Chapter 9
9.1 Compressed version of proportional thinking questions (some additional) Pg 281
9.2 Actual 10 pages of proportional thinking questions Pg283
9.3 Proportional thinking problems 2 Pg 294
- A small collection of miscellaneous questions
9.4 Proportional problems Pg 296
- A page of good proportional problems questions (with answers)
9.5 Bean Salad Pg 297
- A very very good excise (more for the able students) linking ratio / proportion questions into algebra, and solving equations.
9.6 Rational number project proportional concepts Pg 303
Compressed version of Proportional thinking questions presented to the National Numeracy Conference 2006 Workshop: Anne Lawrence and Jim Hogan
(LARGER VERSION WITH PICTURES ATTACHED)
1. Six men can build a house in 3 days. Assuming that all of the workmen work at the same rate, how many men would it take to build the house in 1 day?
2. If seventeen men can build two houses in nine days, How many days would it take twenty men to build five houses?
2. If 6 chocolates cost $.93, how much do 22 cost?
3. Between them, John and Mark have 32 marbles. John has 3 times as many as Mark. How many marbles does each boy have?
4. Mac can mow Mr. Greenway’s lawn in 45 minutes. Mac’s little brother takes twice as long to do the same lawn. How long will it take them if they each have a mower and they work together?
5. Six students were given 20 minutes to clean up the classroom after an eraser fight. They were angry and named 3 other accomplices. The principal added their friends to the clean-up crew and changed the time limit. How much time did she give them to complete the job?
6. If 1 football player weighs 280 pounds, what is the total weight of the 11 starters?
7. Sandra wants to buy a mp3 player costing $210. Her mother agreed to pay $5 for every $2 Sandra saved. How much will each contribute?
8. A company usually sends 9 men to install a security system in an office building, and they do it in about 96 minutes. Today, they have only three men to do the same size job. How much time should be scheduled to complete the job?
9. A motor bike can run for 10 minutes on $1.30 worth of fuel. How long could it run on $.91 worth of fuel?
10. Posh Academy boasts a ratio of 150 students to 18 teachers. How can the number of faculty be adjusted so that the academy’s student-to-teacher ratio is 15 to1?
11. In 3 weeks, a horse eats 10 pounds of hay. How much will he eat in 5 weeks?
12. A dragon’s tail is of its total length. If the tail is 6 feet long, what is the total length of the dragon?
13. Mary lost of her baseball cards. She has 16 left. How many did she lose?
14. It takes Jim and his 2 brothers 4 hours to do the yard work. When one of the boys is sick, how long will it take the other two to do the work?
15. You buy a family-size box of laundry detergent that contains 80 cups of detergent. If your washing machine needs 1 cups per load, how many loads of wash can you do?
16. You watch TV for 12 hours per week. How many hours do you watch in a year?
17. If 15 carrots are 1 of Peter’s daily allowance of carrots, how many carrots will he eat in a week and a half?
18. You bought a box of Grow Fast fertilizer for your plants. The directions on the box say to mix 2 teaspoons of the fertilizer with gallon of water. Your house plants did so well that you decide to uses Grow Fast on your lawn. How much fertilizer will you need to mix up 60 gallons?
19. It takes Steve 1 hours to mow his lawn. Last summer he spent 100 hours mowing the lawn. How many times did he mow it?
20. A 12-person cleaning crew cleans a certain office building every night. It takes them 6 hours to complete the job. One night, 2 people failed to show up for work. How long did it take the rest of the crew to clean the building?
Building houses
Seventeen men can build two houses in 9 days.
How many days would it take twenty men to build 5 houses?
The price of chocolates
This box of chocolates contains 6 chocolates and costs $.93. How much would 22 of these chocolates cost?
Another box of chocolates is selling at 8 for $1.25. Which chocolates are cheaper?
Marbles
Between them, John and Mark have 32 marbles.
John has 3 times as many as Mark.
How many marbles does each boy have?
Mowing the lawn
Mac can mow Mr. Greenway’s lawn in 45 minutes.
Mac’s little brother takes twice as long to do the same lawn.
How long will it take them if they each have a mower and they work together?
Cleaning up
Six students were given 20 minutes to clean up the classroom after an eraser fight.
They were angry and named 3 other accomplices.
The principal added their friends to the clean-up crew and changed the time limit.
How much time should she give them to complete the job?
The football team
If 1 football player weighs 280 pounds, what is the total weight of the 11 starters?
Sandra’s CD player
Sandra wants to buy a cd player costing $210.
Her mother agreed to pay $5 for every $2 Sandra saved.
How much will of them each contribute?
The security system
A company usually sends 9 men to install a security system in an office building, and they do it in about 96 minutes. Today, they have only three men to do the same size job.
How much time should be scheduled to complete the job?
Fueling the motor bike
A motor bike can run for 10 minutes on $1.30 worth of fuel.
How long could it run on $.91 worth of fuel?
Students and teachers
Posh Academy boasts a ratio of 150 students to 18 teachers. How can the number of faculty be adjusted so that the academy’s student-to-teacher ratio is 15 to1?
Enough to feed a horse
In 3 weeks, a horse eats 10 kilograms of hay.
How much will the horse eat in 5 weeks?
The dragon’s tail
A dragon’s tail is of its total length. If the tail is 6 feet long, what is the total length of the dragon?
Mary’s cards
Mary is collecting cards.
She has lost some of them and counts the ones she has left. She has 16 cards.
How many cards did she lose?
