1TTO §6.2 Graphs from formulas PTI Apr24

§6.2 Graphs from formulas
(you may skip some exercises as we do a lot together)



Some TABLES to be made and many
GRAPHS to be drawn in this paragraph.
First we do a part of the paragraph together.
Work hard on the coming tasks,  skipping some exercises later.
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Slide 1: Slide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 1

This lesson contains 31 slides, with interactive quizzes and text slides.

time-iconLesson duration is: 50 min

Items in this lesson

§6.2 Graphs from formulas
(you may skip some exercises as we do a lot together)



Some TABLES to be made and many
GRAPHS to be drawn in this paragraph.
First we do a part of the paragraph together.
Work hard on the coming tasks,  skipping some exercises later.

Slide 1 - Slide

Materials ....
+ Take before you the right things:
+ pencil, pen, geo triangle or ruler, eraser
+ GRAPHS are always drawn with a PEN + GEO/RULER !
+ Notebook and Textbook 1A, p.208

Slide 2 - Slide

7
This is the Theory.
Next slide shows us an example.

Slide 3 - Slide

Slide 4 - Slide

Slide 5 - Slide

> First make a table => variable in top row
                                                 outcome (distance) bottom row

time
distance

Slide 6 - Slide

5



ANS!

Slide 7 - Slide

Steps of 60 are fine, because ...
A
you have to put 300 on the axis; then you need 300 : 60 = 5 cm.
B
the time goes from 0 to 5
C
the distances go up by 60 all the time
D
there is no zigzag needed

Slide 8 - Quiz

6
Points of attention:
+ Scale:  on the vertical axis 60 (km?) is put in 1 cm, so that you cover 300 km.
+ The graph is a straight line because all points lie on one line.
+ Labelling of the axes has not been forgotten.
+ Note that there is no reason for a zigzag.

Slide 9 - Slide


This is Task A.
Question about this task:
What to do first, before plotting the graph?
Answer in next slide.

Slide 10 - Slide

First you ....

Slide 11 - Mind map

Solution:
First you ...
MAKE A TABLE !
As follows:

Slide 12 - Slide


Task A.
You may skip exercises 9, 10 and 11.
Now:
 COPY and MAKE this task in your Notebook,  by copying and filling in the Table above!

timer
2:00

Slide 13 - Slide


Before you go on with this task, there come a few questions about it.




Note: only the EVEN number are used in the top row, because otherwise the line of numbers would be too long.

Slide 14 - Slide

Slide 15 - Slide



Question 1: Is a 'zigzag' a good idea or not?

Slide 16 - Slide

A zigzag: a good idea? (Why?)
A
no
B
yes

Slide 17 - Quiz

Solution:

Yes. Because the height only starts at 120 cm.
(By the way: a Solutionsbook may NOT do this!)

Slide 18 - Slide




Question 2: What is a good scale for the corresponding Graph? Why?
THINK about this for half a minute.
 For the answer see next slide.
timer
0:30

Slide 19 - Slide

QUESTION: What is a good scale for the vertical axis 
of the corresponding Graph?
SOLUTION: 260 - 120 = 140
140 : 20 = 7 , so if you use as a scale:    
 20 cm in table = 1 cm in graph, then you need 7 cm.
That's fine.

Slide 20 - Slide


FOTOVRAAG !
Now PLOT the GRAPH and send in a picture of your work in next slide. Remember:
1.  a zigzag at height 120 cm
2. scale on vertical axis: 20 cm in 1 cm.
Make your teacher happy: draw a beautiful graph!
Of course: USE A PENCIL + GEO/RULER!

Slide 21 - Slide

Slide 22 - Slide

Here are the points again. Now it offers more content!
Sometimes TWO GRAPHS have to be PLOTTED in 
ONE coordinate system.
Why?
Think of a good reason.
ANS

Slide 23 - Slide

TIP for
making TABLES:
The number of years could be LESS than here.
For example: 0, 6 and 12 years is good enough. So only 3 will do!
All the more because all points lie on a STRAIGHT LINE!

Slide 24 - Slide

SOLUTION:
then you can COMPARE both graphs!

Slide 25 - Slide

COMPARING in two examples:
- for number = 0, the green formula
  has as outcome 30, the red one 15.
- the point of intersection is (3, 22);
   in this point the numbers and amounts for both formulas are the same!


Slide 26 - Slide

Slide 27 - Slide

IMPORTANT:
Because two Graphs have to be drawn, also
two Tables have to be made !
How else can we know some points, that lie on the graph?!

Slide 28 - Slide

Is the Graph RISING or FALLING?
Two examples:
The graph for the Formula:             60 + time x 2 = amount
is rising, because per step 2 is added to 60.

The graph for the Formula:             60 - time x 2 = amount
is falling, because per step 2 is subtracted from 60.

Slide 29 - Slide

Above you first see explained: a rising graph.
Below a falling graph is explained.
Most important are the signs        +  and   -.
The minus sign before the multiplication means a falling graph!
Suppose the minus sign was before 60 it only meant that the graph starts
at a lower point. It says nothing about falling or rising.
Next slide says it in other words.

Slide 30 - Slide

Homework time 

Slide 31 - Slide