New
New
Year 7

Determining the whole

I can determine the whole, given one part and the ratio.

New
New
Year 7

Determining the whole

I can determine the whole, given one part and the ratio.

Lesson details

Key learning points

  1. A bar model can help to represent the situation.
  2. A ratio table can also be used to help show the multiplicative relationship.
  3. Both representations help to expose the structure.

Common misconception

Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'.

Offer opportunities to match problems to bar models, ensure the same numbers are used to highlight the differences.

Keywords

  • Proportion - Variables are in proportion if they have a constant multiplicative relationship.

  • Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

During the 2nd learning cycle pose a question e.g. 'The ratio of red:blue cars in a car park is 2:5. Sofia counts the number of blue cars in car park. She counts 9 blue cars. How do you know she has miscounted? How many do you think there were?'''
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).

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6 Questions

Q1.
Fill in the missing word: are in proportion if they have a constant multiplicative relationship.
Correct Answer: Variables, variable, variables
Q2.
Share 189 in the ratio 2 : 7. Which is a correct first step in solving this problem?
189 ÷ 5
189 ÷ 7
189 ÷ 8
Correct answer: 189 ÷ 9
Q3.
Izzy and Andeep share 189 stickers in the ratio of 2 : 7. How many stickers does Izzy get?
Correct Answer: 42, forty-two, forty two, fortytwo
Q4.
Share 132 in the ratio 4 : 6 : 1. What is the value of the largest share?
Correct Answer: 72, seventy-two, seventy two, seventytwo
Q5.
The ratio of flour to butter to sugar in a cookie recipe is 3 : 2 : 1. You want to make a giant cookie weighing 540 grams. How much flour will you need?
Correct Answer: 270 g, 270 grams, 270g, 270grams, 270
Q6.
The perimeter of a triangle is 32.4 cm. The sides are in the ratio 3 : 8 : 7. How long is the longest side?
Correct Answer: 14.4 cm, 14.4cm, 14.4 centimetres, 14.4 centimetre, 14.4

6 Questions

Q1.
Write the ratio 3 to 5 using the correct notation.
Correct Answer: 3 : 5, 3:5, 3: 5
Q2.
What number is represented by the question mark in this bar model?
An image in a quiz
Correct Answer: 88, eighty-eight, eighty eight, eightyeight
Q3.
Sam and Aisha share some stickers in the ratio of 3 : 5. Sam gets 45 stickers, how many stickers are there in total?
Correct Answer: 120, 120 stickers, one hundred and twenty
Q4.
Laura, Jacob and Jun share some sweets in the ratio 5 : 8 : 3. Jun gets 9 sweets, how many sweets are there in total?
Correct Answer: 48, 48 sweets, forty-eight, forty eight, fortyeight
Q5.
Lucas is making necklaces with red, blue and white beads in the ratio 2 : 7 : 5. He uses 16 red beads. How many beads are on each necklace?
Correct Answer: 112, 112 beads, one hundred and twelve
Q6.
The lengths of the sides of a triangle are split in the ratio 3 : 8 : 7. The longest side is 9.6 cm, what is the perimeter of the triangle?
Correct Answer: 21.6 cm, 21.6 centimetres, 21.6 centimetre, 21.6