Lesson Plan: Volume "Popcorn Anyone"

This lesson has students learning about the relationship between volume and dimensions.  Students will construct two rectangular prisms and two cylinders out of 8 1/2" by 11" paper to investigate which holds more popcorn.  The objectives of this lesson are to have students: make a hypothesis and test it, create 3D objects from sheets of paper, compare volume of different 3D shapes, and to discover which dimensions have the largest impact on volume.  This lesson could be used over two-50min class periods where students are working in pairs.  Teacher can model how to construct the objects then turn to the students to have them build the 3D objects and make a conjecture of which object they believe to hold the most popcorn.  There is an accompanying activity sheet that goes along with the activity.

Below are the steps to construct the four different 3D objects.

After students construct all four geometric shapes, have them complete the accompanying worksheet which basically asks them to measure the dimensions and determing the volume of the figures using the formula for volume of a rectangular prism: V = l x w x h and volume of a cylinder: V =

πr ²h.

Next, hand each group a bowl of popcorn and a cup for transferring the popcorn. Suggest to students that one hold the rectangular prism as the other fills the tall prism without spilling the popcorn into the shorter one. If availability allows, watch students during this part of the activity to see their reactions. They can now compare their answers for volume with actually how much popcorn fits into each figure.  Have them tie everything togather by asking well thought of questions and have them explain what they learned from the investigation.

Overall, this lesson allows students to explore how volume effects different geometric figures.

Lesson Plan: Circles

This lesson plan is for introducing a 6th grade class to circles. First ask students what a circle is.  Show them pictures and images of circles on the overhead as students explain.  They'll try to describe it, but usually say what it is not or that it is round or other vague descriptions.

Next, draw a point in the middle of your white board. Then, take a ruler and have students come up one at a time to draw a point anywhere on the board that it 12 inches away from your point (for a smaller class have them each draw 2 or 3 points). The students will start to see that the points form a circle.  Continue this process until you have enough points away from the center where you can see that the points can be joined to form a circle.  Have the last student join the points. Then ask again, using what you just did, what is a circle? They will try to describe what they see, and you can help them refine what they say into a definition: a circle is a set of points that are the same distance away from a given point (called the center of the circle).

From here you define the radius as that distance from the given point (center) to any  point on the circle, and the diameter as the distance from one point on the circle to another going through the center. Then you can use the circle the students made to talk about the circumference of a circle with a 12 inch radius.  This lesson plan will give students a deeper understanding of the definition of a circle by discovering what a circle is for themselves.  It puts a lot more meaning into the definition when students can make the connection between how a circle is made (from making points equidistant from the center in every direction) and how it is defined. 

Lesson Plan: Area Representation of the Distributive Property

In this lesson plan, students use area models to deepen understanding of the distributive property.  Using this visual representation bridges the gap between the concrete and abstract.  Many students struggle with the concept of distributive property when they are first introduced to it.  Simply writing the property, a(b + c) = ab +ac, and showing students some problems, is not an effective way to teach this important property. 

To introduce this lesson, give each student a copy of a rectangle with a base of 6 inches and a height of 3 inches.  Have students use a ruler to determine the base and height.  Then, have them find the area of the rectangle (18in²).  To find the area of a rectangle, multiply the base times height.   Next, have them find the area of a rectangle formed by two smaller rectangles.  Have the students show two ways for finding the area of the rectangle formed by two smaller rectangles.  Here are two methods:

It’s important to let the students discover this relationship without offering too much guidance.  Give them time and have them work through it.  After they figure both methods for finding the area, have them compare and contrast the methods. Some may find the first method to be easier and vice versa but what is important is their understanding that these two expressions are equivalent.  Students can create their own rectangles with dimensions and have their peers solve them using both methods.  Reinforce their knowledge by presenting the property a(b + c) = ab + ac. 

Move onto adding a variable into the rectangles and evaluating both methods.  Continue with reinforcing their knowledge by creating their own problems and sharing them with their peers.  An activity sheet should be distributed in order to practice this concept and work with variations of these types of problems.  This activity uses many instructional strategies that were mentioned like visual representations, creating own problems, working with peers, and comparing and contrasting.  The teacher can use additional methods depending on the needs and culture of the class.

Lesson Plan

As a middle school math teacher, I'm constantly searching for an activity that my students will be engaged with while gaining a deeper understanding of the concepts that are being taught.   I recently came across a lesson plan called “Masterpieces to Mathematics: Using Art to Teach Fraction, Decimal, and Percent Equivalents”.  This lesson plan allows students to express themselves through art while working with rational numbers and their relationship on a grid of 100 squares.

In this lesson plan, the student is given a grid of 100 squares and asked to design their own work of art using color markers or pencils.  To inspire the students prior to beginning this activity, the teacher can show the class images of Op Art (Optical Art) which can be easily found on the internet.  After showing the class the examples, the teacher can begin a class discussion on the concept of a grid with 100 squares.  The teacher can call on students to answer some basic questions:  For example, “what is the decimal equivalent if I color in 10 squares red?” The answer is 0.1 or as a fraction we say 1/10.  The teacher can introduce percent and how a percent relates to fraction and decimals on the grid of 100 squares. 

After a brief discussion with the class, the teacher can have the students begin creating their own piece of artwork.  Tell the students to use at least 4 colors and create any design or pattern they like.  After the student has designed their grid, they can begin labeling all the colors they used and their fraction, decimal, and percent equivalents.  This is a great exercise for students to gain an understanding of the relationship of rational numbers.  This activity can be made more advanced by using a grid of 200, 400 or even 500.  This would require a little more advanced calculations but by all means within the capabilities of a typical middle school math student.