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Welcome!

This is the fourth in a series of teaching aids designed by teachers for teachers at level 6.The worksheets are designed to support the delivery of the National Curriculum in a variety ofteaching and learning styles. They are not designed to take the pedagogy away from the teacher.The worksheets are centred around the shown level, but spiral from the level below to the levelabove. Consult the National Numeracy Strategy for definitive National Curriculum levels.They can be used by parents with the support of the on-line help facility at www.10ticks.co.uk.

Contents and Teacher Notes.

Pages 3/4. Ratio.Cancelling down ratios. Cancelling down ratios in different units. Wordedquestions involving ratio.

Pages 5/6. Ratio Revision.Need some more practice ? Another sheet of questions. This can be used as ageneral revision sheet for GCSE candidates.

Pages 7/8. Menus.A slightly different approach to ratios. All questions are part of genuinerecipes. A good way of generating display work if pupil produce their ownmenus from recipes they may have used in school.

Pages 9/10. Golden Numbers.Practical ratio work. Starting with the Golden Rectangle and how to constructone of varying sizes. Links with the Fibonacci sequence and finishing byconstructing the Golden Section Spiral.

Pages 11/12. Proportion 1.Solve worded questions using the unitary method.

Pages 13/14. Value for Money.Finding best values for money with different items. When attempting the firstside it is best to use the unitary method. On the second, try to get pupils to"cancel" down to a common denominator, rather than all the way down to 1.

Pages 15/16. Proportion 2.This might be best done at a later date than the Proportion 1 sheet as the ideasare distanced. Rather than using the Unitary method now we are usingfractions/decimals to solve the worded questions.

Pages 17/18. Number Work Revision.Revision of some of the number work from level 5. This includes longmultiplication/division, LCM, HCF, Prime Numbers, powers and roots andestimation.

Pages 19/20. Missing Multiplications/Divisions.More number familiarity work without a calculator.

Page 21. Four in a Row (Estimation).A game using estimating skills.

Page 22. Hex-an Estimating Game.A game using estimating skills.

Page 23. Powers of 10 (Multiplication/Division).Graduated mental exercise multiplying and dividing by powers of 10.


Page 24. Number Work (Estimating).Multiplying and dividing by 2, 3 and 4 digit numbers and mentally working outan estimate.

Page 25. Cricket (Estimation).A game for two players using estimation.

Pages 26/27. Trial and Improvement.Solving, mainly linear equations, by trial and improvement. Sections A and Bare primarily for those pupils who struggle to solve these equations by theusually algebraic method. Section C is where the Trial and Improvementtechnique is really tested out.

Pages 28/29. Golf Practice Holes/Royal Idiotdale.An idea that came from a Brian Bolt book that practices Trial and Improvementtechniques. Pupils have to guess the answer inside the par. All guesses are to berecorded. Good wall display material. Get every pupil to make up one hole anddraw it. Put them together and have a whole class golf course wall display.

Pages 30. Glennsparrows.The second, harder Trial and Improvement golf course.

Pages 31/32. Compass and Ruler Constructions.Constructing a triangle given all three side lengths and bisecting an angle.

Pages 33/34. Nets.This sheet should be attempted by the majority of pupils without the aid ofpolydron. The focus is to be able to visualise the nets becoming solids. Torecap the worksheet you may wish that polydron be handed out and pupils spottheir own mistakes.

Pages 35/36. Construct Your Own Calendar.Construction of nets that can build up into a calendar.

Pages 37/40. Calendar Nets.More complicated nets (Square-based Pyramid, Glueless Hexagonal prism,dodecahedron and the Truncated tetrahedron). These can be photocopied ontocoloured card and made into calendars for the next year. They will have to beused in conjunction with the calendar sheets page. A good end of year activity.

Page 41. Santa’s Grotto.This puzzle originates from an Australian detergent manufacturer who used itas a sales gimmick. Here we have adapted it for Christmas. Use it with orwithout a calculator. Especially good to fill up the back of your ChristmasNews letter! Very quick to check if set as a competition.

Page 42. Christmas Investigations.Four Investigations with a seasonal twist.

Copyright in Worksheets. ©Fisher Educational Ltd. 2000.Copyright in the worksheets belongs to Fisher Educational Ltd. Each purchase of the worksheets represents alicence to use and reproduce the worksheets as set out in the Terms and conditions shown on the 10ticks website.

'10TICKS', and '10TICKS.co.uk' and/or other 10TICKS services referenced on this web site or on the Worksheetsare trademarks of Fisher Educational Ltd in the UK and/or other countries.

Details of copyright ownership in the clip art used in these worksheets:Copyright in the clip art used entirely in this pack is owned by Nova Development Corporation, California, USA.


Ratios.

A). Cancel down fully the following ratios.1). 6 : 4 2). 5 : 10 3). 12 : 9 4). 8 : 10 5). 6 : 86). 16 : 12 7). 10 : 25 8). 7 : 28 9). 20 : 8 10). 14 : 811). 9 : 15 12). 22 : 18 13). 9 : 21 14). 28 : 16 15). 15 : 3516). 24 : 18 17). 21 : 35 18). 12 : 30 19). 45 : 18 20). 32 : 6421). 24 : 66 22). 63 : 14 23). 63 : 27 24). 24 : 44 25). 96 : 2426). 200 : 500 27). 480 : 360 28). 360 : 540 29). 640 : 720 30). 220 : 32031). 2000:7000 32). 2100:7000 33). 3500:1500 34). 1400:4200 35). 9600:720036). 2 : 4 : 10 37). 4 : 8 :14 38). 6 : 12 : 15 39). 9 : 12 : 21 40). 8 : 12 : 2841). 10:20:25 42). 16:20:36 43). 7:28:77 44). 18:30:54 45). 33:44:7746). 28:35:56 47). 24:40:48 48). 21:35:77 49). 24:60:84 50). 36:63:81

B). Change the following into the same units, then cancel down the ratio.1). £1 : 50p 2). 3 Kg : 500 g 3). £1.40 : 60p 4). 2 l : 250 ml5). 120 cm : 2 m 6). 24 mm : 3 cm 7). 2 Kg : 400g 8). 45 cm : 3 m9). 4 m : 60 cm 10). 2 l : 150 ml 11). 25 mm : 6 cm 12). £4.32 : £1.8013). 3 Km : 800 m 14). 6 g : 750 mg 15). £2 : £1.50 : 50p 16). 2Kg:1Kg: 250g

17). 3.5 cm : 2.8 cm : 7 mm 18). £3.60 : £2.10 : 90p19). 7 Kg : 3.5 Kg : 350 g 20). 3.9 cm : 1.8 cm : 12 mm

C).1). This month there were 12 sunny days and 18 wet days.

Find the ratio of sunny days to wet days.2). In a bag of sweets 9 are red and 15 blue. Find the ratio of red to blue sweets.3). A bus has room for 30 sitting and 20 standing passengers.

Find the ratio of sitting to standing passengers.4). In a class are 14 girls and 16 boys. Find the ratio of boys to girls in the class.5). In a bag of marbles are 240 blue marbles and 300 red marbles.

Find the ratio of red to blue marbles.6). In a sandwich bar 120 ham, 30 egg and 10 chicken sandwiches are sold.

Find the ratio of ham to egg to chicken sandwiches sold.7). In a survey of cars 560 were British, 800 Japanese and 400 German.

Find the ratio of British to Japanese to German cars.8). In a small wood are 490 Beech trees, 840 Conifers and 70 Oak trees.

Find the ratio of Beech Trees to Conifers to Oak trees in the wood.9). Whilst bird watching 360 Sparrows were spotted, 1080 Thrushes and 1170 Seagulls.

Find the ratio of Sparrows to Thrushes to Seagulls spotted on the watch.10). In School 560 supported Bolton, 490 Manchester United and 140 Bury.

Find the ratio of Bolton to Manchester United to Bury supporters in school.

D). Divide1). £40 in the ratio 3 : 2. 2). £35 in the ratio 4 : 1. 3). £28 in the ratio 5 : 2.4). £48 in the ratio 3 : 1. 5). £54 in the ratio 5 : 1. 6). £35 in the ratio 4 : 3.7). £16 in the ratio 5 : 3. 8). £49 in the ratio 5 : 2. 9). £99 in the ratio 7 : 2.10). £72 in the ratio 5 : 4. 11). £60 in the ratio 7 : 3. 12). £28 in the ratio 3 : 4.13). £42 in the ratio 2 : 5. 14). £65 in the ratio 2 : 3. 15). £77 in the ratio 6 : 5.16). £200 in the ratio 3 : 7. 17). £1040 in the ratio 5 : 8.18). £1540 in the ratio 9 : 5.

19). £30 in the ratio 2 : 2 : 1. 20). £84 in the ratio 3 : 3 : 1.21). £64 in the ratio 5 : 2 : 1. 22). £30 in the ratio 3 : 2 : 1.23). £27 in the ratio 5 : 3 : 1. 24). £140 in the ratio 6 : 3 : 1.25). £990 in the ratio 7 : 2 : 2. 26). £240 in the ratio 5 : 3 : 2.27). £240 in the ratio 5 : 4 : 3. 28). £900 in the ratio 5 : 2 : 2.29). £1320 in the ratio 7 : 4 : 1. 30). £2100 in the ratio 9 : 3 : 2.


E).1). A school collected £272 for charity. It was decided to divide the money between

Dr. Barnados and the RSPCA in the ratio 3 : 5. How much did each charity receive ?2). Pocket money is split between Pete, Alan and Helen in the ratio 2 : 3 : 4. Dad pays out £36,

how much does each person get ?3). £54 is split between Arnie, Barney and Clancey in the ratio 3 : 4: 5. How much does each

one receive ?4). Mr. Allen, Mr. Book and Mr. Collins own 4, 5, and 6 parts of a business respectively. The

business makes £570 profit in a week. How much does each man get ?5). The sides of a triangle are in the ratio 2 : 3 : 5. The perimeter is 35 cm. Find the length of

each side.6). Concrete for foundations is made by mixing cement, sand and aggregate in the ratio

1 : 3 : 6. They need 65 cubic feet of concrete. How many cubic feet of cement, sand andaggregate should they use ?

7). John goes to cookery classes and learns the following:a). To make buttercream you need fat to icing sugar in the ratio 1: 2. He wants to make

276 g of buttercream. How much of each ingredient does he need ?b). To make suet you need fat to flour in the ratio 1: 3. He wants to make 520 g of suet.

