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Question: The monthly charge for a mobile phone is £25. This includes 300 minutes free each week. After that there is a charge of 5p per minute. Calculate the cost of using the phone for 540 minutes, 600 minutes, 310 minutes and 450 minutes for each of the 4 weeks in one month.
2. What would happen to the bill if only 100 minutes were used in the third week?
3. What difference is it likely to make to the bill if calls after 6.00 pm are only 3p per minute?
1. What other questions could you ask about this situation?
4. Is it good value?
5. What other information would you want to know about the charges for this phone before you agreed to have it?
6. Can you make the question more realistic?
Question:
Find the mean, mode, median and range of the numbers:3, 7, 9, 1, 3, 14, 7, 3, 4, 9
3. Can you change one number so that the mean changes but none of the other measures change?4. Can you change one number so that the median changes but none of the other measures change?
2. If I change a 3 for a 4 what happens to the measures?
1. Answer the question.
5. If an extra 3 is added what will change?
6. Can you change one number so that the range is reduced but none of the other measures change?7. How can you change just one number so that two of the measures change?
Question: Tim buys a pack of 12 cans of cola for £4.80. He sells the cans for 50p each. He sells all of the cans. Work out his percentage profit.
2. If he can get 24 cans for £9.20 should he buy them?
3. He wants to make at least 10% profit. What should he do?
1. Change some or all of the numbers so that the percentage profit is still the same.
4. The price has gone up to £5.20 for 12 cans, what should he do to maintain his percentage profit.
5. What else could you ask about this situation?
Question: Rebekah has 35 sweets. She shares then in the ratio 4 : 3 with her brother Daniel. Rebekah keeps the larger share. How many sweets does she keep?
2. What other totals will ‘work’ with the given ratio?
3. What other ratios will ‘work’ with the given total?
1. What happens if Rebekah has miscounted and there are only 33 sweets?
4. Change the question so that Rebekah gets 21 sweets and Daniel gets 15.
5. Change the question so that Rebekah gets 3 more than Daniel.
6. What if there are 3 children instead?
Question:In a sequence u1 = 3, u2 = 9 and u3 = 15. Find u6 and a formula for un.
2. Are all terms a multiple of 3? How do you know?3. Can you find other sequences with the same u3 and u6?Describe their patterns.
4. How could you change the question so that 100 is a term of the sequence?
1. Is 90 a term in the sequence?
5. What would you have to change to get u6 = 40?
6. What difference would it make if u1 = 4?
7. What could the next part of the question be?
Question: Express in the form where a and b are integers to be determined. Hence write down the transformation that sends to the graph
382 xxbax 2)(
2xy 382 xxy
2. What difference would it make to the answers if the 3 was changed to a -3?
1. What difference would it make to the answers if the 8 was changed to a 10?
4. How could you make the question harder?
5. How could you make the question easier?
3. Change the question so that the answer to the second part is a translation of
5
3
Question:
Express in the form
Hence write down (a) the centre and (b) the radius of the circle.
346 22 yyxx222 )()( rbyax
1.Answer the question.
2. What difference will it make to the answer if the 6 is changed to an 8?
3. What would you have to change to get a radius of 5?
4. How could you change the question so that the centre changed but the radius stayed the same?
5. What else could you ask?
6. How could you make the question harder?
Question:
Express in the form
Hence write down (a) the centre and (b) the radius of the circle.
222 )()( rbyax
Alternatively give one of these:
Question:
Express in the form
Hence write down (a) the centre and (b) the radius of the circle.
OR
Question:
Express in the form
Hence write down (a) the and (b) the of the circle.
OR
Prompts to open up closed questions:1. What happens when …..?
2. What happens if I change …..?
3. What difference would it make if …..?
4. What would the next part of the question be?
5. What happens next ….?
6. How could you make it true that …..?
7. What could you change so that …..?
8. How could you make the question easier …..?
9. How could you make the question harder …..?
3. Andy spends one third of his pocket money on a computer game and one quarter on a ticket to a football match. Work out the fraction of his pocket money that he had left.
2. A text book costs £12.99. Work out the cost of 20 books.
A teacher can afford to buy 12 of the books.
Write 12 out of 20 as a percentage.
1. A young person’s railcard gives one third off the normal price. Jenny uses her railcard to buy a ticket. The normal price of the ticket is £36.45. Work out how much she pays for the ticket.
