Understanding Ratio and Proportion ..

Understanding Ratio and Proportion .

20 New England Patriot fans 10 are Washington Redskins fans
Mrs Kedski has 30 students: 20 New England Patriot fans 10 are Washington Redskins fans AIM OF SLIDE To get a feel about ratio and proportion with a simple example. To allow an initial discussion without worrying too much about ‘getting the right answer’. That is, to see that comparing part with part (ratio) and part with whole (proportion) is sometimes more useful to make a decision than to add up totals. TEACHING NOTES: (Note: It might be helpful in remembering which team is red and which is blue using: Red Rovers, Blue United!) The example contains the dilemma that 6A has a higher total of Rover fans – but a lower proportion and ratio. The purpose is to allow pupils to see that totals aren’t always the most useful tool for comparing and drawing conclusions. Accept any relevant comments, perhaps collect on flip chart, eg: ‘outnumbered 2 to 1’ ‘half as many’, ‘twice as many’, ’50-50’, ‘’equal chance’, ‘one in three’, ‘two in three’ etc. The numbers should allow pupils to see easily that there’s twice as many Rovers fans as United fans in 6A – and equal numbers in 6B, but leading questions may be needed: ‘Are there 3 times as many Rovers fans, twice as many …? Which form would you feel more comfortable / happy in? Note: the images are accurate in numbers and therefore pupils can also get a feel for the ratio just by looking: the reds do look outnumbered 2 to 1 by the blues in 6A and the numbers do look equal in 6B.

3 Ways to Compare Numbers
Which question is a … “Mrs. Kedski has 20 out of 30 Patriot fans in her class. That’s 2 out of 3.” Fraction? The Patriot fans outnumbered the other fans 2 to every 1.” Ratio? Proportion? AIM OF SLIDE To consolidate the use of terms ratio, proportion and fraction. TEACHING NOTES Start to point out the language in basic terms, eg: “A ratio is when you looking at 2 United fans to every 1 Rovers fan” (“2 United fans to every 1 Rovers fan” is also correct but will concentrate on using ‘to every’ for ratio in this slideshow). “A proportion is when you’re looking at the total such as ‘1 out of 3 fans are Rovers’ or 10 out 30 pupils are Rovers fans’“. (1 in every 3 fans are Rovers’ is also correct, but will concentrate on using ‘out of’ for proportion in this slideshow). “Only one third of Mrs. Kedski’s class are Redskin fans.

What’s the Difference - Summing Up: .
3 different ways to say the same thing 3 different ways to compare numbers Ratios compare PART WITH PART “1 to every 2” is a Ratio “1 Redskin fan to every 2 Patriot fans” “The ratio of Redskin to Patriot fans is 1 to 2” “The ratio of Patriot to Redskin fans is 2 to 1” “1 out of 3” is a Proportion “1 out of every 3 fans is a Redskin fan” “The proportion of Redskin fans is 1 out of 3” “One third” is a Fraction “One third of all fans are Redskin fans “1/3 of all fans are Redskin fans” Proportions compare PART WITH WHOLE 3 AIMS OF SLIDE* (*Key slide with large amount of content: use mouse to control introduction.) 1. To reinforce the idea that ratio, proportion and fractions are 3 different ways of looking at the same thing. 2. Then to focus on the language which goes with ratio, proportion and fractions, eg: 1 fan to every 2 fans is a Rovers fan’ 3. Finally to consolidate the concept that these are 3 different ways of comparing numbers: - ratios compares part with part, - proportion compares part with whole - fractions also compare part with whole (but saying it another way.) TEACHING NOTES Decide in advance how to use this slide and don’t rush through unless is revision. The slide offers two parts: 3 Ways to Say the Same Thing: reinforces the language to check that pupils are comfortable with the terms. 2) 3 Different Ways to Compare Numbers: clarifies the difference between ratio, proportion and fractions. Fractions compare PART WITH WHOLE using shorthand such as 1/3

