Exponents
Write 10x10x10 in exponential form
103
53
or
5x5x5
Which is written in exponential form?
53
In what shape is an area model made in?
Rectangle
When do you regroup when multiplying using partial products.
a) As you go, when you multiply.
b) At the end only, when you add.
b) At the end only, when you add
Which is the easiest way to multiply in your opinion? Which do you like to use? EXPLAIN
Answers may vary.
Solve: 103
1000
Which number represents the exponent in exponential form?
12,3457
7
Use an area model to solve:
25 x 36
900
54 x 87
4698
What are two ways to estimate a product?
How do you use estimations to decide if your answer is reasonable when multiplying?
Round to a place value OR round using compatible numbers.
First round to compatible numbers or round based on place value, then multiply the rounded numbers together to get an estimate. Then, if your estimate is close to the exact answer you got, then you can say it is reasonable.
Solve:
53
125
Which number represents the base in exponential form?
12,3457
12,345
Factor
Place Value
How are area models and partial products related to each other?
Each of them require you to multiply each digit by the others and use place value to write down its value. Then find the sum of all of these partial products to find the product of the multiplication problem.
When multiplying using the standard algorithm, explain why you need to add a 0 before you start multiplying in the second line
34
21
---
34
0 <---------- This zero... why do you need it?
Because when you multiply in the second line, you are multiplying by a digit in the tens place, which means it is that digit times 10. So adding a zero at the end is done because you are multiplying by 10.
Solve:
28
256
What exponential form completes the equation:
74 x _____________ = 7,400,000 ?
105
Estimate the product, then use an area model to multiply:
158 x 42 =
6,636
Estimate the product, then use partial products to multiply. Show all of your work:
918 x 23 =
21,114
First make an estimate, then find the exact answer, and finally explain if you think your answer is reasonable or not...
708 x 6
4248
What is the equivalent of 3.5 x 104
34,000
How is a square with a side length of 5 related (similar/connected) to the number 52 written in exponential form?
To find the area of a square with side length of 5, you must multiply the length and width together; this is 5x5. Since 5x5 is repeated addition, we can write it in exponential form as 52
Why do we call this strategy of multiplication an area model?
Because it is solved by using the two factors as of a multiplication problem as side lengths of a rectangle. Then partitioning the sides lengths in to smaller, easier to multiply with parts (based on place value).
Why is this strategy called partial products?
The root word of partial is "part". Each factor must be decomposed into parts based on the place value. Then use each of those parts to find products which can be added together to find the answer.
First make an estimate, then find the exact answer, and finally explain if you think your answer is reasonable or not...
708 x 26
18,408