Day 4: Fractions, Subtraction, Multiplication & Polygons

Problem 13: Mind Reading

Step 1: Think of 2 digits & reveal only the 1st e.g. 3

Step 2: Make a number by putting the 2 digits together e.g. 35

Step 3: Add the 2 digits together 3+5=8

Step 4: Subtract the smaller number from the bigger 35 - 8 =27 

 

Prof Yeap guessed the answer correctly on all 4 examples.

How did he do it?

By now, we know it is not magic.

 

Activity: Challenge your partner: Reveal the 1st digit. Ask her to guess the final answer using the steps above. What was the 2nd digit?

 

Her initial response ....

 



0 to 9...so many digits...which one to choose???

She was baffled!#+?!

And so was I:-((
 

To solve the problem, look for patterns!

 

Method 1: The 2nd digit can be any digit from 0-9. The final answer will fit into a pattern that will provide the answers for any 1st digits used! WOW!!

 

     1st digit     Final Answer

  3                     27

  6                     54

  4                     36

  2                     18

 

 Method 2: Take 1st digit and make it a Tens. Next minus the 1st digit and voila, you'll get the final answer!

Example:

40 - 4 = 36

or

60 - 6 = 54 

 

Method 3: Taking a good look at the pattern, you will see that the answers are multiples of 9! So take any 1st digit and multiply by 99 and ta-da you'll have the final answer.

 

1st digit     Final Answer

  3                     27x9 =27

  6                     54x9=54

  4                     36x9=36

  2                     18x9=18

 

Example:

 3 x 9 = 27

2x9=18

 

Being the SloMo (someone who takes forever to understand anything mathematical), I will have to admit that the 3rd method is the easiest for me to understand and share with another person. Just follow the pattern!

 

So what are the Learning Outcomes for the problem solving activity?

 

1. practice subtractions

2. look for patterns

3. explain/communicate to others about how you arrived at the solutions

Problem 14: Fractions and Subtraction

If 1 green bar = 1,

1) show 3 1/4.

2) show 3 /14 - 1/2

 

Method 1

Divide all the bars into 1/4s

 

13 - 2

 4    4 

 

11

 4    which is the same as 2 3/4

 

Method 2

 

3 1/4 - 1/2

 

      31/4

   /   \

11/4     2

  /

from 5

        4 take out 2/4 (1/4+1/4=1/2) remaining 3/4

 

so 31/4 - 1/2 = 2 3/4

 

Problem 15: 3 little Pigs

 

Scenario: The 3 little pigs are famished after their encounter with the wolf. They decided to "pig out" and have some pizzas, only that they are now faced with a problem...

 

             ... they bought 4 whole pizzas.

 

 

Challenge: How can 3 pigs share 4 pizzas equally?

 

Answer: logically, they can't!!

              mathematically .......   

               

Method 1:

 

4 divide by 3 = 3/3 + 1/3 = 1 1/3

Method 2:

 

4 divide by 3

12 thirds (12/3) divide by 3 = 4/3 = 1 1/3

 

so each pig gets 11/3 pizza.....I'd loved to see pigs doing maths at the farm:-)

 

 

Problem 16: Multiplication (with the help of the cutest birds) 

 

Challenge: How do you arrive at answers for multiple rows of bird?

 

 

Method 1: (by doubling) 

 

If 2 x 7= 14 

then 4 x 7= 14+ 14 = 28

Method 2: (by combining) 

 

If 2 x 7= 14 &

   3 x 7= 21

then 5  (2+3) x 7= 14 + 21 = 35 

Method 3: (subtracting)  

 

If 10 x 7= 70 

then 9 x 7= 70 - 7 = 63

 

before this module ends, here's something to reflect upon ....

 

Children must learn

to figure out and also

acquire the belief that

they can figure out.

(the same goes for teachers too!)

 

The T-E-A-C-H-E-R factor

 

A child is better off with a good teacher in a lousy school

than with a lousy teacher in a good school

 

A child is better off with a good teacher in a large group

than a lousy teacher in a small group.

 

(can anyone remember who said this?)