Patterns and Relationships


 Meghan Cummings
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1 Series Techer Ptterns nd Reltionships
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3 Series ontents Topic Section 1 1 Ptterns Answers nd (pp. rules 1 40) (pp. 1 17) repeting ptterns nd ptterns rules 1 trnslting numer reltionships ptterns 18 growing ptterns recording ptterns in tles Section Assessment skip counting with nswers (pp. 41 5) function ptterns rules nd rules 41 numer reltionships 47 Dte completed / / / / / / / / / / / / Topic Numer reltionships (pp ) equlity nd inequlity equivlence fi nding the unknown comintions equivlent sttements turnrounds zero / / / / / / / / / / / / / / Series Author: Rchel Flenley opyright
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5 Ptterns nd rules repeting ptterns We re used to continuing repeted ptterns. But wht if the pttern rule is in the middle? Wht strtegies cn you use to continue these ptterns oth wys? 1 ontinue these ptterns oth wys. J J J u u u rete your own pttern rules in the grey oxes. Swp with prtner nd continue ech other s ptterns oth wys. Answers will vry. 1 1
6 Ptterns nd rules repeting ptterns Ptterns follow very strict rules. Look t this pttern. The rule is The pttern repets circle tringle squre this rule over nd over. 1 ircle the rule in ech repeting pttern. Record it elow. The rule is The rule is Mke up rule nd record it somewhere secret. Drw your rule (or mke it with locks) nd repet it over nd over. Ask prtner to identify your pttern rule nd record it here. heck it if they were right. Answers will vry. 1
7 Ptterns nd rules repeting ptterns If there is no rule, it is NOT pttern. This is not pttern, it is just row of shpes. 1 Look t these rows. heck the ones tht follow pttern rule. c Look t these rows. They strted off s ptterns ut went it stry. Find the errors nd circle the prts tht don t follow the pttern rule. 1 3
8 Ptterns nd rules trnslting ptterns We cn mke ptterns spek in different lnguges. We cll this trnslting. Sy this pttern out loud. We cn chnge it to Sy it out loud now. 1 Look t this pttern. Trnslte it y chnging ech shpe. Pln it here: = = = Answers will vry. Think of simple pttern rule you could mke using 3 different pttern locks. Record it here. Mke your rule with pttern locks nd repet it 5 times. c Ask prtner to trnslte your pttern using different pttern locks. d Record their trnslted rule here. Answers will vry. 4 1
9 Ptterns nd rules growing ptterns Some ptterns repet. Some ptterns grow. When they grow, they must still follow rule. The rule for this pttern is Work out the rule nd drw the next prt of ech pttern. The rule is + 1 The rule is + c The rule is + nd + 1 Mke your own growing pttern with locks. Record the rule nd the fi rst few prts of the pttern here. Answers will vry. 1 5
10 Ptterns nd rules growing ptterns Ptterns cn lso shrink. Look t this pttern It follows rule. In ech stge we hve fewer locks. You will need: prtner counters Wht to do: Strt with 10 counters. Tke some wy so there re only 7 left. Then tke some more wy so there re only 4 left. Now tke some wy so there is only 1 left. How mny counters re you tking wy ech time? 3 Wht is the rule? 3 Wht to do next: Think of different tke wy rule. Write it somewhere secret. Don t let your prtner see! Put out 0 counters in row. Then put out your next row of counters following your tke wy rule. ontinue until your lst row would hve zero counters. Guess ech other s secret rule! Answers will vry. 6 1
11 Ptterns nd rules growing ptterns 1 Follow ech rule nd keep the numer ptterns growing or shrinking. You cn use counters to help The rule is The rule is + 8 c The rule is 1 Look t the ptterns. n you work out ech rule? The rule is The rule is 5 1 7
