The Comparison Concept

The Comparison Concept is one of the three main concepts in the Model Method which all math models are derived from, the other two being the

Part-Whole Concept and the Change Concept . The Singapore Math Primary Curriculum adopts a concrete-pictorial-abstract progressive approach to help pupils tackle seemingly difficult and challenging word problems. Mathematics Teachers in Singapore usually make use of concrete objects to allow students to make sense of the comparison concept by comparing two or more quantities. Once the pupils can visualize how much one quantity is greater than or smaller than another quantity, they will then move on to put these relationships in rectangular bars as pictorial representations of the math models concerned.

To illustrate the comparison concept, take a look at the following problem:

Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?




We can first give the child concrete objects, like 5 pencils and 3 erasers, and let the child put the two groups of objects side-by-side to match the 2 types of items, i.e., 1 pencils match with 1 eraser. Then, he will be able to see that there are 2 more pencils which cannot be matched with any erasers because he has run out of erasers to do that.

When they are comfortable with comparing concrete objects, we can then proceed to teach them to draw pictures of the concrete objects within boxes to illustrate the equation 5 - 3 = 2

comparison-concept-001



After that, we can teach the kids to go on to draw the boxes without the objects.

comparison-concept-002



Eventually, the equation can be visualised as a comparison between the 2 quantities given in the question and the pupils can easily see that to find the difference, they just need to subtract the smaller quantity from the larger quantity.

comparison-concept-003



So, 5 - 3 = 2

Therefore, Peter has 2 more pencils than erasers.

Hence, we can see that the relationship among the larger quantity, the smaller quantity and the difference can be summarised as follows:

comparison-concept-004




To find the difference given two unequal quantities, just subtract the smaller quantity from the larger quantity:

Larger Quantity - Smaller Quantity = Difference


To find the larger quantity given the difference and the smaller quantity, just add the smaller quantity to the difference:

Smaller Quantity + Difference = Larger Quantity


To find the smaller quantity given the difference and the larger quantity, just subtract the Difference from the larger quantity:

Larger Quantity - Difference = Smaller Quantity




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