How much of each ingredient does he need ?c). To make bread you need yeast to flour in the ratio 1: 60. He wants to make 1220 g

of bread. How much of each ingredient does he need ?d). To make puff pastry you need fat to flour in the ratio 3: 4. He wants to make 385 g

of puff pastry. How much of each ingredient does he need ?e). To make choux pastry you need butter to flour in the ratio 3: 5. He wants to make

760 g of choux pastry. How much of each ingredient does he need ?8). £52.50 is split between Alex, Beth and Chloe in the ratio 3 : 5 : 7. How much does each

one receive ?

F).1). To make suet you need fat to flour in the ratio 1: 3. Jane has 180 g of flour. How much fat

does she need to make the suet ?2). General purpose concrete is made by mixing cement, sand and aggregate in the ratio

1 : 2 : 4. Harry needs some concrete to repair a garden wall. He uses 4 buckets of cement.How many buckets of sand and aggregate should he use ?

3). Money is split between Alex, Beth and Chloe in the ratio 2 : 5 : 9. Beth gets £35. Howmuch do the others get ?

4). Mr. Happy has an orchard of apple and pear trees. The trees are planted ina ratio of 3 : 2. He has 30 pear trees.a). How many apple trees are there ?b). How many trees are there altogether in his orchard ?

5). The sides of a triangle are in the ratio 2 : 4 : 5. The middle sized side is 28 cm.a). Find the length of the other two sides.b). Find the perimeter of the triangle.

6). Pocket money is split between Paula, Alan and Henry in the ratio 7 : 3 : 2. Alan gets £3.75.a). How much do Paula and Henry get ?b). How much pocket money does poor old Dad have to pay out altogether ?

7). Mr. Neat, Mr. Tidy and Mr. Perfect own 2, 5, and 6 parts of a business respectively. Theyshare any profits in that ratio. One week Mr. Tidy makes £327 from his share of the profits.a). How much will Mr. Neat and Mr. Perfect make that week ?b). How much profit has the business made that week ?

8). Mr. Jubilant farms cabbages, carrots and cucumbers. They are planted inthe ratio of 4 : 7 : 15. He plants 1575 carrots.a). How many cabbages and cucumbers does he plant ?b). How many vegetables does he grow altogether ?


Ratio Revision Questions.

1). Divide £90 in the ratio 3 : 7.

2). A school collected £180 for charity. It was decided to divide the moneybetween Dr. Barnados and the RSPCA in the ratio 2 : 3. How much did each charity receive ?

3). Pocket money is split between Pete, Alan and Helen in the ratio 4 : 5 : 6. Dad pays out £60,how much does each person get ?

4). £60 is split between Arnie, Barney and Clancey in the ratio 3 : 4: 5. How much does eachone receive ?

5). Mr. Allen, Mr. Book and Mr. Collins own 4, 5, and 6 parts of a business respectively. Thebusiness makes £120 profit in a week. How much does each man get ?

6). The number of pages in a magazine was increased from 48 to 80. If the price, which was75p, is increased in the same ratio, what will the new price be ?

7). A map scale is 1 : 1000. If on the map we travel 4 cm, how far have we actually walked ?

8). The scale on a map is 1 : 2500. Apond is represented on the map as a shape whoseperimeter is 12 cm. Find the actual perimeter of the pond in Kilometres.

9). On a map, scale 1 : 25000, the length of a tunnel is 4.6 cm. What is the tunnels actuallength ?

10). The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter is 36 cm. Find the length ofeach side.

11). Three men form a syndicate for the lottery. Their stakes one week are £4.50, £3.60, £1.80.Express these as a ratio in its simplest form.

12). Anne is twice as old as Bill, who is three times as old as Catherine. Find the ratio of theirages.

13). Ann earns half as much as Beth, Beth earns three times as much as Chris. Find the ratio oftheir earnings.

14). Divide £5 between three friends in the ratio 2 : 3 : 5.

15). Three men invested £2000, £3000 and £4000 in a business. The profit each receives isproportional to the money invested. How much does each receive when the total profits are £4500 ?

16). A sum of money is divided between three women A, B, and C in the ratio 2 : 3 : 5. If Breceives £2.40 less than C, how much does each receive ?

17). In a charity swim, Jim swam 1200 m and Sue 2 Km. What is the ratio ofJim's distance to Sue's ? Give the ratio in its simplest form.


18). A special order for 1200 flowers is for roses and tulips. There are 480tulips in the order. What is the ratio of roses to tulips in its simplest form ?

19). The ages of a mother and daughter are in the ratio 8 : 3. If the mother is48 years old, how old is the daughter ?

20). A paint was made by mixing 12 tins of white paint with 9 tins of green paint.How many tins of white paint should be mixed with 15 tins of green paint ?

21). Two roads have signs warning of a steep hill ahead. One says "1 : 8" another says "12%".Which is the steeper hill ? Show your working out.

22). Which is the larger ratio 3 : 7 or 4 : 9 ?

23). Concrete is made by mixing cement, sand and aggregate in different proportions byvolume. Here are some common ratios for concrete in the order cement : sand : aggregate.For foundations 1 : 3 : 6 and for general purpose 1 : 2 : 4.a). Keith makes some general purpose concrete to repair a garage wall. He uses 6

buckets of cement. How many buckets of sand and aggregate should he use ?b). The Colbys are laying the foundations of a new conservatory. They use 48 cubic feet

of sand. How many cubic feet of cement and aggregate should they use ?c). Jenny needs a new kind of concrete for a pathway. She uses 8 barrow loads of

cement, 20 barrow loads of sand and 36 barrow loads of aggregate. What is the ratiofor this new type of concrete in its simplest terms ?

24). Mr. Happy has an orchard of apple and pear trees. The trees are planted in a ratioof 3 : 2. He has 60 trees altogether. How many of the trees are pear trees ?

25). To make Honey Pot Creams use two parts whiskey to three parts clear honey totwenty parts double cream.a). If 825 ml of ingredients are used in total, how much of each ingredient is used ?b). If the cream comes in a 500 ml carton and it is all used, how much

i). whiskey, ii). clear honey is used ?c). 315 ml of clear honey is used. How much

i). whiskey ii). double cream is used ?

26). A model farm is made using a scale of 1 : 24.a). The height of a model cow is 5 cm. What is the height of the real cow ?b). A real horse is 168 cm long. How long is the model horse ?

27). A green paint is mixed from blue and yellow paint in the ratio 3 : 5. How much of eachcolour is needed to make 80 litres of this green paint ?

28). Three workers, A, B and C hold 120, 200 and 40 shares respectively in their company.A total dividend of £3600 is paid to the three workers in the same ratio as their shares.How much does each worker get ?

29). In order to dilute a bottle of orange squash, it is recommended to mix squashto water in the ratio 2 : 5.a). How much squash should be put in a glass that holds 560 ml ?b). A large jug of juice is to be made up, using a full bottle of orange squash

that holds 0.8 litres. How much drink can be made up from this bottle ?


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Seafood ScallopsSeafood ScallopsSeafood ScallopsSeafood ScallopsSeafood Scallops. One part haddock to two parts peeled potatoes are neededin this recipe. The total weight of these ingredients is 525 g.Find the weight of a). haddock needed, b). peeled potatoes needed.

Eggs with Tarragon CreamEggs with Tarragon CreamEggs with Tarragon CreamEggs with Tarragon CreamEggs with Tarragon Cream. Twelve parts double cream to one part freshly chopped tarragon areneeded in this recipe. The total needed of these ingredients is 130 ml.Find the amount of a). cream needed, b). tarragon needed.

Stilton BitesStilton BitesStilton BitesStilton BitesStilton Bites. Two parts butter to seven parts blue Stilton are needed in this recipe. The totalweight of these ingredients is 225 g.Find the weight of a). butter needed, b). blue Stilton needed.

Prawns with Curry MayonnaisePrawns with Curry MayonnaisePrawns with Curry MayonnaisePrawns with Curry MayonnaisePrawns with Curry Mayonnaise. One part apricot jam to two parts curry powder to twenty partssingle cream are needed in this recipe. The total weight of these ingredients is 345 g.Find the weight of the a). jam, b). curry powder, c). cream.

Haddock & Shrimp GratinHaddock & Shrimp GratinHaddock & Shrimp GratinHaddock & Shrimp GratinHaddock & Shrimp Gratin. One part butter to three parts mature Cheddar to eighteen partshaddock are needed in this recipe. The total weight of these ingredients is 550 g.Find the weight of the a). butter, b). Cheddar , c). haddock.

GoulashGoulashGoulashGoulashGoulash. One part flour to fourteen parts stewing steak are needed in this recipe.The total weight of these ingredients is 750 g.Find the weight of a). flour needed, b). stewing steak needed.

Creamed MushroomsCreamed MushroomsCreamed MushroomsCreamed MushroomsCreamed Mushrooms. Two parts flour to three parts chopped onion are needed in this recipe.The total weight of these ingredients is 90 g.Find the weight of a). flour needed, b). chopped onion needed.

Cauliflower CheeseCauliflower CheeseCauliflower CheeseCauliflower CheeseCauliflower Cheese. Three parts flour to twenty parts milk are needed in this recipe. The totalamount needed of these ingredients is 345 ml.Find the amount of a). flour needed, b). milk needed.

Turkey Escalopes with Hazelnut CreamTurkey Escalopes with Hazelnut CreamTurkey Escalopes with Hazelnut CreamTurkey Escalopes with Hazelnut CreamTurkey Escalopes with Hazelnut Cream. One part Hazelnuts to two parts butter to eighteen partsturkey fillet are needed in this recipe. The total weight of these ingredients is 630 g.Find the weight of the a). hazelnuts, b). butter, c). turkey fillet.

Lamb & Spinach au GratinLamb & Spinach au GratinLamb & Spinach au GratinLamb & Spinach au GratinLamb & Spinach au Gratin. Eleven parts lasagne to twenty eight parts tomato to thirty six partsspinach are needed in this recipe. The total weight of these ingredients is 3375 g.Find the weight of the a). lasagne, b). tomato, c). spinach.

Gooseberry CharlotteGooseberry CharlotteGooseberry CharlotteGooseberry CharlotteGooseberry Charlotte. One part castor sugar to six parts gooseberries are needed in this recipe.The total weight of these ingredients is 525 g.Find the weight of a). castor sugar needed, b). gooseberries needed.

BlancmangeBlancmangeBlancmangeBlancmangeBlancmange. Fifteen parts cornflour to one hundred and forty two parts milk are needed inthis recipe. The total needed of these ingredients is 628 ml.Find the amount of a). cornflour needed, b). milk needed.

Buttered SconesButtered SconesButtered SconesButtered SconesButtered Scones. Four parts flour to one part fat are needed in this recipe. The total weight ofthese ingredients is 725 g.Find the weight of a). flour needed, b). fat needed.

Honey MousseHoney MousseHoney MousseHoney MousseHoney Mousse. One part gelatine to nine parts lemon juice to thirty parts whipping cream areneeded in this recipe. The total weight of these ingredients is 480 ml.