12 Ptterns nd rules growing ptterns You will need: prtner lck pencil Wht to do: Ech week this ldyug develops more spots ccording to secret rule. Work out the secret rule nd drw the spots we would see in Weeks 4, 5 nd 6. Week 1 Week Week 3 Wht is the secret rule? Week 4 Week 5 Week 6 numer of weeks + Wht to do next: n you work out how mny spots the ldyug would hve when it is 10 weeks old without drwing them on? If you cn, explin how you did it. If not, drw them. 1 spots. 8 1
13 Ptterns nd rules recording ptterns in tles We cn record ptterns y drwing them. Look t this growing pttern. We cn lso record the sme ptterns in tle. Stge 1 Stge Stge 3 Stge 1 3 Numer of Record ech growing pttern in its tle. Stge Numer of Stge Numer of c n you work out how mny mtchsticks would e in stge 5? Add it to the tle nd tell someone how you did it. 1 9
14 Ptterns nd rules recording ptterns in tles We cn record repeting ptterns in tles s well. Look t this pttern: The rule is Now we repet it. How mny counters hve we used t the end of Stge 3? 1 Record the repeting pttern in the tle. The rule is Stge 1 Stge Stge 3 Stge 1 3 Numer of 4 6 Numer of 1 3 Stge Numer of Numer of rete your own repeting pttern using different colours of cues. Record the fi rst 5 stges in the tle. Show your pttern nd tle to your techer. The rule is Answers will vry. Stge Numer of Numer of 10 1
15 Ptterns nd rules skip counting When we skip count, we follow numer ptterns. 1 ount y s to fi nd how mny wheels ount y 5s to fi nd how mny toes ount y s to fill in the gps. Wtch out! Your strting point is not. You cn use hundred chrt to help ount y 5s to fill in the gps. Wtch out! Your strting point is not Wht pttern do you notice? Numers end in 3, 8 pttern
16 Ptterns nd rules skip counting 1 Finish the chrt. Try going down the columns, not cross the rows. n you fi nd nd follow the ptterns? Y Y G Y Y YGR Now colour the chrt ove like this. If you sy the numer when you count y s, give it yellow stripe. If you sy the numer when you count y 5s, give it green stripe. c If you sy the numer when you count y 10s, give it red stripe. 3 Wht do you notice: out the numers tht hve 3 stripes? They end in 0. out the numers tht only hve green stripe? They end in 5. c out the numers tht hve yellow stripe? They re even. 1 1
17 Ptterns nd rules skip counting lcultors cn help us lern more out numer ptterns. You will need: clcultor Wht to do: Press 5 + = = Wht numer ppers? 10 Keep pressing = Wht is the clcultor counting y? 5s Press 10 + = = Wht numer ppers? 0 Keep pressing = Wht is the clcultor counting y? 10s Wht to do next: hoose your own numer to skip count y. Write it in the fi rst ox. Press your numer nd + = = Write ech new nswer in the oxes elow. How smrt m I! I cn count y 3s Answers will vry. 1 13
18 Ptterns nd rules function rules Meet the Rule fmily. The Rules like to do everything the sme wy. They ALWAYS get up t the sme time every dy nd they ALWAYS et the sme thing for rekfst. Mr Rule ets oiled eggs, Mrs Rule ets muesli, Freddy likes Weetix nd Fonnie loves + +5 Mr Rule Mrs Rule Freddy Rule tost with jm. They ALWAYS go to work or school the sme wy t the sme time. Get the picture? You cn rely on the Rules. And if you give them numer, ech of them will ALWAYS do the sme thing to it. 1 Fonnie Rule 1 Let s give Mr Rule some numers. He lwys dds to them. Fill in the missing numers elow. Give Mr Rule this + nd he will give you this
19 Ptterns nd rules function rules (continued) Now let s give Mrs Rule some numers. She is + 5 womn. Give Mrs Rule this +5 nd she will give you this Wht out the kids? Freddy likes to nd Fonnie is 1 kind of girl. Give Get Give Get
20 Ptterns nd rules function rules (continued) 4 Uncles Lester nd Leroy Rule hve flown in from New York. Their numers rrived with them, ut unfortuntely their rules seem to e lost in trnsit. Look closely t the numers nd see if you cn work out ech uncle s rule. Write it. Give Get Give Get Uncle Lester Uncle Leroy Aunt Freckle hs lso rrived. She sys you cn mke up the rule. Mke up your own rule nd write it on the sign. Work out wht you ll get Give Aunt Freckle Answers will vry. Get
