Patterns and Algebra. My name. Series

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1 Student Techer Ptterns nd Alger My nme Series D

2 Copyright 009 P Lerning. All rights reserved. First edition printed 009 in Austrli. A ctlogue record for this ook is ville from P Lerning Ltd. ISBN Ownership of content The mterils in this resource, including without limittion ll informtion, text, grphics, dvertisements, nmes, logos nd trde mrks (Content) re protected y copyright, trde mrk nd other intellectul property lws unless expressly indicted otherwise. You must not modify, copy, reproduce, repulish or distriute this Content in ny wy except s expressly provided for in these Generl Conditions or with our express prior written consent. Copyright Copyright in this resource is owned or licensed y us. Other thn for the purposes of, nd suject to the conditions prescried under, the Copyright Act 968 (Cth) nd similr legisltion which pplies in your loction, nd except s expressly uthorised y these Generl Conditions, you my not in ny form or y ny mens: dpt, reproduce, store, distriute, print, disply, perform, pulish or crete derivtive works from ny prt of this resource; or commercilise ny informtion, products or services otined from ny prt of this resource. Where copyright legisltion in loction includes remunerted scheme to permit eductionl institutions to copy or print ny prt of the resource, we will clim for remunertion under tht scheme where worksheets re printed or photocopied y techers for use y students, nd where techers direct students to print or photocopy worksheets for use y students t school. A worksheet is pge of lerning, designed for student to write on using n ink pen or pencil. This my led to n increse in the fees for eductionl institutions to prticipte in the relevnt scheme. Pulished P Lerning Ltd For more copies of this ook, contct us t: Designed P Lerning Ltd Although every precution hs een tken in the preprtion of this ook, the pulisher nd uthors ssume no responsiility for errors or omissions. Neither is ny liility ssumed for dmges resulting from the use of this informtion contined herein.

3 Series D Ptterns nd Alger Contents Topic Section Ptterns Answers nd (pp. functions ) (pp. ) identifying ptterns nd nd functions creting ptterns skip equtions counting nd equivlence completing nd descriing ptterns numer ptterns in tles Section Assessment with nswers (pp. 8) growing shpe ptterns ptterns nd functions mtchstick ptterns equtions nd equivlence 7 function mchines Hrry nd Tortist solve Section Outcomes (p. 9) rows nd columns pply Dte completed / / / / / / / / / / / / / / / / / / Topic Equtions nd equivlence (pp. ) introducing equtions not equl to symol lnced equtions using + nd writing equtions for word prolems lolly weigh in solve symol sums solve / / / / / / / / / / / / Series Author: Nicol Herringer Copyright

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5 Ptterns nd functions identifying nd creting ptterns Look round you, cn you see pttern? A pttern is n rrngement of shpes, numers or colours formed ccording to rule. Ptterns re everywhere, you cn find them in nture, rt, music nd even in dnce! You cn mke pttern out of nything. Ptterns cn grow or repet. Here is pttern mde out of fruit tht repets: Here is pttern mde out of hexgons tht grows: Look t this colour pttern mde with cues. Wht comes next? Write the letters on the lnk cues then colour them in. B B B B B B Blue ed G Green Y Yellow Mke your own colour pttern with these cues using colours from the ox ove. You cn colour them or just write the letter. Answers will vry. In these shpe ptterns, drw the missing shpes. To work out wht comes next, look out for the sequence of shpes tht mke up the rule. c Ptterns nd Alger Copyright P Lerning D

6 Ptterns nd functions identifying nd creting ptterns Complete the shpe ptterns y drwing missing shpes on ech line: Look t the repeting letter pttern nd write in the missing letters. You will see tht ech pttern is word repeted. B I C Y C L E B I C Y C L E B I C Y C L E C O L O U S C O L O U S C O L O U S 6 Follow the directions to crete growing ptterns: Tick squres nd put dot in squres. Tick squres nd put dot in squres. Tick squres nd put dot in squres. Tick squres nd put dot in squres. l l l 7 8 l l l l l l l l l l l Colour squre yellow, squres red. Colour squres yellow, squres red. Colour squres yellow, 6 squres red. Colour squres yellow, squres red. Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y D Ptterns nd Alger Copyright P Lerning

