B1.1 Represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life.
Activity 1: Representation of Whole Numbers Up To 1 Billion
Write or project a large number on the board (represented in 3 different ways).
Example
- ten million five hundred twenty thousand (words);
- 10 520 000 (standard notation);
- \(1 \times {10^8} + 5 \times {10^6} + 2 \times {10^5}\) (expanded notation using powers of ten);
Ask students about these numbers.
- What do you notice?
- What is the largest number? The smallest?
- What are the similarities and differences between the representations?
- Do you encounter these representations in everyday life? If so, in what context?
Ensure that the student realizes that an equivalent number can be written in different representations and represents the same quantity.
Activity 2: Do Large Numbers Exist in Everyday Life? (Representation and Comparison of Numbers)
Have students conduct an internet search so that students can find examples where large numbers are found in everyday life. The student should list the different contexts and notice which notations are used.
Examples
World economy (monetary unit), population, astronomy (distance, size of planets), computer science (memory), provincial and national budget, medicine, etc.
Point out to students that these numbers are not used on a daily basis; they are mostly used in specific situations and in specialized areas.
Invite students to complete a chart based on their research. Students can write down, for example, 5 populations of countries or distances between planets in order to compare and represent them in different ways.
*The first row of this table is an example of each of the representations sought.
| Numbers Expressed in Words | Numbers Expressed in Digits | Numbers Expressed in Expanded Form Using Powers of Ten |
|---|---|---|
| Nine hundred fifty million | 950 000 000 | \(9\; \times \;{10^8}\; + \;5\; \times \;{10^7}\) |
Once the chart is completed, ask students to compare the numbers. Ask them about the different representations.
- Which representation makes it easier to compare numbers? Explain.
Activity 3: Compare Numbers Using Patterns
Choose the smallest number from the table above.
- Why did you choose this number? How do you know it's the smallest number?
Example
12 350
The teacher asks the student about this number.
- What does the number 2 represent in this number? The number 5?
- Can you write a number that is 10 times greater than this number? 100 times? 1 000 times? … 1 000 000 times larger? How do you do it? What do you notice as the number grows?
End with an analysis of the numbers found, trying to highlight certain patterns.