Find the amount of a). gelatine b). lemon juice c). cream needed.

Aperitifs.

Main Courses.

Sweets.


Vegetable PâtéVegetable PâtéVegetable PâtéVegetable PâtéVegetable Pâté. Two parts lemon rind to three parts lemon juice to eighteen parts doublecream are needed in this recipe. The amount of cream needed is 90 ml.Find the amount of a). lemon rind needed, b). lemon juice needed.

Curried EggsCurried EggsCurried EggsCurried EggsCurried Eggs. One part flour to two parts sultanas to nine parts long grain rice are needed inthis recipe. The weight of sultanas used is 64 g.

Find the weight of a). flour needed, b). long grain rice needed,c). all these ingredients.

Lettuce SoupLettuce SoupLettuce SoupLettuce SoupLettuce Soup. Nine parts spring onions to fourteen parts lettuce to twenty four parts chickenstock are needed in this recipe. The weight of lettuce used is 420 g.

Find the weight of a). spring onions needed, b). chicken stock needed,c). all these ingredients.

Souffled Cheese TartletsSouffled Cheese TartletsSouffled Cheese TartletsSouffled Cheese TartletsSouffled Cheese Tartlets. Thirteen parts butter to fifteen parts Cheddar cheese to twenty three partsflour are needed in this recipe. The weight of butter used is 156 g.

Find the weight of a). cheese needed, b). flour needed,c). all these ingredients.

Aperitifs.

Main Courses.

Harvest MackerelHarvest MackerelHarvest MackerelHarvest MackerelHarvest Mackerel. One part breadcrumbs to two parts Cheddar cheese to three parts natural yogurtare needed in this recipe. The weight of Cheddar cheese used is 70 g.

Find the weight of a). breadcrumbs needed, b). natural yogurt needed,c). all these ingredients.

Curried Bacon HamCurried Bacon HamCurried Bacon HamCurried Bacon HamCurried Bacon Ham. One part butter to five parts celery heart to seven parts shortcrust pastry areneeded in this recipe. The weight of the celery heart used is 160 g.

Find the weight of a). butter needed, b). shortcrust pastry needed,c). all these ingredients.

Egg FricasséeEgg FricasséeEgg FricasséeEgg FricasséeEgg Fricassée. One part dried tarragon to fifty seven parts soured cream to eighty parts milkare needed in this recipe. The amount of milk used is 400 ml.

Find the amount of a). dried tarragon needed, b). soured cream needed,c). space these ingedients take up, in ml.

Italian LiverItalian LiverItalian LiverItalian LiverItalian Liver. Three parts beef stock to seven parts lamb liver to nine parts onion are neededin this recipe. The weight of liver used is 280 g.

Find the weight of a). beef stock needed, b). onion needed,c). all these ingredients.

Fruit CrumbleFruit CrumbleFruit CrumbleFruit CrumbleFruit Crumble. One part butter to two parts castor sugar to nine parts mixed fruit are needed inthis recipe. The weight of castor sugar used is 120 g.

Find the weight of a). butter needed, b). mixed fruit needed,c). all these ingredients.

Honey Pot CreamsHoney Pot CreamsHoney Pot CreamsHoney Pot CreamsHoney Pot Creams. Two parts whiskey to three parts clear honey to twenty parts double creamare needed in this recipe. The amount of clear honey used is 45 ml.

Find the amount of a). whiskey needed, b). double cream needed,c). space the combined ingredients take up, in ml.

Bon Appetite!

Sweets.

Rat Ios RestaurantRat Ios RestaurantRat Ios RestaurantRat Ios RestaurantRat Ios Restaurant


Golden Numbers.The Golden Rectangle.

Look at the 4 rectangles below. If these were mirrors which would you hang on your wall?

Do a quick class survey to see which rectangle is the most popular.

Most people will chose rectangle C).. This is the Golden Rectangle.The length and the width of the Golden Rectangle are in a special ratio 1.62 : 1 .Measure the length of these 4 rectangles. Which one is nearest 1.62 ?

width

Follow these instructions to construct your own Golden rectangle.

1). Draw a square of any size. 2). Mark on it the midpoint of the base, X.

3). Extend the baseline. 4). Open up your compass. Put your compasspoint on X and pencil point on A. Draw an arc to the baseline.

5). Construct a perpendicular from Y and finish off your rectangle.

Repeat this for 3 different starting squares.For each one of your constructions, find the ratio length ÷ width.For 10 everyday rectangles (books, mirrors etc.) find the ratio length ÷ width.Are any of them Golden Rectangles ?

A).B).

C).

D).

X

X

A

Y


The Golden Ratio.

The ratio we have used is called the Golden Ratio. TheGreeks developed many patterns and designs using this ratio.It appears on work in circles, pentagons and decagons, but itis the Golden Rectangle that is the most visually satisfying ofall the shapes. Much thought has gone in to why this ratio isso appealing. Pythagoras thought it might be the basis for theproportions of the human body. He was proved right.The height of a man, to his navel height was about 1.62.This picture, “Study of Human Proportions”, attributed toLeonardo da Vinci, was drawn in accordance with

mathematical laws.Find some other parts of the body that are in theGolden Ratio.The Parthenon, an ancient temple, on theAcropolis in Athens was built with the GoldenRectangle proportions.

The Golden Ratio even appears in the Fibonacci sequence. The ratio of any consecutive numbersin the sequence (after 3) is approximately 1.62.Work out the first 10 of these ratios to 2 d.p. for the Fibonacci sequence (after 3).

The Golden Section Spiral.

A Golden Rectangle can be divided into a square and another similar Golden Rectangle. Thisprocess can be repeated to create a Golden Section Spiral. This is an approximation to anequiangular spiral found in seashells such as the nautilus shell.

Follow the instructions to construct your own Golden Section Spiral. You will need alarge piece of paper, A4 or bigger. If you use A4, 28cm x 17.3 cm is an ideal rectangle.

1). Start with a Golden Rectangle.Construct a square using the width as one side.(You have a square and a new Golden Rectangle!)Open up your compass.Put the point on X.Put your pencil point on Y.Draw the arc shown.

2). Repeat these instructions for the new smaller Golden Rectangle.Keep repeating the instructions for each subsequent Golden Rectangle.How many times can you do it ?

Now colour your spiral.

XY


Proportion 1.

Imagine that you have some paint for painting fences.With twice as much paint you could paint twice the area.

With three times as much you could paint three times the area.And so on.

The area you paint is directly proportional to the amount of paint you have.

We can use direct proportion to solve problems.

E.g. In 8 hours a man can earn £40. How much can he earn in 3 hours ?

In 1 hour he earns £40 = £5 , therefore in 3 hours he earns 3 x £5 = £15 . 8

This method is called the Unitary Method because we find 1 (unit) of somethingfirst to solve the question.

Use the Unitary Method to solve the following.

A. 1). Jim walks 3 miles in 51 minutes. How long would it take him to walk 2 miles ?2). In 7 hours Culsoom can earn £52.50. How much can she earn in 4 hours ?3). A car uses 9 litres of petrol to travel 126 km.

How far will it travel on 5 litres of petrol ?4). 13 exercise books weigh 442 grams. What is the weight of 10 of these books ?5). 14 pencils cost £3.36. How much would 8 pencils cost ?6). In 7 hours of steady driving Gill covered 294 miles. How far did she go in 3 hours ?7). £22 can be exchanged for 242 French Francs. What can £17 be exchanged for ?8). In 24 hours the earth turns through 360 degrees.

What angle does it turn through in 20 hours ?9). A watch loses 90 seconds in 15 hours. How much will it lose in 7 hours?10). In 14 minutes a plane climbs 31500 feet, at constant speed.

How far had it climbed after 9 minutes ?11). 9 packets of tea cost £6.57. How much do 8 packets of tea cost ?12). A train travelling at a constant speed covers 319 m in 29 seconds.

How far did it cover in 18 seconds ?13). 15 boxes of cereal weigh 5 Kg 625 g. What will 4 boxes of cereal weigh ?14). A bike at constant speed covers 77 km in 5.5 hours. How far did it cover in 3 hours ?15). 24 cm2 of a map represent a lake of 600 hectares.

How many hectares will an area of 14 cm2 represent on the map ?16). Shirley buys 240 Bighouse shares for £297.60.

How much would 195 Bighouse shares cost ?17). Brian buys 32 bottles of Soy Sauce, in total he has 4 l 800 ml of Soy Sauce.

How much Soy Sauce would he have if he’d bought 23 bottles ?18). £450 can be exchanged for $630. How many dollars would you get for £290 ?19). In 328 days the moon orbits the earth 12 times.

How many times will it orbit the earth in 246 days ?20). A bike has a faulty odometer. It records 56 km for a journey of 40 km.

On another journey the real distance is 28 Km, what will the odometer read ?


B. 1). Mercury orbits the Sun 4 times in 352 days.a). How many days will it take to orbit the Sun 7 times ?b). How many orbits of the Sun has Mercury completed in 264 days ?

2). 75 g of cornflakes provide 270 calories.a). How many calories are in 120 g of cornflakes ?b). There are 360 calories in a portion of cornflakes. What weight is the portion ?

3). 90 Maths text books cost £1125.a). How much will 74 Maths text books cost ?b). If £687.50 is spent on maths text books how many have been bought ?

4). 200g of Cheddar Cheese contains 51 g of protein.a). How much protein is contained in 460 g of Cheddar Cheese ?b). If you want 40.8 g of protein, how much Cheddar Cheese must you eat ?

5). Peter earns £78 for 12 hours work.a). How much will he earn if he works 17 hours ?b). Peter earns £61.75, for how long has he worked ?

6). At a bank Jane changes £50 for 13750 Pesetas.a). How many Pesetas would she get for £80 at this rate ?b). How much is 26400 Peseta worth in Pounds ?

7). 200 g of bacon provides 950 calories.a). How many calories are in 340 g of bacon ?b). A slice of bacon provides 285 calories. What is the weight of the slice of bacon ?

8). A car drives steadily for 9 hours covering 342 miles.a). How far had it travelled after 7 hours ?b). When the car had covered 133 miles for how long had it been travelling ?

9). A front lawn of area 40 m2 cost £188 to turf.a). How much would it cost to turf a lawn of area 65 m2 ?b). Another lawn cost £441.80 to turf, what was the area of the lawn ?

10). Pluto orbits the Sun 6 times in 1491 years.a). How many years will it take to orbit the Sun 5 times ?b). How many orbits of the Sun has Pluto completed in 3479 years ?

11). Jean buys 560 PH Smith shares for £3774.40.a). How much would 800 PH Smith shares cost ?b). Harry spends £2628.60 on PH Smith shares. How many has he bought ?

