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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. Theproject 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 eachinvestigation a student completes a poster or report. The work produced should be levelled and the students shouldhave 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 set Investigation Title Minimum Hours Due inWeek beginning Week beginning5th Sep 2011 Final scores 4 hours 26th Sep 20113rd Oct Ice cream 4 hours 4th Nov 201120117th Nov A piece of string 4 hours 28th Nov 201120115th Dec Jumping 4 hours 9th Jan 2012201116th Jan How many triangles? 4 hours 10th Feb 2012201220th Feb Polo Patterns 4 hours 12th Mar 2012201219th Mar Opposite Corners 4 hours 23rd April 2012201230th April Adds in Order 4 hours 21st May 2012201228th May Match Sticks 4 hours 25th June 201220122nd Jul Fruit Machine 4 hours 16th July 20122012
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Year 7 Homework Record Sheet Date set Investigation Level Target for improvement Week Title beginning Final scores5th Sep2011 Ice cream rd3 Oct2011 A piece of7th Nov string2011 Jumping5th Dec2011 How many16th Jan triangles?2012 Polo20th Feb Patterns2012 Opposite th19 Mar Corners2012 Adds in30th April order2012 Match Sticks th28 May2012 Fruit2nd Jul Machines2012
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Tackling investigationsWhat 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 theinvestigation. Remember your teachers at Queensbury are her to help, if you get stuck at any stage, come and ask one of the Maths teachers.
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Final ScoreWhen Spain played Belgium in the preliminary round of the mens hockey competition in the 2008Olympics, 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 dont miss any out?In the final of the mens 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?
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Final Score Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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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???????
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Ice Cream Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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A piece of StringYou have a piece of string 20cm long. 1) How many different rectangles can you make? Here is one 9cm 1cm 1cm 9cm (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.
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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?
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A piece of String Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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JumpingBen 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 didbefore.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?
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Jumping Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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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 trianglesyou 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 150triangles?Try and draw it to show if it or is not possible.
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How many triangles? Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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Polo PatternsWhen the black tiles surround white tiles this is known as a polopattern.You are a tile designer and you have been asked to design different polopatterns (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 cansurround as many white tiles as you like)?Investigate how the number of tiles in a polo pattern depends on the number ofwhite tiles.
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Polo Patterns Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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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 100The 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 56The products of the numbers in these opposite corners are54 x 66 = 3564 and64 x 56 = 3584The difference between these products is 3584 – 3564 = 20Task: Investigate the difference between the products of the numbers in the opposite cornersof any rectangles that can be drawn on a 100 square.
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Opposite Corners Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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Numbers in order like 7, 8, 9 are called CONSECUTIVE numbers. 4+5=9 12 = 3 + 4 + 6=1+ 517 = 8 + 9 2+317, 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?
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Adds in Order Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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Match SticksLook at the match stick shape below.How many match sticks do you expect to be in pattern 2? Pattern 2 Pattern 3 2 triangles 3 trianglesDraw 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 thereany left over?Think about different shapes you can make using matchsticks, investigate (asabove).
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Match Sticks Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions Fruit MachineIn this task you are going to design your own fruit machine.
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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 AppleThe only way to win on this machine is to get two apples. If you win you get 50 pence back. It costs 10pence 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 thefirst two reels of the machine. Start with lemons in both windows. Move reel 2 one space up – now youhave a lemon and an apple. Try to work logically, and record all the possible combinations in a table,starting like this: Reel 1 Reel 2 How many different ways can the machine stop? Are you likely to win? Lemon Lemon Is it worth playing? Lemon Apple Lemon
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. Maths Fruit Machine Cut out this window Cut out this window Only 10 pence per play. Match two apples to win 50 pence.
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Fruit Machine Mark SchemeLevel Assessment – what evidence is there? Tick What you have done well….3 Describe the mathematics used4 Explain ideas and thinking5 Identify problem solving strategies used6 Give a solution to the question7 Explain how the problem was chunked into smaller tasks8 Relate solution to the original context2 Create their own problem and follow it through3 Discuss the problem using mathematical language4 Organise work and collect mathematical information What you need to do to improve…5 Check that results are reasonable6 Justify the solution using symbols, words & diagrams7 Clearly explain solutions in writing and in spoken language8 Explore the effects of varying values and look for invariance2 Use some symbols and diagrams3 Identify and overcome difficulties4 Try out own ideas5 Draw own conclusions and explain reasoning6 Make connections to different problems with similar Level for this piece of homework… structures7 Refine or extend mathematics used giving reasons8 Reflect on your own line of enquiry examine generalisations or solutions
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