Introduction to Volumes

Learning Goals for the lesson

• Students will be able to effectively use their knowledge of square roots and cubic roots and apply this to area problems using proper mathematical notation, and appropriate vocabulary.

• Students will understand the concept of volume and will be able to utilize this knowledge to solve and make connections to real-world problems.

Standards for the lesson

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

• CCSS.MATH.CONTENT.8.G.C.9

  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world mathematical problems.

Expressions and Equations Work with radicals and integer exponents.​

• CCSS.MATH.CONTENT.8.EE.A.2

  Use square root and cube root symbols to represent solutions to equations of the form ​x²=p and x³=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Standards for the lesson

ELD STANDARDS

• CCSS.ELA-LITERACY.W.9-10.1

  Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

• EXCHANGING INFORMATION/ IDEAS​

  C​contribute to class, group, and partner discussions by following turn-taking rules, asking relevant questions, affirming others, adding relevant information, and paraphrasing key ideas

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Poll

Prior Knowledge: What do you already know?

• Square and Square Root of a Number

• Opposite Operations

• How to multiply numbers

• What area is

We want to work with volumes of spheres, cylinders, and cones!

The Big Picture

• Pool Cleaner

• ​Truck Driver

• ​Video Game Programmer

• ​Artist (Sculptures)

• Entrepreneur (Physical Product)​

• Engineering

• Construction​

Jobs

• To take care of your fish

• ​To know how much it will cost to fill up the gasoline in your car

• ​Baking

• Guitar (amplitude)​

• Sports (psi)​

Everyday

Why?

Warm-Up

(Connection to Prior Learning)​

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​radius

​Area of a Circle

Multiple Choice

If the area of a circle is equal to $$25\pi$$  , what is the length of the radius?

• 25

• $$\pi$$  

• 5

• -5

Draw

Write the equation for the cubic root of 27 (including the answer).

Modeling​ Volume

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Multiple Choice

Each. layer of cubes has a volume of ___ $$cm^3$$ . 

There are ___ layers.

Therefore the volume is: ___ $$cm^3$$  .

• each layer is 11 $$cm^3$$  , 7 layers, $$V=84cm^3$$  

• each layer is 28 $$cm^3$$  , 3 layers, $$V=84cm^3$$  

• each layer is 4 $$cm^3$$  , 3 layers, $$V=12cm^3$$  

• each layer is 7 $$cm^3$$  , 4 layers, $$V=28cm^3$$  

Open Ended

How would you go about solving this problem, using what you know about the volume of cubes and spheres? How did you think of this and why do you think it will work? (Volume of sphere = $$\frac{4}{3}\pi r^3$$  )

• Hands-on exploration of volume​Explore and discover the formulas for the volume of a sphere, cone, and cylinder by identifying relationships using displacement of water.

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​Next Steps for Learning

Open Ended

How did you feel about this lesson? Any questions you are left with? Are there any vocabulary words or concepts that you feel needs to be reviewed more?