21 Ptterns nd rules function rules (continued) You will need: prtner coloured pencils Wht to do: Design your own memer of the Rule fmily. Give them nme nd their own style. My rule Give Get Answers will vry. Wht to do next: Oserve students. Think of simple rule nd write it in the ox. Write some numers in the Give column. Don t mke them too hrd! Work out the nswers tht will pper in the Get column nd write them down somewhere secret. Show your techer. Switch ppers with prtner nd work out the nswers for ech other s chrcter. heck their thinking. 1 17
22 Numer reltionships equlity nd inequlity This is the equls sign = It mens the sme. Things cn e the sme or = in lots of wys. sme length sme weight sme height How else cn things e the sme? 1 Drw: A tree tht is the sme height. = A fi sh tht is the sme length. = If things re not the sme or not equl we put line through the equls sign. Drw: A person who is not the sme height. A cterpillr tht is not the sme length. 18
23 Numer reltionships equivlence You will need: prtner coloured pencils scissors copy of pge 0 Wht to do: olour the rods on pge 0 nd cut them out crefully Look t the rown rod. Now put yellow nd light green rod together. Wht do you notice? Together, yellow nd light green rod re the sme length s rown rod. We cn record this s: yellow + light green = rown or y + lg = How mny different rod comintions cn you fi nd tht re the sme length s the rown rod? Record your fi ndings elow. lck + white = rown drk green + red = rown purple + purple = rown 19
24 Numer reltionships equivlence white copy red light green purple yellow drk green lck rown lue ornge Wht to do next: hoose different rod nd fi nd comintions tht mtch it. Answers will vry. 0
25 Numer reltionships equivlence You will need: prtner the rods from pge 0 Wht to do: This time, cn you work out wht the missing rods might e? olour the words elow nd use the rods from pge 0 to help you. red + light green = yellow yellow + white = drk green c light green + white = purple d yellow = purple + white Wht to do next: Design 3 of your own prolems nd get your prtner to solve them. Record the prolems nd solutions here. Answers will vry. 1
26 Numer reltionships equivlence In mth we often use = when we re tlking out the sme mount of things. To help us decide if mounts re equl, we cn think out lncing them on scle. Are these the sme mount? Yes, there re 4 on ech side. 1 Is ech scle lnced? This mens it hs the sme mount on oth sides. If it is, write =. If it isn t lnced, write. = c = d Drw more counters on the left of ech scle to mke the sides equl. How mny did you drw ech time? Write it in the ox. I drew 3 I drew 5 c d I drew 3 I drew
27 Numer reltionships equivlence Did you know tht we re lncing or mking the sides the sme when we solve numer prolems? Think out + = 4. On the scles it looks like this. + = 4 is nother wy of sying nd is the sme s 4. 1 Write the ddition prolems shown on ech scle wys. Sy them out loud to prtner. 3 + = = 4 3 nd is the sme s 5 1 nd 3 is the sme s 4 c d = = 6 4 nd 3 is the sme s 7 4 nd is the sme s 6 Now drw the missing counters nd fi ll in the missing numers = = 8 5 nd 4 is the sme s 9 4 nd 4 is the sme s 8 3
28 Numer reltionships equivlence We re lncing or mking sides the sme when we solve ll kinds of numer prolems, not just ddition prolems. This shows tht 4 sutrct is the sme s. 4 = 1 Write the sutrction prolems shown on ech scle. 5 = = 4 c d 8 3 = = 6 This shows tht 3 rows of is the sme s 1 row of 6. 3 = 6 Fill in the missing numers to mtch ech scle. 4 = = 9 4
29 Numer reltionships finding the unknown Sometimes we hve to work out the missing prt of prolem. We cll this finding the unknown. We cn use symols like squres or circles to stnd for wht we don t know. Think out + = 5 Look t the scle: How mny more counters do we need to dd to the left side to equl 5? We dd 3 more. Our unknown is = 5 1 Put on your detective cp nd fi nd the unknowns in these prolems. Drw more counters on the left of ech scle to mke the sides equl. Fill in the missing numers elow to mtch. 3 + = = 9 The unknown is = 6 The unknown is = 9 c 1 + = 5 d 4 + = 6 The unknown is 4 The unknown is = = 6 5