Doing chores
It takes Jim and his 2 brothers 4 hours to do the yard work. When Jim is sick how long will it take the other two to do the work?
Laundry detergent
You buy a family-size box of laundry detergent that contains 80 cups of detergent.
If your washing machine needs 1 cups per load, how many loads of wash can you do?
Couch potato?
You watch TV for 12 hours per week.
How many hours do you watch in a year?
Eating carrots
If 15 carrots are Peter rabbit’s daily allowance of carrots, how many carrots will he eat in a week and a half?
Fertilising
You bought a box of Grow Fast fertilizer for your plants. The directions on the box say to mix 2 teaspoons of the fertilizer with one litre of water. Your house plants did so well that you decide to uses Grow Fast on your lawn. How much fertilizer will you need to mix up 60 litres?
The cleaning crew
A 12-person cleaning crew cleans a certain office building every night. It takes them 6 hours to complete the job. One night, 2 people failed to show up for work. How long did it take the rest of the crew to clean the building?
This is a unit (i.e. the area of this shape is equal to one):
You have two pieces this size:
What fraction of the unit would these two pieces be? ____________
What fraction of the circle below is part c?
Pirate Jack buried of his treasure. He gave of the remaining treasure to his trusty mate Pirate Joe. Pirate Joe received $3000 in gold. Exactly how much gold was in Pirate Jack’s whole treasure? Draw a picture to show the solution.
Joshkin built a tower using blocks that linked together. I noticed that he had 27 blocks in of his tower. Exactly how many blocks were in this entire tower?
Provide a clear description of your solution strategy.
The line below is as long as a ribbon I have. Draw a line the same length as my ribbon and another line that is as long as my ribbon. Label the lines.
Proportional Reasoning Challenges
Alice and Blair took two 1 litres containers and filled them with a mixture of water and orange juice. In the first container the ratio of water to juice was 2:1 and in the other container the ratio was 3:1. They then put the combined mixture into a 2 litre container. What was the ratio of water to juice in the mixture in the 2 litre container?
The Lazy Gardener
It takes two gardeners 8 days to mow a lawn. One is lazy and one is energetic. The energetic one would only take 12 days to mow it on his own. How many days would the lazy gardener take to mow the lawn on his own?
The Tree Problem
There is an enchanted forest with many different types of trees in it: pine, oak, beech, and maple. In fact, there are 6 pines trees for every 9 oak trees. There are 4 beech trees for every 13 maple trees. And 6 beech trees for every 8 pine trees. What is the balance of maple trees to oak trees?
Proportion problems
For all questions in the exercise assume that all rates are uniform
- 306 -
1. 6 copies of a magazine cost $41.70. What does
1 copy cost?
2. It takes 5 women 4 hours to chop up some firewood. How long would it take 1woman?
3. Five men take 15 minutes to peel a quantity of potatoes. How long would it take 2 men?
4. A contractor earns $700 for making 5 deliveries of soil in his truck. How much would he earn for making 3 deliveries?
5. It takes 5 hose pipes to fill a swimming pool in 70 minutes. How long would it take 4 hose pipes?
6. A restaurant buys 18 rump steaks for a 5 day period. How many would it need to buy for a 10 day period?
7. Antarctic explorers buried enough food under a cairn of rocks to feed their 8 huskies for 12 days. If two of their huskies had died before they returned to the cairn, how long would the food last the remaining huskies?
8. A watch gains five seconds in. two days. How many seconds would it gain in five days?
9. A large packet of toffees can last three people 18 days. How long will it last nine people?
10. 8 containers of easy-spread butter will make 1200 sandwiches. How many sandwiches will 6 containers make?
11. It takes 10 minutes for a person to pick 40
strawberries.
(a) How long would it take them to pick 60 strawberries?
(b) How many strawberries could they pick in
half an hour?
12. 200 g of roast pork costs $3.40. How much does 300g cost?
13. A power station has enough coal stored to run 6 turbines for 36 days. For how long could the station run 4 turbines on the same amount of coal?
14. l2 bank-tellers took 4 minutes to count a large quantity of bank notes. How long would it take 8 bank-tellers?
15. 3600 mL of milk is enough to feed 8 cats for a week. How much milk would be needed for 3 cats for a week?
16. It takes 5 workers 48 minutes to pack some apples into crates. How long would it take 15 workers to do the same job?
17. A meal for 4 people uses 15 g of salt. How much salt should be used if the meal is to be made for 10 people?
18. 6 survivors from a shipwreck are on a lifeboat, with enough water for 12 days. How long would the water last if there were only 4 people on the boat?
19. It takes 5 people 120 minutes to watch a video. How long would it take 10 people?
20. The recipe for Lasagna Pomodoro starts as follows:
‘For every 500 g of pasta, chop up packets of sun-dried tomatoes.’ How many packets of sun dried tomatoes will be needed for 2 kg of pasta?
21. In a Science exam there are 40 marks for Chemistry questions and 30 marks for Biology. The teacher who set the exam estimates that the Chemistry questions should take 50 minutes to answer. How long should the Biology questions take to answer?
22. Employees at a burger-bar can make 15 burgers in 10 minutes. How many employees would be needed to make 300 burgers in half an hour?
23. 4 people can paint a fence with 30 panels in 3 hours. How long would it take 5 people to paint a fence with 25 panels?
24. If x workers can do a job in n hours, how many hours does it take for x — r workers to do the job?
- 306 -
Bean Salad
Answers:
- 306 -