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<p>Choose the expression that represents the indicated quantity:</p><img src="/qimages/134" />

<p>Find the <strong>surface area</strong>
of a cube that has side length of <code class='latex inline'>3y</code>.</p><p><a href="https://youtu.be/dOssFo3frCY">Similar Example</a></p>

<p>Sketch models to represent each of the following algebraic expressions. The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> do not represent the same number.</p><p><code class='latex inline'>x^2</code></p>

<p>Sketch models to represent each of the following algebraic expressions.</p><p>The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> do not represent the same number.</p><p><code class='latex inline'>x^2
</code></p>

<p>A crawlspace in a space station has the shape of a rectangular prism.
It is about 100 cm high, 10 m wide, and 1 km long. What is the volume enclosed by the crawlspace?</p>

<p>Sketch models to represent each of the following algebraic expressions.</p><p>The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> do not represent the same number.</p><p><code class='latex inline'>x^3
</code></p>

<p>If the footprint of a square building has an area of <code class='latex inline'>50 m^2</code>, which is a bette estimate for the length of the front of the building: <code class='latex inline'>7.2 m</code> or <code class='latex inline'>7.7 m</code>? Explain how you can answer this without using a calculator.</p><img src="/qimages/138" />

<p>The length of the side of a cube is <code class='latex inline'>3^5</code>. Express its surface area and volume using powers and simplify. </p><img src="/qimages/153" />

<p>Sketch models to represent each of the following algebraic expressions. The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> are not equal.</p><p><code class='latex inline'>\displaystyle
(2x)^2
</code></p>

<p>Find the missing value with an integer.</p><p>a) <code class='latex inline'>2^8 = 4^\bigcirc</code> </p><p>b) <code class='latex inline'>2^7 = 4^{\bigcirc}</code></p>

<p>Determine an expression for the are of the square drawn on the hypotenuse. </p><img src="/qimages/152" />

<p>Rob is finishing a floor with square tiles. Each tile has an area of <code class='latex inline'>412 cm^2</code>. Estimate the length of the side of each tile. </p>

<p>Sketch models to represent each of the following algebraic expressions. The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> are not equal.</p><p><code class='latex inline'>\displaystyle
y^2
</code></p><img src="/qimages/2947" />

<p>Sketch models to represent each of the following algebraic expressions.</p><p>The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> do not represent the same number.</p><p><code class='latex inline'>
(2y)^2
</code></p>

<p>The area of some squares are shown. Determine or estimate the length of the sides of each square. use a calculator to check your answers. </p><p><code class='latex inline'>
144 km^2
</code></p>

<p>The length of the side of a cube is <code class='latex inline'>5^3</code>. Express its surface area (SA) and volume (V) using powers and simplify each expression.</p>

<p>Sketch models to represent each of the following algebraic expressions.</p><p>The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> do not represent the same number.</p><p><code class='latex inline'>
y
</code></p>

<p>Sketch models to represent each of the following algebraic expressions. The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> are not equal.</p><p><code class='latex inline'>\displaystyle
2x
</code></p>

<p>Choose the expression that represents the indicated quantity:</p><img src="/qimages/137" />

<p>Draw or build a model of the algebraic expression <code class='latex inline'>ab</code> where <code class='latex inline'>a</code> is not equal to <code class='latex inline'>b</code>. Explain how this model is the same as and how it is different from a model of the algebraic expression <code class='latex inline'>a^2.</code></p>

<p>If <code class='latex inline'>x = \frac{1}{9}</code>, place the following values in order from least to greatest: <code class='latex inline'>x , x^2, x^3, \sqrt{x}, \frac{1}{x}</code></p>

<p>If you know that the product of two numbers is <code class='latex inline'>9^6</code> and quotient is <code class='latex inline'>9^2</code>, which of the following could be the two numbers?</p>

<p>The area of some squares are shown. Determine or estimate the length of the sides of each square. use a calculator to check your answers. </p><p><code class='latex inline'>
75 cm^2
</code></p>

<p>A piece of steel plate is used to make a railway car. The plate is 2.5m wide, 3.2 m long, and 0.5 cm think. Determine the volume of steel in cubic centimeters. </p>

<p>Choose the expression that represents the indicated quantity:</p><img src="/qimages/135" />

<p>Draw or build a model of the algebraic expression abc where <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code> are not equal to each other. Compare this to a model of the algebraic expression <code class='latex inline'>ab^2.</code></p>

<p>Calculate the side length of a square with an area of <code class='latex inline'>49 cm^2.</code></p>

<p>Sketch models to represent each of the following algebraic expressions. The variables <code class='latex inline'>x</code> and <code class='latex inline'>y</code> are not equal.</p><p><code class='latex inline'>\displaystyle
y^3
</code></p>

<p>The area of some squares are shown. Determine or estimate the length of the sides of each square. use a calculator to check your answers. </p><p><code class='latex inline'>
0.01 m^2
</code></p>

<p>The symbol <code class='latex inline'>\sqrt[3]{\bigcirc}</code> represents the cube root. For example, <code class='latex inline'>4 \times 4 \times 4 = 64, \sqrt[3]{64} =4. </code> Create a geometric model to represent <code class='latex inline'>\sqrt[3]{64}</code>. Explain why the model makes sense.</p>

<p>If the length of the side of a square game board is <code class='latex inline'>\sqrt{1000} cm</code>, what is the area of the game board? How can you check your answer?</p>

<p><strong>(a)</strong> Build a volume model to represent a cube with length, width, and height all equal to 4 cm. Sketch the model and label the length, width, and height.</p><p><strong>(b)</strong> What is the volume? Write this as a power.</p><p><strong>(c)</strong> Write an expression for the area of one face as a power. Evaluate the area of one face. </p>

<p>Copy and label each object, then represent it with one of the following algebraic expressions: <code class='latex inline'>c, d, c^2, d^2, d^3 c^3.</code></p><img src="/qimages/133" />

<p>Choose the expression that represents the indicated quantity:</p><img src="/qimages/136" />