7 Ptterns nd functions skip counting Skip counting is good skill to hve ecuse you cn see numer ptterns more esily which mkes you etter t mths. You cn lso count things much fster! This is skip counting pttern of on hundred grid Colour the skip counting pttern on ech hundred grid: Show the s pttern Show the 0s pttern c Wht do you notice? s pttern ends in or 0. 0s pttern ends in 0. Complete these skip counting ptterns: c d Count the ice crems. How mny re there? Ptterns nd Alger Copyright P Lerning 8 D

8 Ptterns nd functions skip counting Colour the skip counting pttern on ech hundred grid: Show the s pttern. Show the s pttern Complete the missing numers in these skip counting ptterns: c d How mny ojects ltogether? Use skip counting. How mny cndles? 6 How mny legs? 8 D Ptterns nd Alger Copyright P Lerning

9 Ptterns nd functions completing nd descriing ptterns Skip counting in the hundred grid strting t zero, is good wy to egin looking t numer ptterns. Now let s look t numer ptterns tht strt t numers igger thn zero. This pttern strts t. 7 7 The rule is: Add Complete the missing numers in ech pttern: ule: Add 7 9 ule: Add c ule: Sutrct Continue the pttern from the strting numer: Add Add c Sutrct Finish ech pttern nd write the rule: ule: ule: + 7 c ule: 9 Ptterns nd Alger Copyright P Lerning D

10 Ptterns nd functions completing nd descriing ptterns Fill these snil grids with these ptterns. You cn use clcultor. Skip count y : Skip count y 9: Check these ptterns with clcultor. They ll hve mistkes in them. Find the mistkes, circle them nd write the corrections underneth These ptterns hve something in common. Cn you discover wht it is? c oll set of dice to mke digit numer. This is the strting numer. Write it in the first spce. Then continue the sequence y following the rule. ule: + 0 ule: + c ule: + 6 D Ptterns nd Alger Copyright P Lerning Answers will vry.

11 Ptterns nd functions numer ptterns in tles When we use numer ptterns in tles it cn help us to predict wht comes next. Look t the tle elow. Once we work out how the pttern works, we cn predict the totl numer of feet for ny mount of students. This tle shows us tht when there is child there re feet. When there re children there re feet nd so on. We cn see tht the rule for the pttern is to multiply the top row y to get the ottom row ech time. Numer of children 0 Numer of feet To find out how mny feet 0 children would hve, we don t need to extend the tle, we cn just pply the rule. Try these numer pttern tles. At prty, one child receives chocoltes. Complete the tle to show how mny chocoltes different numers of students receive. Show how mny 0 receive. Numer of children 0 Numer of chocoltes Alfred is type of lien from the Plnet Trmpolon. The surfce of Plnet Trmpolon is like wlking on trmpoline. Tht is why Alfred nd ll his rce of liens need legs for extr lnce. They lso hve ntenne nd fingers on ech hnd. Complete the numer pttern tles to show the numer of different ody prts for different mounts of liens. Numer of liens 0 Numer of ntenne c Numer of liens 0 Numer of fingers on ech hnd Numer of liens 0 Numer of legs Ptterns nd Alger Copyright P Lerning D 7

12 Ptterns nd functions growing shpe ptterns Let s look t this growing pttern: utterfly uses hexgons. utterflies use hexgons. utterflies use 6 hexgons. How mny hexgons would 0 utterflies use? There is wy we cn do this without using pttern locks. We just look for pttern. The pttern is tht you need to doule the mount of hexgons for ech utterfly. So for 0 utterflies, you would need 0 hexgons. Here re some pictures mde from shpes. Fill in the lnks for ech prt of the pttern nd drw wht comes next: nt uses circles. nts use nts use nts use 6 circles. 9 circles. circles. How mny circles would you use for 0 nts? 0 c The first fish is mde up of shpes. Fill in the oxes for fish nd fish: Try to mke your own growing ptterns from pttern locks. fish uses shpes. fish use fish use 0 shpes. shpes. d How mny shpes would you use for 0 fish? 0 8 D Ptterns nd Alger Copyright P Lerning

