EngageNY
General Prisms and Cylinders and Their Cross-Sections
So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the lesson develops the definition of a general cylinder. Scholars continue on to develop a graphical organizer...
EngageNY
General Pyramids and Cones and Their Cross-Sections
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...
EngageNY
Definition and Properties of Volume
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.
EngageNY
Scaling Principle for Volumes
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...
EngageNY
The Volume of Prisms and Cylinders and Cavalieri’s Principle
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...
EngageNY
The Volume Formula of a Sphere
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...
Institute of Electrical and Electronics Engineers
Coloring Discrete Structures
What's the least number of colors needed to color a U.S. map? The instructional activity begins by having pupils view a video clip on continuous and discrete phenomenon, then launches into an activity reminiscent of Zeno's paradox....
EngageNY
Differences Due to Random Assignment Alone
It takes a lot of planning to achieve a random result! Learners compare results of random assignment, and conclude that random assignment allows results to be attributed to chance. They also realize the set of random means...
EngageNY
Ruling Out Chance (part 1)
What are the chances? Teach your classes to answer this question using mathematics. The first part of a three-day lesson on determining significance differences in experimental data prompts learners to analyze the data by...
EngageNY
Ruling Out Chance (part 2)
Help your classes find the significance in this lesson! Learners analyze the probability of Diff values. They then determine if the difference is significant based on their probability of occurrence.
EngageNY
Ruling Out Chance (part 3)
Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison.
EngageNY
Drawing a Conclusion from an Experiment (part 1)
Challenge your classes to complete an experiment from beginning to end. Learners make their own hypotheses, collect and analyze their own data, and make their own conclusions. They are on their way to becoming statisticians!
EngageNY
Drawing a Conclusion from an Experiment (part 2)
Communicating results is just as important as getting results! Learners create a poster to highlight their findings in the experiment conducted in the previous lesson in a 30-part series. The resource provides specific criteria and...
EngageNY
Evaluating Reports Based on Data from an Experiment
They say you can interpret statistics to say what you want them to. Teach your classes to recognize valid experimental results! Pupils analyze experiments and identify flaws in design or statistics.
EngageNY
Solve for Unknown Angles—Angles and Lines at a Point
How do you solve for an unknown angle? For this sixth installment of a 36-part series, young mathematicians use concepts learned in middle school geometry to set up and solve linear equations to find angle measures.
EngageNY
Construct an Equilateral Triangle (part 1)
Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...
EngageNY
Construct an Equilateral Triangle (part 2)
Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...
EngageNY
Copy and Bisect an Angle
More constructions! In this third installment of a 36-part series, learners watch a YouTube video on creating door trim to see how to bisect an angle. They then investigate how to copy an angle by ordering a given list of steps.
EngageNY
Construct a Perpendicular Bisector
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...
EngageNY
Interpreting the Graph of a Function
Groups sort through NASA data provided in a graphic to create a graph using uniform units and intervals. Individuals then make connections to the increasing, decreasing, and constant intervals of the graph and relate these...
EngageNY
Linear and Exponential Models—Comparing Growth Rates
Does a linear or exponential model fit the data better? Guide your class through an exploration to answer this question. Pupils create an exponential and linear model for a data set and draw conclusions, based on predictions and the...
EngageNY
Solution Sets for Equations and Inequalities
How many ways can you represent solutions to an equation? Guide your class through the process of solving equations and representing solutions. Solutions are described in words, as a solution set, and graphed on a number line....
EngageNY
Solving Equations
Teach solving equations through an exploration of properties. Before pupils solve equations they manipulate them to produce equivalent equations. The activity switches the focus from finding a solution to applying properties correctly.
EngageNY
Some Potential Dangers When Solving Equations
Need a less abstract approach to introducing extraneous solutions? This is it! Young mathematicians explore properties used to solve equations and determine which operations maintain the same solutions. They...