Saturday, September 28, 2013

28/09/2013 Last Lesson but Not The Last of Math

On our last lesson, we had a quiz. We were asked to formulate math word problems using the following equations:

1) 8 ÷ 4
2) 4 ÷ 8
3) 2/3 ÷ 3
4) 3 ÷ 2/3

It was quite challenging as I had to consider if it was appropriate for the children and if they would get confused. After we submitted our answers, we had a discussion about this. I realized that what we deem as simple word problems may actually confuse the children. For struggling learners, the numbers must appear on the word problems so that they do not confuse themselves. When we use fractions, it is not logical to formulate word problems like " sharing 3 fruits among 2/3 friends". We need to keep in mind that living things are all counted in 1s. We can use things that can be measured in fractions such as liquid and pizza.
I find myself trying to read my word problems and do the math at the same time to check if it is really workable and if it is logical. 

These past few days have been very rewarding for me. I have always done badly in math and I think it all started when I was young. I was able to do the math during classes, yet I could never do it when I was given similar word problems or during exams. I lacked the practice and also did not care about finding other possibilities. I did not find a logical reason or find patterns in the problems. I am very enlightened and definitely learned a lot during the past few days. These basic problem solving skills are essential for the children as math is a progressive route. I find myself very eager to find the patterns and try to find logical solutions. This is also the attitude in learning that we as teachers need to cultivate in young children.
This method is not logical and will confuse children.

These are two methods which are logical and workable for children.

Friday, September 27, 2013

27/09/2013 Sum of Angles in a Triangle = 180 degrees

Below are some methods which we found in class!:) I'm eager to also show the 3rd method found outside of class!:P

Method 1: 

Fold the triangle to get a right angle 90 degrees. Triangles are half of a rectangle or square. Quadrilateral shapes have 4 right angles which add up to 360 degrees. So half of that is 180 degrees. 

Method 2: 

Tear out the angles and placed them along a line. You will find that they will fit into a line and the line represents half a circle which is 180 degrees.

Method 3:
The video below explains about how parrallel and vertical angles have corresponding angles on opposite sides.

Thursday, September 26, 2013

26/09/2013 Using Fingers to Count and Multiply

During yesterday's lesson, we worked on multiplication and division. 
Although the problems are more complicating, I observed that all the basic concept of math were continuously used. We were constantly looking out for patterns and counting. We were also constantly exploring possible ways to get the answers. As we explored, we found ways which worked like magic! :P
These so-called tricks help us to understand math better and is very different from memorizing without understanding hands on. Memorizing is robbing children of the opportunity to learn. It is fascinating to find new ways which works and help us count and multiply faster.

Below is a video of a boy counting( addition and subtraction) using just a finger trick he learned.
Can you identify which finger is the special number?
I just learned a faster way to count from a 5 year old!^.^

I also found another amazing way to multiply numbers 6,7,8,9 and 10 using fingers!
obtained from this website: Finger Multiplication of 6,7,8,9,10
Place your fingers as in the below image and consider the value of fingers in each hand to be 6, 7, 8, 9 and 10 - in the order from small finger to thumb.

6th time table finger multiplication trick

Consider the multiplication of 7 × 8.
Make the finger numbered 7 in the left hand to touch the finger numbered 8 in the right hand.

6th time table finger multiplication trick

Step 1:
Now in the left hand, count the finger which is touching (7) and the ones below that = 2 fingers
Similarly in the right hand, count the finger which is touching (8) and the ones below that = 3 fingers
Add the above counted fingers = 2 + 3 = 5 fingers
Multiply the number by 10 = 5 × 10 = 50 -----> (1)

Step 2:
In the left hand, count the fingers above the touching finger = 3 fingers
Similarly in the right hand, count the fingers above the touching finger = 2 fingers
Multiply both = 3 × 2 = 6 -----> (2)

Step 3:
Add (1) and (2),
= 50 + 6 = 56
So, the answer for 7 × 8 = 56 which is easily found through the above trick.

