Minds On
Repeated multiplication
Complete the following multiplication:
2 × 2 × 2 = (Blank)
10 × 10 × 10 × 10 = (Blank)
Is there a more efficient way to express these multiplication statements?
Multiply 8 × 7. Is the answer the same as the sum of 8 + 8 + 8 + 8 + 8 + 8 + 8?
Do you think there is a more efficient way to write 6 × 6 × 6 × 6 × 6 × 6 × 6? What might that be? How could you express that?
Record your ideas in notebook file or share your thinking with a partner.
Action
Multiplying the same factor
Suppose you want to multiply by the same factor more than once. You can use exponents to show what you mean.
Part A: Fundraiser winnings!
Kirra and their family attended the Canadian Roots fundraiser gala last weekend. They entered their names into a lottery draw and won a cash prize. The prize gives them two options. They can only pick one option.
Option A: Collect the $500 dollars today as a prize amount. (June 10th)
Option B: Collect an amount of money that starts at $2 today (June 10th) then doubles each day until June 21st. On June 21st you collect the prize amount.
Help Kirra and their family decide which is the better prize.
Use the Fundraiser Prize Chart in your notebook or use the following fillable and printable document to help you choose the best option.
Press the ‘Activity’ button to access Fundraiser Prize Chart.
|
June 10th $2 |
June 11th $4 |
June 12th $8 |
|---|---|---|
|
June 13th (Blank) |
June 14th (Blank) |
June 15th (Blank) |
|
June 16th (Blank) |
June 17th (Blank) |
June 18th (Blank) |
|
June 19th (Blank) |
June 20th (Blank) |
June 21st (Blank) |
Which prize should Kirra’s family choose?
Why do you think this is the best option?
What mathematical strategies did you apply to figure out the solutions?
How can we express the totals using an expression with an exponent?
Part B: Organizing the fundraiser gala
The organizers of the fundraiser received shipments of the items to set up the gala.
- Forks were placed at the table settings. They received 8 boxes of forks. In each box there were 8 smaller boxes with 8 forks in each.
- Napkins were needed at individual seat settings as well as at the dessert and drink station. Each package of napkins has 12 napkins. There are 12 packages in each box. A shipment of 12 boxes arrived with the order.
- Cups are needed at the drink station. 6 crates arrive. Each crate contains 6 boxes. Each box has 6 groups of 6 cups.
Choose either forks, napkins, or cups and determine how many items were received in all. Can you create an efficient math statement to represent that number of items?
Show your work and steps in a clear and organized manner.
In exponential form, the base is the repeated factor.
The exponent is the number of times the factor is repeated.
A power of a number tells how many times that number is used as a factor.
Example 1:
The above Power is read as:
“five to the third power” or “five to the power of 3” or “five exponent three” or “five cubed”
The following table shows how to write and read positive exponents:
| Repeated factors | Write | Read | Standard form |
|---|---|---|---|
| 2 × 2 | 2² | Two to the second power or two squared | 4 |
| 2 × 2 × 2 | 2³ | Two to the third power or two cubed | 8 |
| 2 × 2 × 2 × 2 | 24 | Two to the fourth power | 16 |
| 2 × 2 × 3 × 3 × 3 | 2² × 3³ | Two squared times three cubed | 108 |
Inquiry question: Can a number have an exponent zero? What will be the answer?
Consolidation
Exponent problem solving
By using exponents to solve our gala questions, we showed that repeated factors create an efficient way to represent that number of items received. Choose one of the following tasks to complete. Be sure to show your work and be able to explain your thinking and how you arrived at your solution.
Task #1
Go back to the Fundraiser in the Action section. Find the totals for the other two items. Can you figure out how many guests were at the gala? Come up with another item you think was needed at the gala and express the quantity as a power.
Task #2
Create your own task involving powers and exponents that is very similar to the ones completed in the Action section of the Learning Activity but takes place in a different setting.
You can exchange tasks with a partner and solve each other’s exponent problems, if possible, or record your solution using a method of choice.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
Press ‘Discover More’ to extend your skills.
Discover More- Can you express the number 64 using three different powers?
- You know that 2 × 5 = 5 × 2. Is it true that 25 = 52? Explain. If it is not true, which is greater, 25 or 52?
- Can a number have an exponent zero? What will be the answer?
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
TVO Mathify (Opens in new window)