## Why is it Important to Draw Bar Models Correctly

In the previous post, we talked about two common mistakes in drawing bar models – not aligning the starting points of the bars being compared and having disjoint bars for parts. Here we want to illustrate why it is important for us to draw bar models correctly from the beginning when we first use them …

## Common Mistakes in Bar Models

Bar Modeling is a very powerful heuristic in Singapore math. Representing unknown quantities and the relationships between them using rectangular “bars” gives an intuitive and visual representation of the problem. More importantly, when used correctly, representing problem using bar models makes students approach the solution in a systematic and algebraic manner. This empowers even young …

## What is Singapore math?

One of the questions we get most often is “What is Singapore math?” and the follow-up question “How is it different from [curriculum]?”. Here is our own definition, interpreted from the point of view of two Singaporeans who grew up in Singapore, went through the public education system learning math using the same concrete-pictorial-abstract techniques, …

## Bar Model example – Before After

Here is a bar model example for “before and after” type of word problems. Tom had \$190 and Jane had \$60.  After each of them received an equal amount of money from their father, Tom had twice as much money as Jane. How much did their father give each of them?   See more 3rd …

## Multiplication and Division – Mastery

This is the final post in our series of blog posts on teaching Multiplication and Division from 2nd through 5th grade. In this post, we discuss the final ingredients needed to master multiplication and division. In fifth grade, we extend our understanding of whole number multiplication and division to general numbers (up to 4-digits), and …

## Multiplication and Division for Higher Order Numbers

In fourth grade, we extend our understanding of multiplication and division concepts to higher order whole numbers. Specifically, multiplication and division for higher order numbers can be divided into: Multiply up to 4 digits by 1 digit, e.g. 7,032×8 Multiply up to 3 digits by 2 digits, e.g. 603×26 Divide up to 4-digits by 1 …

## Using Bar Models for Multiplication and Division

Do you know we can use bar models for multiplication and division problems? In this blog post, we illustrate some of the common types of word problems involving Multiplication and Division and how to solve them using this powerful heuristic. Using Bar Models for Multiplication and Division in One-Step Multiplication Word Problems Example (from Math in …

## Division – Remainder and Regrouping

After we learn about Multiplication of 1-digit numbers with 3-digit numbers, we’ll next go deeper into division. The concept of remainder is specific to division and may be challenging for some students. Hence, before jumping straight into division with remainder, it is better to first understand the concepts of quotient and remainder, and treat cases …

## Multiplying 1-digit numbers with 3-digit numbers

Having learned the basic multiplication tables (please see previous blog posts – 1,2,3) for single digit numbers, i.e. 2 to 9, it is now time to generalize multiplication to multi-digit numbers, starting with multiplying 1-digit numbers with 3-digit numbers. Before jumping into the standard algorithm, it is better to lay some important foundation. Here, a strong …

## Multiplication Tables of 6, 7, 8 and 9

Multiplication tables of 2, 5 and 10 and 3 and 4, are introduced at the 2nd grade level. In third grade, we add the multiplication tables of 6, 7, 8 and 9 to our multiplication tool-belt. There is a reason for this spiral approach to span two grades. Multiplication tables for 6,7,8 and 9 are …

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