Functions (Funktioner)

Ämne / Topic

What a function is, different notations used for functions, and the coordinate system.

Inlärningsmål / Learning Goals

Understand the coordinate system.

Understand what a function is.

Google Slides & Videos

What is a function?

3. Aktiviteter / Key Activities

To explore this concept, the teacher will be doing a examples with the class, before giving the learners two examples to complete on their own.

Example 1: (Teacher led example)

Michelle fills a thermos with hot chocolate and brings the thermos along while she is on the ski slopes.

The temperature of the the hot chocolate is 84 degrees Celsius, but the longer that she is on the slopes, the colder the hot chocolate becomes.

The hot chocolate cools 10% every hour that she is on the slopes.

First we need to find the change factor:

100 - 10 = 90

= 0,9.

We then need to find what the temperature of the hot chocolate will be each hour that Michelle is out there.

After 1 hour: 0.9 x 84 = 76.

After 2 hours: 0.9 x 76 = 68.

After 3 hours: 0.9 x 68 = 61.

After 4 hours 0.9 x 61 = 55.

So after 4 hours, the hot chocolates temperature is 55 degrees Celsius.

So in the case of the example above:

Input (x): Temperature of hot chocolate.

Function: x 0,9

Output (y): New hot chocolate temperature.

So, y = 0,9x

We can even go one step further and plot the drop in the hot chocolates temperature on a graph (coordinate system).

Example 2: (Guided example)

Suppose you buy a share for SEK 100 and that it increases in value by 20% per year over a five year period.

a. calculate how much the share is worth after 1 year, 2 years and so on. Round all values to a whole kronor.

Change factor: 100 + 20 = 120%

= 1,2

Year 1: 100 x 1,2 = 120

Year 2: 120 x 1,2 = 144

Year 3: 144 x 1,2 = 173

Year 4: 173 x 1,2 = 207

Year 5: 207 x 1,2 = 249

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

1. Plot the points below on a coordinate system and name the shape that it makes.

A: (4,2) B: (-2,1) C: (-3,-2) D: (3,-1)

2. Suppose you buy a share for SEK 500 and that it increases in value by 25% per year over a five year period.

a. calculate how much the share is worth after 1 year, 2 years and so on. Round all values to a whole kronor.

b. Draw a graph showing the value of the share as a function of the number of years.

c. When is the change in value greatest in SEK?

5. Stängning / Closure / Summary of lesson

Brain-storm where functions are used in the world and identify which part is the input. function and output.

The amount of gasoline a car consumes depends on the cars speed.

input:

function:

output:

The postage of a letter depends on the the weight of the letter.

input:

function:

output:

The cost of oranges depends on how many kilograms you buy.

input:

function:

output:

Resurser & Materiel / Resources & Materials

http://webbapp.liber.se/matematikboken-z/#

http://webbapp.liber.se/matematikboken-z/#/4-samband-och-forandring

Textbook Practice:

Ett pg. 174 no. 4057 abc, 4059

Två pg. 175/176 no. 4064 abcd, 4065 ab

Tre pg. 176 - 178 no. 4068 abcd, 4069 abc

Fyra pg. 178/179 no. 4072 ab, 4073 ab, 4074 ab, 4075 abc