# Patterns and Algebra

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1 Student Book Series D Mthletis Instnt Workooks Copyright

2 Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing shpe ptterns mthstik ptterns funtion mhines Hrry nd Tortist solve rows nd olumns pply Dte ompleted Topi Equtions nd equivlene introduing equtions not equl to symol lned equtions using + nd writing equtions for word prolems lolly weigh in solve symol sums solve Series Author: Niol Herringer Copyright

3 Ptterns nd funtions identifying nd reting ptterns Look round you, n you see pttern? A pttern is n rrngement of shpes, numers or olours formed ording to rule. Ptterns re everywhere, you n find them in nture, rt, musi nd even in dne! You n mke pttern out of nything. Ptterns n grow or repet. Here is pttern mde out of fruit tht repets: Here is pttern mde out of hexgons tht grows: Look t this olour pttern mde with ues. Wht omes next? Write the letters on the lnk ues then olour them in. B R B R B R B Blue R Red G Green Y Yellow Mke your own olour pttern with these ues. Use one of the olours in the ox ove. You n olour them or just write the letter. In these shpe ptterns, drw the missing shpes. To work out wht omes next, look out for the sequene of shpes tht mke up the rule. D

4 Ptterns nd funtions identifying nd reting ptterns Complete the shpe ptterns y drwing missing shpes on eh line: 5 Look t the repeting letter pttern nd write in the missing letters. You will see tht eh pttern is word repeted. B I C C E B I Y L E B C Y C L C L O R S C O O U R C L U R S 6 Follow the diretions to rete growing ptterns: Tik squres nd put dot in squres. Colour squre yellow, squres red. Tik squres nd put dot in squres. Colour squres yellow, squres red. Tik squres nd put dot in squres. Colour 5 squres yellow, 6 squres red. Tik squres nd put Colour squres yellow, dot in squres. squres red. D

5 Ptterns nd funtions skip ounting Skip ounting is good skill to hve euse you n see numer ptterns more esily whih mkes you etter t mths. You n lso ount things muh fster! This is skip ounting pttern of on hundred grid Colour the skip ounting pttern on eh hundred grid: Show the 5s pttern Show the 0s pttern Wht do you notie? Complete these skip ounting ptterns: d Count the ie rems. How mny re there? D

6 Ptterns nd funtions skip ounting Colour the skip ounting pttern on eh hundred grid: Show the s pttern. Show the s pttern Complete the missing numers in these skip ounting ptterns: d How mny ojets ltogether? Use skip ounting. How mny ndles? How mny legs? D

7 Ptterns nd funtions ompleting nd desriing ptterns Skip ounting 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 eh pttern: Rule: Add 5 7 Rule: Add 8 Rule: Sutrt Continue the pttern from the strting numer: Add 0 Add 5 55 Sutrt 0 Finish eh pttern nd write the rule: 5 8 Rule: 7 Rule: Rule: D 5

8 Ptterns nd funtions ompleting nd desriing ptterns Fill these snil grids with these ptterns. You n use lultor. Skip ount y 5: Skip ount y 9: Chek these ptterns with lultor. They ll hve mistkes in them. Find the mistkes, irle them nd write the orretions underneth These ptterns hve something in ommon. Cn you disover wht it is? Roll set of die to mke digit numer. This is the strting numer. Write it in the first spe. Then ontinue the sequene y following the rule. Rule: + 0 Rule: + Rule: + D 6

9 Ptterns nd funtions numer ptterns in tles When we use numer ptterns in tles it n help us to predit wht omes next. Look t the tle elow. One we work out how the pttern works, we n predit the totl numer of feet for ny mount of students. This tle shows us tht when there is hild there re feet. When there re hildren there re feet nd so on. We n see tht the rule for the pttern is to multiply the top row y to get the ottom row eh time. Numer of hildren 5 0 Numer of feet To find out how mny feet 0 hildren would hve, we don t need to extend the tle, we n just pply the rule. Try these numer pttern tles. At prty, one hild reeives hooltes. Complete the tle to show how mny hooltes different numers of students reeive. Show how mny 0 reeive. Numer of hildren 5 0 Numer of hooltes Alfred is type of lien from the Plnet Trmpolon. The surfe of Plnet Trmpolon is like wlking on trmpoline. Tht is why Alfred nd ll his re of liens need legs for extr lne. They lso hve ntenne nd fingers on eh 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 Numer of liens 0 Numer of fingers on eh hnd Numer of liens 0 Numer of legs D 7

10 Ptterns nd funtions 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 n do this without using pttern loks. We just look for pttern. The pttern is tht you need to doule the mount of hexgons for eh utterfly. So for 0 utterflies, you would need 0 hexgons. Here re some pitures mde from shpes. Fill in the lnks for eh prt of the pttern nd drw wht omes next: nt uses nts use nts use nts use irles. irles. irles. irles. How mny irles would you use for 0 nts? The first fish is mde up of 5 shpes. Fill in the oxes for fish nd fish: Try to mke your own growing ptterns from pttern loks. fish uses 5 shpes. fish use shpes. fish use shpes. d How mny shpes would you use for 0 fish? D 8

11 Ptterns nd funtions mthstik ptterns Numer ptterns in tles n help us with prolems like this. Mi is mking this sequene of shpes with mthstiks. How n she find out how mny she needs for 0 shpes? Shpe Shpe Shpe Shpe numer 5 0 Numer of mthstiks To find out how mny mthstiks re needed for 0 tringles, we don t need to extend the tle, we n just pply the funtion rule: Numer of mthstiks = Shpe numer Complete the tle for eh sequene of mthstik shpes nd find the numer of mthstiks needed for the 0th shpe. Shpe Shpe Shpe Shpe numer 5 0 Numer of mthstiks Shpe Shpe Shpe Shpe numer 5 0 Numer of mthstiks 5 Drw the fourth shpe in the sequene ove: D 9

