Thursday, September 26, 2013

Day 4- Fractions, Subtraction, Polygons

Day 4- Fractions, Subtraction, Polygons

We continued on with Problem 13: Mind Reading
An interesting problem that had me clueless for the first 10 minutes!

Step 1: Think of 2 digits, make known the 1st digit only.
Step 2: Put the 2 digits together, and use that number to minus off the sum of the two digits.
              (eg: 2 1 - 3 = 18)

Have your friend find out: Given the 1st digit only, find out the 2nd digit.

Dr Yeap had us try it out and was able to guess the final answer while being given the 1st digit only.

That baffled us for a while!


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


1st digit     Final Ans

  3                     27

  6                     54

  4                     36

  2                     18

Using this pattern, 2 more methods are found....

Method 2: Take 1st digit and make it a Tens and minus the 1st digit off to get the final answer.

Eg: 30 - 3 -27

Method 3: Have any 1st digits x 9 and you get the final answer.

Eg: 3 x 9 = 27

Personally, I find Method 3 the best and most straight forward method to do!

IMPORTANTLY, this problem allowed 3 levels of teaching here:

1. Learning subtraction
2. Identifying the patterns present
3. Ability to articulate the reasons of the patterns present

This is an example of a problem displaying Differentiation.

Problem 14: Fractions and Subtraction

Using a fairly simple problem, we saw how 2 methods can be used to help children understand ways to calculate the sum 
3 1/4 - 1/2 = ?

Problem 15

Find Out: How do 3 piggies share 4 pizzas equally??

Method 1: 4 divided by 3 = 3/3 + 1/3 = 1 1/3

Method 2: 4 divided by 3 = 12 thirds = 4/3 = 1 1/3

Problem 16 had us thinking about multiplication.

Find Out: How do we get answers for multiple sets of 7 birds?

Method 1: By doubling certain sets 
 Eg:  2x7= 14 , so 4x7= 14+ 14 = 28

Method 2: 2 sets of 7 added up together 
Eg: 2x7= 14 & 3x7= 21,
Therefore, 5x7= 14 + 21 = 35 

Method 3: Subtract 7 from a larger set of 7 
Eg: 10x7= 70 , so 9x7= 70-7 = 63

These provided more efficient ways of using multiplication, addition and subtraction together to arrive at answers at a faster speed!

Problem 17 of exploring Polygons made us think deep into the concept as we...

Find Out: Forming Possible polygons that has 1 dot left in the center

The Geoboard app was a good medium to explore polygons!

It was a fruitful time of consolidating our ideas as we found out the smallest to biggest polygons that can be formed!

From a few ideas...

to a complete set of the best ideas we could come up with!

Ending off, 

Whether you are a good mathematician or not, 

Here's a good Quote to advocate Math as A Math Teacher...

It's not about the answers, but the Concepts of Math that can enrich our everyday lives!

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