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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?
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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
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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
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Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
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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
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Using your planners show me how you found this
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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
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Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
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Extension Task – Problem SolvingFind at least ten different functions that have 50 as one of the output numbers 50
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Using your planners show me how you found this
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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
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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}
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Using your planners show me how you found this
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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
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Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
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What about when we have an inputand an output with two functions...
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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
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Using your planners show me how you found this
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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
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Check:All will find an outputMost will find a rule frominput and outputSome will find the rule fordouble functions when givenan input & output
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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?
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Problem Solving - PlenaryThe function machine for the problem Distance Total time of the taken to race run X9
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