a) b) c) You will need a pegboard and pegs. 1. Arrange 12 pegs in a rectangle. So 3 is a factor of 12, and 4 is a factor of What do these show?

Transcription

1 Smile 00 You will need a pegboard and pegs.. Arrange pegs in a rectangle. = x So is a factor of, and is a factor of.. What do these show? a) b) c). Arrange pegs in a rectangle in as many ways as possible. t Draw each rectangle pattern. ' There is also a straight line pattern. Draw the straight line pattern. Write {factors of } = {,,,, }. Copy and complete: (a) {factors of } = {,,,,, } (b) {factorsof 0} = {,,,,, } (c) {factorsof} = {,,, } (d) {factors of } = }. What are the factors of (a) (b) 0 (c) (d)? Do this for some other numbers.. Describe, in your words, what a factor is. RBKC SMILE 00

2 Prime Numbers Smile 00 A prime number is a number that has only two factors, and itself. ) The factors of are and The number has only two factors. x = So is a prime num ber. The factors of are,, and The number has four factors. So is not a prime number. x = x = ) Which of the following numbers is prime? a) b) c) d) ) List all the prime numbers less than 0. ) Write a definition of a prime number in your book. RBKC SMILE

3 c Smile 00 ) Copy and complete : {factors of \ {factors of } { ' ' ' / I ' ' ' ' ) Copy and complete this Venn diagram, using all the numbers from to. { - } Factors: of Factor-sol ) Which numbers are factors of both and? Write {common factors of and } = { Si, If} Turn over

4 ) Write {factors of 0} {factors of 0} {factors of G} {factors of } {factors of 0} {factors of } {factors of } {,, M,m, M, M] {m,m,m, ^ Bi&J, isssij BES, lisa, Bral, Esa j ) Draw new Venn diagrams to show: (a) The common factors of 0 and 0. (b) The common factors of and. (c) The common factors of 0, and. The Venn diagram for part (c) is shown for you to copy and complete. {-} Factors oil > Factors of'ib;- Write {common factors of 0 and 0} = {common factors of and } = { H, H, H {common factors of 0, and } = { H }

5 Factor Finder Smile 0 I f I ( r i i i f f f ( ( I r f f ( f f I ( f f f e f s t t 0 it a is ft is if i? tt to it a a at & In row there Is a above every multiple of (every number). In row there is a above every multiple of. Copy the table and fill in the numbers along each row. ) Which numbers are written in column? What is special about these numbers? ) Where can you find all the factors of? ) Where are all the factors of? ) How can you find the common factors of and 0? What are they? ) Write down all the numbers with exactly factors. These numbers are called prime numbers. ) What can you say about their factors? Find some more patterns on your table and write about them.

6 Spots in Sequence Smile 0,,,, What is the pattern of the numbers? Turn over

7 Find the first numbers in these sequences. a) b) c) d) e) RBKC SMILE 00

8 You will need dotty paper. Smile 0 Dots in Sequence Draw these squares on dotty paper. (a) Find a sequence of numbers by counting the dots on the perimeter of each square. Continue the sequence and describe it. (b) Do the same for the dots inside each square.

9 Smile 0 Dots in Sequences You will need dotty square paper. Draw these squares on dotty paper. Find a sequence of numbers by counting the dots on the perimeter of each square. Continue the sequence and describe it. Do the same for the dots inside each square. SMILE Mathematics 00 Dots in Sequences You will need dotty square paper. Smile 0 Draw these squares on dotty paper. Find a sequence of numbers by counting the dots on the perimeter of each square. Continue the sequence and describe it. Do the same for the dots inside each square. SMILE Mathematics 00

10 Counting On Smile Worksheet ) > Count on ) » Count on ) Count on ) 0 Count on ) Count on turn over

11 Counting Back Example Count back ) > > Count back ) > * Count back ) * > Count back ) 0) * Count back > Count back RBKC SMILE 00

12 Smile 0 Sequences of Numbers, 0,, 0, >,,,,, 0,, 0,, AddS Double Continue these sequences and describe them..,,,,.,,,,. 0,,,,., ±,, ±, ,,,,, 0, 00, 000,,,,,,,,,,,,,,,, RBKC SMILE 00

13 You will need: scissors, cardboard, drawing pin. Smile 00 Turning Patterns These patterns can be made by turning and drawing around an L shape. Turn over