So comparing totals isn’t the only way to look at these numbers…
…You can compare part with part using RATIO …You can compare part with whole using 1 to every 2 = 1:2 AIM OF SLIDE To reinforce in a different way the concept that these are 3 different ways to compare numbers: - ratios compares part with part, - proportion compares part with whole - fractions also compare part with whole (but saying it another way.) TEACHER NOTES Check pupils are comfortable with the difference between ratio and proportion in preparation for the next 4 slides. PROPORTIONS or FRACTIONS 1 out of 3 1/3

Ratio, Proportion or Fraction?
two out of five This is a … two fifths This is a … proportion fraction four tenths This is a … four to every ten This is a … fraction ratio ten to every four This is a … four out of ten This is a … ratio AIM OF SLIDE (1st of 4) Interaction: pupils decide if each statement is a ratio, proportion of fraction. TEACHER NOTES Unlike other slides, these statements stay on the screen, so you can review the language at the end. You may need to go slowly through the first run, but can revisit slide to practice speed. Speed can be controlled using mouse. Follow-up work can involve pupils creating their own statements: singly, in pairs or whole-class using whiteboards. proportion 4/10 This is a … 4:10 This is a … fraction ratio

3 Bruins fans to every 2 Rangers fans This is a … ratio 9 girls out of 10 use soap This is a … proportion AIM OF SLIDE (2nd of 4) Interaction: pupils decide if each statement is a ratio, proportion of fraction. TEACHER NOTES You may need to go slowly through the first run, but could revisit slide to practice speed. Speed can be controlled using mouse. Follow-up work can involve pupils creating their own statements: singly, in pairs or whole-class using whiteboards. 3 boys out of 10 use deodorant This is a … proportion

3 out of 4 pizza-munchers love olives This is a … proportion Half of all girls in 5th grade love Reading This is a … fraction AIM OF SLIDE (3rd of 4) Interaction: pupils decide if each statement is a ratio, proportion of fraction. TEACHER NOTES You may need to go slowly through the first run, but revisit slide to practice speed. Speed can be controlled using mouse. Follow-up work could involve pupils creating their own statements: singly, in pairs or whole-class using whiteboards. One third of all road accidents involve drinking This is a … fraction

3 out of 4 drivers speed at some time This is a … proportion Three quarters of drivers speed This is a … fraction AIM OF SLIDE (4th of 4) Interaction: pupils decide if each statement is a ratio, proportion of fraction. TEACHER NOTES You may need to go slowly through the first run, but can revisit slide to practice speed. Speed can be controlled using mouse. Follow-up work could involve pupils creating their own statements: singly, in pairs or whole-class using whiteboards. 3 drivers speed to every 1 which does not This is a … ratio

Ratio and Proportion: Different Words!
Ratio: “to every” 1 Redskin fan to every 2 Patriot fans Proportion: “out of” 1 out of 3 football fans is a Redskin fan AIM OF SLIDE To clarify the correct use of language for ratio and proportion. TEACHER NOTES 1) Link language to visual images on slide. Eg for Ratio: 1 (circle red fan) to every 2 (circle blue fan) and then remind pupils that this is what we mean by ‘comparing part with part). Eg for Proportion: 1 (circle red fan) out of (circle all 3 fans) and then remind pupils that this is what we mean by ‘comparing part with whole). 2) Check by asking: “ What ratio is United fans to Rovers fans? What proportion is United fans? 3)Extension: Make up different groups in the classroom (1:3, 1:4, 2:3 etc) and repeat the two questions.

PART 2: Simplest Ratios and Proportions
Part 2 offers teaching support in: the development of the concept of equivalent ratios and proportion, using mental pictures and detailed examples. AIM OF SLIDE Introduction to Part 2: We’re going to use what we know about ratio and proportion to compare different numbers. These should build on the simpler explanations provided in Part 1 and lead to a deeper understanding and confident use of language and equivalent ratios and proportion. TEACHING NOTES These 9 slides uses the everyday context of the dinner queue to demonstrate that you can have different totals but the same ratio or proportion. The ratios 1:2 (and 2:1) and 1:3 (and 3:1) are demonstrated visually. For example for the ratio 1:2: - 1 girl and 2 boys at a time move from the dinner queue to the dinner table, - so the total number of girls and boys can be seen to increase each time, - and the ratios can be successively described as 2:4, 3:6, 4:8 etc, - but the simplest ratio of girls to boys remains as 1 girl to every 2 boys or 1:2. The animated slides allows the teacher to talk these through at each stage.

