Year 7 Investigation HomeworkEach investigation is designed to take a minimum of 4 hours and should be extended as much as the pupil is able. The project should be set in the 1st lesson of week A and collected in at the end of week B. It is the expectation that for each investigation a student completes a poster or report. The work produced should be levelled and the students should have a target for improvement that they copy onto the homework record sheet (which is to be kept in the APP folder).

Outline for the year:

Date setWeek beginning

Investigation Title Minimum Hours Due inWeek beginning

5th Sep 2011 Final scores 4 hours 26th Sep 20113rd Oct 2011

Ice cream 4 hours 4th Nov 2011

7th Nov 2011

A piece of string 4 hours 28th Nov 2011

5th Dec 2011

Jumping 4 hours 9th Jan 2012

16th Jan 2012

How many triangles? 4 hours 10th Feb 2012

20th Feb 2012

Polo Patterns 4 hours 12th Mar 2012

19th Mar 2012

Opposite Corners 4 hours 23rd April 2012

30th April 2012

Adds in Order 4 hours 21st May 2012

28th May 2012

Match Sticks 4 hours 25th June 2012

2nd Jul 2012

Fruit Machine 4 hours 16th July 2012

Year 7 Homework Record Sheet

Date setWeek

beginning

Investigation Title

Level Target for improvement

5th Sep 2011

Final scores

3rd Oct 2011

Ice cream

7th Nov 2011

A piece of string

5th Dec 2011

Jumping

16th Jan 2012

How many triangles?

20th Feb 2012

Polo Patterns

19th Mar 2012

Opposite Corners

30th April 2012

Adds in order

28th May 2012

Match Sticks

2nd Jul 2012

Fruit Machines

Tackling investigations

What are investigations?In an investigation you are given a starting point and you are expected to explore different avenues for yourself.Usually, having done this, you will be able to make some general statements about the situation.

Stage 1 ~ Getting StartedLook at the information I have been given.Follow the instructions.Can I see a connection?NOW LET’S BE MORE SYSTEMATIC!

Stage 2 ~ Getting some results systematicallyPut your results in a table if it makes them easier to understand or clearer to see.

Stage 3 ~ Making some predictionsI wonder if this always works? Find out…

Stage 4 ~ Making some generalisationsCan I justify this?Check that what you are saying works for all of them.

Stage 5 ~ Can we find a rule?Let’s look at the results in another way.

Stage 6 ~ Extend the investigation.What if you change some of the information you started with, ask your teacher if you are not sure how to extend the investigation.

Remember your teachers at Queensbury are her to help, if you get stuck at any stage, come and ask

one of the Maths teachers.

Final Score

When Spain played Belgium in the preliminary round of the men's hockey competition in the 2008 Olympics, the final score was 4−2. 

What could the half time score have been?Can you find all the possible half time scores?

How will you make sure you don't miss any out?

In the final of the men's hockey in the 2000 Olympics, the Netherlands played Korea. The final score was a draw; 3−3 and they had to take penalties.

 

Can you find all the possible half time scores for this match?

Investigate different final scores. Is there a pattern?

Final Score Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Ice Cream I have started an ice cream parlor. I am selling double scoop ice creams. At the moment I am selling 2 flavours, Vanilla and

Chocolate.

I can make the following ice creams:

Vanilla Chocolate Chocolate

+ + +

Vanilla Vanilla Chocolate

Now you choose three flavours. Each ice cream has a double scoop. How many different ice creams can you make?

Extension

Suppose you choose 4 flavours or 5 or 6…

What if you sell triple scoops.

How many then???????

Investigate

Ice Cream Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

A piece of StringYou have a piece of string 20cm long.

1) How many different rectangles can you make?

Here is one

(Check 1 + 9 + 1 + 9 = 20)

Draw each rectangle on squared paper to show your results.

2) I am going to calculate the area of the rectangle I have drawn. Area = base x height so for the one above it is 1 x 9 = 9cm².From the rectangle you’ve drawn, which rectangle has the biggest area?What is the length and width of this rectangle?Write a sentence to say which rectangle has the biggest area.

3) Now repeat the ‘problem’ but the piece of string is now 32xm long.4) Now the string is 40cm long.5) Now the string is 60cm long.6) Look at all your answers for the biggest area. What do you notice?7) Investigate circles when using string of 20cm.8) Look at your answers for the largest area for each string size. What do you

notice?

9cm

9cm

1cm 1cm

A piece of String Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Jumping

Ben is hoping to enter the long jump at his school sports day. One day I saw him manage quite a good jump. However, after practicing several days a week he finds that he can jump half as far again as he did before.This last jump was 3 75 meters long. So how long was the first jump that I saw?

