Teacher Hui Lin has been an educational therapist for over 10 years. She shares 3 of her favourite learning resources for learning and practising math concepts. These 3 tools provide students with a concrete and visual approach to learning, especially in kindergarten and lower primary levels. She will discuss various ways these tools can be used to teach and build a strong foundation.

## Linking/Snap Cubes

Linking Cubes, or Snap Cubes, are useful manipulatives that help students visualise basic math functions such as addition, subtraction, and multiplication, show number bonds, and build number sense and fluency.

**A. Number Bonds**

A number bond visually represents the relationship between addition and subtraction.

In preschool and lower primary levels, number bonds help children visually see that a larger number is made up of other smaller numbers.

Number bonds also drill basic addition functions into a child so that they become familiar with the different variations that make up a number and develop an ability to do mental sums more quickly. For example, 7: 1 + 6, 2 + 5 and 3 + 4.

When first teaching number bonds, I like to use snap cubes. The coloured cubes help children see the 2 parts that make the whole more clearly.

Using two different coloured cubes shows how different combinations of numbers create the same total.

At higher levels, this skill of seeing a whole as made up of smaller parts can later be applied to algebraic thinking where 1 or more parts are unknown.

**B. Addition and Subtraction**

As you put together or take away cubes, introduce mathematical vocabulary such as add, subtract, take away, give, and equals (is the same as).

**C. Multiplication and Division**

When teaching multiplication, form equal groups of cubes and count on them to build familiarity with timetables.

For an additional challenge, show how 4 x 4 is the same as 2 x 8.

**D. Focus on Ten**

In the base 10 number system, each place value corresponds to a power of 10. Form groups of ten cubes and show how 10 tens make a hundred.

Additionally, build on number bond 10 fact fluency by printing out a ten frame and thinking of different number combinations that make ten.

Recall of number bond 10 facts helps with addition and subtraction regrouping.

**E. Part-Whole Model **

When we are solving for the part, we subtract from the whole, as the part is the smaller value. When we want to solve for the whole, we add the parts.

**F. Comparison model**

When comparing two stacks of cubes, you can talk about:

1) Which stack has more cubes and fewer cubes

2) Which parts are the same

3) Which part is the difference

After that, use the maths vocabulary ‘more than’ and ‘less than’ to describe the difference.

For example, A has 5 cubes more than B. B has 5 cubes less than A.

## Fraction Pies

Fraction pies help children develop an initial understanding of fractions. They also present some basic abstract facts in a concrete and visual manner.

**A. Making 1 Whole**

Make abstract fraction representations more concrete by using fraction pies. For example, show how 2/2, 3/3, and 10/10 are the same and equal to one whole.

For example, students might mistakenly think that a fraction with a larger denominator is always larger. Using fraction pies to show that a bigger number in the denominator does not always mean a larger value can help dispel this misconception.

**B. Equivalent and Simplifying Fractions **

Fraction pies can also help build an accurate understanding of abstract computations.

When computing fractions, we can find an equivalent fraction by multiplying the numerator and denominator. This process of breaking down the original fraction into smaller parts allows us to **maintain its value while altering its appearance**. This allows us to work with fractions more easily without changing their properties.

Fraction pies are a great way to show that when we multiply to obtain an equivalent fraction, we do not get a larger value; rather, we split the original fraction and still have the same value.

**C. Addition and Subtraction**

When adding and subtracting, we need to convert to the same denominator to find the answer.

Is 2/9 or 3/6 the right answer?

## Online Math games

Math games are a fun way to provide additional practice. Websites such as __mathplayground.com__ offer games to practise the 4 operations. Guided practice on models is also available as ‘Thinking Blocks'.

Some students like speed/timed games, while others prefer to go at their own pace, depending on their level of mastery and confidence. On __wordwall.net__, use the search function to find practices for specific math goals, such as measurement conversion, identifying angles, or fraction-decimal-percentage conversion. Then, switch templates or select from the various game options to match the child’s learning style and interests.

## Summary

These physical manipulatives and online resources are just some ways you can make learning fun and engaging for students. However, if you sense that your child has challenges that are not being addressed, we recommend you consider seeking advice from an Educational Therapist to have an assessment done. This is to understand your child’s strengths and weaknesses better and have an individualised plan to target underlying difficulties.

The math sessions at The SKILT Centre focus on bridging gaps in conceptual understanding, procedural computation, problem-solving skills, and heuristics.

**Written by:** __Ms Khoo Hui Lin, Educational Therapist__

**Vetted by:** Dr Lian Wee Bin, Developmental Paediatrician & Neonatologist

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