The lunch lineue Ratio of girls to boys? 4 girls to every 8 boys
girls : boys = 4 : 8 Ratio of girls to boys? But the simplest ratio is still 1 : 2 3 girls to every 6 boys girls : boys = 3 : 6 But the simplest ratio is still 1 : 2 2 girls to every 4 boys girls : boys = 2 : 4 AIM OF SLIDE To look at equivalent ratios (where girls : boys = 1:2). TEACHER NOTES See Slide 17 But the simplest ratio is still 1 : 2 1 girl to every 2 boys girls : boys = 1 : 2 This is the simplest ratio is 1 : 2

The dinner queue Ratio of boys to girls? 8 boys to every 4 girls
boys : girls = 8 : 4 Ratio of boys to girls? But the simplest ratio is still 2 : 1 6 boys to every 3 girls boys : girls = 6 : 3 But the simplest ratio is still 2 : 1 4 boys to every 2 girls boys : girls = 4 : 2 AIM OF SLIDE To look at equivalent ratios (where boys : girls = 2:1). TEACHER NOTES See Slide 17 But the simplest ratio is still 2 : 1 2 boys to every 1 girl boys : girls = 2 : 1 This is the simplest ratio is 2 : 1

2 : 1 is a simpler ratio than 4 : 2
Simplest ratios 2 : 1 is a simpler ratio than 4 : 2 but They both mean the same 2 : 1 = 4 : 2 Can you explain why 2 : 1 = 6 : 3 ? 2 : 1 = 8 : 4 ? 2 : 1 = 100 : 50 ?

What proportion is girls?
The dinner queue 4 girls out of 12 Simplest proportion of girls is still 1 out of 3 What proportion is girls? 3 girls out of 9 Simplest proportion of girls is still 1 out of 3 2 girls out of 6 Simplest proportion of girls is still 1 out of 3 1 girl out of 3 This is the simplest proportion of girls = 1 out of 3 AIM OF SLIDE To look at equivalent proportions (for proportion of girls = 1 out of 3). TEACHER NOTES See Slide 17 and next slide. Notice that the example is the same but the focus is now on proportion in stead of ratio. Therefore, while talking through each text box about proportion, links can also be made to the ratio already practised. Introduce slide by referring to previous ratio slide, eg: “Here are the 2 boys and 1 girl again. We know the ratio of boys to girls is 2 to 1. But now we’re going to look at differently – compare part with total instead of part with part – there’s 1 girl out of 3. Next, let’s look at what happens when we have 4 boys and 2 girls … “ The text boxes are mouse-controlled to allow a gradual build up of the whole picture at an appropriate speed. (The next slide repeats this slide but looking at the proportion of boys and includes question boxes. Therefore, you can just talk this slide through if you prefer with just a few questions.)

What proportion is boys?
The dinner queue Proportion of boys? 8 boys out of 12 Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? What proportion is boys? 6 boys out of 9 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 4 boys out of 6 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 2 boys out of 3 Proportion of boys? Simplest proportion of boys? AIM OF SLIDE To look at equivalent proportions (for proportion of boys = 2 out of 3). TEACHER NOTES See Slide 17 and previous slide. This is the simplest proportion of boys = 2 out of 3

The dinner queue What fraction is girls?
4 / 12 What fraction is girls? The dinner queue Simplest proportion of girls? Simplest fraction of girls is still 1 / 3 What fraction is girls? 3 / 9 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? 2 / 6 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? AIM OF SLIDE To look at equivalent fractions (where fraction of girls = 1/3) TEACHER NOTES See Slide 17 and next slide. Talk example through, linking language to ratio and proportion. This is the simplest fraction of girls = 1 / 3 Simplest fraction of girls? What fraction is girls? 1 / 3