If there is no finger above the considered (touched) finger, then consider the value as zero (0).
Play the same for the below multiplications
6 × 6 = ? 6 × 7 = ? 6 × 8 = ? 6 × 9 = ? 6 × 10 = ?
7 × 6 = ? 7 × 7 = ? 7 × 8 = ? 7 × 9 = ? 7 × 10 = ?
8 × 6 = ? 8 × 7 = ? 8 × 8 = ? 8 × 9 = ? 8 × 10 = ?
9 × 6 = ? 9 × 7 = ? 9 × 8 = ? 9 × 9 = ? 9 × 10 = ?
10 × 6 = ? 10 × 7 = ? 10 × 8 = ? 10 × 9 = ? 10 × 10 = ?

And of course, we have the ingenious finger trick of the multiplication of 9.

Wednesday, September 25, 2013

25/09/2013 FUN Activities on Patterns, Division, Mutiplication,

Sharing with you some interesting math activities.

1) Division and Finding Patterns
This is very fascinating. Using your name, find the letter at the 2013th position. The method I used was looking out for patterns. I found that the numbers were formed in way that all the multiples of 10 were moving daigonally downwards as they increased. Using the multiples of 10, I counted to 200. I observed that the 200 was under the same column as 20. I deduced that 2000 would also be at that column. From there, I counted to 13 and got my answer. A faster, shorter and accurate way was to use division. Using 2013 and dividing it by 9 gives a remainder of 6. The 6th letter is the answer. It works with all numbers! The division method is used to find out how many full counts were made from my name. The remainder number if 3 letters short of a full count. Therefore, 'I' is the 2013th letter.

2) Dividing/Parts and Whole
Using a small rectangular paper, fold it so that it can be shared equally among 4 people. How many ways can you come up with? Are u able to create 4 different yet equal shapes? 
Here are some ways:

25/09/2013 Enrichment, Practice and Acceleration

In mathematics, enrichment, practice and acceleration are 3 different goals.
Practice- to work on same goal using the same method.
For example, your child needs practise on AB patterning. Have them make AB patterns using blue beads and red beads. To practice this skill, you can provide them with other objects (two types only). 

Enrichment- to work on the same goal using different methods/objects 
For example, you can have them identify AB patterns in their surroundings. You can also provide them with 3 different types of objects and have them create possibilities of AB patterns.

Acceleration- Progressing onto a new goal. 
For example, drawing AB patterns or making ABC patterns. As long as they are learning new goals, they are accelerating to a next level.

So, if John has no problems making AB patterns with green beans and red beans, which one of those three methods would you suggest doing and what are the activities you can think of?

These three words are essential when it comes to planning activities for your child. You do not want to be planning activities that are not appropriate for them.

Tuesday, September 24, 2013

24/09/2013 Rational Counting, Part and Whole Numbers

To be able to count, one needs to be able to know how to:
1) classify/sort
2) rote count
3) count using one to one correspondence 
4) have a conceptual understanding to use cardinal numbers

Let's DO some Math!

Activity 1(rational counting: subtraction) 

With a small cup of beans (preferably bigger sized beans), play a game with a child or you can also have them play in pairs. 
At every turn, each player should take out at least 1 OR 2 beans. The number can be increased gradually depending on child's readiness. The aim is to count it down to zero and the person who counts it down to zero wins!

For example, start off with 12 beans and take out 2 beans from it. Using rational counting, count the leftover beans and let the child know there is 10 left. If child takes 1 bean out, she will then need to use rational counting and identify 9 beans left. Go on with the game until zero beans are left. The trick to this game is finding out which are GOOD numbers to win this game and which are BAD. If there are 4 beans left, how many should you take in order to win the game? If you take 2, the child wins by taking out the remaining 2. If you take 1 and the child takes 2, you will win with the remaining 1 bean. Hence, 4 is a good number to win. Just remember to take 1 bean out and not 2;). It's quite fun once you know the GOOD and BAD numbers.