30 Numer reltionships finding the unknown You will need: counters Wht to do: Help! While t prty, someone stole some cndies from these children s prty gs. Your jo is to work out how mny cndies re missing from ech g. Pretend counters re the cndies nd work out the unknown mount. Write it in the numer sentence. Melody I hd 8 cndies nd now there re only 3 left! Ho I hd 10 cndies nd now there re only 4 left! Jck I hd 9 cndies nd now there re only left! 8 = 3 10 = 4 9 = 8 5 = = = Wht to do next: These kids on the right hd lredy eten ll their cndies. They sy mum gve them some more ut 1 person is not telling the truth. This person hs exctly the numer of stolen cndies. Who stole the cndies? Thoms 16 cndies Ellie 18 cndies Thoms 1 cndies Dnny 6
31 Numer reltionships comintions We cn mke the sides of prolem equl in mny different wys. How cn we mke 5? = 5 or = 5 or + 3 = 5 or 3 + = 5 or = 5 or = 5 Do you notice the ptterns? 1 How cn we mke 7? hoose coloured pencils. olour the counters to show the different wys. Write the mtching numer sentences = = = = = = = = 7 7
32 Numer reltionships comintions Now you hve the hng of this, cn you fi nd ll the possiilities for these without using counters? If you still wnt to use counters, tht s fi ne too = = = = = = = = = = = = = = = = 8 3 Fill in the missing numers in these ddition comintions = = = 4 + = = + 0 = = = 4 8
33 Numer reltionships comintions You will need: prtner counters Wht to do: Wht sutrction prolems cn you think of tht equl 5? = 5 Work with your prtner to find t lest 10 options. n you find ptterns to help you? Record your nswers elow. 5 0 = = 5 Answers will vry. Wht to do next: n you fi nd more thn 10 options? Answers will vry. 9
34 Numer reltionships comintions You will need: prtner scissors pges 31 nd 3 1 In prk we might fi nd How mny legs does ech creture hve? Write the numers in the oxes ove. If there re 4 legs in the prk one dy, who could e there? There could e: kids irds 1 kid nd 1 ird 1 dog There couldn t e utterfly s it hs 6 legs. There couldn t e spider s it hs 8 legs. 30
35 Numer reltionships comintions (continued) Wht to do: Work with your prtner to work out who could e in the prk if there re 10 legs. You cn cut out the people nd nimls on pge 3 to help you. Record your fi ndings here. Answers will vry. Wht to do next: ompre your findings with those of nother group. Hve they found ny different ones? How will you know when you hve found ll the options? Redy for chllenge? Wht if there were 4 legs in the prk? You will need nother piece of pper to record your fi ndings on. Answers will vry. 31
36 Numer reltionships comintions (continued) copy 3
37 Numer reltionships equivlent sttements Wht is one wy to mke 5? = 5 Wht is nother wy to mke 5? + 3 = 5 They oth mke 5 so they re the sme. They re equivlent sttements = + 3 They oth = 5 1 Fill in the missing numers for these equivlent sttements. c = = = + 6 They oth = 7 They oth = 6 They oth = 8 Use colours nd drw counters on the right side of these scles to crete equivlent sttements. Fill in the missing numers. c = + They oth = 7 + = = + They oth = 4 They oth = 8 Answers will vry. equivlent mens the sme or equl sttement is numer fct 33
38 Numer reltionships equivlent sttements You will need: prtner counters 3 + = = = = = = + 8 Wht to do: Wlly hs creted 6 sets of equivlent sttements nd is very proud of himself. Unfortuntely, 3 of them re wrong. Wlly sked for help to fi gure out the errors. n you help? In ech ox, show how you know which ones re wrong nd which re right. 3 + = = = = = = = = 8 10 = 10 equivlent mens the sme or equl sttement is numer fct 34
