Worksheet Answers G H I D E L M P Q S T U X Y. Numbers. Titles beginning with...

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1 Worksheet s Titles beginning with A B C D E F G H I J K L M N O P Q R S T U V W X Y Z s

2 Page abc Multiply b by then subtract from a Subtract c from a then multiply by b Add b to a then divide into c Multiply a by b then divide by c Divide c by b then multiply by a Multiply a by c then divide into b Add b to a then divide by c Multiply ab by c Multiply a by then subtract c Subtract c from b then multiply by a Divide a by c then subtract b a b b(a c) c a + b ab c c b x a b ac a + b c abc a c a(b c) a c b About How Long Many possible answers Add a square One of the shapes has possible answers or or Take away a square One of the shapes has possible answers or

3 Page Adding Counters One possible solution for each puzzle is shown below Adding Shifts

4 Page Algebra Match a b c (a b) c a (b + c) a + b + c abc a b + c a + b c (a + b) + c a + (b + c) (a x b) x c a x (b x c) (a b) + c a (b c) (a + b) c a + (b c) ab + ac a x (b + c) ab ac ac bc ac + bc a bc a + bc ab + c a x (b c) (a b) x c (a + b) x c a (b x c) a + (b x c) (a x b) + c a bc ab c ac b a b c a + b c a b c a b + c a b + c a b c a + b c a b c a (b x c) (a b) c (a x b) c a x (b c) (a + b) + c a + (b + c) a (b c) a + (b c) (a b) c (a b) + c a (b + c) a (b c) (a + b) c (a b) c ab c (a x b) c Alphabet Symmetry Yes Does it have a horizontal line of symmetry? No Does it have a vertical line of symmetry? Does it have a vertical line of symmetry? Yes No Yes No Diagonal line of symmetry? Diagonal line of symmetry? Diagonal line of symmetry? Diagonal line of symmetry? Yes No Yes No Yes No Yes No Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Half turn rotational symmetry? Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No O X H I B C D E K A M T U V W Y Q N S Z F G J L P R Some students may have different answers if they write their letters differently Most of the boxes are empty because there aren t many letters with more than two different types of symmetry

5 Page An Even Code USE THE CODE KEEP SMILING TWO AND TWO MAKE FOUR I CAN USE THE EVEN CODE EVEN NUMBERS ARE ALL MULTIPLES OF TWO An Islamic Design The pattern can be viewed as a tessellation of the following shape There are squares for every triangles The ratio of hexagons : squares : triangles is : : Angle Fit All the pieces of the jigsaw should fit neatly together Angle facts can be used to check angles around individual points a b c d Angles in a Regular Hexagon

6 Page Anywhere on the Line Many possible answers depending on which starting point was chosen n- n- n- n- n+ n+ n+ n+ n+ (n + ) (n ) (n + ) (n ) n(n + ) (n )(n ) (n + ) n(n )(n + ) Areas of Polygons A cm B cm C cm D cm E cm F cm G cm H cm I cm E, B, G, A & I, C & D & H, F Many possible answers Ask me another There are many ways of completing this sheet Lines can often be reflected or rotated, and explanations may contain a subset of the information given below four congruent isosceles right-angled triangles if you drew a line from the middle of the top side to the middle of the right side, and from the middle of the left side to the middle of the bottom side? if you drew a line from the middle of the top side to the middle of the bottom side and from the bottom left vertex to the top right vertex? two congruent right-angled triangles and two congruent trapeziums one isosceles right-angled triangle and an irregular pentagon if you drew a line from the top left vertex to the bottom left vertex and from the top left vertex to the bottom right vertex? if you drew a line from the top left vertex to the middle of the bottom side and from the top right vertex to the middle of the bottom side?

7 Page Boxes Students can be encouraged to record their scores as they play the game Building Shapes add a line double the height take off a circle halve the width Calculator Flags

8 Page Cardioid The word cardiac means to do with the heart A cardioid is heart shaped Cartoon Co-ordinates The landscape was designed by a girl in a South London school Students may like to design their own cartoon coordinate pictures Centres of Rotation E E M F P M P P E F F M

9 Page Changing Grids Co-ordinate Messages THIS IS A SECRET MESSAGE YOU HAVE UNDERSTOOD IT WELL DONE Counting On ) Count on ) ) ) ) Count on Count on Count on Count on Counting Back ) Count back ) Count back ) ) ) Count back Count back Count back