12). A watch gains 2 minutes in 12 days.a). If the watch gains 4 minutes 30 seconds, for how long has it been working ?b). How long will it gain in 14 days (mins and sec)?

13). Sajid’s bicycle wheel turns 45 times exactly when he cycles 216 metres.a). If his wheel turns round exactly 84 times, how far has he moved ?b). He travels 1.0272 km. How many times has the wheel fully rotated ?

14). To type a 32 page document Peter took 7 hours 28 minutes.a). At this rate how long would it take him to type a 60 page document ?b). Peter was typing for 4 hours 26 minutes, how many pages would you expect him to

have completed ?15). Some of the ingredients for a recipe to make 6 biscuits are 300 g of flour,

240 g of sugar and 120 g of margarine.a). How much of each of these ingredients will you need to make

i). 4 biscuits, ii). 14 biscuits, iii). 35 biscuits ?b). The total weight of flour, sugar and margarine is 1.32 Kg.

i). If I want to make the maximum number of biscuits howmuch of each ingredient do I need ?

ii). How many biscuits will this make in total ?


Value For Money (Unitary Method).Which of the following offer better value for money?

Show all your working.

1). 2). 3).

4). 5). 6).

7). 200 g of coffee at £ 2.40 8). 720 ml of beer at 98p 9). 200 g of butter at 86p75 g of coffee at £1.10 440 ml of beer at 62p 65 g of butter at 24p

10). 5 Kg of fertiliser at £2.40 11). 38 m of rope at £16.40 12). 20 Kg of potatoes at £8.402 Kg of fertiliser at £1.05 50 m of rope at £21.50 9 Kg of potatoes at £4.40

13). 2 Kg of sugar at 54p 14). 18 bananas at £4.30 15). 50 ml of toothpaste at 40p1.6 Kg of sugar at 45p 13 bananas at £2.70 74 ml of toothpaste at 57p

16). 150g box of sweets at 65p 17). 410g of peaches at 35p 18). 340g of marmalade at 29p146g box of sweets at 69p 822g of peaches at 65p 454g of marmalade at 39p

19). 2 litres of conditioner at 84p 20). 1 Kg of butter at 98p 21). 3 litres of pop at 90p700 ml of conditioner at 40p 750 g of butter at 68p 440 ml of pop at 14p

22). 50 ml of toothpaste at £1.05 23). 60 teabags at £1.63 24). 8 bananas at £1.0535 ml of toothpaste at 75p 42 teabags at 87p 6 bananas at 86p

25). 1.3m leather belt at £4.20 26). 200 ml juice at 19p 27). 500ml of paint at £2.3590 cm leather belt at £3.42 1.1 litre juice at 87p 1.1 litre of paint at £4.75

28). 340g of muesli at 52p 29). 1.2Kg crispies at £2.11 30). 9 m of Kitchen foil at 89p680g of muesli at 94p 400g crispies at 76p 4 m of Kitchen foil at 50p2 Kg of muesli at £2.18 150g crispies at 34p 85cm of Kitchen foil at 8p

350 ml80p

225 ml58p

450 g95p

215 g50p

1000 ml60p

440 ml35p

5 litres£3.40

2 litres£1.60

70 g34p

15 g6p

95 metres£7.40

80 metres£6.90


Value For Money.Which of the following offer better value for money?

Show all your working.

1). 2). 3).

4). 5). 6).

7). 200 g of coffee at £ 2.40 8). 700 ml of beer at 88p 9). 210 g of butter at 32p600 g of coffee at £7.10 350 ml of beer at 50p 630 g of butter at 98p

10). 8 Kg of fertiliser at £4.40 11). 12 m of rope at £ 6.00 12). 20 Kg of potatoes at £1.302 Kg of fertiliser at £1.05 60 m of rope at £31.50 80 Kg of potatoes at £5.05

13). 300g of sugar at 64p 14). 40 bananas at £2.65 15). 50 ml of toothpaste at 40p200g of sugar at 46p 30 bananas at £2.10 70 ml of toothpaste at 57p

16). 500g box of sweets at 70p 17). 400g of peaches at 20p 18). 30g of marmalade at 56p600g box of sweets at 82p 900g of peaches at 54p 70g of marmalade at 96p

19). 250ml of conditioner at 80p 20). 150g of butter at 23p 21). 350ml of pop at 34p200ml of conditioner at 68p 550 g of butter at 99p 450ml of pop at 44p

22). 80 ml of toothpaste at £1.15 23). 60 teabags at £1.63 24). 30 bananas at £1.3560 ml of toothpaste at 75p 40 teabags at 97p 20 bananas at 88p

25). 1.2m leather belt at £4.20 26). 200 ml juice at 24p 27). 500ml of paint at £2.5580 cm leather belt at £2.92 1.1 litre juice at £1.12 1.3 litre of paint at £6.75

28). 500g of muesli at 42p 29). 1.2Kg apples at £3.89 30). 2.3m of Tinfoil at 89p600g of muesli at 60p 700g apples at £2.14 4m of Tinfoil at £1.362 Kg of muesli at £1.38 50g apples at 14p 80cm of Tinfoil at 35p

400g90p

200 g40p

1000ml£1.90

500ml£1.00

600 ml80p

300 ml50p

800 ml£4.40 200 ml

£1.20

750 m65p

150 m22p

600 g70p

200 g32p


Proportion 2.

A. For each of the following questions give the proportion stated asa). a fraction, b). a decimal, c). a percentage.

1). The school drinks machine holds 250 cans when full, of these 80 are cola.What proportion of the cans in the drinks machine is cola ?

2). In 800 games of squash Khalid has only lost 204 games.What proportion of games played has Khalid lost ?

3). A 900 g portion of Fish Cakes contains 500 g of potato.What proportion of Fish Cakes is potato ?

4). At a football match 36400 people attended. 25480 were Home fans.What proportion was Away fans ?

5). A farmer has 600 hectares of land. 12 hectares are woods the rest farming land.What proportion of the land is farming land ?

6). A biscuit barrel contains 16 Chocolate Chip Cookies and 12 Digestives.What proportion of the biscuits is Chocolate Chip Cookies ?

7). Dad hands out pocket money to John and Joan. John gets £1.40 and Joan gets £1.80.What proportion of the pocket money that Dad hands out does Joan receive ?

8). In a bag of marbles there are 36 blue marbles and 52 red marbles.What proportion of the marbles in the bag is red ?

9). Betty makes orange squash out of 24 ml of concentrate and 120 ml of water.What proportion of the orange squash is water ?

10). In a school survey 24 wanted a snack bar, 32 didn’t want a snack bar and 4 didn’t know.What proportion of those asked wanted a snack bar ?

B.1). In a fish pond there are 9 green fish out of 36 fish in total.

a). What proportion of the fish is green ?b). In a bigger pond the proportion of fish is the same. There are 92 fish in the

bigger pond. How many green fish are there ?2). The Year 10 netball team played 18 matches last year and won 12 of them.

a). What proportion of matches did they win ?b). This year they won the same proportion of matches. They played 24 matches.

How many did they win ?3). In a class of 32 pupils 20 are girls.

a). What proportion of the class is girls ?b). The school has the same proportion of girls in the whole school as in this class.

There are 928 pupils in the school. How many girls are there ?4). To make purple paint you mix 2 parts red to 7 parts blue paint.

a). What proportion of the purple paint is red ?b). Sue needs to make 31.5 litres of purple paint. How much blue paint will she need ?

5). Dad gives out £8 pocket money in total. Jenny gets £3.60.a). What proportion of the pocket money does Jenny receive ?b). Dad wins £52 on the national lottery and gives it to his children in the same

proportion as the pocket money. How much will Jenny get ?6). Billy gets a packet of chips containing 34 chips. He gives his girlfriend 12 chips.

a). What proportion of the chips does he keep for himself ?b). In the school canteen the next day he gets a plate of rice. He counts the grains!

He has 595 grains of rice. He gives the same proportion to his girlfriend as he did thechips. How many grains of rice does he keep ?


7). In Year 8 there are 96 boys and 84 girls.a). What proportion of Year 8 are girls ?b). Class 7C have the same proportion of girls to boys as Year 8.

There are 30 in the class. How many of the class are girls ?8). A farmer only keeps sheep and goats. He has 92 sheep and 28 goats.

a). What proportion of his animals is goats ?b). He buys a new farm and again only wants sheep and goats in the same

proportion as at his old farm. He has 510 animals. How many goats are there ?9). Last season the football team scored 84 goals, 60 by the strikers.

a). What proportion of the goals was not scored by strikers ?b). This season the goals have been scored in the same proportion.

63 goals have been scored. How many have the strikers scored ?10). In a full football stadium there are 32000 Home supporters and 4000 Away supporters.

a). What proportion of the crowd is Away supporters ?b). The capacity of the ground is raised to 45000. If the proportion of Home and Away

supporters is to stay the same how many Home supporters will there be ?C.1). To make orange paint you mix 13 parts yellow to 7 parts red.

a). What proportion of the orange paint is red paint ?b). Dan has to mix up 90 litres of orange paint. How much red paint does he need ?c). Bill makes orange paint. He uses 451/

2 litres of red paint.

How much orange paint has he made in total ?2). It takes 1.25 kg of damsons to make 3.25 kg of damson jam.

a). What proportion of damson jam is damsons ?b). Ted makes 11.7 kg of damson jam. What weight of damsons does he need ?c). Jenny has 2.4 kg of damsons and uses them all to make jam.

What weight of jam can she make ?3). In a survey of cars passing the school 36 of the 84 cars were red.

a). What proportion of the cars in the survey were not red ?b). The survey was repeated the next day and unusually exactly the same proportions

were found. If 126 cars passed in this survey how many were red ?c). Over the week the survey was repeated everyday and the totals put together.

Oddly the same proportions were found as for the first day. The total number of redcars for the week was 252. What was the total number of cars surveyed ?

4). In September 18 days were rainy.a). What proportion of the days in September weren’t rainy ?b). The weather pattern for the next 65 days was in the same proportion as for September.

How many rainy days were there in this period of time.c). Sarah looks back at a period of time for the previous year and finds exactly the same

patterns and proportions. In this period of time there were 36 rainy days.How long does this period of time last for ?

5). In Year 9 84 pupils eat a school dinner and 126 don’t eat a school dinner.a). What proportion of Year 9 eats a school dinner ?b). The same proportion for the whole school as Year 9 eat school dinners.

If there are 1135 pupils in the school how many don’t eat school dinner ?c). The School Dinner Service find this proportion is the same for the whole Borough.

22040 children eat a school dinner in the Borough.How many school children are there in the Borough ?