12 Ptterns nd funtions funtion mhines This is funtion mhine. Numers go in, hve the rule pplied, nd ome out gin. IN OUT 8 Wht numer will ome out of these funtion mhines? 0 IN 5 OUT 5 IN + 8 OUT Write the rule on these funtion mhines: IN OUT 9 IN OUT 6 Wht numer will ome out of these doule funtion mhines? 8 IN + 5 OUT IN + 6 OUT Write the numer tht went into these funtion mhines: IN OUT 7 IN 8 OUT D 0

13 Hrry nd Tortist solve Getting redy Red the prolem elow nd use your knowledge of numer ptterns to solve the prolem. Wht to do Hrry nd Tortist onstntly rgued over who ws the fster runner out of the pir. To settle the dispute one nd for ll, they deided to re eh other. Hrry ws so onfident tht he ould 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 re? Complete the tle for Hrry nd Tortist to find out: Hrry Tortist km mins km mins D

14 Rows nd olumns pply Getting redy This is gme for plyers. You will need die, this pge nd ounters eh in different olours. Wht to do Plyer rolls ll die, dds them together nd puts this vlue in the first funtion rule. For exmple, if they roll, 5 nd, they should dd these nd get 0. They put 0 into the first rule nd get = 5. Plyer ples one of their ounters on 5. Then Plyer repets these steps. Keep tking turns using different funtion rule eh time. If the nswer is lredy tken, you lose turn. The winner is the first person to get rid of ll their ounters. Funtion Rule + 5 Funtion Rule Funtion Rule Wht to do next Chnge the ojet of the gme. For exmple, the winner might e the person who hs their ounters on the most even numers. D

15 Equtions nd equivlene introduing equtions Look t these lned sles. In eh ox on the left there re dots nd on the other side is the numer 8. This mkes sense euse it shows the eqution + = 8. An eqution is sum 8 with n equls symol. One side must equl or lne the other just like these sles. Blne eh set of sles y writing numer in the ox. Then write the mthing eqution: + = + = Agin, lne eh set of sles ut this time dd the missing dots to the empty ox: 8 + = 0 + = This time, rete your own eqution nd show it on the lned sles: + = D

16 Equtions nd equivlene introduing equtions Blne eh set of sles y writing the missing numer in the ox d These sles re not lned. 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 ould mke these true d 5 5 e 7 7 D

17 Equtions nd equivlene not equl to symol When two sides of n eqution re not lned, it mens tht they re not equl. To show tht n eqution is not equl, we use the not equls symol like this: Blne eh set of sles y writing numer in the ox. Then write the mthing eqution d e 50 f g 50 + h D 5

18 Equtions nd equivlene not equl to symol Prtise using the equls to ( = ) or not equls to ( ) symol in these prolems. Roll die nd write the numer in eh ox. Then, mke the eqution true y either writing = or in the irle d + e + 0 f + 7 Complete the equtions elow only using the numers in the rds. Look refully to see whether it is = or = + + = d + Roll die nd write the numer in ny str tht lnes the eqution. Your im is to lne s mny equtions s you n out of 6 rolls of the die. For numers tht do not lne the equtions, use n symol. 6 +I 0 5 +I 9 9 +I d +I 5 e +I 6 f +I 8 g How did you go? D 6

19 Equtions nd equivlene lned equtions using + nd There re different equtions we ould write for one set of lned sles. + + = = Work out the vlues of the symols in eh prolem = 0 = = = This time work out whih numer should go in the symol = 5 5 = = 7 = D 7

20 Equtions nd equivlene lned equtions using + nd How mny dots re inside eh ox? On one side there re dots nd on the other side, there re oxes. Beuse the eqution is lned, there must e 6 in eh ox. There re different equtions we ould write for one set of lned sles = 6 = How mny dots re inside eh ox? + + = 9 = 9 How mny dots re inside eh ox? + + = 5 = 5 5 If there re 6 dots in these ylinders, how mny dots re there in 6 ylinders? Show your working. = 6 = D 8

21 Equtions nd equivlene writing equtions for word prolems We n use symols to stnd for the unknown numer in word prolems. Red 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 eh eqution. = 9 9 = 6 = = 50 = 5 = d 6 = = Choose n eqution from ove nd write word prolem. Use symol to stnd for the unknown numer. D 9

22 Equtions nd equivlene 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? = Josh sved \$5 of his poket money over 8 weeks. How muh did Josh sve t the end of 8 weeks? = There re 8 hildren in the lss. hildren hve rown hir. How mny hildren do not hve rown hir? = Look t key words for hint out the opertion. d Mx hs \$5 more thn I do. If I hve \$50, how muh does Mx hve? = If the str is worth the sme, wht is it worth in this eqution? + + = 6 = D 0

23 Lolly weigh in solve Wht to do Work your wy through these prolems. Work out wht eh lolly g weighs: 00 g 50 g g 80 g 0 g g 600 g 80 g g D

24 Symol sums solve Wht to do Work out the vlue of eh symol. If the symol is repeted it is the sme numer. + = 0 ª = 0 ª = = ª = = + = ª = ª = = = ª = + + = + ª = ª + = = = ª = = 6 ª 6 = = ª = = ª = D

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