10 Page Cracking the Code a b c d e f g h i j k l m n o p q r s t u v w x y z wait for me meet you after dark Cross Puzzles Crossword o n i n e i g t h t f n c i r c l e t f t h h s q u a r e r y n e s e e e v e n d e l f o u r c e i e e v v d n t w e l v e t t t w w n r i o n s i x m n s a e t h i r t e e n t y x g r t l e f o r t y e s

11 Page Decimals on a number line nought point five seven point six three point seven half three and seven tenths seven and five tenths nought point seven six and a half Decimal flags Using multiplication x x x x x x x Using division Using multiplication or division x x x x x x x Using multiplication x x x x x x x Using division Multiplying by a number is the same as dividing by over that number (its reciprocal) Students might use the reciprocal button on their calculator to help with this

12 Page Decimal Places Match on calculator to decimal place to dp to decimal places to dp to decimal places to dp to dp to dp to dp to dp to dp to dp to dp to dp to dp to dp to dp to dp Decimal Routes Start End

13 Page Decimal Search ways using numbers ways using numbers ways using numbers way using numbers Dissection Pairs ) and ) ) ) and ) and ) ) ) and ) and )

14 Page Doubling Patterns x x x x x x x x x x ) x x x x x x x x x x ) x x x x x x x x x x ) x x x x x ) x x x x x x ) All these patterns can be shown on two diagrams Economical Weaving To develop the most economical colouring, students will need to continue the same colours under a cross-over It can be done using only colours Equal Areas One method is to show all the shapes can be made from triangles One method is to show that all the shapes can be made from of these triangles cm cm Alternatively, students may dissect the shapes to show how each one can be made into the others or apply area formulae to show they all have the same area Alternatively, students may dissect the shapes to show how each one can be made into the others or apply area formulae to show they all have the same area

15 Page Equivalent Expressions a a -a(a ) a + a a a(a + ) + a a + a a(a + ) (a ) a a + a a (a + ) (a + ) a + a a a(a ) (a a) a + a a( + a) (a + a ) (a + ) a + a a + a + a (a ) a + a (a + a) (a + ) + (a + ) (a ) + a( a + ) Equivalent Fractions Sort (,, ), (,,, ),, (,,,, ), (,, ) Any two from,,, etc Even Animal Start

16 Page Evens x x x x x x x x x x x pair pairs pairs pairs pairs pairs pairs Evens Add a Couple Twos Pairs Pages The page numbers should all be even numbers Even Even numbers end in the digits,,, or Favourite Colours ) ) ) ) ) ) Not sure what to write here it seems a bit patronising to tell teachers to check for a key, title etc when we ve included these on the worksheet

17 Page Filing Cards SMILE MATHEMATICS - SMILE MATHEMATICS - SMILE MATHEMATICS - SMILE - SMILE - SMILE - SMILE - SMILE - SMILE - SMILE - SMILE - SMILE Find four squares Find the ) + ) + ) + ) + ) + ) + ) ) ) ) ) ) ) + ) ) ) + ) ) ) + )

18 Page Find the ) x ) ) ) x ) ) x ) x ) ) ) x ) ) ) x ) ) ) x ) x ) x ) ) x Find the ) + false ) false ) of false ) + true ) x true ) of true ) + true ) true ) true ) true ) false ) of true ) + ) x ) ) ) of ) ) ) of Find the operation * b a s increase by as you go right s increase by as you go down ) a * b ab a * b a b a * b (a + b )Mod Find the Route Start x + x x x + + x + + x + x + + x x x + x + + x + x x x + x + End + x x x + + x

19 Page Find the Shape One possible selection of shapes is shown below Rectangle Equilateral triangle Scalene triangle Parallelogram Pentagon Isosceles triangle Right angled triangle Octagon Hexagon Kite Rhombus Find the Uncle The uncle is the man in the bottom left-hand corner Fishing Port Fishing grounds Four Signs x ( ) ( ) + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + x x ( ) x x Fractions to Decimals Match

20 Page Fraction Wall twelth bricks tenth bricks eighth bricks sixth bricks fifthbricks quarter bricks third bricks half bricks whole brick (a) / (b) / (c) / /, /, /, /, /, / Many possible answers Fractions Fractions Fraction unshaded Fraction shaded altogether Fraction shaded grey Fraction shaded with lines of equal parts Example