6). When Mike and June go out for a meal they always pay the bill in the same proportion.a). On Monday Mike pays £26.15 and June pays £10.46. What proportion does June pay ?b). On Tuesday the meal costs £65.66. How much do they each pay ?c). On Wednesday Mike pays £19.65 towards his share of the meal. How much

i). was the meal in total, ii). did June pay ?


Number Work Revision.

A. Work out

1). 13 x 11 2). 17 x 22 3). 14 x 29 4). 38 x 185). 496 ÷ 16 6). 378 ÷ 21 7). 512 ÷ 32 8). 665 ÷ 199). 19 x 33 10). 37 x 25 11). 43 x 14 12). 56 x 2813). 792 ÷ 24 14). 888 ÷ 37 15). 493 ÷ 29 16). 816 ÷ 3417). 72 x 48 18). 39 x 64 19). 58 x 87 20). 63 x 4921). 1512 ÷ 42 22). 2646 ÷ 63 23). 2146 ÷ 37 24). 2538 ÷ 5425). 5112 ÷ 72 26). 4067 ÷ 83 27). 6018 ÷ 59 28). 11232 ÷ 96

B. For each of the following pairs of numbers finda). the sum, b). the difference, c). the product.

1). 4, 7 2). 9, 3 3). 19, 6 4). 25, 75). 32, 9 6). 56, 4 7). 93, 6 8). 8, 1049). 231, 7 10). 423, 6 11). 9, 1723 12). 8, 5632413). 16, 14 14). 24, 12 15). 38, 16 16). 53, 2417). 43, 17 18). 85, 29 19). 94, 32 20). 96, 4821). 136, 24 22). 193, 74 23). 234, 57 24). 63, 39425). 563, 72 26). 974, 57 27). 96, 1472 28). 3592, 84

C. 1). Give the exact definition of a Prime number.2). List all the prime numbers up to 100.

D. Find the prime factors of the following. Leave the answer in index notation.

1). 12 2). 45 3). 144 4). 505). 180 6). 450 7). 245 8). 849). 405 10). 735 11). 2662 12). 157513). 2400 14). 847 15). 1638 16). 5236

E. Find the Lowest Common Multiple (L.C.M.) of

1). 6, 15 2). 5, 6 3). 4, 8 4). 2, 75). 4, 6 6). 3, 8 7). 9, 10 8). 6, 89). 6, 10 10). 5, 9 11). 5, 14 12). 9, 1213). 8, 14 14). 12, 20 15). 16, 20 16). 20, 3017). 15, 20 18). 18, 24 19). 17, 19 20). 25, 4021). 4, 12, 16 22). 5, 12, 24 23). 15, 20, 24 24). 15, 18, 30

F. Find the Highest Common Factor (H.C.F.) of

1). 6, 15 2). 12, 16 3). 12, 30 4). 21, 145). 36, 16 6). 50, 35 7). 45, 27 8). 64, 889). 35, 14 10). 20, 40 11). 28, 84 12). 48, 8413). 99, 77 14). 90, 36 15). 60, 48 16). 88, 6617). 96, 144 18). 140, 252 19). 175, 250 20). 396, 25221). 27, 18, 99 22). 42, 56, 98 23). 108, 54, 90 24). 96, 192, 144


G. Evaluate

1). 4 2 2). 36 3). 3 125 4). 7 3

5). 144 6). 17 2 7). 10 3 8). 3 5129). 3 3 10). 3 64 11). 8 2 12). 40013). 3 1331 14). 361 15). 13 2 16). 9 3

17). 15 2 18). 196 19). 17 3 20). 3 5832

H. Copy the questions and fill in the missing values.

1). 13 x 1000 = ___ 2). ___ x 100 = 5000 3). 72 x ___ = 7204). ___ x 100 = 5700 5). 48 x 1000 = ___ 6). ___ x 1000 = 910007). 4.5 x 10000 = ___ 8). ___ x 10 = 65 9). 9.7 x ___ = 9700010). 0.67 x ___ = 6700 11). ___ x 10 = 5 12). ___ x 1000 = 8013). 0.03 x 10000 = ___ 14). 5.03 x 1000 = ___ 15). ___ x 100 = 716). 800 ÷ ___ = 0.8 17). 120 ÷ 1000 = ___ 18). 6.3 ÷ ___ = 0.6319). 363 ÷ ___ = 3.63 20). ___ ÷ 100 = 12.6 21). ___ ÷ 1000 = 59.322). 475 ÷ ___ = 47.5 23). 50 ÷ ___ = 0.5 24). 21 ÷ 100 = ___25). 14.2 ÷ 1000 = ___ 26). 572 ÷ ___ = 57.2 27). 503 ÷ ___ = 5.0328). ___ ÷ 100 = 54.1 29). ___ ÷ 10 = 3.4 30). 701 ÷ 100 = ___

I. Copy the questions and fill in the missing values.

1). ___ x 104 = 60000 2). 8 x ___ = 8000 3). ___ x 103 = 50004). 16 x 103 = ___ 5). ___ x 102 = 7000 6). 43 x ___ = 4307). ___ x 101 = 5600 8). 38 x 101 = ___ 9). ___ x 103 = 9300010). 9.7 x 102 = ___ 11). ___ x 101 = 37 12). 1.7 x ___ = 17013). 0.4 x ___ = 4000 14). 1.2 x 102 = ___ 15). 4.3 x ___ = 4316). 4000 ÷ ___ = 0.4 17). 19 ÷ 102 = ___ 18). 83 ÷ ___ = 8.319). 5180 ÷ ___ = 5.18 20). ___ ÷ 101 = 15 21). ___ ÷ 103 = 1722). 427 ÷ ___ = 42.7 23). 100 ÷ ___ = 0.1 24). 0.4 ÷ 101 = ___25). 7.02 ÷ 103 = ___ 26). 8.62 ÷ ___ = 0.862 27). 703 ÷ ___ = 0.070328). ___ ÷ 102 = 5.91 29). ___ ÷ 102 = 0.003 30). 8.01 ÷ 102 = ___

J. Without using a pen and paper method, evaluate the following

1). 200 x 50 2). 30 x 400 3). 180 x 20 4). 140 x 305). 40 x 420 6). 50 x 600 7). 20 x 370 8). 250 x 309). 71 x 200 10). 400 x 25 11). 750 x 40 12). 40 x 12513). 320 x 50 14). 70 x 210 15). 50 x 610 16). 320 x 4017). 350 x 200 18). 400 x 810 19). 910 x 500 20). 520 x 600

K. Without using a pen and paper method, evaluate the following

1). 120 ÷ 30 2). 160 ÷ 40 3). 550 ÷ 50 4). 360 ÷ 305). 480 ÷ 40 6). 560 ÷ 70 7). 720 ÷ 90 8). 1440 ÷ 1209). 2000 ÷ 50 10). 1500 ÷ 50 11). 6300 ÷ 70 12). 5600 ÷ 8013). 1230 ÷ 30 14). 2100 ÷ 50 15). 2480 ÷ 40 16). 3060 ÷ 6017). 5760 ÷ 80 18). 2310 ÷ 70 19). 6660 ÷ 90 20). 6800 ÷ 80


Missing Multiplications.

Here are some incomplete multiplication questions.Fill in the empty boxes to complete the sums.

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).

41 8 0x =

22 8 3x =

1 6 8 4x =

33 8 2x =

2 3 8 9x =

2 4 8 8x =

71 9 1x =

32 9 6x =

2 1 9 7x =

42 9 3x =

3 2 9 9 9x =

1 9 9 5x =

43 9 2x =

31 9 3x =

41 9 3x =

82 9 4x =

1 5 9 7x =

2 6 9 3x =

2 7 9 1x =

61 9 2x =

1 2 9 8x =

23 8 9x =

53 8 0x =

1 3 8 2x =

92 8 2x =

81 8 6x =

2 6 8 4x =

2 1 8 9x = 91 8 7x =

71 8 8x =


Missing Divisions.

Here are some incomplete division questions.Fill in the empty boxes to complete the sums.

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).

714 7 =÷

1 44 4 =÷

2 14 1 =÷

415 0 =÷

514 0 =÷

614 2 =÷

815 5 =÷

1 25 7 =÷

425 8 =÷615 8 =÷

316 7 =÷

126 5 =÷

1 86 6 =÷

2 46 6 =÷

616 7 =÷ 417 0 =÷

227 7 =÷ 1 97 7 =÷

617 2 =÷ 2 67 2 =÷

718 3 =÷ 1 98 1 =÷

2 99 7 =÷ 3 29 9 9 =÷

629 8 =÷ 3 49 8 =÷

2 78 3 =÷ 129 4 =÷

238 6 =÷2 48 1 =÷


Four-in-a-Row (Estimation)

A Game for 2 players.

175 1300 403 186 42 325

312 676 1612 364 988 1953

3276 288 1197 247 819 150

589 1488 78 441 1575 3024

114 133 336 1200 378 475

775 2496 912 624 84 217

3125

6

19

7

63

5213 48

Pick 2 numbers. Tell the other player.Multiply them out on a calculator.

Cover the answer on the board below.Now the other player has a go.

The player who gets 4 counters in a row is the winner.


RED

RED

YELLOW

YELLOW

1470

312

3612

1632

1118

923

1653

4828

1368

3010

2494

1218

2394

884

6106

455

4047

377

2982

2380

1704

546

4902

1008

1015

2485

696

5848

1995

2059

741

2064

840

2856

3876

1972

HEX-an Estimating Game

Rules : Two players RED and YELLOW.Take it in turn to take two numbers from the box.Multiply them out on a calculator (or in your head!).Cover up that number on the grid.The winner is the first to make a connected path betweentheir two sides of the board.

24 86 42

71 57 29

68 35

13


Multiplication. Powers of Ten.

