Lesson 4 algebra 1 express simple functions in different forms

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  • These are tricky questions and you should encourage the students to discuss them in pairs/ groups.
  • Go through the answers with the class explaining why.
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Explain the function machine and then get the students to write down the outputs. This can be done using mini whiteboards
  • Outputs shown
  • Questions for students to complete
  • Questions for students to complete Q4 is an extension task
  • Get students to mark work and put a face to describe how they have found the task. This will help you when you are marking their books.
  • To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • This task will encourage the students to think about how they use mathematics. Share some of the students ideas with the class.
  • To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Use this example to show the students how to calculate a double function. This would be a great activity to help to check the understanding using whiteboards.
  • Answers to previous slide
  • Practice questions
  • Practice questions
  • Practice questions, Q4 makes the students think about how they will use a function machine backwards
  • Get students to mark work and put a face to describe how they have found the task. This will help you when you are marking their books.
  • To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Discuss how this will work give examples input 4 function 1 = x 3 then function 2 = - 2 so output would be 10. Ask how they would find the input when given the output and the 2 functions. Then move on to discuss how you would find the functions from several inputs and corresponding outputs.
  • This activity encourages the students to think mathematically. Please explain that each input has 2 functions to make the output.
  • Get students to mark work and put a face to describe how they have found the task. This will help you when you are marking their books.
  • To check progress of the class, mark the task completed and then ask the students to rate how they found the activity, Green = confident, Yellow = OK, Red = Unconfident/don’t get it. Ask the students to draw the corresponding face next to their work so when marking you can see how the students found the task.
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Share objectives with the class and explain to students what they are doing and what progress they have made
  • Get the class to complete the plenary activity – show me answers on the whiteboards. Why? Is the most important part. Can you draw a function machine to help solve this problem?
  • The function machine for the problem solving plenary

Transcript

  • 1. Entry Activity12 Order, add and subtract positive and negative numbers in context10 a) What is in between -4 and -6 on the thermometer?8 b) In my classroom the temperature has fallen to -4 degrees. I put the radiators on and it goes up by 8 degrees. What’s6 the temperature now?4 c) In the next classroom the temperature is 6 degrees, the teacher turns off the radiator and the temperature drops2 by 9 degrees, what is the temperature?0 d) In London on Christmas Day last year it was -5 degrees. It is 30 degrees in Adelaide on the same day. How much-2 warmer is it in Adelaide?-4 e) In Bradford on 30th August it was 19 degrees, I was told that is was 21 degrees colder in the south pole. What-6 temperature is it there? f) I have just got off the plane and at my maximum height I was 7km above group. I am going in a submarine next week and we are going down under the sea by 1.5km. What’s the difference in height between my 2 journeys?
  • 2. Entry Activity - Answers12 Order, add and subtract positive and negative numbers in context10 a) What is in between -4 and -6 on the thermometer? - 58 b) In my classroom the temperature has fallen to -4 degrees. I put the radiators on and it goes up by 8 degrees. What’s6 the temperature now? 4 degrees4 c) In the next classroom the temperature is 6 degrees, the teacher turns off the radiator and the temperature drops2 by 9 degrees, what is the temperature? -3 degrees0 d) In London on Christmas Day last year it was -5 degrees. It is 30 degrees in Adelaide on the same day. How much-2 warmer is it in Adelaide? 35 degrees-4 e) In Bradford on 30th August it was 19 degrees, I was told that is was 21 degrees colder in the south pole. What-6 temperature is it there? – 2 degrees f) I have just got off the plane and at my maximum height I was 7km above group. I am going in a submarine next week and we are going down under the sea by 1.5km. What’s the difference in height between my 2 journeys? 8.5km
  • 3. Today I will learn to:Express simple functions as functionmachines Level 3/4Calculate the rule when given an input andoutput Level 4Challenge Objective:To solve mappings problems Level 5 Key Words Function, Sequence, Generate, Term, Common, Describe, Input, Output
  • 4. Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
  • 5. I will find an output
  • 6. I will find an output
  • 7. Level 3Level 4
  • 8. Level 4
  • 9. Answers1 a output {7, 8, 11, 14} b output {2, 3, 6}, input 11 c output {20, 25, 55}, input 8 d output {10, 8, 6}, input 502 a add 2 b multiply by 3 c divide by 2 (or halve) 3 a {3, 5, 9}, 19 d multiply by 8 b {3, 6, 9}, 20 c input {5, 10}, output {12, 16} d input {1, 3, 10}, output 32
  • 10. Using your planners show me how you found this   
  • 11. Today I will learn to:Express simple functions as functionmachines Level 3/4Calculate the rule when given an input andoutput Level 4Challenge Objective:To solve mappings problems Level 5 Key Words Function, Sequence, Generate, Term, Common, Describe, Input, Output
  • 12. Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
  • 13. Extension Task – Problem SolvingFind at least ten different functions that have 50 as one of the output numbers 50
  • 14. Using your planners show me how you found this   
  • 15. Today I will learn to: Do: Check:Express simple functions as Write All will findfunction machines Level 3/4 functions in an output symbol andCalculate the rule when given an Most will find mappinginput and output Level 4 a rule from input andChallenge Objective: To find the output doubleTo solve mappings function Some will when given find the ruleproblems Level 5 the input and for double output functions Key Words when given Function, Sequence, Generate, Term, an input & output Common, Describe, Input, Output
  • 16. Double functions
  • 17. Double functions
  • 18. Level 3
  • 19. Level 4
  • 20. Level 4
  • 21. Answers1 a 9, 11, 13, 15 b 7, 13, 19, 25 c 9, 12, 15, 18 d 18, 20, 22, 242 A variety of diagrams depending on the starting inputs.3 a multiply by 2; 18, 20 b subtract 1; 14, 17 c multiply by 4; 15, 19 d add 3; 7, 84 a {1, 3, 4, 7} b {2, 3, 5, 8} c {3, 5, 9, 10}
  • 22. Using your planners show me how you found this   
  • 23. Today I will learn to:Express simple functions as functionmachines Level 3/4Calculate the rule when given an input andoutput Level 4Challenge Objective:To solve mappings problems Level 5 Key Words Function, Sequence, Generate, Term, Common, Describe, Input, Output
  • 24. Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
  • 25. What about when we have an inputand an output with two functions...
  • 26. Level 5
  • 27. Answersa multiply by 2 → add 1b multiply by 3 → subtract 1c multiply by 5 → add 2d add 3 → multiply by 2 or multiply by 2 → add 6e add 1 → multiply by 3 or multiply by 3 → add 3f add 2 → multiply by 5 or multiply by 5 → add 10
  • 28. Using your planners show me how you found this   
  • 29. Today I will learn to:Express simple functions as functionmachines Level 3/4Calculate the rule when given an input andoutput Level 4Challenge Objective:To solve mappings problems Level 5 Key Words Function, Sequence, Generate, Term, Common, Describe, Input, Output
  • 30. Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
  • 31. Problem Solving - PlenaryI am have decided to enter a running race. On average I run 1km in 9 minutes.I want to run the race in under an hour. I can enter the following races, 5km, 10km, 15km or 20km. Which race should I enter? Why?
  • 32. Problem Solving - PlenaryThe function machine for the problem Distance Total time of the taken to race run X9