Perfect Percentage Pizza
Level 3 Mathematics Transition Booklet
Mathematical Studies
Name:
Bridging the gap!
Introduction You will be starting a Level 3 Mathematics course in September, and it is important that you are ready for the step up. The best way to prepare yourself is to make sure you have a firm grasp of the knowledge and skills you have already developed at GCSE level. Many areas of this qualification require the confident use and application of numerical concepts. This set of resources is designed to help you check if you are up to speed and to help you fill in any gaps. If you do this you will put yourself in a good position to start the course in September. At the back of this booklet you will find a transition task that needs to be completed before September. All sections should be attempted. There are MyMaths references to provide you with support/revision in these areas The work is to be completed and handed in during your first Maths lesson You will have a transition test during the second week of term which will your understanding of this topic.
Skills you need Below is the list of the skills you should be confident with before starting the course: Rounding Using percentages
Resources to help you For each of the topic areas listed above, there are section on MyMaths to support you. Section
MyMaths Reference
Rounding
https://app.mymaths.co.uk/73-resource/rounding-decimals https://app.mymaths.co.uk/75-resource/significant-figures
Percentages
https://app.mymaths.co.uk/myportal/library/9/84/887
Practical Information You will be provided with an exercise book but you will also need an A4 file, some paper and dividers. Please ensure that all work in your file is kept in a logical, presentable way with all assessments and objective sheets in the correct place.
Useful Websites NRich http://nrich.maths.org/secondary-upper Mathwire http://mathwire.com/archives/enrichment.html The History of Maths https://en.wikipedia.org/wiki/History_of_mathematics https://www.youtube.com/watch?v=cy-8IPVKLIo The joy of Stats https://www.youtube.com/watch?v=jbkSRLYSojo
Transition Task
Perfect Percentage Pizza NB. Where there is an asterisk against a question, it indicates that there is more than one possible solution to the question.
Section A – A Slice of Nutrition Sally buys a 400 g ‘Cheesy Peasy’ vegetarian pizza. It has the following nutritional information:
RDA stands for ‘Recommended Daily Allowance’ – an indication of how much of each nutrient an average person should consume each day.
1. a) What percentage of the carbohydrates are sugars?
b) What percentage of the pizza is protein?
c) What percentage of the pizza is fat?
d) What percentage of the pizza is not accounted for?
e) How many slices is the pizza cut into?
2. Sally eats 3 slices of pizza. a) What percentage of her RDA of protein has she consumed?
b) What percentage of these slices is protein?
3. a) What is the Recommended Daily Allowance of energy for women? (*)
b) How many slices can a man eat to consume his full RDA of protein?
c) If a woman does not want to exceed her RDA in any category, what is the maximum number of slices she can eat?
4. A 400 g low-fat pizza claims to contain 5% less fat than the regular vegetarian pizza. a) How much fat (in grams) is in the low-fat pizza? (*)
b) What percentage of the low fat pizza is fat? (*)
5. A 500 g pepperoni pizza contains 20% fat by mass. If a family has a 500 g pepperoni pizza and a normal 400 g vegetarian pizza for dinner, what percentage of the dinner is fat?
Section B – Some Financial Toppings Sally is shopping around to get the best deal on her ‘Cheesy Peasy’ pizza. She finds the following prices in the shops: Shop
Labelled Price
Special Offer
Buymore
£5
Limited time sale
Cheap and Cheery
£6
25% off labelled price
Pizzas R Us
£10
40% off labelled price
1. Showing your working, explain which shop provides the best value.
2. What is the percentage difference between the cheapest and most expensive prices you would pay for each of these pizzas? (*)
3. In the Buymore sale all of the labelled prices were reduced by 20%. How much will a Buymore Pizza cost when the sale is over?
4. Pizzas R Us have a policy of increasing the labelled cost of their pizza by 10% each year. a) How much will it cost next year?
b) How much will it cost in 3 years? (*)
c) How much will it cost in 100 years?
5. Extension Question: 10 years ago the labelled cost of a Cheap and Cheery Pizza was £4. What was the average annual rate of percentage increase over these 10 years.
