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. 

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...

Three angles in a triangle, three-dimensional space, it all seems connected somehow. Given several different triangles, pupils use the three angles of the triangle as coordinates to plot points in three-dimensional space. They explore...

Learners are asked to find multiples and common multiples of two numbers. They must take their findings and find a pattern between the numbers and explain their reasoning. Use this resource with The Florist Shop activity in this series...

Examine ratio and scale through coordinate geometry. Scholars use two diagrams of different scale to calculate perimeter and area. Then, individuals use the perimeters and areas to find ratios.

Apply concepts of scale and ratio to determine relationships in irregular figures. Learners determine the ratio of the perimeters of two figures composed of rectangles and circles. After, they apply similar concepts to find the ratio of...

Learn the importance of geometry to tailors. Given a shirt sewing pattern, scholars determine the actual size of the shirt. After which they answer questions that require problem solving and extending their understanding of scale.

Develop a solid understanding of the manipulation of expressions to produce equivalent expressions. Given an expression, pupils rearrange it to create a new one. Their new functions must match the structure of the model expressions.

Mathematics can model just about anything—so why not simulate the height of water in a toilet bowl? The lesson asks pupils to create a graphical model to describe the relationship of the height of the water as it empties and fills again....

Develop a new measure of the properties of an object. Scholars develop a definition and formula to measure the bumpy-ness of an object. They utilize their formulas to find the property for several spherical objects.

Apply the concept of similar triangles to design a space in a room. Scholars use similar triangles to determine how a spotlight reflects from a mirror. After drawing the path of the spotlight, individuals find the smallest possible width...

Examine and compare a linear and step function. The task provides two scenarios, one modeled by a linear function and the other a step function. Pupils create a graph for each and explain how each compares to the other.

How many hot dogs does Fenway Park go through in a year? Learners estimate answers to this question and more as they work through the task. Problems require participants to make assumptions and use those assumptions to make estimations.

Explore business problems through mathematical analysis. The task has individuals write and graph a linear system to determine the best business model. They use their models to answer a series of questions that help to make a conclusion.

Creating a definition may be easier than it sounds! Give your classes experience creating their own definition. Scholars examine the meaning of the compact-ness of a scatter plot and create their own definitions based on measurements. 

Apply geometric concepts to a design problem. Individuals examine the structural setup of the chain on a bicycle and use the measurements of the circles to determine the length of the chain. 

Start a trend by using blirts and gorks as your standard unit of measures. The activity asks learners to take a known measures of blirts and gorks and develop a conversion ratio. Individuals use both perimeter and area measures of...

Young mathematicians learn how to solve problems involving stratified sampling. They review concepts of sampling and proportionality by watching a video and then they complete a worksheet of questions on this topic.

Round and round and round we go. Given a diagram of three circles, two of which share a point with the third circle, learners identify the radius of each circle. Doing so requires setting up and solving a system of equations based on the...

Transform your lesson for transforming functions. Scholars transform linear, quadratic, exponential, rational, and trigonometric expressions. They write their expressions to fit specific forms and identify the values of the resulting...

Take a look at a star resource. Young mathematicians use a graphing calculator to draw intersecting lines that look like a star. They then apply translations to move the entire star and also consider what transformations must occur to...

Grab the wheel in learning about functions. A short performance task challenges young mathematicians to develop a function that describes the cars eight people drive. They consider whether the inverse of the function exists. If not, they...

There are zero reasons not to learn about zero coupon bonds. Given information about the interest rate and closing price of a zero coupon bond, future investors determine the purchase price of the bond. They then consider the...

How hard can it be to measure out two pounds? A short performance task introduces a situation where a balance scale is broken. It gives a method for measuring out two pounds and asks learners to evaluate the procedure. They must prove...