number. What did you notice?

"Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number". Which of the below expressions models this?

What number comes next in this sequence? $$n, n+1, n+2, n+3...$$

The result is always "One more than double the smaller of your two numbers".

The result is always "One less than double the bigger of your two numbers".

Add any two consecutive whole numbers. Which of the below are true?

Problem solving with expressions and equations

Lesson outcome