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Use with Ready Instruction Lesson 15 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. ©Curriculum Associates, LLC Copying is not permitted. 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 3 335 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.