This post is about Primary 1 Math Heuristics.

By primary 1 (usually around the ages of 6-7 years old), children should be introduced to basic mathematical concepts and problem-solving strategies. Math heuristics provide simple, practical, and flexible strategies that can really help students to approach problem-solving in a structured way. These math heuristic methods are designed to guide students in finding solutions to mathematical problems.

At Seriously Addictive Mathematics – Hougang, we use the **Concrete-Pictorial-Abstract** approach, among other approaches, to help our pre-primary and primary 1 students to understand an abstract subject such as math.

- Concrete stage is the
**“doing”**stage where children use physical objects such as manipulatives. - Pictorial stage is the
**“seeing”**stage where children use drawings or pictures. - Abstract stage is the
**“symbolic”**stage where children use abstract symbols to represent math.

At primary 1, simple math heuristics are introduced to students in Singapore. As the children progress in age, more math heuristics techniques are added each year while prevailing methods that have been introduced are reinforced with questions of increasing variables or what we call sums with ‘increasing difficulties’ to match their primary level.

## Primary 1 Math Heuristics

Here are some common primary 1 math heuristics taught following the Singapore Math Syllabus:

**Use Manipulatives**

Manipulatives are physical objects like blocks, counting beads, or cubes that help children visualize and manipulate numbers. They can aid in understanding addition, subtraction, and basic arithmetic.

Manipulatives can help young students, in both pre-primary and primary 1, grasp abstract concepts better by letting them pick things up, and move them around. As parents, you, too, can successfully use simple math manipulatives to enhance your kids’ math foundation as they go through the ‘concrete’ or ‘doing’ stage and watch them connect and explain the ideas they are learning.

**Draw a Picture**

Drawing a picture is the most common way for children to get to the second stage of learning mathematics after the concrete stage, that is the ‘pictorial’ or ‘seeing’ stage. Very often, young students need to draw a picture just to understand a simple math story sum. The picture can represent the sum in a way a student can “see” it, understand it, and think about it while he looks for the next step.

Encourage your primary 1 child to draw simple illustrations or diagrams that represent the problem. Visualizing the situation can help him better understand the sum and hence solve the problem or sum more easily.

**Act It Out**

Acting out the problem is a strategy in which young students physically act out what is taking place in a story problem. When given a written word problem in math, the student can discuss the important elements of the story or question, including what the sum is asking for and which aspects are relevant or irrelevant.

Children act out the problem using role-playing or manipulatives or simple objects. This also helps them understand the context and apply math to real-life situations so as to reinforce mathematical concepts better. It fortifies their conceptual understanding of the next stage, that is, the ‘symbolic’ or ‘abstract’ stage.

**Look for Patterns**

Finding a pattern is a strategy in which students look for patterns in the facts or details given in order to solve the problem. Students look for items or numbers that are repeated, or a series of events that repeat.

For younger students at pre-primary or primary 1 level, let them discover and continue using patterns that employ geometric shapes. For example, yellow circle, red square, green triangle, yellow circle, red square, green triangle, and so on. Later encourage such students to identify patterns or relationships in numbers and operations, as it can lead to shortcuts in problem-solving as they grow older.

**Draw a Diagram/ Model**

The main purpose of drawing a diagram or a model method is to visualize the problem sum in question. This is vital for understanding the question at hand and how the mathematical concepts learnt can come in to solve it.

Many older kids fail to answer complex math problems due to their lack of capacity to visualise hence making it difficult for them to estimate the scale and its mathematical relationship, thus deciding which math heuristic method to use.

The diagram/model approach can help students especially in early levels to understand mathematical relationships better and hence strengthen their math foundation in preparation for later years. It is one of the most recommended techniques to be taught in Singapore as it is popularly used to solve most of the problem sums in math tests and exams in schools.

**Conclusion**

It’s important to remember that at this early stage, children are still developing their mathematical foundation. So, while using math heuristics, they should also be given opportunities to explore and play with numbers to develop a deeper understanding of mathematical concepts. These heuristics are meant to guide their thinking and problem-solving skills rather than being strict rules to follow. As they progress in their mathematical journey, they will build upon these problem-solving strategies and learn more advanced math techniques.

At S.A.M. Hougang, we are always ready to answer any queries and to help guide your child to the right path of learning and discovering mathematics the fun and meaningful way. We offer a comprehensive Singapore Math curriculum while incorporating the 12 math heuristics and Polya’s four-step problem-solving process over the full eight odd years leading up to PSLE. Our programme starts as early as four years old.

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