13 Ptterns nd functions mtchstick ptterns Numer ptterns in tles cn help us with prolems like this. Mi is mking this sequence of shpes with mtchsticks. How cn she find out how mny she needs for 0 shpes? Shpe Shpe Shpe Shpe numer 0 Numer of mtchsticks To find out how mny mtchsticks re needed for 0 tringles, we don t need to extend the tle, we cn just pply the function rule: Numer of mtchsticks = Shpe numer Complete the tle for ech sequence of mtchstick shpes nd find the numer of mtchsticks needed for the 0th shpe. Shpe Shpe Shpe Shpe numer 0 Numer of mtchsticks Shpe Shpe Shpe Shpe numer 0 Numer of mtchsticks c Drw the fourth shpe in the sequence ove: Ptterns nd Alger Copyright P Lerning D 9

14 Ptterns nd functions function mchines This is function mchine. Numers go in, hve the rule pplied, nd come out gin. IN OUT 8 Wht numer will come out of these function mchines? 0 IN OUT 0 IN + 8 OUT Write the rule on these function mchines: IN OUT 9 or +6 IN OUT 6 or + Wht numer will come out of these doule function mchines? 8 IN + OUT IN + 6 OUT Write the numer tht went into these function mchines: 9 IN OUT 7 0 IN 8 OUT 0 D Ptterns nd Alger Copyright P Lerning

15 Hrry nd Tortist solve Getting redy ed the prolem elow nd use your knowledge of numer ptterns to solve the prolem. Wht to do Hrry nd Tortist constntly rgued over who ws the fster runner out of the pir. To settle the dispute once nd for ll, they decided to rce ech other. Hrry ws so confident tht he could et Tortist, he gve Tortist hed strt of km. If Hrry runs km every minutes nd Tortist runs km every minutes, who will win the km rce? Complete the tle for Hrry nd Tortist to find out: Hrry Tortist km mins km mins They tie. Both run km in 6 minutes Ptterns nd Alger Copyright P Lerning D

16 ows nd columns pply Getting redy This is gme for plyers. You will need dice, this pge nd counters ech in different colours. Wht to do Plyer rolls ll dice, dds them together nd puts this vlue in the first function rule. For exmple, if they roll, nd, they should dd these nd get 0. They put 0 into the first rule nd get 0 + =. Plyer plces one of their counters on. Then Plyer repets these steps. Keep tking turns using different function rule ech time. If the nswer is lredy tken, you lose turn. The winner is the first person to get rid of ll their counters. Function ule + Function ule Function ule Wht to do next Chnge the oject of the gme. For exmple, the winner might e the person who hs their counters on the most even numers. D Ptterns nd Alger Copyright P Lerning

17 Equtions nd equivlence introducing equtions Look t these lnced scles. In ech ox on the left there re dots nd on the other side is the numer 8. This mkes sense ecuse it shows the eqution + = 8. An eqution is sum 8 with n equls symol. One side must equl or lnce the other just like these scles. Blnce ech set of scles y writing numer in the ox. Then write the mtching eqution: = = Agin, lnce ech set of scles ut this time dd the missing dots to the empty ox: 8 + = = 0 This time, crete your own eqution nd show it on the lnced scles: + = Answers will vry. Ptterns nd Alger Copyright P Lerning D

18 Equtions nd equivlence introducing equtions Blnce ech set of scles y writing the missing numer in the ox c 0 d These scles re not lnced. This shows tht the eqution is not equl. One side is greter thn the other. Write numer in the ox to mke these true. The first one hs een done for you. 6 There re lots of different numers tht could mke these true. 0 < 0 c > 90 d e < > D Ptterns nd Alger Copyright P Lerning