14 Drawing pin Change the position of the drawing pin to make different patterns. Try turning a different shape.

15 You will need cm squared paper, colours, scissors and glue. Smile 0 Cutting up Rectangles ) Draw and colour rectangles like this: ) Cut each rectangle into triangles. Use the triangles to make the shapes below. Stick them in your book. Kite Triangle Triangle Parallelogram Turn over

16 ) Draw and colour rectangles like this: ) Use them to make the shapes below. Stick them In your book. Triangle

17 Smile 0 Use a metre ruler. Is a chair more than a metre high?. Find out some things that are more than a metre.. Find out some things that are less than a metre. Look for a centimetre on the metre ruler.. Find out some things that are less than a centimetre.. Find out some things that are more than a centimetre. RBKC SMILE 00

18 You will need tracing paper. Smile 0 Rotation Copy and complete the following patterns, Turn over

19 Now make up some more of your own. You may like to use LOGO.

20 Smile 0 Tessellations of Quadrilaterals You will need square dotty paper. A tessellation is a repeating pattern of tiles without gaps. Copy this tessellation where the tile is a quadrilateral. turn over

21 Here are different qud^aterals. Draw a tessellation from each one. trapezium parallelogram rhombus kite arrowhead irregular quadrilateral RBKC SMILE 00

22 Smile Worksheet 0 Centre of Rotation You will need tracing paper. Trace one of the A shapes. Put your pencil point on x and rotate the tracing paper. One A shape can be rotated onto the other. x is the centre of rotation. Find the centre of rotation for each of these letters. E M d p n F RBKC SMILE 00

23 Tessellating Pentominoes a group activity Smile 0 The pentomino will tessellate in only one way. The pentomino will tessellate in five different ways. Investigate the tessellations of all pentominoes.

24 Smile 00 You will need hundred squares and Smile Worksheet 00a f On a hundred square ' On this hundred square the multiples of are shaded. n g 0 0 \ This makes a column pattern. 0 0 Take a hundred square. Shade the multiples of. Do you get a column pattern? On other hundred squares find out which other multiples make column patterns. \ 'v. X ' -" - '. ". '- ' "' ', ' -/."*.', ' '-. ***"', '"" : ' "J~>^-~r-* ' ^ i / On a square with six columns Use a square with six columns from Smile worksheet 00a. 0 "», \ Shade the multiples of. Do you get a column pattern? Find out which other multiples make column patterns. Vv._,..., _._ _ « ,...,.... X/ : -... '. : -':"-.'-:- :\., 0 0 J I ij /**"*; ; ""-.- ::^>'. ;'J""j?""*"\ " "". '' * -_-^. ^ «,, " «,, On a square with seven columns! Use a square with seven columns from Smile worksheet 00a 0 \ W Find any multiple which makes column patterns using : a square with seven columns? V-v. ^ C^"' ''-"' '" ' ' ': ": '- ', /^' ^, ' ""'' : ' '"' ' ' ' ' Investigate! Which multiples give column patterns on the: ten square? six square? seven square? -'-] I Ik Can you predict which multiples would give a column pattern on a twelve square? What is the general rule? ~*x \ \ I RBKC SMILE 00

25 Multiple Patterns Smile Worksheet 00a RBKC SMILE 00

26 Prime Factors Smile 0 0,,, 0 and have each been made by multiplying prime numbers, Make the following by multiplying prime numbers,, and 00 Turn over If you need some ideas about how to approach these problems.

27 * 0 + * m *g i = 0 «0 = " ti X 0 = 0 x x 0 x xxxx= 0,and are the prime factors of 0.

28 Smile 0 Equivalent Fractions You may need tracing paper. There are triangles There are squares There are rectangles are shaded. are shaded. is shaded. The fraction shaded is ; The fraction shaded is The fraction shaded is These three fractions, = = T are equal Fractions that are equal are called equivalent fractions. These shape names may help you identify equivalent fractions in the drawings on the back of this page. triangle square rectangle trapezium rhombus hexagon octagon turn over

29 Draw these shapes and fine as many equivalent fractions as you can reach for each one. (You should find at least for each.).. I I \\.. RBKC SMILE 00

30 Egyptian Numbers Smile 0 In about 000 BC mathematics was being engraved on the tomb of a pharoah. The numbers were written very simply: for for 0 for 00 I II III II II III II III III INI III INI INI III III III n 0 00 So that 's and is Translate these: ) ) nnn MI )} MI ); r\r\ ); nnn in Write these as Egyptian numbers: ) ) 0 0) ) 0 ) ) RBKC SMILE 00

31 iummfna the Odds Smile 0 Investigate some more square number patterns like this. Explain how you can work out the sum of the first odd numbers. Can you make this into a general rule?