21 Page From Matches to Mapppings Pattern Mapping diagram Rules and Algebra number of triangles (t) number of matches (m) Pattern down: Rule across: Mapping: Equation: add x + t m t + t + Pattern Mapping diagram Rules and Algebra number of pentagons(p) number of matches(m) Pattern down: Rule across: Mapping: Equation: add x + p m p + p + Pattern Mapping diagram Rules and Algebra number of parallelograms(p) number of matches(m) Pattern down: Rule across: Mapping: Equation: add x + p p + m p + Pattern Mapping diagram Rules and Algebra number of number of Pattern down: hexagons matches Rule across: Mapping: Equation: add x + h h + m h + Pattern Mapping diagram Rules and Algebra number of number of Pattern down: trapezia matches Rule across: Mapping: Equation: add x + t t + m t + Pattern Mapping diagram Rules and Algebra number of number of Pattern down: rectangles matches Rule across: Mapping: Equation: add x + r r + m r + Gelosia Problems

22 Smile Mathematics Worksheet s Page Growing Patterns Halves and Quarters Halves p hexagons minutes Quarters p hexagons minutes Hexagon Puzzle twenty-one one hundred three nine seventeen fourteen seven eight thirty twenty-five forty one one half twelve twenty one quarter eighteen ten six two sixteen eleven four five fifty thirteen seventy-five fifteen seventy nineteen Hexagons Students can be encouraged to consider: Which of their shadings are different do rotations count as different or the same? What fractions can be sensibly and accurately represented why can they not show fifths?

23 Page Hidden Shapes High Powered Matching x + x x + x + Hot and Cold C C A B C C C C Alice Springs ( C) Kingston ( C) - D E F G H I C C C - C - C - C - Delhi ( C) Rome ( C) London ( C) New York (- C) Beijing (- C) Moscow (- C) - J - C - Winnipeg (- C) Any of the winter months Moscow C colder C

24 Page How many cm square? How Many Colours? The least number of colours required for each drawing is: ) colours ) colours ) colours ) colours ) colours ) colours ) colours How Many Routes? ) ) ) ) ) A B C D A B C D A B C D A B C D E A A B B C C D D E A B C D A B C D W X Y Z W X Y Z ) The last tables are the same as the networks are topologically equivalent

25 Page Identical Halves Joining Multiples Joining Odds and Evens Jumping Jack ),,,,, ),,,,, ),,,,, ),,,,, ),,,,, ),,,,, ),,,,, ),,,,, ),,,,, ),,,,,

26 Page Jumps jumps of and x x Twos and fives first meet at jumps of Twos and eights first meet at jump of and jumps of x x jumps of and jumps of x x Fives and threes first meet at jumps of and jumps of x x jumps of and jumps of x x jumps of and jumps of x x Knots knots knots knots knots knots knots knots knots knots knots knots knots knots knots Looking Around Many possible answers

27 Page Making One Mapping Jigsaw

28 Page Mapping Rectangles x x x x x x x x x x Mappings x + x x x then + Square Subtract from + then x then +

29 Page Marks to Percentages Summer They are the same for both terms Art Physical Education, English, French, History, Geography, Mathematics and Music Geography x x % x x x % x x x % x x So is the best mark Autumn Term Summer Term Subject Mark % Mark % Physical Education % % English % % French % % History % % Geography % % Mathematics % % Science % % Art % % Music % % Technology % %

30 x y yz Smile Mathematics Worksheet s Page Matching Algebraic Expressions xy x y x y x y z xy z x yz x y z xyz xyz x z x z y xyz y z xyz xy x y x z x y z x y xy y x x y xyz y x xy Matching Fractions one eighth one quarter one third one half three quarters Matching Pairs A J B D C G E K Matching Weights kg Kg g kg kg kg Kg g g g g g g Kg g g Kg kg kg g g Kg kg Kg

31 Page Mid-Point Sequences Colour can be used to accentuate the pattern Mirror Symmetry Missing Angles y x z Missing digit x x x x Impossible x x x x x

32 Page Missing Pieces More vector messages ) VECTOR CODES ARE EASY )

33 Page Multiplication and Division By Multiplying by Th H T U t h th Dividing by Th H T U t h th The rule for multiplying a number by is: Move the digits place to the left The rule for dividing a number by is: Move the digits place to the right ) ) Multiplying by Th H T U t h th Dividing by Th H T U t h th The rule for multiplying a number by is: Move the digits places to the left The rule for dividing a number by is: Move the digits places to the right ) ) Multipying by Th H T U t h th Dividing by Th H T U t h th The rule for multiplying a number by is: Move the digits places to the left The rule for dividing a number by is: Move the digits places to the right ) )

