The class was asked to write a story problem that can be answered by calculating 4 divided by 2/3.

This does not count!

What is 4 divided by 2/3? (name withheld to protect the innocent)

This is correct but I was hoping for a context:

How many 2/3 are there in 4?

This is pretty close but I think you meant 2/3 cups

How many servings of 2/3 are there in 4 cups? (Nur Ain)

Several people gave responses like hers.

All you need to do is to the 2/3 the same unit as the 4.

I have four pints of ice-cream for a children's day party. If I serve 2/3 of a pint of ice-cream to each child, how many children can be served?

My first reaction is 2/3 pint - is that a lot?

## Technology & Readings

## Wednesday, August 31, 2011

### Final Session

Today is the last session for EDU330.

Lesson 22 Writing a story problem for 4 divided by 2/3. I am glad we see several suitable responses. I randomly selected a few responses.

There are 4 cakes. Each child receives 2/3 of the cake. How many children are there? (Joycelyn)

Inger has 4 pizzas and she needs to cut it into two thirds. How many two thirds can she get out of it? (Ylva)

Lesson 23 How Big is a Foot is a good story to introduce the concept of standard unit in length. One activity I can do in class is to ask students to use the king's foot to measure the size of the bed that fits each of the children in the class. Or for homework, let them bring the 'foot' home and find the dimensions of the beds that fit each member of the kid's family.

Lesson 24 MRT Station. The class was sent to find the height between Level 1 and Basement 1 of the station.

Lesson 25 was to make a container to fill 15 beans.

Lesson 26 was to make a graph to show how we get to school.

We ended with a caterpillar story to remind us that shortcuts can 'damage' a child, easpecially in early childhood education.

The course has ended but learning continues ...

Lesson 22 Writing a story problem for 4 divided by 2/3. I am glad we see several suitable responses. I randomly selected a few responses.

There are 4 cakes. Each child receives 2/3 of the cake. How many children are there? (Joycelyn)

Inger has 4 pizzas and she needs to cut it into two thirds. How many two thirds can she get out of it? (Ylva)

Lesson 23 How Big is a Foot is a good story to introduce the concept of standard unit in length. One activity I can do in class is to ask students to use the king's foot to measure the size of the bed that fits each of the children in the class. Or for homework, let them bring the 'foot' home and find the dimensions of the beds that fit each member of the kid's family.

Lesson 24 MRT Station. The class was sent to find the height between Level 1 and Basement 1 of the station.

Lesson 25 was to make a container to fill 15 beans.

Lesson 26 was to make a graph to show how we get to school.

We ended with a caterpillar story to remind us that shortcuts can 'damage' a child, easpecially in early childhood education.

The course has ended but learning continues ...

## Monday, August 29, 2011

### Multiplication in Hort Park

These are photographs taken at Singapore's Hort Park.

Each flower has 5 petals. How many petals are there in 2 flowers? 4 flowers? 5 flowers? This is a 'rate' situation that can be modelled using multiplication

Another is the 'array' situations. How many pots of plants are there in the photograph. In an array, the number of objects in each row is equal.

## Friday, August 26, 2011

### Pick's Theorem

At the top of this blog is a link to one of the many, many sites on Pick's Theorem. There is an applet there that you can use - it gives the area automatically, so no need to calculate the area yourself.

There is also a proof of the theorem. It is a little involved so be warned that it is not a walk in the park.

For those of you mathematical types, there are other things on this site. Enjoy.

There is also a proof of the theorem. It is a little involved so be warned that it is not a walk in the park.

For those of you mathematical types, there are other things on this site. Enjoy.

### Session 5

Lesson 17 continues which is looking at division of fractions in a visual way. Then we did Lesson 18, which is actually the homework of the children of one of the participants.

We went on to Lesson 19 on area. Today we did some work on measurement.

See photo.

Lesson 20 revealed an interesting pattern! Who would think that the area of the polygon is realted to the number of dots inside it. And the relationship that someone came up with (add the number of dots minus three) is awesome!

George Pick would have been impressed. The link to Pick's Theorem is available above.

We had been focusing on whole numbers and fractions the last few sessions.

We also used graphs to document the number of 'pegs' for good ideas. That is Lesson 21.

Selamat Hari Raya to all. Final session for EDU330 on 31st August. But the learning journey continues ...

## Thursday, August 25, 2011

### Addition & Subtraction Situations

There are three basic situations for addition and subtraction - part-whole, change and comparison situations.

In Change Situation, there is an initial quantity, a change in quantity and a final quantity. In Part-Whole Situation, there are at least two parts and the whole. In Comparison Situation, there are two quantities that are compared.

### Session 4

Are the four parts equal?

We started with Lesson 14 The Mind Reading Game - the class came up with at least four different ways to figure out the final difference. We explained how the trick works using base ten materials and algebra.

Lesson 15 was on Subtraction 37 - 19. We wrote different word problems based on this.

After dinner, we did several lessons on Fractions. Lesson 16 was on Equal Parts. Lesson 17 was on Dividing Fractions.

See you tomorrow.

We started with Lesson 14 The Mind Reading Game - the class came up with at least four different ways to figure out the final difference. We explained how the trick works using base ten materials and algebra.

Lesson 15 was on Subtraction 37 - 19. We wrote different word problems based on this.

