Session Four

Lesson 14:

Mind Reading Game (using only digits from 1 to 9).

This was another “magic trick” by Dr. Yeap. Well, actually there is a logical solution to the problem again…convincing me that math is actually a science and not magic. 
The "mind reader" will ask the person to think of a two digit number. Then follow three steps:
1. The two digit number, for example 72
2. Then add the two digits 7+2=9
3. Then difference between the first number 72 and the second number 9 which is 63. 
The person will call out the first number in the tens place and think about the other number in the ones place. Then the person will do the three step computation. The mind reader will actually get the same result.  

Column A will tell you the number that was called out and Column B is the number that Dr. Yeap figured out (which was indeed the same number).

Column A: Column B:

8 3 9 4 6 5

72 27 81 36 54 45

 

There were a variety of methods for the “mind reader” to figure out the person’s number.

1. Multiply by 10 then minus the 1^st number that the person says. For example, 8, I then think 80 – 8 = 72.

2. If the person say 5, you think 51 (5+1=6) then 51-6=45 (4+5 must add up to 9) or think 57 (5+7=12) then 57-12=45.

3. We see that it is multiples by 9.

4. Person says 8 then I will go back one number 7 (7 + 2 to make 9) so number is 72.

I thought this was an excellent introduction to Algebra. Very interactive and it made sense eventually.

For example, 3 (call it x) is in the tens value and 2 (call it y) in the ones value.

(30x +2y)=32

(3x +2y)=5

32 -5=27

There is still some hope even for someone like me!

Lesson 15:

Subtraction 37 – 19 = ?

We discussed a variety of ways to subtract and how to teach the concept of place value. This is important for children to effectively calculate. They need to be able to count in tens and ones. Explain to children that each place has a value, for example, 37 (3 is in the tens place hence 30 but we don’t write it out). We also discussed that children should explore different strategies. However, the teacher needs to bring it back and anchor the lesson to introduce the new idea to effectively help them to count.

Word problems:

It was interesting to discuss the necessity to introduce a variety of different word problems. Thus, elicit thinking and problem solving skills. The problems should have different structures such as: Join Problems, change situation (before and after), part-part-whole situation and compare. We discussed Zoltan Dienes who has emphasized the importance of variation in mathematics (vary the unknown). Also, a math problem can be introduced at any grade level just knowing which approach to use (Concrete, Pictorial or Abstract). Teachers need to be aware of their language when discussing math. For example, do not say when there is the word “more” in word problems always use addition and when there is the word “less” then you should say take away. This may cause confusion for children when looking at the word problem such as:  Valentino has 12 cookies and Sandra has 8 cookies. How many more cookies does Valentino have than Sandra?

Lesson 16:

Equal Parts

The square is divided into 4 equal parts:

¾ is colored blue. We discussed that the parts are equal and you can name them. Also, it is important to start by introducing the name, three fourths instead of writing the fraction ¾. We also talked about the importance that we can count only the same sets of things (no difference in nouns). In addition, be aware of our language; do not say 2 upon 5 or 2 out of 5 (as this may confuse the child and interfere with his/her conceptual understanding).

How to do two fifths plus one half? It has to belong to the same set.

Well, cut it in half…now you can do it.

Always introduce informally then move to formal math.

One piece is one fourth.

Now if you cut each piece into halves they will become one eighths. Thus one fourth is equal to two eighths.  

Being equal does not mean being identical. As long as the area is the same it will represent the same amount.

It is interesting to see that a math exercise can be done at any grade level using the CPA approach. 

Concrete Approach: Children have a piece of paper and cut it out.

Pictorial Approach: Use drawings to explain the concept.

Abstract Approach: Use the formula to find out the area of the triangle. Multiply the base by the height, and then divide by 2.

Lesson 17:

Dividing Fractions

Division have two meanings; sharing and grouping.

12 divided by 4 equals 3

 

How many fourths are there?

¾ divided ¼ = 3 (simply put, how many fourths are there in three fourths…)

12 divided by 4 =3 (simply put, how many fourths there are in 12…)

So ¾ divided by ¼ = 3

Thank you Dr. Yeap!