Patterns And Algebra - 3P Learning

Patterns and AlgebraStudent Book – Series EMathleticsInstantWorkbooksCopyright

Series E – Patterns and AlgebraContentsTopic 1 – Patterns and functionsDate completed identifying and creating patterns// skip counting// predicting repeating patterns// predicting growing patterns// function machines// that’s my number – apply// understanding equivalence// not equal to symbol// greater than and less than// balanced equations using and // using symbols for unknowns// fruit values – solve// mystery snacks – solve//Topic 2 – Equations and equivalenceSeries Author:Nicola HerringerCopyright

Patterns and functions – identifying and creating patternsLook around you, can you see a pattern? A pattern is an arrangement of shapes,numbers or colours formed according to a rule. Patterns are everywhere, youcan find them in nature, art, music and even in dance! Patterns can grow orrepeat depending on the ruleRecognising number patterns is an important part of feeling confident inmaths. In this topic we will look at different number patterns but first let’s lookat shape patterns.1Look at these repeating shape patterns. Draw the last two shapes: ab c2In these repeating shape patterns, draw the missing shapes:ab3Complete what comes next in this growing pattern:Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC1

Patterns and functions – identifying and creating patterns4Look at these repeating shape patterns. Draw the next 2 shapes:abcde5If the patterns (above) continued, what would the 10th shape be on each row:a6bcdWrite your name by putting each letter inthe grid as a repeating pattern. For example,if your name is Ben, you would write:12345e123456789 10BENBENBEN6789B10a Which letter of your name will be under the letter 32?b How did you work this out?Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC2

Patterns and functions – skip countingThere are many skip counting patterns to discover on a hundred grid.1Colour the skip counting pattern on each hundred grid:b Show the 3s and 6s pattern. Shadethe 3s and circle the 6s.a Show the 4s pattern.12345678910234567891011 12 13 14 15 16 17 18 19 2011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 10091 92 93 94 95 96 97 98 99 100d Shade the 9s pattern, then put acircle around all the numbers 5 lessthan numbers ending in 9.c Show the 11s pattern.12123456789101234567891011 12 13 14 15 16 17 18 19 2011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 10091 92 93 94 95 96 97 98 99 100Complete these number patterns by looking for skip counting patterns.a6b9c322418303620Patterns and AlgebraCopyright 3P Learning Pty Ltd548E1SERIESTOPIC3

Patterns and functions – skip counting3Colour the skip countingpattern for 3s up to 30.If you kept going on a completehundred grid, would 52 becoloured in?1234567891011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30How can you tell without using a whole hundred grid?4Only 3 numbers are shaded in each of the skip counting patterns below. Work outthe pattern and complete the shading:a123456789b10234567891011 12 13 14 15 16 17 18 19 2011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 10091 92 93 94 95 96 97 98 99 100This shows a skipcounting pattern of:51This shows a skipcounting pattern of:Shade these sequences on the hundred grid: Sequence 1: start at 1 and showa skip counting pattern of 11. Sequence 2: start at 1 and showa skip counting pattern of 98081828384858687888990919293949596979899 100Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC4

Patterns and functions – completing and describing patternsSo far we have looked at skip counting patterns that begin at zero.Here is a skip counting pattern of 5s that begins at 7.This pattern starts at 7.The rule is: Add 5.123712 517 522 527 5Continue the pattern from the starting number:aAdd 1011bAdd 555cSubtract 440Practise counting backwards by 10 and 100.Backwards by 10:Backwards by 100:a112a673b219b798c583c1 010Look carefully at these number pattern grids. There are 4 rules: across, down, andalong each diagonal.ab1526322741413844474750Patterns and AlgebraCopyright 3P Learning Pty Ltd5356E1SERIESTOPIC5

Patterns and functions – completing and describing patterns4Figure out the missing numbers in each pattern and write the 56Rule:Some number patterns can be formed with 2 operations each time.For example:2 2 37 2 317 2 337The rule is to multiply by 2 and add 3 each time.5Complete these number patterns, by following the rules written in the diamondshapes. Describe the rule underneath.3 5x2 5x2 5x2The rule is6Roll a die to make the starting number. Continue the sequence by following the rule:aRule: 4 2bRule: 1 3cRule: 3 2Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC6

Patterns and functions – predicting repeating patternsWhen we use number patterns in tables, it can help us to predict what comesnext. Look at the table below and how we can use it to predict the total numberof sweets needed for any number of children at a party.This table shows us that 1 sweet bag contains 8 sweets and 2 bags contain 16sweets. We can see that the rule for the pattern is to multiply the top row by 8to get the bottom row each time.Number of sweet bags1234510Number of sweets81624324080 8To find out how many sweets are in 10 bags, we don’t need to extend the table,we can just apply the rule.10 8 80. So, 10 bags contain 80 sweets. This helps us plan how manysweets are needed for a party.1Complete the table for each problem:a Tom receives 5 a week pocket money as long as he does all his chores. Howmuch pocket money does Tom get after 10 weeks?Weeks12Pocket money51034510b A flower has 7 petals. How many petals are there in a bunch of 10 flowers?Flowers12Number of petals71434510510c A flag has 6 stars. How many stars are there on 10 flags?Flags12Number of stars61234d At a pizza party, each person eats 3 pieces of pizza. How many pieces of pizza do10 people eat?GuestsPizza pieces1234912Patterns and AlgebraCopyright 3P Learning Pty Ltd510E1SERIESTOPIC7

