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Dr Yeap talks about one of the fundamental ideas in mathematics: that items can only be counted, added, and subtracted if they have the same nouns. He uses a simple example with concrete objects, chocolates and glue sticks to illustrate the point and then shows how it relates to column addition and the addition of fractions.

Dr. Yeap explains how young children can use concrete materials and later use pictorial representations as number bonds. Number bonds represent how numbers can be split up into their component parts. Children can explore number bonds using a variety of concrete materials, such as counters with containers and ten frames or with symbols.

Dr. Yeap explains how standard column subtraction can be taught meaningfully by using children's knowledge of number bonds. Once children can explain how numbers can be split into their component parts, they can adapt their understanding to the conventional column subtraction method.

Dr. Yeap discusses how children can develop an ability to calculate the four operations (addition, subtraction, multiplication and division) in their heads without the use of paper and pencil or calculators.

Dr. Yeap discusses how children can learn their times tables meaningfully by using visualisation and other strategies.

Dr Yeap discusses how children can learn to do long division meaningfully by first using concrete apparatus, such as base-10 materials, to perform the operations. They can then explore how this idea is represented in the long division algorithm.

Dr. Yeap discusses how diagrams can be used to represent a situation in a problem: such as rectangles representing (unknown) quantities. This method of visualising problems is known as the bar model.

Dr. Yeap gives another example of the bar model: how diagrams can be used to represent situations in a problem.