Lesson 4 algebra 1 express simple functions in different forms
1. Entry Activity
12 Order, add and subtract positive and negative numbers in context
10 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’s
6 the temperature now?
4
c) In the next classroom the temperature is 6 degrees, the
teacher turns off the radiator and the temperature drops
2
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 - Answers
12 Order, add and subtract positive and negative numbers in context
10 a) What is in between -4 and -6 on the thermometer? - 5
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’s
6 the temperature now? 4 degrees
4
c) In the next classroom the temperature is 6 degrees, the
teacher turns off the radiator and the temperature drops
2
by 9 degrees, what is the temperature? -3 degrees
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? 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 function
machines Level 3/4
Calculate the rule when given an input and
output Level 4
Challenge Objective:
To solve mappings problems Level 5
Key Words
Function, Sequence, Generate, Term, Common,
Describe, Input, Output
4. Check:
All will find an output
Most will find a rule from
input and output
Some will find the rule for
double functions when given
an input & output
9. Answers
1 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 50
2 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
11. Today I will learn to:
Express simple functions as function
machines Level 3/4
Calculate the rule when given an input and
output Level 4
Challenge Objective:
To solve mappings problems Level 5
Key Words
Function, Sequence, Generate, Term, Common,
Describe, Input, Output
12. Check:
All will find an output
Most will find a rule from
input and output
Some will find the rule for
double functions when given
an input & output
13. Extension Task – Problem Solving
Find at least ten different functions that
have 50 as one of the output numbers
50
15. Today I will learn to: Do: Check:
Express simple functions as Write All will find
function machines Level 3/4 functions in
an output
symbol and
Calculate the rule when given an Most will find
mapping
input and output Level 4 a rule from
input and
Challenge Objective: To find the
output
double
To solve mappings function Some will
when given find the rule
problems Level 5 the input and for double
output functions
Key Words when given
Function, Sequence, Generate, Term, an input &
output
Common, Describe, Input, Output
21. Answers
1 a 9, 11, 13, 15 b 7, 13, 19, 25 c 9, 12, 15, 18
d 18, 20, 22, 24
2 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, 8
4 a {1, 3, 4, 7} b {2, 3, 5, 8} c {3, 5, 9, 10}
23. Today I will learn to:
Express simple functions as function
machines Level 3/4
Calculate the rule when given an input and
output Level 4
Challenge Objective:
To solve mappings problems Level 5
Key Words
Function, Sequence, Generate, Term, Common,
Describe, Input, Output
24. Check:
All will find an output
Most will find a rule from
input and output
Some will find the rule for
double functions when given
an input & output
25. What about when we have an input
and an output with two functions...
27. Answers
a multiply by 2 → add 1
b multiply by 3 → subtract 1
c multiply by 5 → add 2
d add 3 → multiply by 2 or multiply by 2 → add 6
e add 1 → multiply by 3 or multiply by 3 → add 3
f add 2 → multiply by 5 or multiply by 5 → add
10
29. Today I will learn to:
Express simple functions as function
machines Level 3/4
Calculate the rule when given an input and
output Level 4
Challenge Objective:
To solve mappings problems Level 5
Key Words
Function, Sequence, Generate, Term, Common,
Describe, Input, Output
30. Check:
All will find an output
Most will find a rule from
input and output
Some will find the rule for
double functions when given
an input & output
31. Problem Solving - Plenary
I 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 - Plenary
The function machine for the problem
Distance Total time
of the taken to
race run
X9
Hinweis der Redaktion
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