Today we looked at how to make lessons problem-solving in nature as well as how to differentiate instruction for advanced learners as well as remedial students. We looked at the idea of tiered instruction as well.

This group even included me in the problems they created. Can you identify the other characters in the problems?

Why is this a problem?

What can you ask an advanced learner to do?

# I Teach K

This blog is on all things related to early mathematics and science. I use this blog for all the early childhood degree programmes I teach at SIM University as well as SEED Institute / Wheelock College and other early childhood programmes for Ministry of Education, Singapore and PCF Kindergartens.

## Technology & Readings

## Monday, December 2, 2013

## Monday, November 18, 2013

### BSc08 Reading 1 Poster Sharing - Polya's Model

The class was asked to make a poster to share with fellow educators. Some of the students made a poster to share their understanding about Polya's Model and the kind of questions suitable at each stage.

I encourage fellow educators to have a poster of Polya's Model - Let's Understand, Let's Plan, Let's Carry Out and Let's Look Back in our classrooms ...and make it suitable for the age group.

I encourage fellow educators to have a poster of Polya's Model - Let's Understand, Let's Plan, Let's Carry Out and Let's Look Back in our classrooms ...and make it suitable for the age group.

**BSc08 Polya**from

**Jimmy Keng**

## Sunday, November 17, 2013

### MAT150 Developing Problem-Solving Skills Session 3 on 18/11/2013

Don't forget we meet this evening and tomorrow to discuss instructional strategies and also linking mathematics to other domains.

After these two days, the assigned reading is Chapter 4 - Planning in the Problem-Based Classroom.

Based on your reading, compile five photographs to remind colleagues in early childhood sector what is important in planning for exciting problem-solving lessons for young children. Please bring these five photographs (can be simply printed on your own printer) with annotation (limited to three sentences) for the next class meeting in December. You can use the guiding questions at the end of Chapter 4 to guide you.

An example will be shown here later.

Today we look at instructional strategies and assessment methods.

We solve Problem 31 - How Many Pieces?

Along the way we reviewed important bits about teaching beyond ten, choice of materials for shapes, and the language of measurements.

We also saw the creation of the English Language as a problem-solving process.

Problem 32 - How Many Coins in the Can?

We discussed some differentiated instruction strategies via a discussion on a lesson to compare length of paper strips.

Several challenging topics were brought up.

After these two days, the assigned reading is Chapter 4 - Planning in the Problem-Based Classroom.

Based on your reading, compile five photographs to remind colleagues in early childhood sector what is important in planning for exciting problem-solving lessons for young children. Please bring these five photographs (can be simply printed on your own printer) with annotation (limited to three sentences) for the next class meeting in December. You can use the guiding questions at the end of Chapter 4 to guide you.

An example will be shown here later.

Today we look at instructional strategies and assessment methods.

We solve Problem 31 - How Many Pieces?

Along the way we reviewed important bits about teaching beyond ten, choice of materials for shapes, and the language of measurements.

We also saw the creation of the English Language as a problem-solving process.

Problem 32 - How Many Coins in the Can?

We discussed some differentiated instruction strategies via a discussion on a lesson to compare length of paper strips.

Several challenging topics were brought up.

## Sunday, November 3, 2013

### Development of Numeracy in Early Childhood Education

This course, customized by Marshall Cavendish Institute for Ministry of Education Singapore, reviewed the question - how children learn mathematical ideas.

Dr Yeap Ban Har's email is yeapbanhar@gmail.com

Resources

Manipulative Materials

Classroom Warehouse Products website

EAI Education's website

The (clothes) number pegs etc are available in many neighbourhood stores and I saw some in Popular as well.

The 'eggs' are from a shop behind Ang Mo Kio Market (Ang Mo Kio Avenue 10) ... I will get the exact address on my next visit. Watch this space.

The giant playing cards are about $3 a pack from 'pasar malam' type stores.

The music videos are from Debbie and Friends

My favourites include Jack and the Beanstalk, Cinderella and Goldilocks. Actually I like all the Debbie and Friends videos!

Dr Yeap Ban Har's email is yeapbanhar@gmail.com

Resources

Manipulative Materials

Classroom Warehouse Products website

EAI Education's website

The (clothes) number pegs etc are available in many neighbourhood stores and I saw some in Popular as well.

The 'eggs' are from a shop behind Ang Mo Kio Market (Ang Mo Kio Avenue 10) ... I will get the exact address on my next visit. Watch this space.

The giant playing cards are about $3 a pack from 'pasar malam' type stores.

The music videos are from Debbie and Friends

My favourites include Jack and the Beanstalk, Cinderella and Goldilocks. Actually I like all the Debbie and Friends videos!

