Securing understanding of ratio as a multiplicative relationship | Maths

Starter quiz

Use the ratio table to work out how many slices of cheese are needed to make 7 sandwiches. ______ slices.
- '21' ✓
Use the ratio table to work out how many slices of cheese are needed when there are 12 slices of tomato. ______ slices.
- '24' ✓
Here is a recipe for vanilla cake. How much sugar is needed if you use 6 eggs? ______ grams of sugar.
- '225' ✓
Here is a recipe for vanilla cake. How much vanilla is needed if you use 125 g of flour? ______ ml of vanilla.
- '5' ✓
Lucas has some red and blue marbles. For every 4 red marbles, he has 5 blue marbles. Lucas has 20 red marbles altogether. Lucas has ______ blue marbles.
- '25' ✓
Laura has some red and blue marbles. For every 4 red marbles, she has 5 blue marbles. She has 36 marbles altogether. Laura has ______ blue marbles.
- '20' ✓

Exit quiz

A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole. The relationship between parts and/or the whole is always ______.
- additive
- multiplicative ✓
- constant
- subtractive
A robot in travelling around a toxic planet. The protective clothing is heavy, so for every 6 protective items, there must be 2 batteries. Match the equipment list to its effect on the robot.
- 18 protective and 6 batteries
  
  ⇔
  
  This means the robot is fully protected and quick. ✓
- 3 protected and 2 batteries
  
  ⇔
  
  This means the robot is quick but not fully protected. ✓
- 12 protected and 2 batteries
  
  ⇔
  
  This means the robot protected but slow. ✓
To make a "Sunrise" orange paint, 2 cans of yellow paint for every 1 can of red paint is used. Match the paint shades to the recipes.
- "Sunrise" Orange
  
  ⇔
  
  4 cans of yellow and 2 cans of red ✓
- Darker than "Sunrise" orange
  
  ⇔
  
  6 cans of yellow and 4 cans of red ✓
- Lighter than "Sunrise" orange
  
  ⇔
  
  10 cans of yellow and 4 cans of red ✓
To make lemonade, 1 lemon and 2 tablespoons of sugar are used for every 500 ml of water. Jun uses 750 ml of water to make lemonade. Jun should use ______ tablespoons of sugar.
- '3' ✓
Select all the statements that are correct.
- A ratio describes the relationship between values. ✓
- Ratio uses an additive relationship.
- Adding the same amount to each part in a ratio keeps the ratio the same.
- Multiplying the same amount to each part in a ratio keeps the ratio the same. ✓
"Choko Milk chocolate" bars are made with 2 parts cocoa, 5 parts milk powder and 1 part sugar. Too much cocoa makes it too bitter, too much sugar makes it too sweet. Match each result with its recipe
- Too sweet
  
  ⇔
  
  18 parts cocoa, 45 parts milk powder and 10 parts sugar. ✓
- Too bitter
  
  ⇔
  
  15 parts cocoa, 35 parts milk powder and 7 parts sugar. ✓
- Perfect
  
  ⇔
  
  10 parts cocoa, 25 parts milk powder and 5 parts sugar. ✓
- Too much milk powder
  
  ⇔
  
  20 parts cocoa, 55 parts milk powder and 10 parts sugar. ✓

Worksheet

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Lesson Details

Key learning points

A ratio describes as connection between two values.
This relationship is multiplicative, not additive.
Adding the same amount to each part of the ratio changes the ratio.

Common misconception

Using multiplication as repeated addition leads to incorrect additive strategies of ratios.

Focus on the multiplicative relationships between parts to whole or whole to parts. Ratio allow the multiplicative relationship to be seen.

Keywords

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.