Representing Decimals Through Illustrations

Instructor: Anna Reinking

Anni taught elementary school for eight years and is currently teaching college. She received her Ed.D. in Curriculum and Instruction.

In this lesson we will briefly review decimals and the relationship to place value. We will learn how decimals can be represented in illustrations, specifically using a grid.

Decimals

You are getting ready for a party and have three big pizzas and each one of them is cut into 10 pieces.

Pizza

What's left of your pizza relates to understanding how to illustrate decimals. However, we are going to use a grid rather than a pizza.

A decimal number is based on the idea of 10. When you see a decimal in written form, such as 2.4, you would read it as two and four tenths. That is how many pizzas are left when you come back from the store. You have two whole pizzas, which goes before the decimal point, and only four of the 10 original pieces left in the third pizza, which goes after the decimal point. Therefore, you end up with 2.4 pizzas.

Decimals and Place Value

Place value is the value given to a specific place in a number. For example, in the number 154, the number one is in the hundreds place, the five is in the tens place, and the four is in the ones place.

This is the same with decimals. Before the decimal point the numbers have the same value as any other number; after the decimal the numbers begin to represent a piece or portion of the whole number. Remember, when we start to work with numbers on the right side of the decimal point we start stating the values from the left to the right. That means the number directly to the right of the decimal point is in the tenths place, then the hundredths, then the thousandths, and so forth.

Decimals and Illustrations

Decimals can be written using only numbers, like 2.4, but they can also be represented through illustrations on a grid, helping us visually see the decimal.

grid paper

In the example above, you had pizzas with 10 pieces each. Now, imagine it takes you a total of 10 bites to finish each of the individual pieces of pizza. If that is the case, then the grid would help you in the following way:

Each of your 10 bites would be one unit or square.

Each piece of pizza would be one column because there are 10 single units within a column.

Each whole pizza would be the entire grid because there are 100 single squares or units within the whole grid.

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