34 Page Multiples of Ten There are six groups in this shape There are six groups in this shape

35 Page Multiplication Facts Students shading will vary according to the multiplication facts they already know Having identified the multiplication facts which they need to learn, students can be encouraged to return to this activity periodically until they have learnt all of the multiplication facts Multiplication flags x x x x x x x x x Multiplying by then multiplying by is the same as multiplying by x x x x x x x x x Multiplying by then multiplying by is the same as multiplying by Multiplying by then multiplying by is the same as multiplying by Multiplying by then multiplying by is the same as multiplying by Multiplying by then multiplying by is the same as multiplying by

36 Page Multiplication Table Booklet Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

37 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

38 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

39 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

40 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

41 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

42 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

43 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

44 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

45 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

46 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

47 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

48 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

49 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

50 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

51 Page Page Page Match the multiples of In Out x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

52 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

53 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

54 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

55 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

56 Page Tables Page Page Page Page Complete the times table x x x x x x x x x x x x

57 Page Page Page Match the multiples of x x x x x x x x Mark the test paper x x x x x x x x x x Page Try these questions to make sure x x x x x x x x x x

58 Page Mystic Rose A mystic rose with points has lines ( x ) The circles with an odd number of points have a hole at the centre, whilst circles with an even number of points do not Students could be encouraged to investigate how many lines are needed for a circle with a given number of points The MicroSMILE program ROSE is a useful aid for this Nephroid Nines Complete this pattern Complete this Here is the way to check the times pattern of s multiplication tableyou have to add the tens digit to the units digit gives + gives + gives + gives + gives + gives + gives + gives + gives + gives + gives +

59 Page Nodes paths go to B, path goes to C paths go to A, path goes to C C is a -node D is a -node of -Nodes of -Nodes of -Nodes of -Nodes Total of Nodes (a) (c) (b) (d) (e) (a) of -Nodes of -Nodes of -Nodes of -Nodes Total of Nodes of -Nodes of -Nodes of -Nodes of -Nodes Total of Nodes (b) (d) (c) (e) Puzzle The rule is: add the two numbers together Sorts The rule is: multiply the two numbers together The rule is: subtract the top number from the side number six seventeen twenty-nine forty-two fifty sixty-four seventy-one ninety-three eighty-eight

60 Page Square Words + Total in numbers Total in words + One thousand and ninety-nine One thousand three hundred and seven One thousand six hundred and forty-eight Total in numbers Total in words One thousand one hundred and eight One thousand and thirty-seven One thousand nine hundred and nine Squares ) ) ) ) ) ) ) ) ) ) ) )

61 Page Squares ) ) ) ) ) ) ) ) O ) ) ) ) Squares ) ) ) ) ) ) ) ) )

62 Page Odd Animal Start One Straight Cut A C or B E G D F H Out of One possible shading is shown below % % % % % % % % % %

63 Page OXFAM Collection Sam s total Shelene s total is Kieu s total Dean s total Oxford Street A B C D Regents Park Tottenham Court Road Piccadilly Circus Bond Street Marble Arch Bond Street Marble Arch Regents Park Tottenham Court Road Piccadilly Circus Tottenham Court Road Piccadilly Circus Bond Street Marble Arch Regents Park Fold Fold Fold Fold Glue here Glue here Glue here Glue here Patterns on a line Pentagons Students patterns should be checked for accuracy Percentage Estimation % % % % a) % shaded % unshaded b) % shaded % unshaded c) % shaded % unshaded d) % shaded % shaded with lines % unshaded Percentage Puzzle % of OR % of % of OR % f % of OR % of % of OR % of

64 Page Percentages % % % % % % % % Shading Fraction Decimal % Shading Fraction Decimal % ) % ) % ) % ) % ) % ) % ) % ) % ) % ) % ) % ) % Percentages of Money Original amount p p p p % % % % p p p p p p p p p p p p p p % of is p % of p is % of is % of is % of is % of is p

