Mixing Paint

Introduction

In this lesson, you will learn about ratios. Take a look at the 4 questions below. Which one is the odd one out? Can you explain why?

Ratio Starter - Odd One Out p1.pdf
Ratio Starter - Odd One Out p2.pdf

Application

Instructions

Part 1

  1. In your groups, sort the cards into order with the “reddest” paint at one end and the “yellowest” paint at the other end. You might think that some of the cards are the same as other cards. Click here if you need some help.

  2. When you are sure that you have your answer make a record of it on Desmos. You could right down the letters or take a photo and save it on your laptop.

  3. Now talk to the next group on your table and see if you agree with them.

  4. If you don’t agree then try to resolve your differences. Explain as carefully as you can why you have made the decisions that you did, and listen to the other group’s explanation.

  5. When you have reached an agreement make a note of the result. Ask a teacher to come and look at what you have done. Explain to the teacher how you chose the order of your cards.


Part 2

Now work in your original (small) group and try to answer each of these questions.

  1. For each of the following pairs of cards, say how you would make a shade of paint that was somewhere between the two shades.

  • Card E and Card L (use 7 tins of paint altogether)

  • Card F and Card N (use 4 tins of paint)

  • Card B and Card K (use as many tins as you think you need)

  • Card A and Card J (use as many tins as you think you need)

  • Card G and Card P (use as many tins as you think you need)


  1. Look at Card D and Card K.

    • Which paint is more red and which is more yellow?

    • If you combined D and K, which card would that give you?

    • Is your answer more red or more yellow than D?

    • Is your result more red or more yellow than K?


  1. Card B uses 6 tins of paint in total, 4 tins of red paint and 2 tins of yellow paint. Now imagine that you made this shade of paint using 24 tins in total.

  • How many of the 24 tins would be red?

  • How many of the twelve tins would be yellow?


  1. Card K uses 4 tins of paint, 3 red and 1 yellow.

  • If you made this shade of paint using 24 tins, how many tins of red would you need?

  • How many of yellow tins would you need?

  • Are you still happy with your answer to Question 1(c) above, or do you want to change it?

  • Use this technique to check your answers to the rest of Question 1.


  1. If you want paint of the shade it Card N, but the paint you have is actually the one in Card D, it’s easy to make the right shade by adding an extra tin of red paint.

For each of these situations, describe how much red paint or yellow paint you would have to add to the card that you have to get the one you want.

You might have to make more of the paint than is shown on the card, but it must be the same shade.

Remember, you can’t take paint away – once it is mixed, it’s impossible to separate!

  • You have J, but you want E

  • You have O, but you want C

  • You have O but you want E

  • You have K, but you want D

  • You have H, but you want J

  • You have M but you want G

  • You have H, but you want M

  • You have G, but you want P

Further Practice

Ratio is an important topic to learn and practise. The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.


Transum

  • Pattern Clues: An interactive activity challenging you to reproduce a pattern of coloured squares according to given clues.

  • Ratio: A self marking exercise on using ratio notation, reducing a ratio to its simplest form and dividing a given quantity into a number of parts in proportion to a given ratio.

  • Ratio Clues: Arrange the ratio clues in the clouds in a logical order to work out the values of the twelve letters.

  • Ratios vs Fractions: Relate the language of ratios and the associated calculations to the arithmetic of fractions.

  • Recipe Ratios: Learn the mathematics required to adapt recipes to serve a different number of people.

  • Unit Pricing: Calculate the unit cost of items to earn jigsaw pieces that make a joke.

  • Unitary Method: Ten questions which can be solved using the unitary method.

For more goodies on Ratio on Transum, click on the hyperlink.


Have a look at the attached worksheet below (Answers can be found here).

Ratio (SMP 7C Interact).pdf

Extension

Here are some further mixing activities on nRich:

  • Mixing Paints - Can you work out how to produce different shades of pink paint?

  • Mixing More Paints - Can you find an efficient way to mix paints in any ratio?


You may wish to take a look at some of the following Desmos activities:

  • Paint - where you will develop use ratio tables to mix paint that is the same colour as a given paint colour. You will also decide which mixtures from a list will make the same paint colour.

  • Water Slide - where you will use equivalent ratios to create a smooth ramp for a water slide.

  • Balloon Float - where you will use ratios to determine the number of balloons needed to float different objects.

  • Nana's Chocolate Milk - where you will use double number lines and proportional reasoning to help Dan fix his chocolate milk mix-up.

  • Click Battle - where you will explore unit rate in the Click Battle arena.