Now Mia has been practicing for the high jump.I saw that she managed a fairly good jump, but after training hard, she managed to jump half as high again as she did before.

This last jump was 1 20 meters. So how high was the first jump that I saw?You should try a trial and improvement method and record you results in a table. Use a number line to help you.

Please tell us how you worked these out.Can you find any other ways of finding a solution?Which way do you prefer? Why?

Jumping Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

How many triangles?Look at the shape below, how many triangles can you see?

I can see 5. Am I correct or can you see more or less? Highlight all the triangles you can see.

How many triangles can you see in the shape below?

Can you draw a triangle like the ones above that have over 20 but less than 150 triangles?

Try and draw it to show if it or is not possible.

How many triangles? Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Polo Patterns

When the black tiles surround white tiles this is known as a polo pattern.

You are a tile designer and you have been asked to design different polo patterns (this is be made by surrounding white tiles with black tiles). The drawing shows one white tile surrounded by 8 black tiles.

What different polo patterns can you make with 12 black tiles (you can surround as many white tiles as you like)?

Investigate how the number of tiles in a polo pattern depends on the number of white tiles.

Polo Patterns Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Opposite Corners.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

The diagram shows a 100 square.

A rectangle has been shaded on the 100 square.

The numbers in the opposite corners of the shaded rectangle are54 and 66 and 64 and 56

The products of the numbers in these opposite corners are

54 x 66 = 3564 and

64 x 56 = 3584

The difference between these products is 3584 – 3564 = 20

Task: Investigate the difference between the products of the numbers in the opposite corners of any rectangles that can be drawn on a 100 square.

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

91 92 93 94 95 96 97 98 99 100

Opposite Corners Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Numbers in order like 7, 8, 9 are called CONSECUTIVE numbers.

17, 9, 6 and 12 have all been made by adding CONSECUTIVE numbers.

What other numbers can you make in this way? Why?

Are there any numbers that you cannot make? Why?

17 = 8 + 9

4 + 5 = 9

6 = 1 +

2 + 3

12 = 3 + 4 + 5

Adds in Order Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…

Match SticksLook at the match stick shape below.

How many match sticks do you expect to be in pattern 2?

Pattern 2 Pattern 32 triangles 3 triangles

Draw the next 5 patterns.

What do you notice about the number of matchsticks used, is there a pattern?

Extension - Can you write it in algebra?

How many matchsticks do you need to make the 50th pattern?

What’s the biggest number pattern can you make with 100 matchsticks? Are there any left over?

Think about different shapes you can make using matchsticks, investigate (as above).

Match Sticks Mark SchemeLevel Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

Fruit Machine

What you have done well….

What you need to do to improve…

Level for this piece of homework…

In this task you are going to design your own fruit machine.

Start with a simple one so you can see how it works.

Use two strips for the reels – each reel has three fruits.

Lemon

Banana

Apple

The only way to win on this machine is to get two apples. If you win you get 50 pence back. It costs 10 pence to play.

Is it worth playing?

You need to know how many different combinations of fruits you can get.

Use the worksheet. Carefully cut out two strips and the slotted fruit machine. Fit the strips into the first two reels of the machine. Start with lemons in both windows. Move reel 2 one space up – now you have a lemon and an apple. Try to work logically, and record all the possible combinations in a table, starting like this:

How many different ways can the machine stop? Are you likely to win? Is it worth playing?

Reel 1 Reel 2

Lemon Lemon

Lemon Apple

Lemon

.

Maths Fruit Machine

Only 10 pence per play.

Match two apples to win 50 pence.

Cut out this window Cut out this window

Fruit Machine Mark Scheme

Level Assessment – what evidence is there? Tick

3 Describe the mathematics used

4 Explain ideas and thinking

5 Identify problem solving strategies used

6 Give a solution to the question

7 Explain how the problem was chunked into smaller tasks

8 Relate solution to the original context

2 Create their own problem and follow it through

3 Discuss the problem using mathematical language

4 Organise work and collect mathematical information

5 Check that results are reasonable

6 Justify the solution using symbols, words & diagrams

7 Clearly explain solutions in writing and in spoken language

8 Explore the effects of varying values and look for invariance

2 Use some symbols and diagrams

3 Identify and overcome difficulties

4 Try out own ideas

5 Draw own conclusions and explain reasoning

6 Make connections to different problems with similar structures

7 Refine or extend mathematics used giving reasons

8 Reflect on your own line of enquiry examine generalisations or solutions

What you have done well….

What you need to do to improve…

Level for this piece of homework…