The dinner queue What fraction is boys? 8 / 12 What fraction is boys?
Simplest proportion of boys? Simplest fraction of boys is still 2 / 3 What fraction is boys? 6 / 9 What fraction is boys? Simplest fraction of boys? Simplest fraction of boys is still 2 / 3 4 / 6 What fraction is boys? Simplest fraction of boys is still 2 / 3 Simplest fraction of boys? 2 / 3 What fraction is boys? This is the simplest fraction of boys = 2 / 3 Simplest fraction of boys? AIM OF SLIDE To look at equivalent fractions (where fraction of boys = 2/3) TEACHER NOTES See Slide 17 and previous slide Talk example through, linking language to ratio and proportion.

Does order matter? There are 20 boys and 10 girls in room 102.
Which of these are correct? boys : girls = 2 : 1 b) girls : boys = 2 : 1 c) boys : girls = 1 : 2 AIM OF SLIDE To draw attention to the need to get the order right in ratio notation. TEACHER NOTES A good initial question is: “Two of these mean the same thing. Which ones are they?” boys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy Click to check your answer ORDER MATTERS! Be careful what you write!

True or Not True? Ratio of students to teachers = 20 : 1
GUESS! TRUE! Ratio of students to teachers = 20 : 1 Ratio of fans to players = 1 : 1000 This would mean all the players would be sitting in the stadium! Ratio of weekdays to weekend days = 2 : 5 You wish! Ratio of porridge lovers to hamburger guzzlers = 100 : 1 - Not until they invent McPorridge .. TRUE! TRUE! AIM OF SLIDE To provide an opportunity to apply correct order of ratio notation in other everyday contexts. TEACHER NOTES Talk through each statement using a variety of wording so that pupils are linking the formal language to everyday language. Reinforce with questions, such as - “If the ratio of teachers to pupils really was 30:1, what would this classroom look like? Would you prefer to come to school?! “ - “What do you think is the ideal ratio of teachers to pupils?” - “What do you think is the ratio of Villa fans to Blues fans?” TRUE!

PART 3: Recipes and Proportion
How to scale a recipe for 10 people down to 4 people without disaster! Part 2 offers teaching support in: the development of the concept of equivalent ratios and proportion, using mental pictures and detailed examples. the concept of scaling up and down in recipes, keeping the ingredients in proportion AIM OF SLIDE Introduction to Part 3: We’re going to use what we know about proportion to work out some recipes. TEACHING NOTES This could be introduced with questions such as: - ‘You know if you haven’t kept a recipe in proportion by the taste! How would you know if you’ve made twice as much squash by doubling the squash and not the water?” - “If you normally add one teaspoon of sugar to your cup of tea, how much would you add to large mug?”

Biscuits and Bananas Skins
Enjoy cooking? Check out these fantastic recipes! Some of them need changing to suit the number of people, - But remember to keep them in proportion, - And watch out for the or else … AIM OF SLIDE The next 3 slides allow pupils to look at ratio/proportion problems about scaling a recipe up or down. TEACHER NOTES The examples use simple numbers so pupils can have a go at solving them mentally. This allows you to avoid formal methods initially and support pupils to build confidence in their calculation skills. (The tables needed are 2, 4, 5 and 10.) After 3 slides, a further slide allows pupils to reflect on how they are already successfully working out answers. It suggests a 3-step process, two of which they will have had to already used: 1) CHOOSE the maths: x or ÷ (eg: half the biscuits means halve all the ingredients. Decide to use ÷2. ) 2) DO the maths (eg: divide ALL ingredients by 2) 3) CHECK the maths (eg: if you have halved everything correctly, the total must be halved as well.) Whoops !

