You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has led the world in math mastery for over a decade; its students become competent and proficient mathematicians at very early ages. Even better, they grow to be capable problem solvers who think mathematically with ease. Wouldn’t it be nice if your child could enjoy the same success with math? Well, there’s good news: We’re teaching Singapore Math to your child. So let’s discover what it’s all about and how you can help your child succeed. It all begins with understanding the curriculum and seeing some examples.
First, you need to know that Singapore Math takes a slightly different mathematical approach than what you may be used to. It revolves around several key number‐ sense strategies:
- building number sense through part‐whole thinking,
- understanding place value, and
- breaking numbers into decomposed parts or friendlier numbers, ones that are easier to work with in the four operations (addition, subtraction, multiplication and division).
Second, Singapore Math does something dramatically different when it comes to word problems. It relies on model drawing, which uses units to visually represent a word problem. Students learn to visualize what a word problem is saying so they can understand the meaning and thus how to solve the problem.
Third, we have mental math, which teaches students to calculate in their heads without using paper and pencil. Sure, your child will still need to commit some facts to memory, but mental math will teach him or her to do calculations using proven strategies that don’t require pencil and paper.
Fourth, the strategies taught in Singapore are layered upon one another. One strategy is the foundation for another one. You’ll notice this as you read through this letter. For example, students need prior knowledge of bonding in order to be successful at strategies they will learn later on (like vertical addition).
Last, Singapore Math teaches students to understand math in stages, beginning with concrete (using manipulatives such as counters, number disks, dice, and so on), then moving to pictorial (solving problems where pictures are involved), and finally working in the abstract (where numbers represent symbolic values). Through the process, students learn numerous strategies to work with numbers and build conceptual understanding. With time and practice, they eventually master the traditional methods and algorithms. Let’s take a closer look at all the layers of Singapore Math.
Singapore Math is a base‐10 system. A number’s place value is determined from right to left, starting with the ones and moving through the tens, hundreds, thousands, ten thousands, one hundred thousands, to a million and beyond. In fourth grade, we add the study of decimals into the mix. In class, we use tools such as place value boards with disks and cards to help us organize, visualize, and understand what these numbers actually mean and how they relate to one another. As we perform mathematical operations, we can move place value disks from column to column on the place value board to demonstrate regrouping (making a en out of 10 ones).
An algorithm is a systematic, step‐by step procedure to solve a problem using a mathematical operation. For example, with subtraction, we have learned to line our numbers up vertically so that the digits are in the correct place value columns. We’ve learned to subtract the digits moving from right to left, using regrouping or borrowing, in order to get the correct answer to the problem. In Singapore, traditional algorithms are taught and mastered with the help of the place value mat. However, we also teach alternative algorithms or strategies to solving equations often before we teach the traditional ones. This helps us build and reinforce our understanding of number sense and place value. This also allows students to use a strategy that they are competent at using for any problem. Rather than having one strategy, they may have several to choose from, and they can use the one that’s most intuitive for them.
Number Bonds: Part Whole Thinking
The beginning of number sense is viewing each digit as a part of a whole. This is very similar to fact families, where a number has specific “relatives” in its family. Let’s take the number 6 as an example. 6 is 6 and 0, 5 and 1, 4 and 2, and last, 3 and 3. This understanding becomes very important when students start doing operations with the number 6. After students learn digits 1–9, they master what combinations make 10. 10 is an anchor number in Singapore. So, in K and grade 1, students will spend a significant amount of time learning their bonds through 10. Number bonds can also be created with multiplication and division fact families, using two factors and a product. For example, 16 is 16 and 1, 2 and 8, and 4 and 4. Once students know the parts that make up each number, they can add any numbers together by making 10s. For example, when students add 7 + 5, they find how many 10s they can make, and label the leftover parts as 1s. In this example, there is one 10 nd two 1s remaining, so the answer is 12. Instead of memorizing just the fact, the tudent has a strategy to work with addition.
Decomposing and Branching
Students spend time learning how to break numbers into place value groupings on the place value board. This is called decomposing numbers or using expanded notation. After students practice breaking numbers apart into place value groupings, we teach them to add and subtract by place value. This is branching. The goal with branching is for students to break numbers into place value groupings and then do the operation with those place value groups. or example, 23 + 42 would be branched into tens and ones. Then students will add and then add the groupings together. F each place value grouping separately, Take a look at how branching works.