Student Book SERIES. Patterns and Algebra. Name

Transcription

1 E Student Book Nme

2 Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing ptterns function mchines tht s my numer pply Dte completed Topic Equtions nd equivlence (pp. 3 ) understnding equivlence not equl to symol greter thn nd less thn lnced equtions using + nd using symols for unknowns fruit vlues solve mystery sncks solve Series Author: Nicol Herringer Copyright

3 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! Ptterns cn grow or repet depending on the rule. Recognising numer ptterns is n importnt prt of feeling confident in mths. In this topic we will look t different numer ptterns ut first let s look t shpe ptterns. Look t these repeting shpe ptterns. Drw the lst two shpes: c In these repeting shpe ptterns, drw the missing shpes: 3 Complete wht comes next in this growing pttern: E

4 Ptterns nd functions identifying nd creting ptterns 4 Look t these repeting shpe ptterns. Drw the next two shpes: c d e 5 If the ptterns (ove) continued, wht would the 0th shpe e on ech row: c d e 6 Write your nme y putting ech letter in the grid s repeting pttern. For exmple, if your nme is Ben, you would write: B E N B E N B E N B Which letter of your nme will e under the letter 3? How did you work this out? E

5 Ptterns nd functions skip counting There re mny skip counting ptterns to discover on hundred grid. Colour the skip counting pttern on ech hundred grid: Show the 4s pttern. Show the 3s nd 6s pttern. Shde the 3s nd circle the 6s c Show the s pttern d Shde the 9s pttern, then put circle round ll the numers 5 less thn numers ending in Complete these numer ptterns y looking for skip counting ptterns. c E 3

6 Ptterns nd functions skip counting 3 Colour the skip counting pttern for 3s up to 30. If you kept going on complete hundred grid, would 5 e coloured in? How cn you tell without using whole hundred grid? 4 Only 3 numers re shded in ech of the skip counting ptterns elow. Work out the pttern nd complete the shding: This shows skip counting pttern of: This shows skip counting pttern of: 5 Shde these sequences on the hundred grid: Sequence : strt t nd show skip counting pttern of. Sequence : strt t nd show skip counting pttern of E

7 Ptterns nd functions completing nd descriing ptterns So fr we hve looked t skip counting ptterns tht egin t zero. Here is skip counting pttern of 5s tht egins t 7. This pttern strts t 7. The rule is: dd Continue the pttern from the strting numer: c Add 0 Add 5 Sutrct Prctise counting ckwrds y 0 nd 00. Bckwrds y 0: Bckwrds y 00: c 583 c 00 3 Look crefully t these numer pttern grids. There re four rules: cross, down, nd long ech digonl E 5

8 Ptterns nd functions completing nd descriing ptterns 4 Figure out the missing numers in ech pttern nd write the rule Rule: Rule: c d Rule: Rule: Some numer ptterns cn e formed with two opertions ech time. For exmple: The rule is to multiply y nd dd 3 ech time. 5 Complete these numer ptterns, y following the rules written in the dimond shpes. Descrie the rule underneth x + 5 x + 5 x The rule is 6 Roll die to mke the strting numer. Continue the sequence y following the rule: Rule: + 4 Rule: + 3 c Rule: E

9 Ptterns nd functions predicting repeting ptterns When we use numer ptterns in tles, it cn help us to predict wht comes next. Look t the tle elow nd how we cn use it to predict the totl numer of sweets needed for ny numer of children t prty. This tle shows us tht sweet g contins 8 sweets nd gs contin 6 sweets. We cn see tht the rule for the pttern is to multiply the top row y 8 to get the ottom row ech time. Numer of sweet gs Numer of sweets To find out how mny sweets re in 0 gs, we don t need to extend the tle, we cn just pply the rule So, 0 gs contin 80 sweets. This helps us pln how mny sweets re needed for prty. Complete the tle for ech prolem: Tom receives $5 week pocket money s long s he does ll his chores. How much pocket money does Tom get fter 0 weeks? Weeks Pocket money 5 0 A flower hs 7 petls. How mny petls re there in unch of 0 flowers? Flowers Numer of petls 7 4 c A flg hs 6 strs. How mny strs re there on 0 flgs? Flgs Numer of strs 6 d At pizz prty, ech person ets 3 pieces of pizz. How mny pieces of pizz do 0 people et? Guests Pizz pieces 9 E 7

10 Ptterns nd functions predicting repeting ptterns Ech of these kids wrote the first 3 numers of skip counting pttern of 6, strting t different numers. Ech kid s sequence goes down the column. Imgine the sequence continues. Mel Brinn Brd Gen Jo Kte Who hd the numer 4 in their column? Who hd the numer 50 in their column? 3 Look t ech pttern of shpes nd complete the tle elow: Repet section Numer of circles Numer of tringles Show wht this entire sequence would look like with 0 repet sections: Look for the section tht repets. Wht is it mde up of? This is the rule. 8 E

11 Ptterns nd functions predicting growing ptterns Numer ptterns in tles cn help us with prolems like this. Mi is mking this sequence of shpes with mtchsticks nd wnts to know how mny she will need for 0 shpes. Shpe Shpe Shpe 3 Shpe numer 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 3 Complete the tle for ech sequence of mtchstick shpes nd find the numer of mtchsticks needed for the 0th shpe. Shpe Shpe Shpe 3 Shpe numer Numer of mtchsticks 4 Shpe Shpe Shpe 3 Shpe numer Numer of mtchsticks 6 c Shpe Shpe Shpe 3 Shpe numer Numer of mtchsticks 7 E 9