39 Numer reltionships equivlent sttements You will need: prtner copy of this pge 10 counters in 4 different colours, 40 in ll copy Wht to do: Divide up the coloured counters so you hve different colours ech. You should hve 0 counters. Mix up your own counters. Decide who will go fi rst. Plyer 1: tke hndful of your own counters. ount how mny counters you hve ltogether nd how they re mde up. For exmple, you might hve 1 counters: 4 red nd 8 lue. Write 1 in the smll ox nd the ddition sttement you hve mde. Answers will vry. Smple nswers = Plyer : mke n equivlent sttement with your own counters. Fill in your sttement on the other side of the equls sign. Wht to do next: Swp jos nd mke 3 more sets of equivlent sttements. If you wnt to dd some excitement, you could dd time limit or penlty for n incorrect nswer. How out 5 push ups for n incorrect sttement? + = + Answers will vry. + = + + = + 35
40 Numer reltionships turnrounds A turnround mens we cn put the numers efore the equls sign in ny order nd we still get the sme numer fter the equls sign. n we mke turnrounds when we dd? Wht out when we sutrct? = 13 6 nd 7 re efore 13 is fter 1 Answer these pirs of ddition prolems = = = = 14 c = = 9 d 5 + = = 7 e 1 + = = 3 f = = 18 g n we mke turnrounds when we dd? Yes. Now try these sutrction prolems. If you cn t work out the nswer, drw. 5 = = 5 = 4 6 = 4 7 = d n you do ll these prolems? Do the nswers in ech pir mtch? No. e n we mke turnrounds when we sutrct? No. c 7 4 = 3 36
41 Numer reltionships turnrounds We know we cn mke turnrounds when we dd. We know we cn t mke turnrounds when we sutrct. Wht out when we multiply? 1 Use the dots to help you solve these pirs of multipliction prolems. If you think they re turnrounds, check them. 3 rows of 5 = 15 5 rows of 3 = 15 5 rows of 4 = 0 4 rows of 5 = 0 c 4 3 = = 1 d 6 = 1 6 = 1 e n we mke turnrounds when we multiply? Yes. This is row. 37
42 Numer reltionships turnrounds Look t these scles. We cn see tht 3 rows of re the sme s rows of 3. Our turnrounds re: = 6 3 = 6 1 Look t the scles nd write the turnrounds to mtch. 4 = 8 4 = 8 Rememer this is row! 4 3 = = 1 c 5 1 = = 5 Drw some turnrounds on the scles nd get prtner to write the mtching sttements. Are they right? = = = = Answers will vry. 38
43 Numer reltionships zero 1 Do you know ny other words for zero? Write them here. nought none nil nothing Answers will vry. Wht hppens when we dd zero to numer or numer to zero? Try these = = 19 c = 3 d = 4 e = 7 f = 38 g Wht do you notice? The numer stys the sme. 3 Wht out if we sutrct zero from numer? Try these = = 13 c 8 0 = 8 d 67 0 = 67 e 16 0 = 16 f 8 0 = 8 g Wht do you notice? The numer stys the sme. 4 Wht is the lrgest dd zero prolem you cn think of? Write it here. Answers will vry. 39
44 Numer reltionships zero Wht hppens when we use zero in multipliction prolems? Think out 6 0 = or 0 6 = Let s explore. 1 You re t frmstnd. There re 6 pltes, nd on ech plte there re pples. Drw the pples on the pltes. How mny pples do you hve? 6 = 1 Now drw 0 pples on ech of the pltes. How mny pples do you hve now? 6 0 = 0 3 The frmer sys you cn hve s mny pples s you like ut only if you put them on pltes. You look everywhere ut cn t fi nd ny pltes. How mny pples cn you hve? 0 0 = 0 4 Wht hppens when you multiply y zero? The nswer is zero. 40
45 Ptterns nd rules Nme 1 Wht is the rule? The rule is ontinue this pttern oth wys. 3 hnge the shpes to trnslte this pttern. 4 Find the rule nd continue ech growing pttern. J J JJ JJ JJ Series Topic 1 Assessment 41
46 Ptterns nd rules Nme 5 Look t the ptterns. n you work out ech rule? The rule is The rule is 6 Record the growing pttern in the tle. Stge 1 Stge Stge 3 Stge 4 Stge 5 Stge 1 Numer of 7 ount y 5s to fi nd how mny toes. 4 Series Topic 1 Assessment
47 Ptterns nd rules Nme 8 ount y s to fill in the gps. Wtch out! Your strting point is not. You cn use hundred chrt to help ount y 10s to fill in the gps. Wtch out! Your strting point is not Follow the rules to find the missing numers. Give Get Give Get Skills nd understndings Not yet Kind of Got it Recognizes nd continues simple repeting ptterns Finds the rule for simple repeting ptterns Trnsltes simple repeting ptterns Recognizes nd continues simple growing ptterns Records simple ptterns in tles Skip counts in s, 5s nd 10s Recognizes nd pplies simple function rules Series Topic 1 Assessment 43
