# Tze-Ping Low

## Understanding Fractions as Equal Parts

Fractions is often formally introduced in 3rd Grade. When this topic is introduced, it usually starts with naming fractions or fraction of a set. Students often skipped over the very fundamental concept of fraction – EQUAL PARTS. Without a strong visual understanding of equal parts, fraction often gets reduced to number operations. In this blog post, we describe the progression that teachers and parents can take to lay the foundation for fractions, i.e. understanding fractions as equal parts through visual representations using geometric shapes.

## Why are we learning Greatest Common Factor (GCF)?

It is important for educators to recognize that teaching the various procedures for finding GCF and LCM is not a standalone topic, but rather a foundation skill required for more advanced applications a few years down the road. More importantly, for higher grade teachers, when dealing with students with anxiety over algebraic manipulations and fractions operations, to identify if procedural fluency of finding GCF and LCM might be the root cause.

## Finding Greatest Common Factor by Prime Factorization

We received a question regarding the 2nd method of finding Greatest Common Factor by Prime Factorization in the Math In Focus Grade 4 materials. This example is from Math In Focus workbook 4A page 23, The “Method 2” mentioned above uses prime factorization as a procedure to find the GCF between two numbers. Procedure In each …

## Math Strategies for Teaching Addition and Subtraction – Part 4: Numbers to 1000

Once students learn the foundation for adding and subtracting up to 100, extending to 1000 and beyond is more straightforward than the previous two progressions, i.e. from numbers within 10 to numbers within 20, and to numbers within 100. However, there are still a few new pitfalls and common challenges when first trying to teach addition and subtraction beyond the hundreds. Here we discuss some of our observations and suggestions about how to overcome the challenges faced by teachers and students.

## Singapore Strategies for Teaching Addition and Subtraction – Part 3: Numbers to 100

Learning about addition and subtraction for numbers to 100 is the next phase after numbers to 20. In this series, we’ll talk about the teaching approaches we recommend for numbers from 20 to 100 and the common problems faced by students.

## Singapore Strategies for Teaching Addition and Subtraction – Part 2: Numbers to 20

Addition and Subtraction to 20 is an unique milestone because it is the first time kids are exposed to concepts like place value and regroup. Many rely on counting for addition and subtraction within 20; while this is perfectly fine for young learners, they should also be exposed to concepts like making ten, decomposing ten and derived facts. This would go a long way in building a strong foundation in number sense.

## Singapore Strategies for Teaching Addition and Subtraction – Part 1: Numbers to 10

Singapore Math, with it’s strong emphasis on visualization, is especially well-suited to introducing this topic to young learners who have just started their journey in math education. In this discussion, we explore some of the less obvious misconceptions when first introducing addition and subtraction for numbers to 10.

## Subtraction Within 20 – The Cost of Working Memory

Part of our role as educators is to continually reflect on the teaching methods and evolve them as we adjust to students’ learning. One such adjustment came about from teaching our first graders addition and subtraction for numbers within 20. Specifically, the problem of subtraction with regrouping was a major hurdle the kids had to get through. Let us look at some examples from the textbooks and workbooks, and why we decide to tweak the method for our classes.

## About the counting problem last Christmas

Last Christmas, we gave out a free worksheet based on the familiar carol “The Twelve Days of Christmas”, where students are asked to count the number of gifts they will receive on each day and cumulatively the total number of gifts received up to the n-th day. While working through the exercises, we (and our …

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