Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 7

Problem solving with expressions and equations

I can use my knowledge of expressions and equations to solve problems

Download all resources
arrow-right
Share activities with pupils
arrow-right
New
New
Year 7

Problem solving with expressions and equations

I can use my knowledge of expressions and equations to solve problems

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
View new resources
arrow-right

Lesson details

Key learning points

  1. Standardised notation is important when using algebra.
  2. Algebra allows us to generalise real life problems.
  3. Algebra allows us to express relationships so that everyone can understand them.

Keywords

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

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

Common misconception

A variable and an unknown are the same thing.

A variable's value is not fixed. It can take any value within a given range. This means algebraic statements using variables can form proofs

In Task B, pupils may spot that the middle value is the second factor. Encourage them to explore what happens when there is an even number of numbers.
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

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
Which of the below accurately completes the sentence? An algebraic term __________
must contain an $$x$$
must contain a constant.
Correct answer: contains at least one variable or unknown.
must have an equals sign after it.
Q2.
Simplify $$a+2b+c+b+2c+d$$ by collecting like terms.
Correct answer: $$a+3b+3c+d$$
$$a+2b^2+2c^2+d$$
$$a+2bc+2bc+d$$
$$a+4bc+d$$
Q3.
Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number. What did you notice?
There is no pattern.
The answer is always the number you started with.
Correct answer: The answer is always 5.
The answer is always 5 but it only works for whole numbers.
Q4.
"Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number". Which of the below expressions models this?
$$n \times 2 +10 \div 2-n$$
Correct answer: $$(n \times 2 +10) \div 2-n$$
Q5.
What number comes next in this sequence? $$n, n+1, n+2, n+3...$$
$$4$$
$$4n$$
Correct answer: $$n+4$$
$$4n+6$$
Q6.
Add any two consecutive whole numbers. Which of the below are true?
Correct answer: The result is always odd.
Correct answer: The result is always "One more than double the smaller of your two numbers".
Correct answer: The result is always "One less than double the bigger of your two numbers".
The result is always even.
The result can be odd or even.

Exit quiz

Download exit quiz

6 Questions

Q1.
$$n + (n+1) + (n+2)$$ is an algebraic __________ for the sum of three consecutive numbers.
term
Correct answer: expression
equation
formula
Q2.
Some ink has spilled onto this addition pyramid. What would the expression in the top box of the pyramid be?
An image in a quiz
$$a + b + c$$
$$2(a + b + c)$$
$$a + 2b + 2c$$
Correct answer: $$a + 2b + c$$
Q3.
If we were working on a proof about six consecutive whole numbers, which expressions would we use?
$$n, n, n, n, n, n,$$
$$n, n+6$$
$$n, 2n, 3n, 4n, 5n, 6n$$
$$n, n+1, n+2, n+3, n+4, n+5, n+6$$
Correct answer: $$n, n+1, n+2, n+3, n+4, n+5$$
Q4.
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?
We end up with the number we started with.
Correct answer: We always end up with double the number we started with.
We always end up with 2.
Q5.
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?
$$n+(n+1)+(n+2)$$ are not consecutive numbers.
Adding $$n+(n+1)+(n+2)$$ incorrectly.
Correct answer: Incorrectly factorising $$3n+3$$
Q6.
Which of the below algebraic expressions supports the proof that the sum of two consecutive whole numbers is always odd?
$$n + 2n \equiv 3n$$
$$(n) + (2) \equiv n+2$$
Correct answer: $$n + (n+1) \equiv 2n+1$$