19 Equtions nd equivlence not equl to symol When two sides of n eqution re not lnced, it mens tht they re not equl. To show tht n eqution is not equl, we use the not equls symol like this: Blnce ech set of scles y writing numer in the ox. Then write the mtching eqution. + < 0 > + + > + < 0 c < 6 d > < > e 0 f 0 + <60 + > 00 Answers will vry. + > < g 0 + <0 h >9 0 + < > 9 0 Ptterns nd Alger Copyright P Lerning D

20 Equtions nd equivlence not equl to symol Prctise using the equls to ( = ) or not equls to ( ) symol in these prolems. oll dice nd write the numer in ech ox. Then, mke the eqution true y either writing = or in the circle. Answers will vry c + 8 d + e + 0 f + 7 Complete the equtions elow only using the numers in the crds. Look crefully to see whether it is = or = Possile nswers. c 6 + = 0 d oll die nd write the numer in ny str tht lnces the eqution. Your im is to lnce s mny equtions s you cn out of 6 rolls of the die. For numers tht do not lnce the equtions, use n symol. 6 +I 0 +I 9 c 9 +I d +I e +I 6 f +I 8 g How did you go? Answers will vry. 6 D Ptterns nd Alger Copyright P Lerning

21 Equtions nd equivlence lnced equtions using + nd There re different equtions we could write for one set of lnced scles. + + = = Work out the vlues of the symols in ech prolem = 0 0 = = 6 = This time work out which numer should go in the symol. + + = = = 7 = Ptterns nd Alger Copyright P Lerning D 7

22 Equtions nd equivlence lnced equtions using + nd How mny dots re inside ech ox? On one side there re dots nd on the other side, there re oxes. Becuse the eqution is lnced, there must e 6 in ech ox. There re different equtions we could write for one set of lnced scles = 6 = How mny dots re inside ech ox? + + = 9 = 9 How mny dots re inside ech ox? + + = = If there re 6 dots in these cylinders, how mny dots re there in 6 cylinders? Show your working. = 6 6 = 8 D Ptterns nd Alger Copyright P Lerning

23 Equtions nd equivlence writing equtions for word prolems We cn use symols to stnd for the unknown numer in word prolems. ed this word prolem. Jess nd Jo went on n Ester egg hunt. Jess found eggs nd Jo found 7 eggs. How mny did they find ltogether? The eqution for this prolem is: + 7 = I I = 0 Now red this prolem: Jess nd Jo went on n Ester egg hunt. If 0 eggs were found ltogether nd Jo found 7 eggs, how mny did Jess find? The eqution for this prolem is: 7 + I = 0 I = Wrm up with these. Find the vlue of the symols in ech eqution. = 9 9 = 6 = = c 0 = d 6 = = = 7 Choose n eqution from ove nd write word prolem. Answers will vry. Use symol to stnd for the unknown numer. Ptterns nd Alger Copyright P Lerning D 9

24 Equtions nd equivlence writing equtions for word prolems Write n eqution for these word prolems. Write n eqution using for the unknown numer. Mi did 6 push ups every dy for 7 dys. How mny push ups did she do ltogether? 6 7 = = Josh sved $ of his pocket money over 8 weeks. How much did Josh sve t the end of 8 weeks? $ 8 = = $0 c There re 8 children in the clss. children hve rown hir. How mny children do not hve rown hir? 8 = = Look t key words for hint out the opertion. d Mx hs $ more thn I do. If I hve $0, how much does Mx hve? $0 + $ = = $6 If the str is worth the sme, wht is it worth in this eqution? + + = 6 = 0 D Ptterns nd Alger Copyright P Lerning

25 Lolly weigh in solve Wht to do Work your wy through these prolems. Work out wht ech lolly g weighs: 00 g 0 g 0 g 80 g 0 g 0 g c 600 g 80 g 80 g Ptterns nd Alger Copyright P Lerning D

26 Symol sums solve Wht to do Work out the vlue of ech symol. If the symol is repeted it is the sme numer. + = 0 ª = 0 ª = = ª = = 0 + = ª = ª = = = ª = = + ª = ª + = = = ª = 7 = 6 ª 6 = = ª = = ª = 6 D Ptterns nd Alger Copyright P Lerning