65 Page Pictures from Multiples Pie Chart Match in women between and years old live on their own Source: General Household Survey % One third of the world s surface is land (Atlas) out of a pack of playing cards are red % % out of eggs for sale in Britain come from battery hens Source: Compassion in World Farming in people in the UK are pensioners Source: Keydata - % % Just under half of households in Inner London have a car Source: Guardian report on Census % Two thirds of the water used in the home is flushed down the toilet Source: Independent / / By, a quarter of the petrol delivered to petrol stations each week was unleaded Source: Digest of Environmental Protection and Water Statistics Approximately p in each of Health Spending is used for Hospital Services Source: Regional Trends Approximately in households do not have a computer Source: Keydata - % % % % Plaited Cube No answers required

66 Page Plus and Minus Grids Pounds and Pence p p p p p p p p Power Match x x Powers of Ten x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

67 Page Powers of Ten Flags x x x x x x x x x x x x Prism or Pyramid B and C make pyramids A and D make prisms Put them in their Places Directed numbers A, -,, -,, -, -, -, -,,,, B C D, -,, -,, -, -,,, -,, -,, -, -, -, -, -, -, -,,,, -, -, -,,,, -, -, -, -,, Decimals AA,,,,,,,,,, BB,,,,,,,,,, CC,,,,, DD,,,,,,,,,,,,,,, Fractions A,,,,,,,,,,,, B,,,,,,,,,,,, C,,,,,,,,,,,, D,,,,,,,,,,,, Powers A,,,,,,,,,,,, B,,,,,,,,,,,, C D,,,,,,,,,,,,,,, and,,,,,,,, A mixed bag A,,,, -,, -,,,,,, B,,,,,,,,,,,, C,,,, -,, -,,,,,, - -, -, -, D, -, -,,,, - -,,,

68 Page Putting in Order s A,,,,,, B,,,,,, C,,,,,,,, D,,,,,,,, E,,,,,,,,, F,,,,,, G,,,,,, H,,,, J,,,,,,, K,,,,,,, In order,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, L M,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Puzzle Worksheet How many Scramble? Hidden Picture tandoush erunddh hundred net ten inthegee eighteen tow two eno one wytent twenty eisnext sixteen Rifle Range/ Pat won Quiz Times Route Climb One possible solution is shown here x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

69 Page Smile Mathematics Worksheet s Race Track No answers required Radar Object Polar co-ordinates A B C D E F G H I J (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) North km i a b c d e f g h Rectangles width area length cm cm cm area length x width Reflect Right-angled Triangles ) cm ) cm ) cm ) cm ) cm ) cm ) cm ) cm

70 Page Rolling Two Dice The highest possible score is ( + ) The lowest possible score is ( + ) Column is most likely to be full However some students may find that columns or are full Columns or (or possibly or ) are most likely to have the least squares shaded There are ways to make ; ( + ), ( + ), ( + ), ( + ), ( + ), ( + ) but only way to make ( + ) Rotate this Way B A C B l O A l C l Reduced to % Rotational and Line Symmetry Review shapes with line symmetry shapes with rotational symmetry Rotations B C A F J E D L G H I K M - -

71 Page Sam Shape No answers required Satellite Signals Turn Estimate Clockwise or anticlockwise Measure A to B B to C C to D D to E E to F F to G G to H Anticlockwise Clockwise Clockwise Anticlockwise Anticlockwise Anticlockwise Anticlockwise Self-Portrait January February March April May June July August September October November December Sequence Jigsaw Across and down has the pattern add one more than the time before (The first row and column contain the triangle numbers) The leading diagonal contains x the triangle numbers, and follows the pattern add more than the time before The square numbers can be found either side of the leading diagonal Sequences in Squares + -

72 Page Shading Fractions Shape Names A rectangle All the angles of this shape are right-angles Not all the sides are equal B scalene triangle This shape has three sides None of the angles are equal It has no right-angle C equilateral triangle This shape has three sides The angles are all equal D square All the sides of this shape are equal All the angles are right-angles E right-angled trapezium This shape has four sides Two sides are parallel It has two right-angles F right-angled triangle This shape has three sides It has one right-angle G isosceles triangle This shape has two equal sides Two of the three angles are equal Shape-tiles

73 Page Shapes that can grow Silver Earrings Sim No answers required Solids cube cylinder triangular prism tetrahedron square-based pyramid cuboid Vertices Vertices Vertices Vertices Vertices Vertices Surfaces Surfaces Surfaces Surfaces Surfaces Surfaces Edges Edges Edges Edges Edges Edges Some sums for your mind Q A Q A Q A Just over One and ( ) a quarter Q A Q A Q A Q A Q A Q A A bit more About six than ( ) and a half Q A Q A Q A Q A Q A Q A and a bit - - something Q A Q A Q A Q A Q A Q A - - something Q A Q A Q A

