Progression in Mastery Year 6 Find a Rule

Let’s revisit what we should know… A one-step function machine performs one operation on

Let’s revisit what we should know… A one-step function machine performs __________ on the

Let’s revisit what we should know… Sometimes more than one function is possible… 21

Let’s learn A two-step function machine performs two operations on the input. INPUT 7

Let’s talk What is the output for each two-step function machine? 20 × 5

Let’s learn If both functions are addition and/ or subtraction, we can write it

Let’s learn If both functions are multiplication, we can write it as a one-step

Let’s learn If both functions are division, we can write it as a one-step

Let’s learn If both functions are multiplication and division, we can write it as

Let’s talk Rewrite the two-step function machines as one-step machines. 3 x 10 ÷

Let’s learn A two-step function machine performs _________ on the input. We can use

Let’s talk What is the input for each two-step function machine? x 2 +

Let’s learn We can explore the relationship between the input, output and function that

Let’s talk Find the missing functions for each two-step machine. 4 × 10 79

Let’s talk Use the function machine to complete the table. input Input 1 2

Let’s talk Use this pattern to work out the output when the input is

Let’s develop our learning What is the same and what is different? 126 ÷

Independent Task Let’s showcase our learning ©Deepening Understanding LTD 2020

Inpu t Output 24 © White Rose Maths 2019

Exit task – Dong Nao Jin How many different ways can you complete the

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Progression in Mastery Year 6 Find a Rule (Two Step) It’s time to try two-step function machines! ©Deepening Understanding LTD 2020

Let’s revisit what we should know… A one-step function machine performs one operation on the input. INPUT FUNCTION OUTPUT 6 × 9 54 38 + 56 94 INPUT FUNCTION OUTPUT 840 ÷ 40 21 87 − 17 70 ©Deepening Understanding LTD 2020

Let’s revisit what we should know… A one-step function machine performs __________ on the input. We can use the inverse operation to work out the input. × 7 42 ___ ÷ ___ = ___ so the input must be ___. + 91 244 ___ − ___ = ___ so the input must be ___. ©Deepening Understanding LTD 2020

Let’s revisit what we should know… A one-step function machine performs __________ on the input. We can explore the relationship between an input and output to work out the missing function. 114 79 193 158 The difference between 114 and 79 is ____ and the difference between 193 and 158 is ____. The function must be __ ____. ©Deepening Understanding LTD 2020

Let’s revisit what we should know… Sometimes more than one function is possible… 21 63 98 49 How many possibilities can you find for each function machine? ©Deepening Understanding LTD 2020

Let’s learn A two-step function machine performs two operations on the input. INPUT 7 INPUT 975 FUNCTION 1 FUNCTION 2 OUTPUT + 15 29 FUNCTION 1 FUNCTION 2 OUTPUT × 2 ÷ 10 − 5. 5 We say You I all say it!it!it! ©Deepening Understanding LTD 2020 92

Let’s talk What is the output for each two-step function machine? 20 × 5 − 37 120 ÷ 3 + 74 34 x 2 + 19 850 ÷ 10 − 46 ©Deepening Understanding LTD 2020

Let’s learn If both functions are addition and/ or subtraction, we can write it as a one-step function machine. 8 + 24 − 4 28 is the same as… 8 + 20 We say You I all say it!it!it! ©Deepening Understanding LTD 2020 28

Let’s learn If both functions are multiplication, we can write it as a one-step function machine. 5 × 3 x 2 30 is the same as… 5 × 6 We say You I all say it!it!it! ©Deepening Understanding LTD 2020 30

Let’s learn If both functions are division, we can write it as a one-step function machine. 84 ÷ 3 7 is the same as… 84 ÷ 12 We say You I all say it!it!it! ©Deepening Understanding LTD 2020 7

Let’s learn If both functions are multiplication and division, we can write it as a one-step function machine. 12 × 6 ÷ 2 36 is the same as… 12 × 3 We say You I all say it!it!it! ©Deepening Understanding LTD 2020 36

Let’s talk Rewrite the two-step function machines as one-step machines. 3 x 10 ÷ 2 280 ÷ 8 × 2 68 + 35 − 14 304 − 64 + 37 ©Deepening Understanding LTD 2020

Let’s learn A two-step function machine performs _________ on the input. We can use the inverse operation to work out the input. × 4 − 6 82 + 6 = ____ ÷ 4 = ____ We say You I all say it!it!it! ©Deepening Understanding LTD 2020 82

Let’s talk What is the input for each two-step function machine? x 2 + 19 109 ÷ 10 − 15 68 − 20 × 8 96 +7 ÷ 5 10 ©Deepening Understanding LTD 2020

Let’s learn We can explore the relationship between the input, output and function that we know to work out a missing function. 7 × 5 60 7 × 5 = ____ The difference between ____ and 60 is ____. The missing function must be __ _____. We say You I all say it!it!it! ©Deepening Understanding LTD 2020

Let’s learn We can explore the relationship between the input, output and function that we know to work out a missing function. 17 × 8 72 72 ÷ 8 = ____ The difference between ____ and 17 is ____. The missing function must be __ _____. We say You I all say it!it!it! ©Deepening Understanding LTD 2020

Let’s talk Find the missing functions for each two-step machine. 4 × 10 79 68 77 127 × 2 + 31 150 33 ÷ 4 ©Deepening Understanding LTD 2020 16

Let’s talk Use the function machine to complete the table. input Input 1 2 × 4 3 4 +9 5 6 7 output 8 9 Output Describe the pattern you can see. ©Deepening Understanding LTD 2020 10 11 12

Let’s talk Use this pattern to work out the output when the input is 13. input Input × 4 +9 output 1 2 3 4 5 6 7 8 9 10 11 12 Output 13 17 21 25 29 33 37 41 45 49 53 57 What will the output be when the input is 15? ©Deepening Understanding LTD 2020

Let’s develop our learning What is the same and what is different? 126 ÷ 2 126 87 × 4 × 2 252 + 78 ©Deepening Understanding LTD 2020 252

Exit task – Dong Nao Jin How many different ways can you complete the two-step function machine? 58 200 ©Deepening Understanding LTD 2020