1TH/Vwo §7.1 Calculating with numbers

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

A look back at the Practice test from Ch6 first!

What many people did not pick up yet was:

CHECKING by two CALCULATIONS if the 

point of intersection that you read off REALLY is the p.o.i.!

Let's Study the following instruction slide together.

So for these two graphs we are going to 

- read off the p.o.i. which is (5, 3.5) and also

- check this by filling in 5 in both formulas and seeing IF

   the outcome is 3.5 both times!

§7.1 Calculating with numbers

Homework:  2, 4  t/m  10

Some new words will come up!

It's important to know their meaning.

That's what this LessonUp is useful for.

§7.1 Calculating with numbers

Homework:  3  t/m  8

learning goals:

- what is a sum, a difference, a product and a quotient ?

- how to do calculations IN THE RIGHT ORDER

The new words:

brackets           product       quotient

sum             difference                   

Try to TAKE IN the following information.

Later in this LessonUp there will be several questions about it!

You get the Sum when ...

adding up two (or more) numbers together,

 Like  35 + 12 = 47

In fact 'the sum' is our 'de som'!

Indeed, awe-sum!      

Difference:

When you subtract 2 numbers from each other, 

the result is the Difference.

For example:          45 - 16 = 29,  

so 29 is the Difference of 45 and 16.

Product:

Multiplying 2 (or more) numbers by each other,

gives us the Product of the numbers.

Like 23 x 3 = 69, 

so 69 is the Product of 23 and 3.

Quotient:

When you divide 2 numbers by each other, the result is called the Quotient of them.

For example:  14 : 7 = 2,  

so the Quotient of 14 and 7 is 2.

Mention the most important 4 words from the previous slides.

The Product of 15 and 3 is ......

1. 18
2. 5
3. 45
4. 12

The Product of 15 and 3 ....

means the Multiplication of 15 and 3, so:

15 x 3 = 45

The Sum of 34 and 13 is .........

1. 21
2. 21
3. 57
4. 47

The Sum of 34 and 13 is ...

47, because the Sum means Adding!

The quotient of 27 and 9 is ........

What has to do most with arithmetic?

1. Sam
2. Siem
3. Sum
4. Sem

Maybe you remember from your old school ..

that x  and  :  go before  +  and   -.

This is still true.

However, there can be exceptions...

See next slide!

Brackets are the New Things!

Brackets? There are several kind of brackets!

In dutch 'beugels' comes nearest.

Next slide shows you brackets for arithmetics.

Amazing stuff, down here:

Amazing stuff, down here:

So, thanks to the Brackets (=haakjes), the old Priority (=voorrang) is changed.

In the first calculation we do   2 x 5   first,

but because of those Brackets we first do:     8 + 2.

What is the result of:
(6 + 6) : 3 ?

1. 3
2. 4
3. 9
4. -5

Explanation:       (6 + 6) : 3 =

First work out the Brackets:

(6 + 6) : 3 = 12 : 3 =4              (Notice that the Brackets have gone in the 2nd step, as they have no meaning any more.)

That's why the good answer is 4!

FINALLY:  Try to understand the meaning of the next slide!

In the next slide the meaning is explained!

A correct notation is important.

In the next slide, find the mistake!

5 + 5 x 3 = 15 = 5 + 15 = 20

The outcome is good, but the way of writing it all down contains a mistake.

Think hard about this. Which step above is not good?

Some of you get the turn.

Next slide gives the answer.

5 + 5 x 3 = 15 = 5 + 15 = 20

The outcome is good, but the way of writing it all down contains a mistake.

The Mistake:    ' = 15 '

It suggests that 15 is equal to the final outcome, 20.

Why? Well, there are ' = ' signs between every step, so every step must be equal to any other step!

5 + 5 x 3 = 5 + 15 = 20

One more time the good answer, above.

Work out:
4 : 2 + 7 x 3 - 4 x 2 = .......

1. 31
2. 2 = 2 + 21 = 23 - 8 = 15
3. 2 + 21 - 8 = 15
4. 15

Fotovraag:

1. Work this task out in your Notebook.

2. take a picture of this and

3. send it in in the next slide!

4. so show us your Calculation and

5. NOTA = not only the Answer!

Calculate 7 + 3 x 4 : 6 - 5 = .........

Solution:

Homework time

+ You may skip exercises  1 and 3.

+ Next slide tells more about exercises  7 and 8.

Homework time-additional remark:

Exercises 7 and 8:

NOT ONLY THE ANSWERS!

1.  Copy the task in your Notebook

2. Make a CALCULATION for every task, just like you see 

    in the two EXAMPLES on p.12, right above exercise 7.