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Year 6

Represent and solve problems with two unknowns efficiently

I can represent problems with two unknowns and solve using an efficient strategy.

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New
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Year 6

Represent and solve problems with two unknowns efficiently

I can represent problems with two unknowns and solve using an efficient strategy.

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Share activities with pupils
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Lesson details

Key learning points

  1. The model can represent a scaling structure with one part being __ times the size of the other.
  2. The model can represent an additive structure.

Keywords

  • Coefficient - A coefficient is number used to multiply an unknown value.

  • Efficient - To solve something efficiently means to solve a problem quickly whilst also maintaining accuracy.

Common misconception

Pupils think that the removal of the multiplication symbol can result in the number becoming a two-digit number rather than two, single digits being multiplied together.

Using the language of 'lots of' may support pupils to see that an algebraic equation with coefficients represents multiplication. For example: 40 can be read as 'four lots of 0'.

Whilst many examples show the variable being represented with a letter that is relevant to the context, ensure pupils understand that any letter can be used and that common letters used are usually the beginning or end of the alphabet (a,b,c or x,y,z).
Teacher tip

Equipment

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

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Starter quiz

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6 Questions

Q1.
When the sum and the multiplicative relationship between two unknown numbers is known, how many possible solutions are there?
Correct answer: 1
2
3
4
Infinite
Q2.
What is the value of a in this equation? a × 6 = 42
Correct Answer: 7
Q3.
a represents a larger numbers and b represent a smaller number. The sum of a and b is 340, and the difference between them is 40 What number does b represent?
150
160
170
180
Correct answer: 190
Q4.
Grace is 32 years younger than her father. The sum of their ages is 64 years. How old is Grace’s father? years old.
Correct Answer: 48
Q5.
The sum of two numbers is 240 One number is five times the size of the other number. What are the two numbers?
30 and 210
Correct answer: 40 and 200
50 and 190
60 and 180
Q6.
The sum of two numbers is 500 One number is one-third times the size of the other number. What is the value of the largest number?
Correct Answer: 375

Exit quiz

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6 Questions

Q1.
5 × a + 7 × b can also be written as:
5 × 7 + b × a
Correct answer: 5a + 7b
5a × 7b
b7 + a5
Q2.
Tick the problems that, when written as a pair of equations, would share the same coefficient.
Correct answer: 5 apples and 3 pears cost £3.10; 4 apples and 3 pears cost £3.60
3 apples and 3 pears cost £2.50; 4 apples and 5 pears cost £3.80
2 apples and 2 pears cost £3.00; 1 apple and 3 pears cost £3.60
Q3.
What is the value of the gap marked ? in the bar model? Give your answer in pence. p
An image in a quiz
Correct Answer: 80, 80 p, 80 pence
Q4.
What is the value of b in the bar model? Give your answer in pence. p
An image in a quiz
Correct Answer: 40, 40 p, 40 pence
Q5.
What is the value of k? Give your answer in pence. p
An image in a quiz
Correct Answer: 60, 60 p, 60 pence
Q6.
Cereal is sold in big boxes and small boxes. 3 big boxes and 2 small boxes costs £9.50. 2 big boxes and 3 small boxes costs £8.00 What is the cost of the big box of cereal?
£1.50
£2.00
£2.20
Correct answer: £2.50
£2.80