48 Ptterns nd rules Nme 1 Wht is the rule? The rule is ontinue this pttern oth wys. 3 hnge the shpes to trnslte this pttern. Answers will vry. 4 Find the rule nd continue ech growing pttern. J J JJ JJ JJ JJ JJ JJJ JJ 44 Series Topic 1 Assessment
49 Ptterns nd rules Nme 5 Look t the ptterns. n you work out ech rule? The rule is The rule is +5 6 Record the growing pttern in the tle. Stge 1 Stge Stge 3 Stge 4 Stge 5 Stge Numer of ount y 5s to fi nd how mny toes Series Topic 1 Assessment 45
50 Ptterns nd rules Nme 8 ount y s to fill in the gps. Wtch out! Your strting point is not. You cn use hundred chrt to help ount y 10s to fill in the gps. Wtch out! Your strting point is not Follow the rules to find the missing numers. Give Get Give Get Skills nd understndings Not yet Kind of Got it Recognizes nd continues simple repeting ptterns Finds the rule for simple repeting ptterns Trnsltes simple repeting ptterns Recognizes nd continues simple growing ptterns Records simple ptterns in tles Skip counts in s, 5s nd 10s Recognizes nd pplies simple function rules 46 Series Topic 1 Assessment
51 Numer reltionships Nme 1 Are the groups equl? Drw = or etween them. Drw lines to = this grey line. Drw 4 lines to = this lck line. 3 Drw more counters on the left side of ech scle to mke the sides equl. How mny did you drw ech time? Write it in the ox. I drew I drew 4 Write the numer prolems shown on these scles. + = = c d = + = Series Topic Assessment 47
52 Numer reltionships Nme 5 Find the unknown in these prolems. Drw counters on the left side of ech scle to mke the sides equl. Finish the numer sentences. 1 + = = The unknown is + = The unknown is + = 6 Find the unknown in this prolem. Show or explin how you did it. 4 + = 9 7 How mny different wys cn you dd to mke 6? Write nd or drw them = 6 48 Series Topic Assessment
53 Numer reltionships Nme 8 Look t ech ox. Are the sttements equivlent? Show how you know. 3 + = = 9 + c = Write the fcts nd their turnrounds. + = + = + = + = c d = = = = Skills nd understndings Not yet Kind of Got it Recognizes different forms of equivlence nd nonequivlence retes equivlent mounts Finds the unknown in simple ddition nd sutrction sttements retes ddition comintions (with more thn 1 vrile) Recognizes simple ddition equivlent sttements (to 10) Writes simple ddition nd multipliction turnrounds Series Topic Assessment 49
54 Numer reltionships Nme 1 Are the groups equl? Drw = or etween them. = Drw lines to = this grey line. Drw 4 lines to = this lck line. 3 Drw more counters on the left side of ech scle to mke the sides equl. How mny did you drw ech time? Write it in the ox. I drew 3 I drew 5 4 Write the numer prolems shown on these scles = = 6 c d 8 3 = = 7 50 Series Topic Assessment
55 Numer reltionships Nme 5 Find the unknown in these prolems. Drw counters on the left side of ech scle to mke the sides equl. Finish the numer sentences. 1 + = = 6 The unknown is 5 The unknown is = = 6 6 Find the unknown in this prolem. Show or explin how you did it. 4 + = = 9 Explntions will vry. 7 How mny different wys cn you dd to mke 6? Write nd or drw them = = = = = = = 6 Series Topic Assessment 51
56 Numer reltionships Nme 8 Look t ech ox. Are the sttements equivlent? Show how you know. 3 + = = 9 + c = = Write the fcts nd their turnrounds. 3 + = = = = 5 c d 4 = 8 4 = = = 15 Skills nd understndings Not yet Kind of Got it Recognizes different forms of equivlence nd nonequivlence retes equivlent mounts Finds the unknown in simple ddition nd sutrction sttements retes ddition comintions (with more thn 1 vrile) Recognizes simple ddition equivlent sttements (to 10) Writes simple ddition nd multipliction turnrounds 5 Series Topic Assessment
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