Activity 2 (Part and Whole Numbers)

Here is another fun math activity you can do with your child based on red beans and ten frames. You can buy of create your own ten frames.

With this number of beans in each frame, come up with as many ways to count the total number of beans. Some ways are:
1) rote counting 
2) making sets of 10s
3) making sets of 5s 

Have your child explore and come up with more ways? Explore the possibilities of more than one way to a correct answer.
You can also try it this way:) 

Monday, September 23, 2013

Skills I Picked Up For Teaching

  1. Hands on activities are crucial for learning mathematics. (DOING the math)
  2. While solving problems, we were going through the process of constructing new knowledge from our prior knowledge.
  3. More heads are better than one. As we share ideas, we learn new methods and possibilities in problem solving.
  4. We were also learning to articulate our ideas and giving logical explanations to our solutions.
  5. Patterns can be found in problems. (So far, yes)
Math is a life long skill and the skills can be used for life.

23/09/2013 There Is No One Way In Mathematics

Math is scary to me. I have never done well in mathematics and never liked it. Perhaps it was the thinking that caused me to stop exploring mathematics. After yesterday's lecture, I reflected on it and found that I actually liked mathematics for it is FUN. It was the RIGHT answer that stopped me from exploring problems and possibly the lack of patience too. I learned a few important values of learning mathematics yesterday and it was through these hands on activities that I actually learned to DO mathematics. There is no one way to mathematics.

We did a total of 4 problems from yesterday's lecture.
1) Counting Name
-figuring out the letter in our names that takes up the 99th spot.
2) Spell Count Card Trick
-arranging the cards in a way that when you spell the number of the card, the card will appear at the top of the deck.
3) Fractions
-finding out the time it takes to shred a truckload of paper if both old and new machines are operating at the same time.
4) Tangrams
-exploring ways to create a rectangle using different shaped and sized tangrams.

There are many possibilities in creating a rectangle.

Sunday, September 22, 2013

Note to Parents

"Mathematics ability is not inherited - anyone can learn mathematics." - Van de Walle, Karp and Bay-Williams(2014)

In the past, when we think about math, we think about words like "listen, copy, memorize, drill and compute". Math was driven into our heads and forced on us through piles and piles of practicing on worksheets. Many students who could not understand the concepts just gave up and never liked math again. This is something we educators would like to change and parents, you play an important partnering role with us in adding math into their life.

Firstly, I would like to introduce The Five Content Standards from Principles and Standards to you. Knowing what your child is learning will help you set appropriate goals and expectations for what they need to know about math from elementary through middle school. They are : 

.Number and Operations
.Data Analysis and Probability

Following these, Principles and Standards lists five process standards. These are mathematical process which your child should acquire and use when doing math. These processes are skills which will aid your child in tackling mathematics. They are:

.Problem Solving Standard
.Reasoning and Proof Standard (logical thinking)
.Communication Standard (able to explain mathematical ideas verbally)
.Connections Standard ( connecting mathematical ideas and using math in the real world)
.Representation Standard (use of mathematical tools to symbolize mathematical ideas)

Of course, the above requires us to have knowledge of the math we are teaching. We also need persistence, a positive attitude, readiness for change and a reflective disposition. Our attitude towards the teaching affects how the children learn.

Mathematics is the science of pattern and order. You can find pattern of regularity and logical order in mathematics. Students are taught to develop ideas of math, connect the materials together, respond and build on those ideas and make conjectures and predictions. In connecting dots between theories and practices, we need to encourage students using an inquiry approach whereby they develop their own ideas and use their prior knowledge in trying to assimilate or accommodate new knowledge. They will in turn need our help and guidance in providing then with the environment for learning math. An important note to remember is that the students are the ones doing the thinking, the talking and the mathematics.

 "Mathematics requires effort, and it's is important that students, families, and the community acknowledge and honor the fact that effort is what leads to learning in mathematics" (National Mathematics Advisory Panel, 2008).