|Programme of Study statements
|solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
|solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
|solve problems involving similar shapes where the scale factor is known or can be found
|solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Activity set A
You could give the children, for example, one green and three yellow counters, the children could identify, for example, the ratio of green to yellow, the proportion of green. They could then work out other numbers of counters that would give the same ratio, for example two green and six yellow, three green and nine yellow,. This would help them to understand that the numbers of counters might change but the ratio does not change, if the relationship between the different parts remains the same. You could ask them to explore what they need to do to find a formula for ‘g’ green and ‘y’ yellow so that they can work out any number of these counters that give the same ratio and proportion.
Give the children some blue and white interlocking cubes and ask them to show you different ratios and proportions, such as:
- a 5:2 ratio of blue to white
- a 2:5 ratio of blue to white
- blue is 2/5 of white
- blue is 5/2 or 2½ of white
- the proportion of cards from a normal pack of 52 that is red
- the proportion of cards from a normal pack of 52 that are aces
You could give the children a selection of recipes from the internet and ask them to work out the ratio of, for example, flour:sugar:margarine in a sponge cake, or the proportion of a ready meal that should be eaten by 2 people if the meal is intended to serve 6 people. You could then ask them to rewrite a list of ingredients for a recipe, originally written for 4 so that it will serve 6 or 12 people.
You could give the children problems such as:
- Tom and Nafisat win £750 between them. They agree to divide the money in the ratio 2:3. How much do they each receive?
- A necklace is made using gold and silver beads in the ratio 3:5. If there are 80 beads in the necklace:
- How many are gold?
- How many are silver?
- To make a tasty chocolate milkshake James needs one part chocolate sauce to six parts milk. Each part is 150ml
- If he used 4 parts of chocolate sauce how much milk would he need?
- If he had 420 ml milk, how much chocolate sauce?
Activity set B
The children could construct a pie chart and then make up and solve problems from it. You could set scenarios such as: the local health authority are surveying the eating habits of school children and want to know how many of the 360 children in a local school have school dinners, packed lunches or go home. If appropriate the children could find out this information or could make up the data. They could then construct a pie chart using a protractor with every degree representing one child. They could then find the numbers, fractions or percentages of children having each type of lunch.
Set problems such as this for the children to solve:
- Tammy was saving for a laptop. The laptop she wanted cost £360. She has saved 60% of the amount. How much more money does she need?
Encourage the children to use effective methods to find 60%, such as find 50% by halving and then 10% by dividing £360 by ten and adding the two amounts together.
- In the sale a coat has been reduced by 20%. It now costs £56. What was its original price?
The children could use the bar model to help them solve this:
Each section of the bar is worth £14 so the original cost of the coat must be £70.
You could give the children the Nrich activity ‘Rod Ratios’ or, as a challenge, ‘Weekly Problem 27’
Activity set C
- Children could look at photographs of themselves or famous buildings and discuss why they are smaller than the actual children or buildings. Establish that they have been scaled down. Discuss where else they might see scaled down images, for example, maps, models, architects plans.
- The children could measure the lengths/heights and widths of objects around the classroom, scale these measurements down by an amount they choose and then sketch the object to that size on paper. Other children could estimate by how much these have been scaled down.
- The children could look at maps and work out distances from one place to another using the given scale.
- You could discuss when objects might need to be scaled up – explain that this is called ‘enlarged’. A good example would be looking at very small objects under a magnifying glass or microscope. If you have any available the children could use the equipment to see what different objects, such as an apple pip or the head of a pin, would look like if scaled up by the magnification on the apparatus.
Activity set D
- The children could look at paintings such as ‘Tiger in a storm’, by Henri Rousseau. They could explore mixing blue and yellow paints to get the colours that Rousseau has achieved. What ratios of blues and yellows have they made? What are these as proportions or fractions of the total paint mix? They could paint a jungle scene using their mixed paints.
- See The Art of Mathematics for other ideas of how to link ratio and proportion to art