Patterns and functions recursive number patterns Write the next 3 numbers in each sequence by following the rule:

Transcription

1 Ptterns n funtions reursive numer ptterns Look roun you, n you see pttern? A pttern is n rrngement of shpes, numers or ojets forme oring to rule. Ptterns re everywhere, you n fin them in nture, rt, musi n even in ne! In this topi, we re looking t numer ptterns. A numer pttern is sequene or list of numers tht is forme oring to rule. Numer ptterns n use ny of the four opertions (+,,, ) or even omintion. In the exmple elow, if we follow this instrution: strting t eh time we get this numer pttern: Write the next numers in eh sequene y following the rule: Rule: Rule: sutrt Rule: multiply y Figure out the missing numers in eh pttern n write the rule. Cirle the sening ptterns. 0 0 e f Complete these gri ptterns. Look losely t the numers in the gri n follow the ptterns Ptterns n Alger Copyright P Lerning

2 Ptterns n funtions funtion numer ptterns There re ifferent types of rules tht numer pttern n e se upon: A reursive rule use to ontinue the sequene y oing something to the numer efore it. A funtion rule use to preit ny numer y pplying the rule to the position of the numer. A funtion rule is rule se on the position of numer. Consier this. Lui ws given this numer pttern: 0 0 Her teher ske her to work out wht the 0th numer woul e without ontinuing the sequene. Lui use tle to work out the rule etween the position of numer n the numer in the pttern. She worke out the rule to e. Position of numer 0 Numer pttern So, following the rule se on the position of numer, the 0th numer is 00. This is funtion rule. Use the funtion rule n then pply the rule to position 0. Position of numer 0 Numer pttern 0 Position of numer 0 Numer pttern 0 HT: In the lst pttern, the rule hs opertions. Position of numer 0 Numer pttern 0 Position of numer 0 + Numer pttern 9 Ptterns n Alger Copyright P Lerning

3 Ptterns n funtions funtion numer ptterns s with opertions re esy to work out when we look t how they re linke to the multiplition tles. Position of numer times tle Numer pttern 9 Multiply y n then This tle shows tht the numer pttern is the sme s the times tle with e to eh nswer. Complete eh tle to show how funtion rules with opertions n e linke to multiplition tles. Position of numer times tle Numer pttern 0 9 Multiply y n then Position of numer times tle Numer pttern 0 Multiply y n then Position of numer times tle + Numer pttern 9 Complete this tle to show the times tles with e. Position of numer times tle + Numer pttern Wht woul the numer in the 0th position e? Ptterns n Alger Copyright P Lerning

4 Ptterns n funtions funtion mhines This is funtion mhine. Numers go in, hve the rule pplie, n ome out gin. 0 0 Look refully t the numers going in these funtion mhines n the numers oming out. Wht rule re they following eh time? 9 0 Wht numers will ome out of these funtion mhines? 9 Wht numers go in to these numer funtion mhines? Ptterns n Alger Copyright P Lerning

5 Ptterns n funtions funtion mhines Write the rule in eh oule funtion mhine. Eh rule is me up of opertions ( then +) Whih funtion mhine will win this gme of ingo? Write the numers tht ome out n olour eh mhine s numers in ifferent olour. Chek whih mhine hs numers in line in ny iretion. + FREE 9 SPACE Ptterns n Alger Copyright P Lerning

6 Ptterns n funtions reursive numer ptterns Look roun you, n you see pttern? A pttern is n rrngement of shpes, numers or ojets forme oring to rule. Ptterns re everywhere, you n fin them in nture, rt, musi n even in ne! In this topi, we re looking t numer ptterns. A numer pttern is sequene or list of numers tht is forme oring to rule. Numer ptterns n use ny of the four opertions (+,,, ) or even omintion. In the exmple elow, if we follow this instrution: strting t eh time we get this numer pttern: Write the next numers in eh sequene y following the rule: Rule: 9 Rule: sutrt Rule: multiply y 0 Figure out the missing numers in eh pttern n write the rule. Cirle the sening ptterns e f Complete these gri ptterns. Look losely t the numers in the gri n follow the ptterns Ptterns n Alger Copyright P Lerning

7 Ptterns n funtions funtion numer ptterns There re ifferent types of rules tht numer pttern n e se upon: A reursive rule use to ontinue the sequene y oing something to the numer efore it. A funtion rule use to preit ny numer y pplying the rule to the position of the numer. A funtion rule is rule se on the position of numer. Consier this. Lui ws given this numer pttern: 0 0 Her teher ske her to work out wht the 0th numer woul e without ontinuing the sequene. Lui use tle to work out the rule etween the position of numer n the numer in the pttern. She worke out the rule to e. Position of numer 0 Numer pttern So, following the rule se on the position of numer, the 0th numer is 00. This is funtion rule. Use the funtion rule n then pply the rule to position 0. Position of numer 0 Numer pttern 0 0 Position of numer 0 Numer pttern 0 0 HT: In the lst pttern, the rule hs opertions. Position of numer 0 Numer pttern 0 0 Position of numer Numer pttern 9 Ptterns n Alger Copyright P Lerning

8 Ptterns n funtions funtion numer ptterns s with opertions re esy to work out when we look t how they re linke to the multiplition tles. Position of numer times tle Numer pttern 9 Multiply y n then This tle shows tht the numer pttern is the sme s the times tle with e to eh nswer. Complete eh tle to show how funtion rules with opertions n e linke to multiplition tles. Position of numer times tle Numer pttern 0 9 Multiply y n then Position of numer times tle Numer pttern 0 Multiply y n then Position of numer times tle Numer pttern 9 Multiply y then Complete this tle to show the times tles with e. Position of numer times tle Numer pttern 0 Multiply y then Wht woul the numer in the 0th position e? 0 + = Ptterns n Alger Copyright P Lerning

9 Ptterns n funtions funtion mhines This is funtion mhine. Numers go in, hve the rule pplie, n ome out gin. 0 0 Look refully t the numers going in these funtion mhines n the numers oming out. Wht rule re they following eh time? Wht numers will ome out of these funtion mhines? 9 9 Wht numers go in to these numer funtion mhines? Ptterns n Alger Copyright P Lerning

10 Ptterns n funtions funtion mhines Write the rule in eh oule funtion mhine. Eh rule is me up of opertions ( then +) Whih funtion mhine will win this gme of ingo? Write the numers tht ome out n olour eh mhine s numers in ifferent olour. Chek whih mhine hs numers in line in ny iretion. + 0 This one oes. FREE 9 SPACE Ptterns n Alger Copyright P Lerning