Patterns and functions – predicting repeating patterns2Each of these kids wrote the first 3 numbers of a skip counting pattern of 6,starting at different numbers. Each kid’s sequence goes down the column.Imagine the sequence 1415161718a Who had the number 42 in their column?b Who had the number 50 in their column?3Look at each pattern of shapes and complete the table below:Repeat section1234510Number of circles24681020Number of triangles1234510a Show what this entire sequence would look like with 10 repeat sections:Look for the section thatrepeats. What is it madeup of? This is the rule.Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC8

Patterns and functions – predicting growing patternsNumber patterns in tables can help us with problems like this. Mia is makingthis sequence of shapes with matchsticks and wants to know how many shewill need for 10 shapes.Shape 1Shape 2Shape 3Shape number1234510Number of matchsticks369121530 3To find out how many matchsticks are needed for 10 triangles, we don’t needto extend the table, we can just apply the function rule:Number of matchsticks Shape number 31Complete the table for each sequence of matchstick shapes and find the numberof matchsticks needed for the 10th shape.abcShape 1Shape 2Shape number1Number of matchsticks4Shape 1Shape 3234Shape 2Shape number1Number of matchsticks6Shape 11Number of matchsticks710Shape 3234Shape 2Shape number5510Shape 32Patterns and AlgebraCopyright 3P Learning Pty Ltd34510E1SERIESTOPIC9

Patterns and functions – predicting growing patterns2Look at these growing patterns. Complete the table and follow the rule to drawPicture 5:aPicture 1Picture 2llllPicture 4llllllllllllPicture number1234Number of dots1357RulebPicture 35Picture number 2 – 1 Number of dotsPicture 1Picture 2Picturenumber1234Number ofsquares46810RulePicture 5Picture 3Picture 4Picture 55Picture number 2 2 Number of squaresHow many squares will Picture 8 have?Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC10

Patterns and functions – function machinesThis is a function machine.INNumbers go in, have the ruleapplied, and come out again.2OUTRULE:6 3824101Look carefully at the numbers going in these function machines and the numberscoming out. What is the rule?abIN5230OUT15IN4824742927954RULE:What numbers will come out of these function machines?baIN34RULE:OUTIN24 84873OUT24RULE:OUTRULE: 872What numbers go in to these number function machines?abINRULE:– 10OUT3652INOUT78RULE: 10287112Patterns and AlgebraCopyright 3P Learning Pty Ltd122E1SERIESTOPIC11

That’s my number!GettingreadyWhatto doapplyThis is a game for 2 players. You will need sometransparent counters each in 2 different colours and2 dice.copyPlayer 1 rolls 2 dice. The first die shows the starting number andthe second die shows the skip counting pattern. Player 1 writesdown the first 4 numbers of their sequence.For example, if Player 1 rolls a 2 and a 6, the starting number is 2and the rule is 6. So Player 1 writes 2, 8, 14, 20 and chooses oneof these numbers to cover with their counter.Player 2 has their turn, following the same steps as above. Theychoose one number to cover with their counter. If the number isalready covered, they can’t put down a counter. The winner is thefirst player to have their counters in a group of 4 (2 2223241234Patterns and AlgebraCopyright 3P Learning Pty LtdE1SERIESTOPIC12

Equations and equivalence – understanding equivalenceLook at these balanced scales.On one side there is the sum 4 3 andon the other side there is a total of7 triangles. This makes sense because itshows the equation 4 3 7.Equation is another word for a sum. Withequations, both sides must be equal.14 34 3 7Balance each set of scales by writing a number in the box that is equivalent to thetotal number of shapes. Then write the matching equation.5 a5 b2Balance each set of scales by writing a number in the box. Then write thematching equation. 5585 100 a45 bPatterns and AlgebraCopyright 3P Learning Pty LtdE2SERIESTOPIC13

Equations and equivalence – not equal to symbolWhen two sides of an equation are not balanced,it means that they are not equal. To show thatan equation is not equal, we use the not equalssymbol like this:1 12 920Write numbers in each box to show equations that are not balanced:a50b704565200 c d35 30185160 2 Complete the equations below by using only the numbers in the cards.Look carefully to see whether it is an or symbol.201535a 50b 50c 35d 35Patterns and AlgebraCopyright 3P Learning Pty LtdE2SERIESTOPIC14