After dinner, we did several lessons on Fractions. Lesson 16 was on Equal Parts. Lesson 17 was on Dividing Fractions.

See you tomorrow.

## Wednesday, August 24, 2011

### Session 3

Photo Credit: Raudha

I hope you see how maths emphasizes visualization in the cubes lesson and tangram homework.

The cubes lesson is to help children learn the idea of conservation of number. That is, no matter how the cubes are arranged, the number remains the same.

By the way did you watch the two kids in Jasmine's blog playing a variant of the sticks game that you played in class (Session 2)? I enjoy reading many of your blogs.

If you were absent, please complete the three tasks and do a write-up on lesson study and the two case study done in this lesson. You may read your classmates' blogs to find out more.

I hope you see how maths emphasizes visualization in the cubes lesson and tangram homework.

The cubes lesson is to help children learn the idea of conservation of number. That is, no matter how the cubes are arranged, the number remains the same.

By the way did you watch the two kids in Jasmine's blog playing a variant of the sticks game that you played in class (Session 2)? I enjoy reading many of your blogs.

If you were absent, please complete the three tasks and do a write-up on lesson study and the two case study done in this lesson. You may read your classmates' blogs to find out more.

## Tuesday, August 23, 2011

### Session 2

We have covered key ideas in Chapter 8 to 14. Tomorrow we will do some lessons in kindergarten and lower primary and explore ways to develop key components of mathematical thinking.

Today we completed our discussion on what constitute mathematics. The class came up with Problem Solving & Thinking with five key components - Generalization (patterns, relationship, connections), Visualization, Communication (language, representation, reasoning, justification), Number Sense and Metacognition.

Lesson 6 was on Take 1 or 2 Game where we decide bad numbers are multiples of three. There was some attempt to generalize to when the rule allows taking one, two or three sticks. Lesson 7 was a favourite - Making Largest Even Number.

Lesson 8 was on Long Division. The photograph shows Lesson 9.

Lesson 10 was a word problem in response to a question raised.

Make-up work for absentees. Please solve all the problems we discussed and prepare a set of short notes for three key ideas discussed in class today.

## Monday, August 22, 2011

### Session 1

We had the first meeting today.

We did tasks in Lesson 1 (Name Problem), Lesson 2 (Sound of a Number), Lesson 3 (Jun-Jun, Lasene & Siti), Lesson 4 (Spelling Card Trick), Lesson 5 (Arrange Five Numbers).

If you are absent from the session

(1) solve these problems and submit them - you may need to consult a classmate to find out the details;

(2) explain the diferent uses of numbers - ordinal, nominal, cardinal and measurement numbers;

(3) describe in order of increasing complexity different strategies to do 5 + 7; and

(4) four pre-requisites to counting.

If you were present, you must have learnt, minimally, all the above. You may also recall two 'mistakes' that teachers make in designing ordinal number tasks and patterning tasks.

Hopefully, you will review Chapter 2 and Chapter 8.

Do not forget to write your daily reflections - even if it is just one paragraph.

For your class participation, I have given out pegs. Please trade them for a 'good idea token' when you have ten of the pegs.

See you tomorrow. Do not be late if you want to do the Quiz.

I randomly went to a few blogs and saw that Ain had done up an entry where she shared a bit of what she learnt with other teachers who were not with us, and reminded those of us who were there with what we learnt.

Session 1 has as a goal to give teachers a correct mindset about mathematics and teaching. When I read more blogs I will know if this goal has been achieved and to what extent.

## Sunday, August 21, 2011

### Information on Quiz

During the course you will be given some quizes for you to demonstrate your learning of the course materials. These are 15-minute tasks to be done between 1800 and 1815. You must hand in your responses by 1815 for it to be graded. If you are late for classes, you will have to forgo the opportunity to attemp the quiz.

Some tasks are content based. Others are based on pedagogy.

Sample Quiz Items are available at http://mmepdpm.pbworks.com . Please request access the first time you log in. This site requires a password (created by yourself).

Here are the sample tasks for those who have difficuly accessing the site.

Content Type Task

Sally added 8 and 7 by thinking that 8 is 3 and 5. Thus, 3 and 7 is ten. Hence, 8 + 7 = 5 + 10 = 15.

Use Sally's Method to add 6 and 9.

Pedagogy Type Task

Miss Lim uses three types of materials to teach numbers to twenty (e.g. 18) - ice-cream sticks, 1-cent and 10-cent coins and base ten blocks.

Are these three unique materials or they can replace each other? Give your reason.

Some tasks are content based. Others are based on pedagogy.

Sample Quiz Items are available at http://mmepdpm.pbworks.com . Please request access the first time you log in. This site requires a password (created by yourself).

Here are the sample tasks for those who have difficuly accessing the site.

Content Type Task

Sally added 8 and 7 by thinking that 8 is 3 and 5. Thus, 3 and 7 is ten. Hence, 8 + 7 = 5 + 10 = 15.

Use Sally's Method to add 6 and 9.

Pedagogy Type Task

Miss Lim uses three types of materials to teach numbers to twenty (e.g. 18) - ice-cream sticks, 1-cent and 10-cent coins and base ten blocks.

Are these three unique materials or they can replace each other? Give your reason.

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