ARC (Singapore) Teaching Numeracy Skills

ARC (Singapore) from Jimmy Keng

Weston Public Schools 23 August 2013 CPA Approach

Weston 2013 K-1 Sdr yeapession from Jimmy Keng

Weston Public Schools 22-23 August 2013 MAP111 Bar Models in Primary Mathematics

The course for teachers of Grades 2 to 6 classes (23 August)

Weston 2013 Bar Models 2-5 from Jimmy Keng

The course for teachers of Grades 7 and 8 classes (22 August).

Weston 2013 Bar Models Upper Grades from Jimmy Keng

Weston Public Schools 22 August 2013 MAP101 Fundamentals of Singapore Math

This was covered in 2012 sessions.

Weston Public Schools 2012 from Jimmy Keng

The sessions is 2013 is an mix of review and extension.

Session 1
Fundamentals of Singapore Math for Grade 3, 4, 7 and 8

Photographs of the session are available here.

Wheelock College EDU330 Elementary Mathematics at SEED Institute

The 8th BSc cohortor completed their module on elementary mathematics today. I t is good to see that a degree in early childhood requires students to know something about primary level mathematics. I have been teaching this course for several years now.

One of the tasks the students did in class was to write story problem for 3/4 divided 1/8.

Some do not show the required division 

There are 3/4 of a pizza left at a party. 

Sam cut 1/8 of the the remaining pizza into equal parts.

Advil calculated the division correctly (8) but wrote 

Peter has 8 pizzas.

He ate 3/4 of it (them).

How many slices did he eat?

This could have been correct if it was

Peter cut a pizza into 8 equal slices.

He ate 3/4 of it.

How many slices did he eat?

Adil's story is answered by doing 3/4  x 8.

Masterclass for New Syllabus Primary Mathematics in Manila

In this invite-only class to train a core group of Filipino educators to provide professional development for teachers using a Singapore mathematics textbook series aligned with the Philippines new K-12 Initiative, the focus is on helping teachers understand the Problem-Solving Approach, the CPA Approach as well as the three-part lesson format with some references to Differentiated Instruction, Assessment and Model Method.

Photographs of the sessions are available here.

Technology tools used during the sessions include NLVM and Ultimath.
The apps used on the iPad include Bamboo Paper, Geo Board and Thinking Blocks, all available from Apple Store (free apps).

Professional Development at Island School

The course is on Problem-Solving Approach and CPA Approach.

Photographs are available here.

We discussed anchor task:
(1) extended time over one problem
(2) use of concrete materials
(3) collaborative format

Anchor Task : Think about ways to do 32 - 19

NSMSI Open Grade 5 Lesson in Westminster Colorado

Today I taught two open lessons to one group of 'volunteer' students (they gave up a day of their summer because their parents made them come; thanks, guys), Many did not know each other before today. This is the best option we have given that the conference was held during the summer break and yet we want to provide teachers with some opportunities to observe learning in action.

Lesson 1 was a problem-solving lesson on algebraic thinking designed to show teachers the implementation of anchor tasks. The anchor task for this lesson is taken from Primary Mathematics Grade 6 textbook for algebra but for the fifth graders, we did not move to formally writing expressions. The problem is to arrange five consecutive whole numbers in the arrangement seen in the photos such that the vertical sum and horizontal sum are equal. Students articulate the general pattern they saw using words. They saw several patterns. With little guidance, one student saw that "in a population, if there are more even numbers then the numbers in the middle are even". With some help a girl saw that one of the totals can be obtained by "times-ing 3".

Anchor Task

Guided Practice

Lesson 2 is the first lesson on finding 1/2 of 3/4. Students used paper folding to discuss the anchor task. Two main ideas emerged - halving the entire 3 fourths and halving each of the fourths.The focus today is to review a fraction of a whole number and using it to do say 1/2 of 6 eighths as 1/2 of 6 apples.

This open lesson is for teachers to study the three-part lesson format and differentiated instruction.

A student later articulated that what helped were (1) the paper and (2) the 'advice' which is essentially is instruction between desks or differentiated instruction - different kids got different advice based on their current level of understanding.

It was gratifying to see a good student who started off using the procedure to get 3/8 got the conceptual idea during independent practice.

Independent Practice

National Singapore Math Summer Institute at Westminster Colorado Day 3

NSMSI Day 3 Session 1 from Jimmy Keng

Photos are available.