Even doordenken! Wiskundepuzzels.

Even doordenken!
For a change and for getting a little more flexible in your Maths skills, you are going to solve a number of 
Math Puzzles!   
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Slide 1: Diapositive
WiskundeMiddelbare schoolhavo, vwoLeerjaar 1

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Even doordenken!
For a change and for getting a little more flexible in your Maths skills, you are going to solve a number of 
Math Puzzles!   

Slide 1 - Diapositive

Slide 2 - Diapositive

18 Math Puzzles will come your way ...
+ simple 
+ tricky
+ even difficult, but all ..
+ worth while thinking over!
+ in Pairs or on your own.

Slide 3 - Diapositive

after a while you may ...
+  read out a Puzzle to your own choice to the class, and
+  show the way how you found the Solution!
+ First let's look at a few examples.
+ In English, although all Puzzles are in dutch.

Slide 4 - Diapositive

Example 1:
The three of us eat a pie.
A eats      ,  B   eats        and C eats the rest.

How much did C get?

41
85
87
81
timer
1:00

Slide 5 - Diapositive

How much did C get?
(Explanation next slide.)
A
1/7
B
1/4
C
1/3
D
1/8

Slide 6 - Quiz

Example 1:
The 3 of us eat a pie. We are A, B and C. 
A eats      ,  B eats        and C eats the rest.
T solve this, we have to add up the following fractions:         and  
      +        =   

So for C there is         left.  Because  1 =               and        -          =   
41
85
87
81
41
85
82
85
87
81
88
88
87

Slide 7 - Diapositive

Example 2:
Warning: this one is more difficult. However, maybe you find a way to tackle it?!
Three friends, Amy, Brenda and Cathy, win a price in the Lottery.
They divide it up as follows:
1.    Amy gets three times as much as Brenda
2.   Cathy gets two times as much as Amy.
3.   Together they divide up 40 euros.
QUESTION: How much do Amy, Brenda and Cathy get?
timer
2:00

Slide 8 - Diapositive

How much does Cathy get?
A
16 euros
B
24 euros
C
12 euros
D
4 euros

Slide 9 - Quiz

Explanation:
A new method is introduced here. Just try and follow this. (Maybe you can use it to solve a few of the Math Puzzles!)
They divide it up as follows:
1.  Amy gets three times as much as Brenda
2. Cathy gets two times as much as Amy.
3. Together they divide up 40 euros.

Solution: the key step is the first:
a. Let's call the part Brenda gets:   h                   (This may seem mysterious to you but it turns out to be very helpful!)
b. Then Amy gets 3 x h     and    Cathy gets 2   x   3 x h = 6 x a. 


Slide 10 - Diapositive

Example 2 - follow up
Solution: the key step is the first:
a. Let's call the part Brenda gets:   a                   (This may seem mysterious to you but it turns out to be very helpful!)
b. Then Amy gets 3 x a     and    Cathy gets 2   x   3 x a = 6 x a. 

Now we add up the parts the 3 girls get:     a + 3 x a + 6 x a = 1 x a + 3 x a + 6 x a = 10 x a 
So   10 x a = 40 euros, because 40 euros is what they may divide up.
Then a = 40 euros : 10 = 4 euros.
ANSWER: Brenda gets 1 x a  = 1 x 4 euros = 4 euros                Amy gets 3 x a = 3 x 4 euros = 12 euros   and finally
Cathy gets   6 x a = 6 x 4 euros = 24 euros.    Check:    4 + 12 + 24 = 40 euros.              Checks out all right.


Slide 11 - Diapositive

Maybe this last example was pretty difficult for you.
+ That's only logical as a complete new Math technique was used here!
+ However, not all Puzzles are that complicated.
+ Some are even very easy.
+ Some have more to do with Language than with Maths.
+ So there is something for everyone! (See next slide.)

Slide 12 - Diapositive

MCMLXX is a Roman number
What year does it mean in our number system?
A little help:
M = 1000        C = 100      L = 50     X = 10
timer
2:00

Slide 13 - Diapositive

SOLUTION:
MCMLXX is a Roman number.
It means:                1970.  How to find that out?
M = 1000,        C = 100,         L = 50       and       X = 10
Rules for Roman numbers:
If a lower number preceeds (voorafgaan) aan a higher one then it is subtracted.
So we get:  1000 - 100 + 1000 + 50 + 10 + 10 =  1970

Slide 14 - Diapositive

Solve a few Math Puzzles now!
Have fun!
+  Note: the Puzzles are not connected in any way.
+ That's why you may choose which one you do first.
+  Do this with a neighbour or on your own.
+  You don't have to finish them all. Better do a few good!
+  Write down your answers on the paper I'll give you.
timer
15:00

Slide 15 - Diapositive

In 4 minutes time I ask some of you to explain one of the Puzzles.
timer
4:00

Slide 16 - Diapositive

Time to explain a few Puzzles to the class!

Slide 17 - Diapositive

Try to solve a few more Puzzles.

Slide 18 - Diapositive

What is your opinion of this lesson?

Slide 19 - Carte mentale