An Introduction to Singapore Maths

During your child’s year in first grade, you will have many opportunities to learn more about the Singapore Math curriculum.  Here is a brief introduction:

• Singapore Maths revolves around several key number sense strategies: (1) building number sense through part‐whole thinking, (2) understanding place value, and (3) breaking numbers into decomposed parts or friendlier numbers, ones that are easier to work with in the four operations of addition, subtraction, multiplication and division.

• Singapore Maths 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.

• Mental math teaches students to calculate in their heads without using paper and pencil. 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.

• Strategies taught in Singapore are layered upon one another. One strategy is the foundation for another one.

• Singapore Math teaches students to understand math in stages, beginning with concrete (using manipulatives such as counters, number disks, cubes, 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.

While we differentiate instruction to meet individual student needs, the chart on the opposite page is a road map to show progression of computational strategies across the grade levels:

Kindergarten	Making bonds to build numbers 1-10. Using the place value mat.
First grade	Making bonds to build numbers 11-20. Branching bigger numbers into smaller ones to make them more manageable. Using place value mats to decompose, add, and subtract numbers. Adding horizontally from left to right (instead of adding vertically).
Second grade	Using place value mats for more complex addition and subtraction. Branching with even larger numbers. Adding vertical addition to the mix. Using model drawing.
Third grade	Using place value mats with multiplication and division problems. Branching with larger numbers. Using model drawing. Using the distributive property to decompose numbers.
Fourth grade	Using the area model for multiplication and using partial quotient division. Using model drawing for increasingly complex problems.
Fifth grade	Using model drawing proficiently.

Examples of First Grade Strategies

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 plus 0, 5 plus 1, 4 plus 2, and 3 plus 3. This understanding becomes very important when students are challenged to use operations with the number 6. After students learn digits 1–9, they master what combinations make 10. 10 is an anchor number in Singapore as we use a Base 10 system. In K and grade 1, students will spend a significant amount of time learning their bonds through 10. 

  

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. For example, 23 + 42 would be branched into tens and ones. Then students will add and then add the groupings together.

23 + 42 =(20 + 3) + ( 40 + 2)

20 + 40 = 60 + 3 + 2 = 5

60 + 5 = 65

The goal for branching is for students to eventually be able to look at the problem and work it out mentally.

Place Value: Singapore Maths 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 class, we use tools such as place value boards with disks and cards to help us organize, visualize, and understand value of numbers and how they relate to one another.

Algorithms 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 have traditionally 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.

Model Drawing: Model Drawing is the key strategy we use to solve word problems.

Read the problem to get a sense of what is asking.

Decide who and what the problem is about.

Draw units for each who and what.

Reread the problem and adjust our units to match the word problem.

Decide what the question is asking of us and place a ? in place.

Work our computation.

Write our answer in a complete sentence

Mental Math: Mental math is one of the cornerstones of Singapore Math as its emphasis is on helping students to calculate mathematically in their heads, thus developing number sense and place value. It encourages flexibility and speed when working with numbers. We practice mental math strategies and do lots of fun activities that support the skill. Please come to class and participate with us one day!