Nutty Mixture
Use the ratio of cashew nuts to peanuts to find out how many peanuts Rachel has. What would the ratio be if Rachel and Marianne mixed their bags?
Problem
Rachel has a bag of nuts.
For every cashew nut in the bag, there are two peanuts.
There are 8 cashews in Rachel's bag. How may peanuts are there?
In Marianne's bag, for every two cashew nuts, there are three peanuts.
Marianne's bag contains 12 peanuts in total. How many cashews are in her bag?
Rachel and Marianne decide to mix their bags of nuts together.
What is the ratio of cashew nuts to peanuts in the mix?
Getting Started
Might it help if you group the nuts?
Have you tried using counters or cubes to stand for nuts? Or perhaps you could draw a picture?
Student Solutions
A lot of you had a really good attempt at this question. In addition to Ruth, Tom and Ollie (whose solutions are given below), well done to those of you who got the answer correct:
Talia and Maelona from Jebel Ali school, Dubai; Tom from C.P.S.; Katie, Oliver and Daniella from Portsmouth Grammar School; Amy from Stoke by Nayland Middle School; Daniel from Camberwell South Primary School, Melbourne, Australia; Zak from Clavering Primary School; Andrew Mott from Aldermaston C.E. primary school; Alice and Miriam from Aldermaston Primary; Alara from IK Primary School; Jason (school unknown) and Ben from Short Wood Primary School.
Ruth from Oxford High sent in this clearly explained solution:
In the first problem Rachel has double the number of peanuts to cashew nuts. She has 8 cashew nuts in her bag so you double the number of cashew nuts and you get 16 peanuts.
In the second problem Marianne also has a bag of nuts but this time she has 3 peanuts for every 2 cashew nuts. Marianne has 12 peanuts which is 4 times bigger than 3. So she will have 8 cashew nuts because this is 4 times bigger than 2.
When you add the two bags together they make the following:
| Bag Owner | Cashews | Peanuts |
| Rachel | 8 | 16 |
| Marianne | 8 | 12 |
| Total | 16 | 28 |
Tom and Ollie of Ardingly College had a slightly different way of explaining it:
Teachers' Resources
Nutty Mixture
Rachel has a bag of nuts.
For every cashew nut in the bag, there are two peanuts.
There are 8 cashews in Rachel's bag. How may peanuts are there?
In Marianne's bag, for every two cashew nuts, there are three peanuts.
Marianne's bag contains 12 peanuts in total. How many cashews are in her bag?
Rachel and Marianne decide to mix their bags of nuts together.
What is the ratio of cashew nuts to peanuts in the mix?
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem is a good introduction to ratio. It can also be used to emphasise the language of "for every".
Possible approach
As an introduction, tou may demonstrate the idea of "for every" with the help of counters or cubes (representing the nuts). For example, you could physically group each cashew nut with two peanuts. At first children might need to use equipment to solve the problem or they should be encouraged to draw sketches. If appropriate, a plenary could address how the solution could be reached using mental calculations.
Key questions
Possible extension