27 Ptterns nd functions Nme Drw the missing shpe in these shpe ptterns: Complete these skip counting ptterns y filling in the missing numers Finish ech pttern nd write the rule: 6 8 ule: 9 7 ule: c ule: Skills Not yet Kind of Got it Completes shpe pttern Completes skip counting pttern Completes numer pttern nd write the rule in words Copyright P Lerning Series D Topic Assessment

28 Ptterns nd functions Nme Drw the missing shpe in these shpe ptterns: Complete these skip counting ptterns y filling in the missing numers Finish ech pttern nd write the rule: ule: ule: + c ule: Skills Not yet Kind of Got it Completes shpe pttern Completes skip counting pttern Completes numer pttern nd write the rule in words Series D Topic Assessment Copyright P Lerning

29 Ptterns nd functions Nme Complete this tle nd nswer the questions: Numer of pckets 0 Numer of sweets How mny sweets in 0 pckets? How did you work this out? Write the rule on these function mchines: 7 IN OUT 0 IN OUT 9 6 Look crefully t this growing pttern. Drw wht comes next: How mny squres will e needed for the 0th shpe? c How do you know? Skills Not yet Kind of Got it Completes shpe or numer pttern y following function rule Cn write rule to descrie input nd output reltionships Copyright P Lerning Series D Topic Assessment

30 Ptterns nd functions Nme Complete this tle nd nswer the questions: Numer of pckets 0 Numer of sweets How mny sweets in 0 pckets? 00 How did you work this out? Multiply the numer of pckets y 0. Write the rule on these function mchines: 7 IN + OUT 0 IN OUT 9 6 Look crefully t this growing pttern. Drw wht comes next: How mny squres will e needed for the 0th shpe? c How do you know? This pttern grows y ech time. Skills Not yet Kind of Got it Completes shpe or numer pttern y following function rule Cn write rule to descrie input nd output reltionships 6 Series D Topic Assessment Copyright P Lerning

31 Equtions nd equivlence Nme Crete your own eqution nd show it on the lnced scles: + = Blnce ech set of scles y writing numer in the ox. Then write the mtching eqution Write n eqution for this word prolem. Use symol for the unknown numer. Sils te pples every dy for dys. How mny pples did he et ltogether? Skills Not yet Kind of Got it ecognises tht equls symol mens equivlence ecognises the not equls to symol Cn mtch numer sttement tht uses symol for the unknown in simple story prolem Copyright P Lerning Series D Topic Assessment 7

32 Equtions nd equivlence Nme Crete your own eqution nd show it on the lnced scles: + = Answers will vry. Blnce ech set of scles y writing numer in the ox. Then write the mtching eqution Answers will vry. + + > < 0 00 > 0 < 00 Write n eqution for this word prolem. Use symol for the unknown numer. Sils te pples every dy for dys. How mny pples did he et ltogether? = = * Choice of symol will vry. Skills Not yet Kind of Got it ecognises tht equls symol mens equivlence ecognises the not equls to symol Cn mtch numer sttement tht uses symol for the unknown in simple story prolem 8 Series D Topic Assessment Copyright P Lerning

33 Series D Ptterns nd Alger Curriculum Outcomes Ntionl Curriculum NSW AusVELS ACMNA060 MA-WM MA-WM MA-WM MA-8NA ACMNA060 Descrie, continue, nd crete numer ptterns resulting from performing ddition or sutrction Uses pproprite terminology to descrie, nd symols to represent, mthemticl ides Selects nd uses pproprite mentl or written strtegies, or technology, to solve prolems Checks the ccurcy of sttement nd explins the resoning used Generlises properties of odd nd even numers, genertes numer ptterns, nd completes simple numer sentences y clculting missing vlues Descrie, continue, nd crete numer ptterns resulting from performing ddition or sutrction Copyright P Lerning Series D Outcomes 9