Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

Apply the Pythagorean Theorem to coordinate geometry. Learners find the distance between two points on a coordinate plane by using the Pythagorean Theorem. The vertical and horizontal change creates a right triangle, which allows...

Class members are introduced to probability using terms such as impossible, unlikely, likely, and certain. Numbers between zero and one are associated with the descriptions of probability. Pupils find the likelihood of chance experiments...

Be 100 percent confident who has the most and by how much. Pupils use percentages to help make the comparisons by finding what percent one quantity is of the other. They also determine the percent differences between the two...

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...

Who knew the sum of a number's digits gives such interesting information? The 18th installment of a 21-part module has scholars investigate division by three and nine. After looking at several examples, they develop divisibility tests...

It's said that opposites attract, but what about opposites of opposites? Individuals learn about the opposite of opposites using number lines. They complete a group activity in which members determine the opposite of opposites of...

The original drawing is eight units — how big is the scale drawing? Classmates determine the scale percent between a scale drawing and an object to calculate the length of a portion of the object. They use the percent equation to find...

Add an outstanding resource to your repertoire. The first installment of a 36-part module looks at the relationship between addition and subtraction through an activity using tape diagrams. Pupils develop the identities w – x + x =...

Everyone does their fair share. The sixth segment in a 22-part unit presents the mean as a fair share. Groups build a conceptual understanding of the mean of a data set, rather than simply learn an algorithm. Learners use the...

See how division and subtraction go hand-in-hand. The fourth installment of a 36-part module has scholars investigate the relationship between subtraction and division. They learn using tape diagrams to see that they can use repeated...

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...

How do you find arc lengths and areas of sectors of circles? Young mathematicians investigate the relationship between the radius, central angle, and length of intercepted arc. They then learn how to determine the area of sectors of...

Fold, fold, and fold some more. In the first installment of a 35-part module, young mathematicians fold a piece of paper in half until it can not be folded any more. They use the results of this activity to develop functions for the area...

Statistics can be manipulated to say what you want them to say. Teach your classes to be wise consumers and sort through the bias in those reports. Young statisticians study different statistical reports and analyze them for...

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...

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....

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.

Can an equation have an infinite number of solutions? Allow your class to discover the relationship between the input and output variables in a two-variable equation. Class members explore the concept through tables and graphs and...

How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...

Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application...

Everyone knows that opposite sides of a parallelogram are congruent, but can you prove it? Challenge pupils to use triangle congruence to prove properties of quadrilaterals. Learners complete formal two-column proofs before moving on to...

Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a...