Math is everywhere

Ways to represent a number

We can find math in words, patterns, pictures and numbers. Just like math can be represented in many ways, a single number can be represented in many ways.

Think of a number from 23 to 100. How many ways can we represent that number?

Record all of the ways that you can show the number 23.

Access the following strategies to help you think about different ways to represent a number. How many did your group use?

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Place value chart

In this learning activity, we are going to learn different strategies to represent whole numbers.

Place value is the value of each digit in a number based on its place in the number. 

For example, we can use the following place value chart to represent the number 1,247. Each digit of the number 1,247 is recorded in the column that represents its place value.

Let’s practice

Now it’s your turn! Access the following fillable and printable Place Value Chart and record the numbers 259, 47, and 1,034 in the chart. You can also complete the activity in your notebook.

Base ten form

We can represent the place value of different numbers using base ten blocks as follows:

• single units = ONES
• rods (made up of ten single units) = TENS
• flats (made up of ten rods) = HUNDREDS
• cube (made up of ten flats) = THOUSANDS

In the following example, the number 1,247 is represented using base ten blocks.

Identify the number

Complete Identify the Number in your notebook or use the following fillable and printable document to write the number represented by each set of base ten blocks.

Standard form

When we use standard form to represent a number, we simply write the number.

In standard form the same number from the base ten form above is written as: 1247.

Word form

When we use word form to represent a number, we write out the number in words.

In word form, the same number is written as: one thousand two hundred forty-seven.

Practice writing the following numbers using word form:

1. 133
2. 1,005
3. 729

Expanded form

When we represent a number in expanded form, we write the number to show the place value of each digit in the number.

In expanded form, the same number is shown as 1,247 = 1,000 + 200 + 40 + 7.

Composing and decomposing numbers using place value

When we combine two or more numbers to make a greater number, we are composing the number.

Example: 1,000 + 200 + 40 + 7 = 1,247

When we break apart a number into two or more smaller numbers, we are decomposing the number.

Example: 1,247 = 1,000 + 200 + 40 + 7

Compose and decompose using place value

Compose and decompose the following numbers in your notebook:

1. 354
2. 162
3. 971

What strategies did you use to help you?

Math is everywhere

We’ve learned that numbers are represented in different ways all the time. We also talked about the types of math we can find in our classroom.

Counting money

There is an envelop that contains $100. Explore the following carousel of images and determine which example contains $100. Record your thinking in a method of your choice.

Press ‘Hint’ to access the correct answer.

Hint

Celebrate a number!

Celebrate a number of your choice by creating a poster to show the different ways in which it is represented. Which representation of your number is the easiest to understand?

Include:

• place value chart
• using base ten blocks
• standard form
• word form
• expanded form
• where it is represented in everyday life
• why your number is important in everyday life
• if your number is used or seen every day

Your poster should have:

• a title with your number included
• pictures and diagrams
• words
• numbers
• colour to add interest

Refer to the following example when making your poster.

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.