What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...

Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...

Review the principles of scaling areas and draws a comparison to scaling volumes with a third dimensional measurement. The exercises continue with what happens to the volume if the dimensions are not multiplied by the same...

Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder. 

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

How do 2-D properties relate in 3-D? Lead the class in a discussion on how to draw and see relationships of lines and planes in three dimensions. The ability to see these relationships is critical to the further study of volume and...

Using a similar process from the first activity in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference...

What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.

What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...

Do you have a class that gets excited about technology? Bring in a lesson that allows learners to explore linear equations. Using spreadsheet software, individuals find key features of linear equations and then compare slopes...

What was your age the first time you lost a tooth, broke a bone, or learned to ride a bike? Young mathematicians choose a set of data to examine with an educational lesson on statistical measurements. After they collect data...

Geometric design makes a fashion statement! Challenge learners to design a hat to fit a Styrofoam model. Specifications are clear and pupils use concepts related to three-dimensional objects including volume of irregular shapes and...

If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...

Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two...

So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the lesson plan develops the definition of a general cylinder. Scholars continue on to develop a graphical...

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

Just how big would it really be? Young mathematicians determine if different toys are proportional and if their scale is accurate. They solve problems relating scale along with volume and surface area using manipulatives. The...

Fibonacci numbers are not only found in the classroom but also in nature. Explore the concept of Fibonacci numbers through a series of lessons designed to gain insight into the mathematical reasoning behind the number pattern, and spark...

Reinforce the concept of probability with a series of lessons highlighting the idea of likelihood, probability formulas, relative frequency, outcomes, and event predictions. The collection is made up of four lessons offering informative...

From start to finish this skills practice resource provides a way for individuals to explore the standard form equation of a line. Begin with a warm-up, work through the problems, and then discover the relationship between the...

Explore surface area and calculate how much wrapping paper one needs to cover a whole box with this math video. The resource gives a nice visual of surface area and explains the use of a square unit.

Young mathematicians may solve for cubic units but do they know what that is? This video does a great job of visually explaining not only how to find cubic volume, but what it means in relatable terms. 

This is not your ordinary farm! Using a case study, small groups study two proposed locations for a wind farm. After researching all the information about the sites, the groups choose a site. Each team member writes up the proposal...

How hard can it be to split something in half? Learners investigate how previously learned concepts from angle bisectors can be used to develop ways to construct perpendicular bisectors. The resource also covers constructing a...