Mathematical Studies
Name:
Bridging the gap!
Introduction You will be starting a Level 3 Mathematics course in September, and it is important that you are ready for the step up. The best way to prepare yourself is to make sure you have a firm grasp of the knowledge and skills you have already developed at GCSE level. Many areas of this qualification require the confident use and application of numerical concepts. This set of resources is designed to help you check if you are up to speed and to help you fill in any gaps. If you do this you will put yourself in a good position to start the course in September. At the back of this booklet you will find a transition task that needs to be completed before September. All sections should be attempted. There are MyMaths references to provide you with support/revision in these areas The work is to be completed and handed in during your first Maths lesson You will have a transition test during the second week of term which will your understanding of this topic.
Skills you need Below is the list of the skills you should be confident with before starting the course: Rounding Using percentages
Resources to help you For each of the topic areas listed above, there are section on MyMaths to support you. Section
MyMaths Reference
Rounding
https://app.mymaths.co.uk/73-resource/rounding-decimals https://app.mymaths.co.uk/75-resource/significant-figures
Percentages
https://app.mymaths.co.uk/myportal/library/9/84/887
Practical Information You will be provided with an exercise book but you will also need an A4 file, some paper and dividers. Please ensure that all work in your file is kept in a logical, presentable way with all assessments and objective sheets in the correct place.
Useful Websites NRich http://nrich.maths.org/secondary-upper Mathwire http://mathwire.com/archives/enrichment.html The History of Maths https://en.wikipedia.org/wiki/History_of_mathematics https://www.youtube.com/watch?v=cy-8IPVKLIo The joy of Stats https://www.youtube.com/watch?v=jbkSRLYSojo
Transition Task
Perfect Percentage Pizza NB. Where there is an asterisk against a question, it indicates that there is more than one possible solution to the question.
Section A – A Slice of Nutrition Sally buys a 400 g ‘Cheesy Peasy’ vegetarian pizza. It has the following nutritional information:
RDA stands for ‘Recommended Daily Allowance’ – an indication of how much of each nutrient an average person should consume each day.
1. a) What percentage of the carbohydrates are sugars?
b) What percentage of the pizza is protein?
c) What percentage of the pizza is fat?
d) What percentage of the pizza is not accounted for?
e) How many slices is the pizza cut into?
2. Sally eats 3 slices of pizza. a) What percentage of her RDA of protein has she consumed?
b) What percentage of these slices is protein?
3. a) What is the Recommended Daily Allowance of energy for women? (*)
b) How many slices can a man eat to consume his full RDA of protein?
c) If a woman does not want to exceed her RDA in any category, what is the maximum number of slices she can eat?
4. A 400 g low-fat pizza claims to contain 5% less fat than the regular vegetarian pizza. a) How much fat (in grams) is in the low-fat pizza? (*)
b) What percentage of the low fat pizza is fat? (*)
5. A 500 g pepperoni pizza contains 20% fat by mass. If a family has a 500 g pepperoni pizza and a normal 400 g vegetarian pizza for dinner, what percentage of the dinner is fat?
Section B – Some Financial Toppings Sally is shopping around to get the best deal on her ‘Cheesy Peasy’ pizza. She finds the following prices in the shops: Shop
Labelled Price
Special Offer
Buymore
£5
Limited time sale
Cheap and Cheery
£6
25% off labelled price
Pizzas R Us
£10
40% off labelled price
1. Showing your working, explain which shop provides the best value.
2. What is the percentage difference between the cheapest and most expensive prices you would pay for each of these pizzas? (*)
3. In the Buymore sale all of the labelled prices were reduced by 20%. How much will a Buymore Pizza cost when the sale is over?
4. Pizzas R Us have a policy of increasing the labelled cost of their pizza by 10% each year. a) How much will it cost next year?
b) How much will it cost in 3 years? (*)
c) How much will it cost in 100 years?
5. Extension Question: 10 years ago the labelled cost of a Cheap and Cheery Pizza was £4. What was the average annual rate of percentage increase over these 10 years.