It’s supper time! You make a simple omelette like this:
= 2 eggs teaspoon of butter = 1 omelette Your omelette tastes amazing! - So of course your mates start turning up. Can you scale up your ingredients to feed them all? ? eggs ? tsp of butter = 2 omelettes 4 eggs tsp of butter = 2 omelettes AIM OF SLIDE See Slide 28 TEACHER NOTES It is important to use the opportunity to use the language of ratio and proportion here and talk through each question rather than just read as written. The key approach to scaling recipes up and down is to one of proportion, (eg: ‘2 eggs needed for 1 omelette’) - rather than one of ratio (eg: ‘2 eggs needed to every 1 teaspoon of butter’). Both approaches are valid, but the suggestion here is to focus on one approach when approaching recipes. Therefore, the starting point is to find all missing numbers from the TOTAL (omelettes / biscuits etc). That is, if you know the amount of ingredients for 1 omelette (or 24 biscuits …), then 4 times as many omelettes means 4 times as many ingredients, and so on. 6 eggs tsp of butter = 3 omelettes ? eggs ? tsp of butter = 3 omelettes 8 eggs tsp of butter = 4 omelettes ? eggs ? tsp of butter = 4 omelettes ? eggs ? tsp of butter = 5 omelettes 10 eggs tsp of butter = 5 omelettes

2 eggs + 1 teaspoon of butter = 1 omelette
And the next week … = 2 eggs teaspoon of butter = 1 omelette … word’s getting around and more mates turn up the next day. Can you scale up your ingredients to feed them? 4 eggs tsp of butter = 2 omelettes 4 eggs ? tsp of butter = ? omelettes AIM OF SLIDE See Slide 28 TEACHER NOTES These questions offer a different approach to the last slide: they start by specifying quantity of an ingredient rather than number of omelettes. 10 eggs tsp of butter = 5 omelettes 10 eggs ? tsp of butter = ? omelettes 20 eggs tsp of butter = 10 omelettes ? eggs tsp of butter = ? omelettes 22 eggs tsp of butter = 11 omelettes ? eggs tsp of butter = ? omelettes

RECAP How did you work these out?
STEP 1: CHOOSE the maths! x or ÷ ? BIGGER AMOUNTS mean X SMALLER AMOUNTS mean ÷ RECAP How did you work these out? STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients (This is called ‘keeping it in proportion’) STEP 3: CHECK the maths! - using ratio ! Eg: If there are 2 eggs to every 1 tsp butter, the ‘eggs number’ is ALWAYS twice the ‘butter number’. AIM OF SLIDE To recap the approach used to work out the new proportions. TEACHER NOTES Step 1: Emphasise that choosing the maths from 4 possible operations (+, -, X and ÷) is the 1st step for all problem-solving. In ratio and proportion it’s even simpler – choose from X or ÷. Step 2: Why should you halve the ingredients if you halve the total number of biscuits? Step 3 suggests solving the original problem using proportion and checking using ratio. This step has not been carried out in the slideshow in order to avoid overload. Step 3 also reinforces the connection between ratio and proportion. It also allows for the fact that sometimes the numbers lend themselves to solving a recipe problem using ratio and we need to be allow for more than one approach. Eg: If pupils notice the easy number pattern that the ‘eggs number’ is always twice the ‘butter number’, they will use this to work out missing quantities. That is, they are using ratio instead of looking at the total and using proportion. Hungry for more? Try these recipes … REMEMBER THE 3 STEPS

Recipe for Shortbread Biscuits
Makes 20 shortbread biscuits Ingredients 200g butter 200g plain flour 100g golden caster sugar 100g fine semolina Pre-heat the oven to gas mark 2, 300°F (150°C). You will also need an 8 in (20 cm) diameter fluted flan tin, 1¼ in (3 cm) deep with a loose base. AIM OF SLIDE View a recipe in preparation for some questions about scaling it up or down. TEACHING NOTES Draw attention to the quantities of the ingredients and that the recipe is for 20 people.