12 Ptterns nd functions predicting growing ptterns Look t these growing ptterns. Complete the tle nd follow the rule to drw Picture 5: Picture Picture Picture 3 Picture 4 Picture 5 l l l l l l l l l l l l l l l l Picture numer Numer of dots Rule Picture numer Numer of dots Picture Picture Picture 3 Picture 4 Picture 5 Picture numer Numer of squres Rule Picture numer + Numer of squres How mny squres will Picture 8 hve? 0 E

13 Ptterns nd functions function mchines This is function mchine. Numers go in, hve the rule pplied, nd come out gin. IN 8 RULE: 3 OUT Look crefully t the numers going in these function mchines nd the numers coming out. Wht is the rule? IN 5 RULE: OUT 5 IN 4 RULE: OUT Wht numers will come out of these function mchines? IN 3 4 RULE: 8 OUT IN 4 48 RULE: 8 OUT Wht numers go in to these numer function mchines? IN RULE: 0 OUT 36 5 IN RULE: + 0 OUT E

14 Tht s my numer! pply Getting redy This is gme for plyers. You will need some trnsprent counters ech in different colours nd dice. copy Wht to do Plyer rolls dice. The first die shows the strting numer nd the second die shows the skip counting pttern. Plyer writes down the first 4 numers of their sequence. For exmple, if Plyer rolls nd 6, the strting numer is nd the rule is + 6. So Plyer writes, 8, 4, 0 nd chooses one of these numers to cover with their counter. Plyer hs their turn, following the sme steps s ove. They choose numer to cover with their counter. If the numer is lredy covered, they cn t put down counter. Continue with Plyer nd Plyer rolling gin until there is winner. The im is to e the first to hve their counters in group of 4 ( ) E

15 Equtions nd equivlence understnding equivlence Look t these lnced scles. On one side there is the sum nd on the other side there is totl of 7 tringles. This mkes sense ecuse it shows the eqution Eqution is nother word for sum. With equtions, oth sides must e equl Blnce ech set of scles y writing numer in the ox tht is equivlent to the totl numer of shpes. Then write the mtching eqution Blnce ech set of scles y writing numer in the ox. Then write the mtching eqution E 3

16 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: Write numers in ech ox to show equtions tht re not lnced: c 35 d Complete the equtions elow y using only the numers in the crds. Look crefully to see whether it is n or symol c + 35 d E

17 Equtions nd equivlence greter thn nd less thn When two sides of n eqution re not lnced, one side is greter thn the other. We cn show this with greter thn (>) nd less thn (<) symols like this: < > 5 Complete the equtions elow y using only the numers in the crds. Look crefully to see whether it is n > or < symol. The first one hs een done for you < 50 + > c d > + < Alex is older thn Gilly ut younger thn Tylor. Their ges could e descried s: 6 > > 9 How old is ech person? Alex is Gilly is Tylor is E 5

18 Equtions nd equivlence greter thn nd less thn 3 Complete the numer sentences elow y writing numers in the lnk oxes: 38 + > < 00 c > d 500 < e + > 000 f + < 000 g + > h + < 4 Sm nd Will s mother is trying to work out how much to udget for her children s dily lunch orders. She is wondering if $50 is enough for When you dd these mounts, look for onds to $. For exmple: $.40 + $.60 (40c + 60c) + $ + $ $3 oth Sm nd Will. Add up the cost of ech child s lunch order for the week nd then complete mtching numer sentence. Sm s lunch orders Mondy Tuesdy Wednesdy Thursdy Fridy $4.60 $5.40 $7.30 $3.70 $6 Will s lunch orders Mondy Tuesdy Wednesdy Thursdy Fridy $5.0 $3.80 $5.90 $6.0 $5 + $50 Sm s totl Will s totl 6 E

19 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: c d E 7

20 Equtions nd equivlence lnced equtions using + nd Find the vlues of these symols: If is 5, wht is the vlue of? 5 5 If is 8, wht is the vlue of? Find the vlues of oth symols from the clues: If oth sides re equl to 36, wht is the vlue of ech symol? 3 If oth sides re equl to 0, wht is the vlue of ech symol? E

21 Equtions nd equivlence using symols for unknowns Write n eqution for these word prolems. Write n eqution using s for the unknown numer. Bec collects stickers. She hs 48 umper stickers, glitter stickers nd 5 smiley fce stickers. How mny stickers does Bec hve in her collection? s s Chrlie sved $5 week of his pocket money over 8 weeks ut then spent $5. How much did Chrlie hve t the end of 8 weeks? s c people re specttors t footll mtch. 700 re there to support Tem A while the rest re there to support Tem B. How mny specttors support Tem B? s In this tringle, the numers on the sides re the totls. So Work out the vlue of the other symols: 0 E 9

22 Fruit vlues solve Wht to do Work out the vlue of ech type of fruit: E

23 Mystery sncks solve Wht to do Work out wht is the snck ox from the clues. Clue Clue Hint: Keep the scle lnced y dding Crunchy Os to ech side in Clue. Then work out wht else pckets of chips is equl to. From there, you cn work out your nswer. E