New Buzzmath Activity – Surface Area of Triangular and Rectangular Prisms

At one time or another you may have folded a flat piece of cardboard into a gift box, or maybe a box for mailing a package. The flattened box may have had creases to show you where to fold in order to create the sides of the box. In this way, you had taken a two-dimensional flat object and changed it into a three-dimensional object. But the amount of cardboard did not change! So, to find the amount of cardboard the box is made of, you could simply find the area of the unfolded box.

Triangular prisms

In the activity, Surface Area of Triangular and Rectangular Prisms, students find the surface area of triangular and rectangular prisms by adding the areas of the faces of the prisms. They use flattened out prisms called nets to help them figure this out. The dynamic nature of this activity allows students to fold and unfold prisms to help them see the two-dimensional net of the prism as well as the three-dimensional solid.

Nets and boxes

New Buzzmath Activity – Volume of Rectangular Prisms with Fractional Edges

A puzzle game called Rubik’s Cube was very popular in the 1980’s. The classic Rubik’s Cube is made up of 27 smaller cubes with different colors on the visible faces of the smaller cubes. The object of the game is to pivot the larger cube so that each face has a consistent color. The Rubik’s Cube is a perfect example of how a larger cube can be packed with smaller cubes to demonstrate volume.

Now, imagine an even smaller cube, where each side of this cube is one-half the length of a side of one of the smaller cubes in the Rubik’s Cube. You would need eight of these much smaller cubes to make up one of the small cubes in a Rubik’s Cube. Now imagine that each of the 27 cubes in a Rubik’s Cube is made up in this way. How many of the smallest cubes will it take to create the Rubik’s Cube? Well, that’s the kind of problem students will need to figure out in the activity, Volume of a Rectangular Prism with Fractional Edges. Not only will students pack prisms with cubes to solve problems, but they will also use formulas.

New BuzzMath Activity – Using Ratio Reasoning to Convert Measurement Units

In Gallon Land, King Gallon is the leader of the land. King Gallon lives with four queens (don’t judge). Each Queen has 2 Princes and each Prince goes on to have two children. OK, so there is no Gallon Land and there is no King Gallon, but this is a great story to help remember how many quarts are in a gallon, how many pints are in a quart and how many cups are in a pint. So now how do we find how many cups are in a quart? Or how many inches are in a yard? Or how many ounces are in 10 pounds? We can use ratios and proportions!


In the activity, Using Ratio Reasoning to Convert Measurement Units, students will use tables, tape diagrams, double number line, and images to identify ratios and use them to convert measurement units. They will practice converting both units of length and capacity. This is not only a fun activity, it also reinforces a skill that is so useful in our everyday lives.

New BuzzMath Activity – Mean and Mean Absolute Deviation

There is nothing mean about this activity; unless, of course, you are talking about the average kind of mean. Conceptually the mean is much more than finding the sum of the values and dividing the quantity of values. In the activity Mean and Mean Absolute Deviation, students get to actively explore the concept of finding the mean by manipulating stacks of books. Once they have explored the concept they are then given the opportunity to practice finding the mean with the algorithm.

Mean Books

As the student’s progress through the activity they are then asked to use their prior knowledge of mean and absolute value to find the mean absolute deviation of a variety of data sets. This activity introduces students to finding the mean absolute deviation based on concepts they have already explored, and provides plenty of practice to support the introduction.

Mean Absolute Deviation

New Buzzmath Activity – Representing Situations with Two Variables

Some things depend on other things! That’s a fact in nature, society, and so on. One thing may be independent, while the other depends on the independent thing. For instance, a parent is independent, in that the parent can live where he or she chooses. A child is dependent on the parent since where the child lives depends on where the parent lives. Another example, is that the number of points in a basketball game depends on the number of baskets scored.

In math, we often deal with independent and dependent variables. The activity Representing Situations with Two Variables uses variables to represent real-world quantities that change in relationship to each other–one dependent and the other independent. Students analyze the relationship between these variables and use graphs, tables, and equations to represent this relationship.