## Thursday, October 10, 2013

### MAT150 Developing Problem Solving Skills 10 October 2013

We reviewed problem solving using this video

We solve a problem connected to polygons with area 5 square units and ended up observing a pattern.

We also solved a problem connected to packing 19 beans in bags of 2 or 3 beans as well as two other related problems - 10 bicycles and tricycles have 28 wheels and the possible values of 10 coins of two types - 5-cent and 20-cent coins.

We reviews the CAT to DOG problem by trying to do TOAD to FROG (how about STEPSISTER to CINDERELLA?)

We looked at various heuristics - some concrete, others pictorial and yet others abstract.

Five core competencies - visualization, number sense, looking for patterns, metacognition and communication.

If you are absent or missed the discussion please submit a solution to the problem with one main point that you can discuss based on the solving of the problem.

Reading to be done before November's sessions - Chapter 3 and complete on of the tasks by presenting it in the form of an A4 poster for sharing with colleagues. Submit this when you come back in November.

Yi Yang (age 1.5 year) pretending to solve a maths problem |

We also solved a problem connected to packing 19 beans in bags of 2 or 3 beans as well as two other related problems - 10 bicycles and tricycles have 28 wheels and the possible values of 10 coins of two types - 5-cent and 20-cent coins.

We reviews the CAT to DOG problem by trying to do TOAD to FROG (how about STEPSISTER to CINDERELLA?)

We looked at various heuristics - some concrete, others pictorial and yet others abstract.

Five core competencies - visualization, number sense, looking for patterns, metacognition and communication.

If you are absent or missed the discussion please submit a solution to the problem with one main point that you can discuss based on the solving of the problem.

Reading to be done before November's sessions - Chapter 3 and complete on of the tasks by presenting it in the form of an A4 poster for sharing with colleagues. Submit this when you come back in November.

## Wednesday, October 9, 2013

### MAT150 Developing Problem-Solving Skills 9 October 2013

Experiencing and Discussing

Show two halves.

Polya Four-Stage Model was discussed.

1. Understand

2. Plan

3. Do

4. Look Back

Problem solving includes exploring, specialising and generalising. (Mason)

Problem solving include self checking.

We completed three other tasks to understand what is problem solving.

CAT to DOG

CAT > COT > DOT > DOG

In three steps, we changed CAT into DOG.

Only one letter can be changed each time.

Each word must be an English word.

John and Mary agreed to meet at 6 o'clock at a restaurant. John's watch is fast by 2 minutes. Mary's watch is slow by 5 minutes. John arrived at the restaurant, looked at his watch and said, " I am 5 minutes early." Mary did the same and said, "Oh no! I am 5 minutes late."

How long does one person have to wait for the other?

We also looked at Mrs Lim's happy problem (PSLE Preliminary Examination Problem from a school).

Mrs Lim usually spent $290 on several bottles of vitamins at Healthway Pharmacy. During a storewide discount of 20%, Mrs Lim found that she could buy 2 additional bottles of vitamins with the same amount of money.

Were you able to make the connection that the 20% discount is the cost of the two additional bottles?

If you are absent or missed the discussion please submit a solution to the problem with one main point that you can discuss based on the solving of the problem.

Reading to be done before November's sessions - Chapter 3 and complete on of the tasks by presenting it in the form of an A4 poster for sharing with colleagues. Submit this when you come back in November.

More photos on my Facebook.

## Thursday, September 26, 2013

### EDU330 Elementary Mathematics Session 4 on 26/09/13

Do you see multiplication in this arrangement of lanterns for the Mid Autumn Festival in Chinatown in Singapore?

Problem 13 is based on a 'mind-reading' read. Choose two digits A and B.

Make a 2-digit number AB and add the numbers A and B to get a sum.

Find the difference between AB and the sum.

If you know A you can figure out what the difference is.

In Problem 14 we explored ways to subtract 3 1/4 - 1/2

In Problem 15, the three little pigs shared 4 pizzas equally.

Problem 16 is to figure out the multiplication facts for 7 by the doubling method, the distributive property and the subtraction method.

Problem 17

Draw a polygon on geoboard paper. How many times is it as large as the square?

Jessica shares her solutions at her blog.

Problem 13 is based on a 'mind-reading' read. Choose two digits A and B.

Make a 2-digit number AB and add the numbers A and B to get a sum.

Find the difference between AB and the sum.

If you know A you can figure out what the difference is.

In Problem 14 we explored ways to subtract 3 1/4 - 1/2

In Problem 15, the three little pigs shared 4 pizzas equally.

Problem 16 is to figure out the multiplication facts for 7 by the doubling method, the distributive property and the subtraction method.

Problem 17

Draw a polygon on geoboard paper. How many times is it as large as the square?

Jessica shares her solutions at her blog.

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