A). 1). 30 x 2 2). 40 x 3 3). 5 x 40 4). 6 x 305). 9 x 50 6). 20 x 7 7). 8 x 40 8) 9 x 309). 5 x 70 10). 12 x 30 11). 40 x 11 12). 80 x 913). 30 x 60 14). 20 x 80 15). 70 x 20 16). 40 x 3017). 50 x 50 18). 70 x 30 19). 80 x 60 20). 30 x 9021). 50 x 70 22). 40 x 70 23). 80 x 70 24). 90 x 6025). 80 x 90 26). 120 x 30 27). 110 x 40 28). 120 x 6029). 70 x 110 30). 90 x 120 31). 120 x 120 32). 120 x 11033). 500 x 30 34). 700 x 40 35). 50 x 700 36). 600 x 8037). 700 x 300 38). 600 x 400 39). 1200 x 300 40). 1100 x 1200

B). 1). 0.4 x 0.3 2). 0.6 x 0.5 3). 0.8 x 0.3 4). 0.2 x 0.35). 0.7 x 0.4 6). 0.5 x 0.2 7). 0.4 x 0.2 8). 0.03 x 0.49). 0.12 x 0.04 10). 0.11 x 0.3 11). 0.34 x 0.002 12). 1.3 x 0.00313). 0.023 x 0.04 14). 1.5 x 0.4 15). 0.007 x 0.5 16). 3.7 x 0.517). 9.2 x 0.4 18). 8.6 x 0.6 19). 3.12 x 0.8 20). 8.25 x 0.0421). 4.56 x 0.05 22). 8.2 x 1.2 23). 0.26 x 0.9 24). 0.11 x 3.425). 0.243 x 0.4 26). 0.054 x 0.03 27). 3.45 x 0.6 28). 5.67 x 1.229). 1.24 x 0.05 30). 4.56 x 0.2 31). 2.3 x 4.6 32). 0.23 x 6.733). 0.051 x 0.98 34). 4.3 x 5.6 35). 45.6 x 2.2 36). 94.6 x 3.437). 234.5 x 0.7 38). 19.4 x 3.5 39). 17.5 x 9.4 40). 200.4 x 0.67

Division. Powers of Ten.

A). 1). 40 ÷ 2 2). 27 ÷ 3 3). 48 ÷ 4 4). 88 ÷ 85). 42 ÷ 6 6). 60 ÷ 5 7). 144 ÷ 12 8). 63 ÷ 39). 80 ÷ 5 10). 96 ÷ 6 11). 126 ÷ 7 12). 207 ÷ 913). 400 ÷ 20 14). 180 ÷ 30 15). 240 ÷ 60 16). 350 ÷ 5017). 240 ÷ 20 18). 390 ÷ 30 19). 520 ÷ 40 20). 800 ÷ 2021). 420 ÷ 60 22). 480 ÷ 80 23). 280 ÷ 70 24). 810 ÷ 9025). 650 ÷ 50 26). 910 ÷ 70 27). 960 ÷ 60 28). 690 ÷ 3029). 960 ÷ 40 30). 720 ÷ 120 31). 550 ÷ 110 32). 390 ÷ 13033). 840 ÷ 120 34). 840 ÷ 60 35). 680 ÷ 40 36). 1040 ÷ 4037). 1350 ÷ 90 38). 1920 ÷ 60 39). 1890 ÷ 70 40). 2280 ÷ 120

B). 1). 0.6 ÷ 3 2). 0.8 ÷ 4 3). 0.75 ÷ 3 4). 0.98 ÷ 75). 0.864 ÷ 6 6). 1.281 ÷ 7 7). 2.439 ÷ 9 8). 3.705 ÷ 159). 6.048 ÷ 12 10). 0.085 ÷ 5 11). 0.336 ÷ 8 12). 8.645 ÷ 713). 0.275 ÷ 11 14). 0.824 ÷ 4 15). 5.424 ÷ 6 16). 16.159 ÷ 1317). 8.48 ÷ 0.4 18). 8.37 ÷ 0.9 19). 7.08 ÷ 0.6 20). 1.12 ÷ 0.721). 3.45 ÷ 0.5 22). 15.2 ÷ 0.8 23). 10.8 ÷ 0.9 24). 0.48 ÷ 0.0325). 1.35 ÷ 0.09 26). 3.65 ÷ 0.05 27). 264 ÷ 0.4 28). 837 ÷ 0.0929). 325.5 ÷ 0.07 30). 380.7 ÷ 0.09 31). 197.4 ÷ 0.003 32). 680.4 ÷ 1.233). 732.6 ÷ 0.11 34). 483.2 ÷ 0.08 35). 36.072 ÷ 0.012 36). 3.366 ÷ 0.1137). 180.24 ÷ 0.006 38). 120.84 ÷ 0.004 39). 4732 ÷ 0.13 40). 456.9 ÷ 0.015


Number Work (Estimating).

A. Getting up to Speed.See how quickly you can answer the following questions.

1). 4 x 9 = 2). 7 x 8 = 3). 12 x 4 = 4). 8 x 12 = 5). 6 x 7 =6). 9 x 3 = 7). 4 x 13 = 8). 9 x 6 = 9). 15 x 3 = 10). 12 x 11 =11). 7 x 12 = 12). 34 x 2 = 13). 14 x 5 = 14). 25 x 4 = 15). 9 x 12 =16). 8 x 4 = 17). 13 x 6 = 18). 22 x 4 = 19). 12 x 13 = 20). 15 x 6 =21). 81 ÷ 9 = 22). 56 ÷ 8 = 23). 108 ÷ 9 = 24). 55 ÷ 5 = 25). 39 ÷ 3 =26). 45 ÷ 9 = 27). 84 ÷ 7 = 28). 60 ÷ 15 = 29). 42 ÷ 3 = 30). 56 ÷ 2 =31). 60 ÷ 12 = 32). 132 ÷ 11 = 33). 54 ÷ 6 = 34). 72 ÷ 3 = 35). 76 ÷ 4 =36). 78 ÷ 6 = 37). 88 ÷ 8 = 38). 63 ÷ 9 = 39). 42 ÷ 7 = 40). 105 ÷ 5 =41). 7 x 9 = 42). 18 x 5 = 43). 100 ÷ 4 = 44). 17 x 3 = 45). 60 ÷ 5 =46). 56 ÷ 7 = 47). 121 ÷ 11 = 48). 24 x 3 = 49). 60 ÷ 15 = 50). 14 x 6 =

B. Multiplying and Dividing by Powers of 10.Work out the answer to the following questions.

1). 3 x 50 2). 6 x 20 3). 80 x 4 4). 9 x 30 5). 20 x 86). 7 x 60 7). 30 x 9 8). 6 x 30 9). 50 x 9 10). 12 x 7011). 40 x 30 12). 50 x 70 13). 90 x 20 14). 40 x 80 15). 20 x 7016). 60 x 70 17). 40 x 50 18). 50 x 90 19). 70 x 30 20). 120 x 9021). 30 x 800 22). 90 x 500 23). 400 x 700 24). 600 x 40 25). 20 x 90026). 70 x 500 27). 500 x 60 28). 90 x 300 29). 110 x 500 30). 120 x 110031). 90 ÷ 3 32). 240 ÷ 4 33). 200 ÷ 5 34). 150 ÷ 3 35). 420 ÷ 736). 810 ÷ 9 37). 240 ÷ 8 38). 450 ÷ 3 39). 720 ÷ 6 40). 880 ÷ 841). 320 ÷ 40 42). 450 ÷ 50 43). 560 ÷ 80 44). 680 ÷ 20 45). 540 ÷ 6046). 390 ÷ 30 47). 800 ÷ 40 48). 750 ÷ 50 49). 630 ÷ 90 50). 910 ÷ 7051). 4000 ÷200 52). 4500 ÷ 50 53). 7500 ÷ 30 54). 1400 ÷700 55). 2400 ÷ 8056). 6000 ÷150 57). 7200 ÷900 58). 8400 ÷400 59). 9600 ÷120 60). 12100 ÷ 1100

C. Estimating.Estimate the answers to the following questions without a calculator.Now check the estimate with a calculator to see if it is about the right size.

1). 41 x 58 2). 32 x 29 3). 87 x 44 4). 93 x 76 5). 26 x 546). 18 x 58 7). 45 x 93 8). 28 x 32 9). 57 x 83 10). 14 x 9711). 104 x 37 12). 59 x 296 13). 912 x 18 14). 47 x 394 15). 206 x 4216). 595 x 67 17). 29 x 603 18). 704 x 83 19). 36 x 887 20). 414 x 6721). 452 ÷ 49 22). 346 ÷ 68 23). 461 ÷ 21 24). 418 ÷ 32 25). 315 ÷ 1826). 476 ÷ 77 27). 364 ÷ 42 28). 614 ÷ 47 29). 532 ÷ 61 30). 431 ÷ 7831). 887 ÷ 302 32). 1493 ÷489 33). 4842 ÷618 34). 4478 ÷879 35). 7118 ÷61136). 5369 ÷877 37). 5004 ÷682 38). 5132 ÷421 39). 7154 ÷579 40). 7880 ÷ 97841). 47 x 93 42). 444 ÷ 38 43). 342 ÷ 72 44). 685 x 28 45). 3549 ÷ 38446). 2641 ÷331 47). 693 x 67 48). 75 x 674 49). 2908 ÷ 64 50). 91 x 4851). 42 x 58 52). 7098 ÷ 93 53). 89 x 908 54). 18 x 67 55). 7463 ÷ 4656). 6942 ÷17 57). 72 x 89 58). 9007 ÷779 59). 2379 ÷78 60). 123 x 6982


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Trial and Improvement.

A). Use trial and improvement techniques to solve the following equations.All the answers are whole numbers.

1). 3x + 4 = 19 2). 2d - 6 = 10 3). 49 = 4c + 1 4). 37 = 2e + 75). 5v - 9 = 81 6). 191 = 9 + 13a 7). 5 + 8g = 189 8). 12w - 13 = 1919). 1 x + 16 = 27 10). 70 = 59 + 1 k 11). 38 = 47 - 1 t 12). 32 = 38 - 1 u

2 4 3 713). 113 - 2x = 87 14). 20 = 56 - 4k 15). 28 = 172 - 6t 16). 50 = 203 - 9u17). 9 + 2.5x = 99 18). 234 = 7.2p - 18 19). 200 - 1.8k = 83 20). 262 = 6 + 6.4n21). 5 + 14q = 383 22). 354 = 12w - 18 23). 321 - 16y = 97 24). 524 = 56 + 18r25). 259 = 532 - 7h 26). 23x - 36 = 930 27). 1321 = 67 + 57b 28). 978 - 26v = 94

B). Use trial and improvement techniques to solve the following equations.All the answers are to 1 d.p..

1). 5r = 76 2). 87.6 = 6p 3). 2k + 7 = 20 4). 54 = 4h + 85). 3r - 2 = 23.2 6). 14.6 = 6q - 4 7). 4 + 7z = 153.1 8). 11b - 23 = 80.49). 1 f + 13 = 16.2 10). 25.2 = 21 + 1 x 11). 3.1 = 20 - 1 a 12). 17.1 = 18 - 1 d

3 4 2 613). 200 - 5t = 36 14). 14.2 = 241 - 12y 15). 20 - 5g = 1 16). 27.7 = 372 - 11c17). 1.76 + 1.4v = 60 18). 138.1 = 9.5e - 31 19). 537-4.2k =366.9 20). 69.3 = 3 + 10.2n21). 6 + 22b = 201.8 22). 5.8 = 16h - 7 23). 121 - 19j = 14.6 24). 486.7 = 16 + 9n25). 316.3 = 751 -7h 26). 43c - 32 = 32.5 27). 61 = 23 + 95x 28). 1809 - 32f = 100.2

C). Use trial and improvement techniques to solve the following equations.All the answers are to 2 d.p..

1). 4x + 7 = 24 2). 8f - 9 = 13 3). 21 = 4t - 8 4). 11 = 12y + 25). 5v - 2 = 15.7 6). 96.4 = 7 + 10u 7). 3 + 2a = 27.68 8). 14s - 33 = 138.789). 1 h + 6 = 14.22 10). 12.67 = 9 + 1 j 11). 5.66 = 27 - 1 k 12). 7.88 = 8 - 1 x

3 5 4 1213). 220 - 8g = 31.68 14). 14 = 41 - 12y 15). 175.52 = 302- 6t 16). 49.7 = 263 - 6u17). 4.5y = 134.235 18). 608.482 = 9.8p 19). 10 - 3.8j =1.222 20). 8.664 = 6 + 7.4n

D). Use trial and improvement techniques to solve the following equations.All the answers are to 3 d.p..

1). 8f - 9 = 12 2). 16d - 7 = 63 3). 36 = 10c - 0.28 4). 33.608 = 2e + 215). 9v - 0.522 = 9 6). 40 = 0.76 + 15a 7). 25 + 3g= 48.673 8). 12w - 8.38 = 509). 1x + 12 =40.218 10). 12.141 = 9 + 1 k 11). 7.132 = 10 - 1 t 12). 9.583 = 12 - 1 u

2 4 3 1513). 13 - 2x = 6.984 14). 2.946 = 36 - 14k 15). 5.844 = 8 - 7t 16). 4.829 = 163 - 23u17). 0.79 + 5x = 19 18). 90.268 =7p - 80 19). 10 - 19k = 4.148 20). 140 = 2.083 + 13n


E). Use trial and improvement techniques to find the exactsolutions to the following equations.All the answers are exact negative numbers.They may be whole, or to 1 or 2 decimal places.

1). 3h + 7 = 1 2). 8k - 2 = -50 3). -50 = 3w - 2 4). 9 = 7h + 1005). 6j - 7 = -20.8 6). 0 = 32 + 5u 7). 0.2 + 8f = -51 8). 17t - 10 = -127.39). 1 i + 10 = 2 10). 2 = 9 + 1 p 11). 19.3 = 12 - 1 h 12). 16.8 = 15 - 1 y

2 5 3 1013). 100 + 7x = 60.52 14). 31.64 = 7 - 8c 15). 91.83 = 2 - 13v 16). 100.45 = 4 - 15u17). 5y + 6 = 1.2 18). -170.4 = 9d - 3 19). 10 - 3q = 59.11 20). 10.88 = 12 + 14n21). 1 + 25b = -409 22). -179.71 =19n -7 23). 21 - 25j = 107.5 24). -57.2 = 46 + 12g25). 388.45 =71 -5m 26). 32c - 2= -130.96 27). -794.5 = 3 +55x 28). 9 - 72x = 37.8

F). Use trial and improvement techniques to solve the following equations.These answers will not be exact answers. Leave all the answers to 2 d.p..

1). 6r = 86 2). 45.6 = 7p 3). 11k + 3 = 26 4). 54 = 3h + 85). 13r - 1 = 23 6). 12 = 9q - 2 7). 2 + 7z = 53 8). 14b - 3 = 809). 11 f + 3 = 46.2 10). 75 = 9 + 17 x 11). 3 = 20 - 3a 12). 1 = 18 - 19 d13). 100 - 14t = 36 14). 14 = 41 - 7y 15). 90 - 6g = 1 16). 27 = 172 - 11c17). 9 + 7.4v = 80 18). 173 = 3.5e - 3 19). 237 - 4.2k = 36 20). 508 = 9 + 16.2n21). 6 + 22b = 571 22). 4 = 31h - 7 23). 421 - 19j = 34 24). 401 = 16 + 9n25). 16 = 751 -37h 26). 43c - 832 = 32 27). 61 = 53 + 93x 28). 1809 - 78f = 7

G). Use trial and improvement techniques to solve these equations.All the answers are to 1 d.p..1). 6 = 10 2). 5 = 7 3). 15 = 2 4). 7.5 = 54

t g m q5). 8 = 0.64 6). 20 = 38 7). 42 = 20 8). 80 = 128

n t d e

All the answers are to 2 d.p..9). 35 = 20 10). 6.4 = 8 11). 112 = 50 12). 34 = 70.04

e w y u13). 18 = 8 14). 15 = 110.55 15). 415.38 = 46 16). 26 = 602.68

k r b p

These answers will not be exact answers. Leave all the answers to 2 d.p..17). 19 = 47 18). 13 = 97 19). 615 = 14 20). 705 = 34

a s v c21). 69 = 7 22). 54 = 7 23). 198.5 = 29 24). 739 = 544

t x m f


A). Green (Putting).

1). 17 ≤ 3x ≤ 182). 22 < 4x ≤ 233). 16 < 7y < 174). 10 < 8d ≤ 115). 3.6 < 2x < 3.96). 22.1 ≤ 9u < 22.87). 39.2 < 6h ≤ 40.18). 2.5 < 5c ≤ 2.6

B). Bunkers (Sand Wedge).

1). 24 ≤ 2x + 3 ≤ 252). 31 ≤ 4 + 3r < 333). 34 ≤ 5w - 3 < 364). 15 < 7k - 4 ≤ 185). 12.2 ≤ 2x - 6 ≤ 12.86). 21.3 ≤ 3y + 5 < 22.17). 41.7 < 4n - 9 ≤ 43.68). 53.4 ≤ 3 + 7h < 54.8

D). Driving ( 2-Wood).

1). 50 < x 3 < 562). 4.6 < √ x < 4.93). 32 < f 2 + f < 364). 8.3 < 80 ≤ 8.9

v5). 11.2 < √ b < 11.76). 92 < c + c 2 < 967). 9.2 ≤ 24 < 9.8

n8). 165 < x 3 ≤ 168

C). Chipping ( 5-Iron).

1). 17 ≤ x 2 ≤ 202). 37 < k 2 < 403). 12.2 ≤ g 2 < 12.94). 21.4 < r 2 ≤ 22.65). 34 < x 2 + 7 < 396). 2 ≤ m 2 - 8 < 57). 14.6 ≤ 2 + t 2 ≤ 15.98). 0.4 ≤ x 2 - 16 < 3.2

Golf Practice Holes.


Royal Idiotdale Golf Course.

1. 16 ≤ 3y < 17 Par 32. 26 < y2 < 27 Par 43. 42 < 5y ≤ 43 Par 34. 4 < y÷3 ≤ 5 Par 35. 18 < 2y + 5 < 19 Par 36. 70 < y3 < 73 Par 57. 27 ≤ 8 ÷ y < 30 Par 58. 53 < 1.5y < 55 Par 49. 12 < y ÷ 1.3 ≤ 14 Par 310. 0.5 ≤ 4y < 0.8 Par 311. 7 < 13 ÷ y ≤ 8 Par 512. 25 < 3y + 7 < 29 Par 313. 90 < 2y2 ≤ 95 Par 414. 22 < 4y - 5 < 23 Par 415. 28 ≤ y3 + 7 < 31 Par 516. 14 < 100 ÷ y < 15 Par 517. 14 < 4y - 5 ≤ 15 Par 318. 35 < 3y2 < 37 Par 5


Glennsparrows Golf Course.

1. 17≤ 14y < 20 Par 32. 38 < y2 ≤ 39 Par 33. 31 < 6t ≤ 32 Par 34. 4 ≤ 12 - 9y < 5 Par 55. 18 < 6y - 5 ≤ 19 Par 46. 150 < y3 < 160 Par 47. 25 ≤ 30 ÷ y < 30 Par 58. 63 < 1.5y + 4 ≤ 65 Par 49. 18 ≤ y ÷ 1.8 < 19 Par 410. 0.5 < 7y < 0.9 Par 411. 17 ≤ 2 ÷ y < 22 Par 512. 1 < 3 ÷ y < 1.5 Par 413. 51 < 2y2 ≤ 55 Par 414. 26 < 4y + 5 ≤ 27 Par 315. 38 ≤ y3 + 7 ≤ 41 Par 516. 19 < 50 ÷ y ≤ 20 Par 517. 18 < 12 - 3y ≤ 19 Par 318. 41 < 6y2 < 46 Par 4


Compass and Ruler Constructions.

To construct a triangle given all three sides.

Eg. Construct the triangle below using a pencil, compass and ruler only. (Diagrams not to scale).

1). Draw out a baseline and mark on a startpoint A. Open the compass to 9 cm.Place the point on A and draw an arc acrossthe baseline, C.

2). Open the compass to 5 cm. Place the 3). Open the compass to 7 cm. Place thepoint on A and draw an arc above the point on C and draw an arc to cross thebase line. other arc. Join up the triangle.

Construct the following triangles using a pencil, compass and ruler only.With a protractor measure each angle in every triangle. Diagrams not drawn to scale.

1). 2). 3). 4).

5). 6). 7). 8).

9). 10). 11). 12).

7 cm

9 cm

5 cm

B

CAA C9 cm

A C9 cm

A C9 cm

B

9 cm

5 cm 7 cm

4 cm7 cm

5 cmA

C

B

A

A A

A

A A A

A

A

A A

B B

B

B

B

B

B

B

B B

B

C

C

C

C C

C

C

CC

C

C

6 cm

6 cm

4 cm6 cm

9 cm

5 cm

5 cm 6 cm

7 cm

5.8 cm

5.5 cm 6.5 cm51 mm 62 mm

43 mm

87 mm

37 mm

62 mm4.8 cm 4.8 cm

4.8 cm

9.8 cm5.4 cm

69 mm

6.1 cm 53 mm

69 mm33 mm

55 mm

44 mm

5.5 cm 9.2 cm

8.4 cm


Bisecting an angle.

Eg. To bisect an angle using a pencil, compass and ruler only. (Diagrams not to scale).NB. Throughout this construction keep the compass open to the same distance apart.

1). Put the compass point on 2). Put the compass points 3). Join the vertex ofthe vertex A. Open to any on X and Y and draw the angle to wheredistance and draw an arc. 2 more arcs, the arcs cross, AZ.

Construct the following triangles using a pencil, compass and ruler only.Bisect ∠ ABC, label the end of the bisector Z (as above).For each triangle use a protractor to measure ∠ ABZ. Diagrams not drawn to scale.

1). 2). 3). 4).

5). 6). 7). 8).

Construct the following shapes using a pencil, compass and ruler only.For each shape use a protractor to measure ∠ QPR and ∠ QRS.

9). 10).

11). 12).