Representing situations with 2 variables

But don’t forget the DRY MIX when teaching about independent and dependent variables. That is,

Dependent variable, Resulting, Y (goes on the y-axis)

Manipulated, Independent variable, X (goes on x-axis)

X-Y variables

Very positive feeback from New London-Spicer Middle School!

Seven grade teacher Brittany Valentien from New London-Spicer Middle School, MN, made our day by sending us a very encouraging email joined by this article about Buzzmath (click on the image to read the full article):

We love to receive our user’s comments and suggestions, because it gives us an opportunity to constantly improve Buzzmath. But, we must admit that when a teacher writes us to say that she has incorporated Buzzmath into her everyday lessons as a way to have the students do some extra practice, we are thrilled!

Thanks again, Brittany!

Alfred letters

New BuzzMath Activity – Histograms

A picture is worth a thousand words! That saying couldn’t be truer than when it comes to data. It is so much easier to understand data when placed in picture form, such as a histogram, than to have a lot of numbers and/words describing the data. A histogram is simply a picture that shows data in ranges using bars of different heights.


In the activity, Histograms, students organize data in frequency tables and create histograms. First, they learn to divide the data into equal intervals. Then they determine the frequency in each interval to create the bars for the histograms. The dynamic nature of this activity allows students to “click” to add or remove tallies when creating frequency tables, and drag bars to desired heights to create the histograms. Creating these histograms helps students to better understand and interpret the data.

Welcome to the Carnival… of Functions!

Last week, we learned that our good friends Dan Meyer and Christopher Danielson collaborated with Desmos to create Function Carnival, an online math tool to address the misconceptions students may have about graphs.

As Dan and Christopher explain on Desmos’ blog:

It’s often challenging for students to distinguish between (1) values, (2) the rate of change of those values, and (3) the rate of change of the rate of change.

Students also tend to have the idea that graphs are pictures—that the graph always describes the position of an object in space.

Their solution was to create this online tool, where students can watch a little animation, draw a graph of what they see, observe the animation again next to their graph to determine if they were right, and then revise and re-draw the graph so that it fits the image. They not only know if they had a right or wrong answer, they see it! Dan actually calls this process “echoing“. So simple and brilliant!

Correct Graph

The student can graph the motion on three rides:

The Cannon Man‘s graph is piecewise quadratic and linear.
The Bumper Car‘s graph is piecewise linear, which has thrown a bunch of students.
The Ferris Wheel‘s graph is sinusoidal.

Three rides

Furthermore, the students can make arguments on incorrect graphs, which help them have a stronger understanding of the concept by putting it into words.

Incorrect graph

Function Carnival also include filters for common misconceptions. With this tool, teachers can quickly see which students evoke those misconceptions about function graphs. A good way to start the conversation! Give it a try!

Buzzmath likes graphing too!

More advanced students can draw graphs too in the Buzzmath activity Graphing Linear Equations.

Graphing linear equations

New BuzzMath Activity – Evaluate Algebraic Expressions

Everyday routines become easier when there is order and connection. A cake cannot be made by placing  the ingredients in an oven before mixing the ingredients together. Only by following the same steps can a recipe be duplicated over and over again. The same is true when evaluating expressions.

In the activity Evaluate Algebraic Expressions, students learn that the “recipe” is to substitute a value for a variable and then use the order of operations to find the value of the expression. This includes expressions with exponents involving formulas. In the first few pages of the activity, students learn that an algebraic expression contains a variable and at least one operation, and then learn to write verbal expressions with math symbols. Since the variable in an expression can vary, students evaluate the expression using a specific value for that variable.

Evaluate Algebraic Expressions

New BuzzMath Activity – Polygons in the Coordinate Plane

Before GPS (Global Positioning Systems), most people were familiar with maps, since maps helped them to find unknown locations. Today, maps are still used in different areas, such as city planning, to map out communities, buildings, landmarks, and so on. A map is simply a coordinate plane.

The activity Polygons in the Coordinate Plane is a dynamic activity in which students drag points to given locations on a grid. Students plot given coordinates for different points that form a polygon, and must sometimes determine the coordinates of a missing point to complete the polygon.

Who knows…maybe there will be some city planners in the making!


Get every new post delivered to your Inbox.

%d bloggers like this: