B2.7 Evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts.
Activity 1: Measurements (Conversion of Units of Measurement Using Exponential Notation)
Prepare problems involving the conversion of units of measurement (links to E 2.2). Ask students to write measurements in standard notation and in exponential notation. Transcribe to a table (see below) to support the student see and understand some of the patterns.
Examples of problems
- A flag for an amateur show is made by the students in the sewing class. It is 10 m long. What is the length of the flag in centimetres? Express your final answer in exponential notation.
- A company builds a warehouse with a capacity of 100 m3. What is the capacity of the warehouse, in cubic centimetres, expressed in exponential notation?
- How many metres are there in 5 km? Express your answer in exponential notation.
Structure of solutions:
| Number With Initial Measurement | Number With Desired Unit (Current Notation) | Number With Desired Unit (Exponential Notation) |
|---|---|---|
| 10 m | \(10\; \times \;(100\;{\rm{cm}})\) | \(10\; \times \;10\; \times \;10\; = \;{10^3}\;{\rm{cm}}\) |
| 100 m3 | \(100\; \times \;(100\;{\rm{cm}}\; \times \;{\rm{100}}\;{\rm{cm}}\; \times \;{\rm{100}}\;{\rm{cm}})\;{\rm{ = }}\;{\rm{100}}\; \times \;({\rm{1}}\;{ \rm{000}}\;{\rm{000}}\;{\rm{cm}}^{\rm{3}})\;{\rm{ = } }\;{\rm{100}}\;{\rm{000}}\;{\rm{000}}\;{\rm{cm}}^{\rm{ 3}}\) | \({10^2}\; \times \;{10^2}\;{\rm{cm}}\; \times \;{10^2}{\rm{ cm}}\; \times \;{\rm{10}}^{\rm{2}}\;{\rm{cm}}\;{\rm{ = }}\;{10^8}\;{\rm{cm}}^3\) |
| 100 km | \(100\; \times \;1\;000\;{\rm{m}}\;{\rm{ = }}\;{\rm{100}}\;{\rm{000}}\;{\rm{m}}\) | \({10^2}\; \times \;{10^3}\;{\rm{m}}\; = \;{10^5}\;{\rm{m}}\) |
Activity 2: Which of the Amounts of Money Do You Choose? (Meaning of Operations, Exponential Notation)
Project this statement on the board.
Statement
A person comes to visit you and tells you that they have an amount of money to give you. They give you two options.
Option A: I'll give you $2 the 1st day, $4 the 2nd day, $8 the 3rd day, and so on, until the 30th day.
Option B: I'll give you $1750 on day 1 , $1750 on day 2 , $1750 on day 3, and so on, until day 30 .
Which of the options do you choose?
Give students a maximum of one minute to make a choice: Option A or B. (No calculator allowed) Have students write their choices on a piece of paper and collect them. Write on the board the number of students who chose Option A and the number of students who chose Option B.
Afterwards, divide the students into teams of two. Each team analyzes the two options in more depth with the help of their tools (pencil, calculator, computer). After about 10 minutes, ask each student again (paper and tally) which option they prefer. Compare with the initial choices.
Debrief and discuss students' strategies/justification.
Extensions:
Problem
A colony of bacteria doubles every 10 minutes. If it contains 20 bacteria at the beginning, how many will it contain after one hour?
Problem
More than half of Ontario's electricity comes from nuclear power. The energy comes from an atom releasing 3 particles, called " n ", on a collision. If left unchecked, these particles will cause the release of 3 more " n " particles on each collision, which will cause the release of 3 more particles each.
Express in exponential notation, how many particles " n " will be released after 6 collisions.
Estimate how many " n " particles there will be in total.