Changing ratios make for interesting problems. Pupils solve problems that involve ratios between two quantities that change. Groups use tape diagrams to represent and solve classroom exercises and share their solutions. 

Build tables by understanding their structure. Scholars take a closer look at the structure of ratio tables in the 10th segment in a 29-part series. Individuals realize that the tables can be built using an additive or...

Make all the ratio representations fit together. The 15th segment in a series of 29 presents ratio problems to solve. Scholars use a variety of representations to respond to the questions. The problem set has pupils show how the...

Represent ratios using a variety of methods. Classmates combine the representations of ratios previously learned with the coordinate plane. Using ratio tables, equations, double number lines, and ordered pairs to represent...

Find a way to work with rates. The 23rd part in a 29-part series presents work problems for the class to solve given work rates. Pupils compare rates to determine which is faster. Some problems require learners to convert the rates to...

How do you convert from one measurement to another? Pupils use unit rates to convert measurements from one unit to another in the 21st segment in a 29-part series. They convert within the same system to solve length, capacity,...

Scholars learn to order rational numbers in the seventh lesson in a series of 21. Reasoning about numbers on a number line allows for this ordering.

Individuals build on prior knowledge to order a set of rational numbers from least to greatest or greatest to least. As part of the lesson, they order rational numbers written in different forms.

Young mathematicians compare two fractions with like denominators and then move to the next level to compare fractions with unlike denominators. They will first try to use mental math to make educated guesses. There are a few guidelines...

Tenth graders investigate the history of Pi and how it relates to circles. In this geometry instructional activity, 10th graders measure the circumference of a circle and the diameter of a circle. They relate these measurements to the...

Everything you wanted to know about calculus—and more! The resource is a complete Calculus textbook with explanations, examples, and practice problems. 

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...

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.

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. 

Using a similar process from the first instructional 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...

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...

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...

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...

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...

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...

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...

Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison. 

Do homework grades really determine test scores? Learn whether lines of best fit, correlation coefficients, and residuals can be used to determine test scores when given homework grades. (It would certainly save teachers time in grading...

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.