10 Mouth-watering Shortbread Biscuits!
STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ This is the recipe for 20 biscuits. Can you scale down the recipe for 10? Remember to keep your recipe in proportion – if you halve the sugar, remember to halve the rest as well or it won’t taste good! STEP 3: CHECK the maths! - using ratio. Eg: The weight of the butter is always 2 times the weight of the sugar. STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients = 400g flour 400g butter 200g sugar 200g semolina 20 biscuits ÷ 2 ? ÷ 2 ? ÷ 2 ? ÷ 2 ? ÷ 2 ? AIM OF SLIDE To use recipe on previous slide to work out the quantity of ingredients for half as many people. TEACHER NOTES Reinforce the idea that we need to ‘scale down’ the quantities and that is called ‘keeping it in proportion’. This slide walks pupils through the 3 step process for a correct calculation. Subsequent slides will ask pupils to identify mistakes in calculations and what difference it makes to the biscuits, so this slide can just be used to emphasise the 3 steps. = 200g flour 200g butter 100g sugar 100g semolina 10 biscuits

3 Steps for Scaling RECAP STEP 1: CHOOSE the maths! CHOOSE FROM x or ÷
… BIGGER means X … SMALLER means ÷ RECAP STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients AIM OF SLIDE To reinforce the 3 steps and clarify any questions or issues before trying out the next slide. STEP 3: CHECK the maths! - using ratio. Eg: If the weight of the butter is always 2 times the weight of the sugar…

… Nirmal makes 2 shortbread biscuits
Whoops ! … Nirmal makes 2 shortbread biscuits Mistake in STEP 1: Choose the maths! CHOOSE FROM + - x ÷ BIGGER means X SMALLER means ÷ BUT… Nirmal did X 10 instead of ÷ 10 Nirmal scaled down the recipe for 2 biscuits, but they don’t taste right! Did he scale down correctly and keep the recipe in proportion? Check his working out Then click to see if you’re right = 20 biscuits 400g flour butter 200g sugar semolina 20 biscuits ÷ 10 ÷ 10 ÷ 10 ÷ 10 x 10 x10 ? x 10 ? x 10 ? x 10 ? ? AIM OF SLIDE To consolidate the need for Step 1: Choose the Maths: multiply or divide? Pupils are asked to identify the error and correct it. TEACHER NOTES Talk through each stage as appropriate. Emphasise the need to choose the correct operation. ÷ 10 200 BISCUITS INSTEAD OF 2! WHAT DIFFERENCE DID THE MISTAKE MAKE? = 40 g flour 4000 g flour 40 g butter 4000 g butter 2000 g sugar 20 g sugar 2000 g semolina 20 g semolina 2 biscuits

… Liana makes 5 shortbread biscuits
Whoops ! … Liana makes 5 shortbread biscuits Mistake in STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients BUT …Liana did not do ÷ 2 to the sugar. Check her working out Then click to see if you’re right Liana scaled down the recipe for 5 biscuits, but they don’t taste right! Did she scale down correctly and keep the recipe in proportion? = 20 biscuits 400g flour butter 200g sugar semolina ÷ 4 ÷ 4 ÷ 4 ÷ 2 ÷ 4 ÷ 4 ? AIM OF SLIDE To consolidate the need for Step 2. Pupils are asked to identify the error and correct it. TEACHER NOTES Talk through each stage as appropriate. Emphasise that the same operation has to be done to each quantity. If necessary, rephrase the problem using division by 2, an easier mental concept - half the number of biscuits means only needing half the flour, half the butter, etc... THE BISCUITS WERE TOO SWEET! WHAT DIFFERENCE DID THE MISTAKE MAKE? = 100 g flour 100 g butter 100 g sugar 50 g sugar 50 g semolina 5 biscuits

Further Practical Examples Recipe No.1 Melon Merenga
Serves 8 people Ingredients 300 g raspberries 200 g bananas 100 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour and serve with ice or ice-cream. AIM OF SLIDE View a recipe in preparation for some questions about scaling it up or down. TEACHING NOTES Draw attention to the quantities of the ingredients and that the recipe is for 8 people.

