Evaluating Expressions with Exponents: IM 6.6.14
[url=https://im.kendallhunt.com/MS/teachers/1/6/14/preparation.html]“Evaluating Expressions with Exponents”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table des matières
- Lesson 6.6.14
- IM 6.6.14 Lesson: Evaluating Expressions with Exponents
- Practice 6.6.14
- IM 6.6.14 Practice: Evaluating Expressions with Exponents
IM 6.6.14 Lesson: Evaluating Expressions with Exponents
Based on the given information, what other measurements of the square and cube could we find?
A cube has side length 10 inches. Jada says the surface area of the cube is [math]600[/math]in[math]^2[/math], and Noah says the surface area of the cube is [math]3,600[/math]in[math]^2[/math]. Here is how each of them reasoned:[br][br][table][tr][td]Jada's Method:[/td][td]Noah's Method:[/td][/tr][tr][td][math]6\cdot10^2[/math][br][math]6\cdot100[/math][br][math]600[/math][/td][td][math]6\cdot10^2[/math][br][math]60^2[/math][br][math]3,600[/math][br][/td][/tr][/table][br]Do you agree with either of them? Explain your reasoning.[br]
Evaluate the expressions in one of the columns. Your partner will work on the other column. Check with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error.
Consider this equation: [math]\boxed{\phantom{3}}^2+\boxed{\phantom{3}}^2=\boxed{\phantom{3}}^2[/math]. An example of 3 different whole numbers that could go in the circles are 3, 4, and 5, since [math]3^2+4^2=5^2[/math]. (That is, [math]9+16=25[/math].)[br][br][br]Can you find a different set of 3 whole numbers that make the equation true?
How many sets of 3 different whole numbers can you find?
Can you find a set of 3 different whole numbers that make this equation true? [math]\boxed{\phantom{3}}^3+\boxed{\phantom{3}}^3=\boxed{\phantom{3}}^3[/math].
How about this one? [math]\boxed{\phantom{3}}^4+\boxed{\phantom{3}}^4=\boxed{\phantom{3}}^4[/math].
Once you have worked on this a little while, you can understand a problem that is famous in the history of math. (Alas, this space is too small to contain it.) If you are interested, consider doing some further research on [i]Fermat’s Last Theorem[/i].
IM 6.6.14 Practice: Evaluating Expressions with Exponents
Lin says, “I took the number 8, and then multiplied it by the square of 3.” Select [b]all [/b]the expressions that equal Lin’s answer.
Evaluate each expression.
[math]7+2^3[/math]
[math]9\cdot3^1[/math]
[math]20-2^4[/math]
[math]2\cdot6^2[/math]
[math]8\cdot\left(\frac{1}{2}\right)^2[/math]
[math]\frac{1}{3}\cdot3^3[/math]
[math]\left(\frac{1}{5}\cdot5\right)^5[/math]
Andre says, “I multiplied 4 by 5, then cubed the result.” Select [b]all [/b]the expressions that equal Andre’s answer.
Han has 10 cubes, each 5 inches on a side.
Find the total volume of Han’s cubes. Express your answer as an expression using an exponent.[br]
Find the total surface area of Han’s cubes. Express your answer as an expression using an exponent.[br]
Priya says that [math]\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}=\frac{4}{3}[/math]. Do you agree with Priya? Explain or show your reasoning.[br]
Answer each question. Show your reasoning.
125% of [math]e[/math] is 30. What is [math]e[/math]?
35% of [math]f[/math] is 14. What is [math]f[/math]?
Which expressions are solutions to the equation [math]2.4y=13.75[/math]? Select [b]all [/b]that apply.
[size=150]Jada explains how she finds [math]15\cdot23[/math]:[br][br]“I know that ten 23s is 230, so five 23s will be half of 230, which is 115.[br]15 is 10 plus 5, so [math]15\cdot23[/math] is 230 plus 115, which is 345.”[/size][br][br]Do you agree with Jada? Explain.