4. Bronze is made from copper and tin.
The ratio of the weight of copper to the weight of tin is 3 : 1.
(a) What weight of bronze contains 36 grams of copper?
(b) Work out the weight of copper and the weight of tin in 120 grams of bronze.
5. (a) Change 10 kilograms to pounds.
(b) Change 7 pints to litres.
6cm
8cm
x cm
Type 1
7cm
13cm
x cm
Type 2
x cm
12cm
13cm
Type 3
x cm
8cm
11cm
Type 4
8cm
15cm
Type 5
Find the length of the diagonal of the rectangle.
y
15
x18
24
Find x and y.
Type 6
8 cm and 10cm are the lengths of two sides of a right angled triangle. Find possible triangles and use Pythagoras to justify that they are indeed right angles triangles.
The hypotenuse of a right angled triangle is 10cm. Find possible triangles and use Pythagoras to justify that they are indeed right angles triangles.
One of the sides of a right angled triangle that is adjacent to the right angle is 10cm. Find possible triangles and use Pythagoras to justify that they are indeed right angles triangles.
One side of a right angled triangle is 10cm. Find possible triangles and use Pythagoras to justify that they are indeed right angles triangles.
Instead of :
y
15
x18
24
Find x and y.
39
15
18
24
Is this diagram possible? Justify your answer.
How about:
Or this one:
Not to scale.
Put possible lengths on the diagram so that the right angles work. Justify your decisions. Can you generalise?
Not to scale.
12 cm
13 cm
8 cm
5 cm
Find the perimeter of this shape.
Not to scale.
12 cm
13 cm
8 cm
5 cm Find the area of this shape.
Not to scale.
The perimeter of this shape is 56 cm. Give possible dimensions.
Not to scale.
The area of this shape is 120 cm². Give possible dimensions.
The area of this shape is 120 cm². Give possible dimensions.
The perimeter of this shape is 56 cm. Give possible dimensions.
OR
The area of the shape is 120 cm².
The perimeter of the shape is 56 cm.
Find a possible shape.
OR
6 cm9 cm
8 cm
Original Problem: Find the volume of this triangular prism. State the units of your answer.
Thinking Problem:
Find possible dimensions for the prism. Which give the maximum volume? Does this prism have the largest surface area?
Area of the sloping face is 48cm²
Original Problem:
Construct two box plots from the stem and leaf:
3 4 8 7 3 3
1 3 5 5 7 3
6 8 6 2 1 1 0
3 4 4 5 7 5 5 5 2 1
6 8 8 8 9 5
7 7 9 6 3 1
4/5 represents 4.5 cm
Thinking Problem:
Construct a possible back to back stem and leaf that is represented by these box plots.
Original Problem:
A driver covers 110 km in 3 hours and then travels at 70 km h-1 for a further 2 hours.
What is his average speed?
Thinking Problem:
The average speed of a journey is 60 km h-1. Construct a possible travel graph.
Justify that its average speed is 60 km h-1 and describe the journey.
Original Problem:
Does the point (3, 5) lie on the circle with equation x² + y² + 4x + 6y = 76?
Justify your answer.
Thinking Problem:
The circle has equation x² + y² + 4x + 6y = 76?
Find possible coordinates for A, B and C and justify your answers.
C xx A
B x
Original Problem:
Find the mean, median and mode of the set of numbers:
3, 5, 7, 2, 4, 3, 5, 8, 3, 2, 4, 1, 0, 5
Thinking Problem:
Find a possible set of numbers with mean 6, median 5 and mode 3.
10 cm
30º
What questions could you ask?
(1, 4)x
x(3, 10)
What questions could you ask?
What questions could you ask?
x
(5, 2)
53 23 xxxy
What questions could you ask?
Distance from home
Time
What questions could you ask?
What information would you need in order to answer each question?
Trapezoidal tables are put together in pairs so that they will seat 6 students.
What questions could you ask?
What information would you need in order to answer each question?
What questions could you ask?
What information would you need in order to answer each question?
A
B
C D
A baker offers a 3 tiered wedding cake. Each layer is cylindrical. The bottom layer has diameter 29cm, the middle layer has diameter 23cm and the top layer has diameter 17cm.
Write questions based on the situation above that use as many different aspects of mathematics as you can think of.
What extra information would you need in order to answer your questions?
What questions could be asked from the information given?