Can you work out the missing amounts?
STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The bananas’ weight is ALWAYS twice the melons’ weight. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Melon Merenga for 8 600 g = 400 g 200 g Melon Merenga for 4 ? g = ? g ? g 300 g 200 g 100 g General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 2 people. 2) X 3 (easier than X6) Melon Merenga for 2 ? g = ? g ? g 150 g 100 g 50 g AIMS OF SLIDE To use proportion to work out the missing ingredients using Steps 1 to 3. To understand that there is often more than one route. (Eg: wok out recipe for 1 from the recipe for 8, 4 or 2 people) To understand that some routes are easier than others (See shortcut for recipe for 6 people). TEACHER NOTES 1) Recipe for two can be found by dividing recipe for eight by 4 – or by dividing recipe for four by 2. Similarly, the recipe for one can be calculated from the recipes for 4 or 2. Encouraging more than route is good practice and also provides a way to check results. 2) Hopefully, pupils will work out that any amount can be worked out from the recipe for one. If not, it would be useful to point out. Extension: The recipe for 6 allows both the general approach (work out the recipe for one and multiply by 6) and a shortcut (work out the recipe for 2 and multiply by 3). Such shortcuts are conceptually more difficult, but allow access for more able pupils to extend their problem-solving strategies. Melon Merenga for 1 You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? ? g = ? g ? g 75 g 50 g 25 g Melon Merenga for 6 ? g = ? g ? g 450 g 300 g 150 g

Further Practical Examples Recipe No
Further Practical Examples Recipe No.2 Raspberry Fruitloop (Same ingredients. Different amounts) Serves 10 people Ingredients 500 g raspberries 250 g bananas 150 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour and serve with fresh raspberries AIM OF SLIDE View a recipe in preparation for some questions about scaling it up or down. TEACHING NOTES Draw attention to the quantities of the ingredients and that the recipe is for 10 people.

STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The raspberries’ weight is ALWAYS twice the melons’ weight. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Raspberry Fruitloop for 10 500 g = 250 g 150 g Raspberry Fruitloop for 5 ? g = General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it! (Easier than X8) 250 g ? g 125 g ? g 75 g Raspberry Fruitloop for 1 ? g = ? g ? g 50 g 25 g 15 g AIMS OF SLIDE To use proportion to work out the missing ingredients using Steps 1 to 3. To understand that there is often more than one route. (Eg: wok out recipe for 1 from the recipe for 8, 4 or 2 people) To understand that some routes are easier than others (See shortcut for recipe for 8 people). Raspberry Fruitloop for 4 You can work this out from the quantities for 1 person, BUT … Can you see any shortcuts? ? g = 200 g ? g 100 g ? g 60 g Raspberry Fruitloop for 8 ? g = 400 g ? g 200 g ? g 120 g

Further Practical Examples Recipe No
Further Practical Examples Recipe No.3 Bombastic Banana Boat (Same ingredients. Different amounts) Serves 12 people Ingredients 120 g raspberries 600 g bananas 120 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour into a scooped out melon half . Serve with fresh raspberries AIM OF SLIDE View a recipe in preparation for some questions about scaling it up or down. TEACHING NOTES Draw attention to the quantities of the ingredients and that the recipe is for 12 people.

STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The weight of bananas is always 5 times the weight of the melon. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Banana Boat for 12 120 g = 600 g 120 g Banana Boat for 6 ? g = ? g ? g 60 g 300 g 60 g General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it! (Easier than X8) Banana Boat for 4 ? g = ? g ? g 40 g 200 g 40 g AIMS OF SLIDE To use proportion to work out the missing ingredients using Steps 1 to 3. To understand that there is often more than one route. (Eg: wok out recipe for 1 from the recipe for 8, 4 or 2 people) To understand that some routes are easier than others (See shortcut for recipe for 6 people). Banana Boat for 1 You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? ? g = ? g ? g 10 g 50 g 10 g Banana Boat for 8 ? g = ? g ? g 80 g 400 g 80 g

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