Download Lesson 15 - Numerical Expressions with

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Dear Family,
Your child is learning about numerical
expressions with exponents.
A numerical expression shows a mathematical relationship using
numbers and symbols, but it does not have an equal sign. You can
evaluate any numerical expression to find its value. Here are some
examples of numerical expressions:
1,0953.6 1 8
0.75 3 24
6 2 ​  7 ​ 4 ​ 5 ​ 8
··
6
··
9(5 1 2) 2 6  8
The expression 6 2 is an exponential expression because it contains an
exponent. You can read 6 2 as “six squared” or “6 to the second power.”
6 is the base. 6 2 2 is the exponent.
To find the value of an exponential expression, multiply the base by
itself the number of times indicated by the exponent. For example, to
find the value of 6 2, multiply 6 by itself two times: 6 3 6. The value of
6 2 is 36.
Consider this situation:
Art students created a mural
using tiles. They placed 3 tiles
during the first class as they
established their design. During
each of the next 4 classes, the
students tripled the number of
tiles placed in the previous class.
How many tiles did the students
place during the fifth class?
On the next page you will see two ways your child may write and
evaluate a numerical expressions to find the number of tiles placed in
the fifth class.
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Lesson 15 Numerical Expressions with Exponents
159
Numerical Expressions with Exponents:
Sample Solution
Students placed 3 tiles in a mural during one class. For each of the
next 4 classes, the students tripled the number of tiles they had
placed in the previous class. How many tiles did the students
place during the fifth class?
One way: Use multiplication to represent the problem.
Find the number of tiles that the students placed during each class.
Because the students tripled the number of tiles placed in the previous
class each time, multiply the number of tiles in each previous class by 3.
First Class
Second Class
Third Class
Fourth Class
Fifth Class
3
335 9
9  3 5 27
27  3 5 81
81  3 5 243
The number of tiles placed during the fifth class is 243.
Another way: Represent the problem with repeated multiplication.
The expression in each row of the table shows the expression from the
previous row multiplied by 3.
Class
Number of Tiles Placed
First
3 5 31
Second
3  3 5 32
Third
3 ∙ 3 ∙ 3 5 33
Fourth
3  3  3  3 5 34
Fifth
3  3  3  3  3 5 35
The expression in the last row of the table shows that the number of
tiles placed during the fifth class is 3  3  3  3  3, which can be
written as the exponential expression 35. Evaluate the expression.
35 has a value of 243.
Answer: The methods show that the numerical expressions 81  3,
3  3  3  3  3, and 35 all represent the number of tiles the students
placed during the fifth class. The expressions all have a value of 243,
so the students placed 243 mosaic tiles during the fifth class.
160
Lesson 15 Numerical Expressions with Exponents
©Curriculum Associates, LLC Copying is not permitted.