32 Vector Messages Smile 0 Tr// if These vectors spell out DOG Start A C D E F M L K J H G N O P Q R S T Space Z Y X W V U From Start takes you to D From takes you to From T T» takes you to. What does this say? H > Ll ^>. Show how to spell out the word VECTORS.. Make a vector message for a friend. RBKC SMILE.

33 Smile 00 You will need: geo-strips, split pins Use geo-strips to make a triangle. Is it rigid (firm)? Make some different triangles and see it they are rigid. Make some different quadrilaterals using geo-strips each time. Add a diagonal to each one to make them rigid. Can you see why the diagonal makes them rigid? Make a pentagon, a hexagon, and polygons with more than sides. Add the right number of diagonals each time to make them rigid. How many diagonals do you need each time? Find a rule- if you can. RBKC SMILE 00

34 Smile Worksheet 0 Nodes Four paths lead from node A. One of the paths goes to D. ) Where do the others go? A is a -node. A is a node of order.

35 ) How many paths lead from B? ) Where do they go? B is a -node. B is a node of order ) C is a D is a -node. -node. ) Complete the table: Number of -Nodes Number of -Nodes Number of -Nodes Number of -Nodes Total Number of Nodes

36 Next to each node write the order of the node. Some of (a) has been done for you. Complete the table: Number of -Nodes Number of -Nodes Number of -Nodes Number of -Nodes Total Number of Nodes (a) 0 (b) (c) turn over

37 Mark in the nodes on these networks. By each node, write in the order. (d) (e) Complete the table: Number of -Nodes Number of -Nodes Number of -Nodes Number of -Nodes Total Number of Nodes (d) (e) RBKC SMILE 00

38 r Smile 0 About Nodes To draw a network, it is a good idea to set out the nodes first and then join up the loose ends. For a network with two -nodes and one -node: Sef out the nodes Join them up There may be more than one possible answer. Try to draw networks for (a) to (h). You will find that two are impossible. Number of -nodes Number of -nodes Number of -nodes Number of -nodes (a) (b) 0 0 (c) (d) (e) 0 0 (f) (g) 0 0 (h) Make up some examples of your own and fry to find a rule to decide whether or not a network can be drawn.

39 You will need: 0 counters smile 0 Counter Hopping Puzzle Put 0 counters in a row. You may move any counter over the nearest counters and onto the rd nearest. Your first moves could be the ones shown You must finish with pairs of counters - equally spaced like this:

40 Smile Worksheet 0 Smile Worksheet 0 Sequences In Squares. + Sequences In Squares Complete the sequences in these squares. 0 Complete the sequences in these squares O RBKC SMILE 00 I RBKC SMILE 00

41 Sequences ^^ B in Squares ^^ Smile OIIMIC Worksheet VVUII\0 0 Here is an example of a completed square Complete the sequences in these squares. o r + + VI ' I - * + -

42 How Many Rectangles? Smile 0 This rectangle has dividing line. How many rectangles are there altogether? (The answer's not.) This rectangle has parallel dividing lines. Can you see that there are rectangles altogether? How many rectangles are there with parallel dividing lines? dividing lines? What about dividing lines? Can you see a pattern? Turn over

43 These rectangles have one horizontal dividing line. If you add one more vertical dividing line each time, is there a new pattern? How new? horizontal dividing lines. A pattern? horizontal lines? A pattern of patterns?

44 Tangram Teasers You will need a piece tangram. Smile 0 Here is one way to make triangle with tangram ieces. Make other triangles using different combinations of pieces. Can you make a triangle with pieces pieces pieces pieces? How many different ways can you make a square using the tangram pieces?

45 You will need a tetrahedron, isometric paper and scissors. Smile 0 TETRAHEDRON NETS Get a tetrahedron from the box of solids.. How many FACES has it?. What shape is each face?. How many triangles are there in the shapes below? (e) (c) is the net of a tetrahedron. Find which of the other drawings are nets of tetrahedrons.

46 Tetrahedron Nets You will need a tetrahedron, Isometric paper and scissors. Smile 0 Get a tetrahedron from the box of solids.. How many faces has it?. What shape is each face?. How many triangles are there in the shapes below? (a). (e) is the net of a tetrahedron. Find which of the other drawings are nets of tetrahedrons. RBKC SMILE Mathematics 00