Entry 4 | Patterns, patterns, patterns!

With all the discussions on how recognizing number patterns when problem-solving is important, I hereby declare that yes, solving a problem requires recognizing number patterns, just like what I did for the past few problem activities. 

If you see a pattern when you look systematically at specific examples, you can use that pattern to generalize what you see into a broader solution to a problem.

Here is a video that may be of help. It talks about patterns in fractions.
















Here is also a link that talks a little on patterns.

http://www.brighthorizons.com/family-resources/prepare-your-child-for-school/teaching-patterns-to-children/

At the end of the day, it is all about encouraging our little ones to recognize patterns, thick critically and solve problems. Feeding them with the answers will not help. Communicate why patterns work.

Entry 3 | Talk Math!

Picture this.

Now, can you guess how many went to St Ives? How can you work it out?

Think about these...
1)   How many cats are there?
2)   How many kittens are there?

Could there have been

1 man + [ 7 women x 7 sacks ] sacks + [ 7 x ( 7 women x 7 sacks ) cats ] + { [ 7 x ( 7 women x 7 sacks ) cats ] x 7 kittens ) kittens?

You figure it out! Remember it is not about getting it right. It is about how you explain how you derive to your answer.

Do you know that you cannot count things that have different nouns? Ah huh! You cannot count 1 apple and 3 oranges. Apple is of a different noun than orange. However, you can add 1 fruit to 3 fruits. Get it?

Bruner says after all, "Handle counting with same names." In early stages of learning, we should not leave out nouns. We should be using same names or identical nouns as they learn through concrete experiences.

Remember the Tortoise and Hare race? Which came first? How do you know?

Look at the picture below. Can you tell who came first?

Ah ah ah! You can never know until they finish the race! Just like the story of the tortoise and the hare. You only knew when the tortoise finished the race at the finishing line. Anything can happen before they reach the finishing lines you know. :)

Touching on this, do you know that you can use ordinal in 2 situations? First in the race is talking about time. When you are seated on the first row in the cinema, we are talking about space. Get it?

Let's try these!
1)  Third in class - Ordinal number in time or space?
2)  4th in the queue for popcorn - Ordinal number in time or space?
3)  Sarah came 5th for the lucky draw - Ordinal number in time or space?

So which is which?


















Time for 1 and 3! Space for 2! Did you get it right too?

Entry 2 | BORING First night - NOT!

When was the last time, I got thrilled over what was taught in class? Hmm… YESTERDAY! I lost all my energy solving the Mathematical problems last night that I ended up with none by the time the class ended. That explains why I only blog today! Hah!

Problems came after one another. No. Not the kind of problems that worry you, causing you to have sleepless nights. They were good problems. Good problems that put members together to think critically. Good problems that led us to come up with different solutions. Good problems that involve cognition.

How many letters do you have in your name? Which of those letters do you think is the 99^th? My name is Herma. There are five letters in my name and the letter ‘r’ is the 99^th. No matter what method I used from the 5 methods introduced by Dr Yeap yesterday, the 99^th is still ‘r’.

 

Find the connection or pattern in each method to facilitate your 99^th!

Problem 2 was my favourite! I will save talking about that at the end of my ramblings today. Now, read on. J

For problem 3, you got to imagine a truckload of paper if you are an American. A lorryload of paper if you are a Singaporean. Get it? Truckload? American? Lorryload? Singaporean? Oh well! Just imagine a big vehicle full of paper.

The question is… How long does it take for both machines, working at the same time, to shred one truckload of paper? Oh man! When was the last time I did a problem sum? Many years ago?

My group had a different answer from the correct one. Knowing that one of the machines (Let’s call it Machine A) takes 4 hours to shred 1 truckload of paper, we concluded that in 2 hours, Machine A will be able to shred ½ truckload of paper. The other machine (This one, we call it Machine B OK?) takes 2 hours to shred 1 truckload of paper. So, altogether, while Machine A worked hard to shred ½ truckload of papers in 2 hours, Machine B shredded 1 truckload of paper with the same timing. Thus, we thought,

2 hours = ½ truckload of papers (Machine A) + 1 truckload of papers (Machine B) = 1 ½ truckload of papers (3 units represented by ½ truckload of papers each)

So if it is just 1 truckload of paper we are talking about here, we took 2 units out of the 3 units (2 units represented 1 truckload of papers).

The equation à 3 divide by 2 = 1 1/2  hour

We thought we thought deeply. We explained our reasoning but well, we did not get it right but that is alright. When it comes to Math, we explore, guess and check!

We thought inventively when it came to Problem 4. Tangrams!

We made rectangles with different shapes. Yes, big rectangles. Small rectangles. Those were all “spatial” ideas. The foundation of children’s early cognitive development is spatial thinking. Do you know that research has showed that working with and combining shapes improves the Math skill and IQ of the young children?

Yikes! 50 minutes to 2nd day of this module. Let me wrap off this blog with my favourite Problem 2.

First, watch this video at this link.

https://www.youtube.com/watch?feature=player_embedded&v=9OqKyfytOvA

Are you wondering how this is done? Let me show you a fast one!

Now who in the world has created this trick? GENIUS!

P/S: Urgh! I cannot upload the video as of now! I'll be back!





 

Entry 1 | Note to parents

Gone were the days where 6 x 4 = 4 x 6. Not only should our new generation understand that 6 x 4 = 4 x 6, they should know that six fours make 24 too. 

Math is no longer what it used to be in the past. Worksheets, black boards and drilling are all things from the past. The new generation learn best when they interact with the environment. They do not learn as effectively when they are passive. They should be active while they learn from first-hand and concrete experiences, as they create or re-create Mathematical relationships. Given problems, they persevere to get them right through “productive struggle”. They listen, ask questions, share, try, err and discuss connections. Through their senses, they go through the process of learning and building knowledge of concepts.

Do you know that your kitchen is opulent with fun ways for your child to learn counting and measuring?

Start with a recipe!

When measuring, parents teach children how to make comparisons and estimations, while exploring fractional parts. When adding 2 large eggs or 1 cup of chopped nuts, your child is obviously counting. Talk Mathematics. Engage in rich interaction as they internalize concepts. Encourage multiple approaches. Adding two half cups of sugar is similar to adding a whole cup of sugar! Reason out. Discuss why this can be done.

According to NCTM, “Technology is essential in teaching and learning Mathematics. It influences the Mathematics that is taught and enhances students’ learning.” With kitchen technology so advanced, the working timer on your oven can provide an educational opportunity in learning to tell time!

Positive environment promotes positive learners. When your child has the ability to grasp and understand Mathematical ideas, you have successfully instilled that thing called "self confidence" in them.

Now, go and whip some cookies!