74 Page Something and a half s and words Halves and the number line twenty-one two and a half seven and a half a half six and a half nine and a half four and a half seven eleven and a half six and a half three two and a half eight and a half twenty-three and a half a half five and a half nine and a half Halves and the a ruler Weights and scales cm kg kg kg cm cm Spirals Student patterns should be checked for accuracy

75 Page Square Diagonals + + The numbers on the leading diagonal go up in s The numbers on the other diagonal are all the same () + + The numbers on the leading diagonal go up in s The numbers on the other diagonal are all the same () + + The numbers on the leading diagonal The numbers on the other diagonal go up in s go up in s The numbers on the leading diagonal go up by the sum of the addition numbers The numbers on the other diagonal go up by the difference of the addition numbers Squares, Cubes and Roots

76 Page Straight Lines Sum and Product sum product Sum and Product Again sum product Sum Message target x + x target x x + + x x + target x + x target x x + x + target + + The word is target The word is x + T x + A O C + P x E

77 Page Surfaces Many possible answers Surrounding Right-angle Triangle cm cm cm cm cm cm cm cm cm cm cm cm cm cm The area of square R is equal to the sum of the areas of squares P and Q cm cm Symmetrical Triangles Many possible answers Symmetry

78 Page Symmetry Codes ) This shape has and sides lines of symmetry This shape has and sides lines of symmetry This shape has code This shape has code ) ) Code: Code: ) ) Code: ) Code: Code: Symmetry Match Table Squares x x x x x x

79 Page Tangram Arrows Tangram Arrows Tangram Sea Harder Tangrams Tens and Fives Multiples of ten Multiples of five x x x x x x x x x x x x Multiples of ten end in a Multiples of five end in a or a The Key to Success One set of possible solutions is shown below

80 Page The Mode Letter A B C D E F G H I J K L M Tally Frequency Letter N O P Q R S T U V W X Y Z Tally Frequency O is the most frequently used letter Letter O is the mode Many possible answers Many possible answers Many possible answers Ties ties would require about cm of m wide plain material Tom the Bowling Champ or or or or or or or or or or or or or or or

81 Page Turning Green Students answers will depend upon their interpretation of the objects and of the bins They could be encouraged to explain why they have placed items in particular bins Two cuts Investigation Many possible answers Unmarked Angles Using Brackets Many possible answers Vehicle Survey Many possible answers Weaving C and G represent the same pattern from opposite sides B D F A C E G

82 Page What Shapes? isosceles triangle right-angle triangle scalene triangle equilateral triangle equilateral triangle rectangle trapezium rhombus kite arrowhead kite pentagon pentagon pentagon pentagon pentagon regular hexagon hexagon hexagon hexagon heptagon What s the difference? Question Can you eat it? Yes No Question Is it a vegetable? Question Does it have two wheels? Yes No Yes No, and Many possible answers potato apple bicycle car Which has the largest area? b (a cm, b cm ) a (a cm, b cm ) b (a cm, b cm ) b (a cm, b cm )

83 Page Word Match cylinder minus triangle octagon kite x multiply pentagon equals ruler centimetre circle plus cube rectangle hexagon calculator + cm divide square Words wont fail me! The product of a and c is divided by b Divide a by c then subtract b Subtract b from a and then divide into c Multiply a by c then divide into b Subtract b from a then divide by c Divide the sum of a and c into b a b c c a b b a + c a c b b ac ac b The sum of a and b is divided by the sum of c and d a is added to b then divided into the product of c and d Add a to b and divide by the product of c and d The sum of a divided by c and b divided by d a + b c + d cd a + b a + b cd a + b c d a + b c c + d a + b cd ab c a + b Add a to b and then divide by c The sum of c and d is divided by the sum of a and b The product of c and d is divided by the product of a and b c is divided by the sum of a and b

84 Page Zigzag Each line is the same length It is not possible to draw a longer zigzag Search There are ways altogether: horizontal vertical diagonal

85 Page Smile Mathematics Worksheet s Search There are ways of making horizontal ways vertical ways diagonal ways Search horizontal ways vertical ways diagonal ways There are ways of making

86 Page Squares ) Colour them in s ) Colour them in s ) Colour them in s ) Colour them in s ) ) ) ) ) ) ) ) ) ) ) ) square patterns A B C Many possible answers