The Areas of Squares and Their Side Lengths: IM 8.8.1
[url=https://im.kendallhunt.com/MS/teachers/3/8/1/preparation.html]“The Areas of Squares and Their Side Lengths”[/url] from IM Grade 8 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 of Contents
- Lesson 8.8.1
- IM 8.8.1 Lesson: The Areas of Squares and Their Side Lengths
- Practice 8.8.1
- IM 8.8.1 Practice: The Areas of Squares and Their Side Lengths
IM 8.8.1 Lesson: The Areas of Squares and Their Side Lengths
In the applet below, which shaded region is larger below? Explain your reasoning.
Find the area of shaded square (in square units).
Find the area of shaded square (in square units).
Find the area of shaded square (in square units).
[size=150]Any triangle with a base of 13 and a height of 5 has an area of [math]\frac{65}{2}[/math].[br][/size][br]Both shapes in the figure have been partitioned into the same four pieces. Find the area of each of the pieces, and verify the corresponding parts are the same in each picture. There appears to be one extra square unit of area in the right figure. If all of the pieces have the same area, how is this possible?
Find the areas of squares D, E, and F.
Which of these squares must have a side length that is greater than 5 but less than 6? Explain how you know.
[size=150]Use the applet below to determine the total area of the five shapes, [math]D[/math], [math]E[/math], [math]F[/math], [math]G[/math], and [math]H[/math]. Assume each small square is equal to 1 square unit.[/size]
IM 8.8.1 Practice: The Areas of Squares and Their Side Lengths
Find the area of each square. Each grid square represents 1 square unit.
Find the length of a side of a square if its area is:
81 square inches
[math]\frac{4}{25}cm^2[/math]
0.49 square units
[math]m^2[/math] square units
Find the area of a square if its side length is:
3 inches
7 units
100 cm
40 inches
[math]x[/math] units
Evaluate [math](3.1\times10^4)\cdot(2\times10^6)[/math]. Choose the correct answer:
Noah reads the problem, “Evaluate each expression, giving the answer in scientific notation.” The first problem part is: [math]5.4\times10^5+2.3\times10^4[/math].[br][br]Noah says, “I can rewrite [math]5.4\times10^5[/math] as [math]54\times10^4[/math]. Now I can add the numbers: [math]54\times10^4+2.3\times10^4=57.3\times10^4[/math]."[br][br]Do you agree with Noah’s solution to the problem? Explain your reasoning.
Select [b]all[/b] the expressions that are [math]3^8[/math].