A

X

Y

X

Y

Z

AA

A

BC

56 mm 68 mm

71 mm

B

C

3.6 cm9.0 cm

7.7 cmA

B

C

9.5 cm4.0 cm

8.3 cm

A

B

C

4.9 cm 5.2 cm

8.4 cm

A B

C

6.4 cm 6.4 cm

6.4 cm

A

BC

65 mm 55 mm

61 mm

A B

C

10.8 cm7.1 cm

4.4 cm

A

C

64 mm 80 mm

48 mmBA

S

RP

Q6.5 cm

5.1 cm6.6 cm

6.2 cm

3.9 cm

PQ

R S72 mm

72 mm

57 mm51 mm

51 mm

Q

P R

T S

80 mm80 mm

80 mm

80 mm

80 mm

129 mm

129 mmR

ST

Q

P

5.5 cm

4.5 cm

2.7 cm8.1 cm

6.8 cm 9.5 cm

6.3 cm


Nets.

A). Below are some nets. Some are correct, some don’t make solids.Draw the net and state if the net is a solid or not.If it is a solid write the name of the solid.

2). 3). 4). 5).

6). 7). 8). 9).

10). 11).

12).

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1). 2). 3). 4).

1).

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Draw each net.When the net is folded into a solida). how many other points meet at, (name them) i). A, ii). D, iii). G ?b). which other edge joins i). AB, ii). FG, iii). GH ?

5). 6). 7). 8).

Draw each net.When the net is folded into a solida). how many other points meet at, (name them) i). B, ii). C, iii). H ?b). which other edge joins i). BC, ii). DE, iii). FG ?

9). 10). 11). 12).

C). The following nets will fold up to make the solid shown. They have one face missing.Draw each net.a). Name the shape of the missing face,b). Show, by using diagrams, all the places where that face can be placed

so the net will make the solid.

1). 2). 3). 4).

5).

Square-basedPyramid

TriangularPrism

Cube

Cube

Tetrahedron

BA

NM

L

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E

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Construct Your Own Calendar.

Below are 4 nets for you to construct.Each net doesn’t have any glue flaps drawn on. Work out where they should be placed.

If you get stuck, put one on each edge and cut off the ones you don’t need!Each net will fit on an A4 piece of paper.

Glue on the calendar dates for next year before you make the solid.

1). Cube.

Square side length 6 cm.2 months on each face.

A4 paper orientation: portrait.

2). Cuboid.

Rectangle 15 cm x 4.5 cm.Square side length 4.5 cm.3 months on each rectangular face.

A4 paper orientation: landscape.

3). Hexagonal Prism.

Rectangle 8 cm x 3 cm.Regular hexagon side length 3 cm.2 months on each rectangular face.

A4 paper orientation: portrait.

4). Tetrahedron.

Equilateral triangle side length 12 cm.3 months on each face.A4 paper orientation: landscape,but angled. See below.


Sun 7 14 21 28 Mon 1 8 15 22 29 Tues 2 9 16 23 30 Wed 3 10 17 24 31 Thur 4 11 18 25 Fri 5 12 19 26 Sat 6 13 20 27

Calendar Dates.Teacher notes: Shown below are dates for calendars. The spaces at the top are for the month andyear. Work out which ones you need for next year. Cut them out and stick them on another pieceof paper for photocopying. Some may be needed more than once. Cut in or outside of the linesdepending if you want a border.

Sun 1 8 15 22 29 Mon 2 9 16 23 30 Tues 3 10 17 24 Wed 4 11 18 25 Thur 5 12 19 26 Fri 6 13 20 27 Sat 7 14 21 28

Sun 1 8 15 22 Mon 2 9 16 23 Tues 3 10 17 24 Wed 4 11 18 25 Thur 5 12 19 26 Fri 6 13 20 27 Sat 7 14 21 28

Sun 1 8 15 22 29 Mon 2 9 16 23 Tues 3 10 17 24 Wed 4 11 18 25 Thur 5 12 19 26 Fri 6 13 20 27 Sat 7 14 21 28

Sun 1 8 15 22 29 Mon 2 9 16 23 30 Tues 3 10 17 24 31 Wed 4 11 18 25 Thur 5 12 19 26 Fri 6 13 20 27 Sat 7 14 21 28

Sun 7 14 21 28 Mon 1 8 15 22 29 Tues 2 9 16 23 30 Wed 3 10 17 24 Thur 4 11 18 25 Fri 5 12 19 26 Sat 6 13 20 27

Sun 7 14 21 28 Mon 1 8 15 22 29 Tues 2 9 16 23 Wed 3 10 17 24 Thur 4 11 18 25 Fri 5 12 19 26 Sat 6 13 20 27


Sun 6 13 20 27 Mon 7 14 21 28 Tues 1 8 15 22 29 Wed 2 9 16 23 30 Thur 3 10 17 24 31 Fri 4 11 18 25 Sat 5 12 19 26

Sun 6 13 20 27 Mon 7 14 21 28 Tues 1 8 15 22 29 Wed 2 9 16 23 30 Thur 3 10 17 24 Fri 4 11 18 25 Sat 5 12 19 26

Sun 6 13 20 27 Mon 7 14 21 28 Tues 1 8 15 22 29 Wed 2 9 16 23 Thur 3 10 17 24 Fri 4 11 18 25 Sat 5 12 19 26


Sun 5 12 19 26 Mon 6 13 20 27 Tues 7 14 21 28 Wed 1 8 15 22 29 Thur 2 9 16 23 30 Fri 3 10 17 24 31 Sat 4 11 18 25

Sun 5 12 19 26 Mon 6 13 20 27 Tues 7 14 21 28 Wed 1 8 15 22 29 Thur 2 9 16 23 30 Fri 3 10 17 24 Sat 4 11 18 25

Sun 5 12 19 26 Mon 6 13 20 27 Tues 7 14 21 28 Wed 1 8 15 22 29 Thur 2 9 16 23 Fri 3 10 17 24 Sat 4 11 18 25


Sun 4 11 18 25 Mon 5 12 19 26 Tues 6 13 20 27 Wed 7 14 21 28 Thur 1 8 15 22 29 Fri 2 9 16 23 30 Sat 3 10 17 24 31


Sun 4 11 18 25 Mon 5 12 19 26 Tues 6 13 20 27 Wed 7 14 21 28 Thur 1 8 15 22 29 Fri 2 9 16 23 Sat 3 10 17 24

Sun 4 11 18 25 Mon 5 12 19 26 Tues 6 13 20 27 Wed 7 14 21 28 Thur 1 8 15 22 29 Fri 2 9 16 23 30 Sat 3 10 17 24

Sun 3 10 17 24 Mon 4 11 18 25 Tues 5 12 19 26 Wed 6 13 20 27 Thur 7 14 21 28 Fri 1 8 15 22 29 Sat 2 9 16 23 30

Sun 3 10 17 24 Mon 4 11 18 25 Tues 5 12 19 26 Wed 6 13 20 27 Thur 7 14 21 28 Fri 1 8 15 22 29 Sat 2 9 16 23


Sun 2 9 16 23 Mon 3 10 17 24 Tues 4 11 18 25 Wed 5 12 19 26 Thur 6 13 20 27 Fri 7 14 21 28 Sat 1 8 15 22 29


Sun 2 9 16 23 30 Mon 3 10 17 24 Tues 4 11 18 25 Wed 5 12 19 26 Thur 6 13 20 27 Fri 7 14 21 28 Sat 1 8 15 22 29

Sun 2 9 16 23 30 Mon 3 10 17 24 31 Tues 4 11 18 25 Wed 5 12 19 26 Thur 6 13 20 27 Fri 7 14 21 28 Sat 1 8 15 22 29

Sun 3 10 17 24 31 Mon 4 11 18 25 Tues 5 12 19 26 Wed 6 13 20 27 Thur 7 14 21 28 Fri 1 8 15 22 29 Sat 2 9 16 23 30


The Square-basedPyramid

Cut out the net.To make a calendar, stick 3months on each triangular face.Score along all lines.Fold and glue.


Hexagonal Prism(Glueless)

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Dodecahedron.

Cut out around the edge.Score along other lines.

Stick 1 calendar month on each pentagon face.

Fold into shape.When you are sure this is correctglue the tabs in the order shown.Start with A tabs working through to J.

E

A

JJ

I H

G

G

F

H

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I

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D

J

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B


TruncatedTetrahedron.

(A tetrahedron withthe points cut off!)

Cut out around the edge.Score along other lines.

Stick 3 calendar months oneach hexagon face.

Fold into shape.When you are sure thisis correct, glue the tabs down.


SSSSaaaannnnttttaaaa’’’’ssss

GGGGrrrroooottttttttoooo

32 80 19 98 1 90 14 85

66 22 73 52 72 57 83 31

30 84 41 73 16 74 45 92

77 6 70 24 28 67 11

32 99 44 81 27 75 42 98

68 21 72 56 59 42 75 17

34 87 19 92 5 99 27 88

Santa's GrottoSanta's GrottoSanta's GrottoSanta's GrottoSanta's Grotto !!

Santa has his elves working in 55 different room, centred around his Grotto.In each room is the number of toys that each elf has made.

Santa wakes up late and is in a rush.He only has time to collect toys from 13 rooms.

He starts in his Grotto and runs from room to room either up/down or sideways.Diagonal moves are not allowed and the same room cannot be visited twice.

Find the route where he will collect most toys (remember from only 13 rooms).


Christmas Investigations.Christmas Investigations.Christmas Investigations.Christmas Investigations.Christmas Investigations.Christmas Trees

Santa decides to build a Christmas tree out ofcubes. He can't decide on which of the twodesigns to build. Here are the start patterns.The first is 7 levels high and the second is 5levels high. He has 150 cubes. Which onedoes he build ?As you're doing this, make a note of anything you discover.

Christmas

How many ways can you spellChristmas in each diagram. If youhave more time, can you find arelationship between the two answers ?

The Snowflake

You will need squared paper.Follow these rules to produce the diagrams below.1). At the centre of your paper colour (colour 1) in one square.2). Use another colour (colour 2). Colour in the four squares which are

next to the first square.3). Use colour 1. Colour in the squares which have only one edge next

to the squares in the second set.4). Use colour 2. Colour in the squares which have only one edge next

to squares in the third set.

Try to predict what the diagram will look like next.Draw the next 6 diagrams following these rules.Record in a table the number of squares for each colour in the first 10 diagrams.

Three Dimensional Snowflakes.

Snowflakes tends to have six axes of symmetry rather than the four above.Snowflakes are also three dimensional, rather than two dimensional.Use multilink cubes and build some three dimensional snowflakes.Try to use similar rules to those used above. Write them down.(You can adapt the above rules, e.g. only cubes which haveone face (not edge) adjacent to existing cubes can be built on).

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