This collaborative activity investigates the meaning of a trapezoid and a parallelogram. It begins by presenting two different definitions of a trapezoid. Learners are to reason abstractly the difference between the two definitions and...

Learners follow a series of instructions for drawing and coloring different shapes in order to learn the difference between the perimeter and area of a polygon. Then they are asked to find the perimeter and area of a 3x4 rectangular...

An exercise in finding the area of polygons by decomposing into triangles and composing into rectangles is the focus of this resource. Make several copies of the worksheet for each participant. Ask learners to use colored pencils to...

Investigate the attributes of polygons. A thorough set of lessons presents problem scenarios for elementary through high school classes. The first lessons focus on basic characteristics of polygons, including the line of symmetry. As the...

Now you'll never have trouble cutting a cake evenly again. Here is a set of five problems all about partitioning shapes into a given number of pieces and identifying the fractional amount of each piece. As learners progress through the...

Try five problems on triangles. Levels A and B focus on shapes that can be created from right triangles. Level C touches upon the relationship between the area of a six-pointed star and the area of each triangle of which it is composed....

Scholars crave practical application. Let them use the different models of a quadratic function to plan the size and shape of a school playground. They convert between the different forms and maximize area.

Investigate polygons from rectangles to triangles to octagons. Each level of the five-problem series targets a different grade level. Beginning with the level A problem, learners examine the relationship between area and perimeter by...

Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required.  From calculating the volume of a composite shape through the...

How long do we have to wait? Given several days of times between eruptions of Old Faithful, learners create a graphical representation for two days. Groups combine their data to determine an appropriate wait time between eruptions.

Present the class with a question on whether the water level of a pond will rise they take a large rock out of a boat and drop it into the pond. Groups come down on all sides of the question and try to justify their answers. The activity...

An excellent lesson that encourages learners to discover how complex figures can be broken into simpler shapes when measuring area. Working with block letters, learners are given the freedom to develop their own strategies for...

Farming is full of mathematics, and it provides numerous real-world examples for young mathematicians to study. Here, we look at a cylinder-shaped storage silo that has one flat side. Given certain dimensions, students need to determine...

Investigating the large numbers of science is the task in a simple but deep activity. Given a one-sentence problem set-up and some basic assumptions, the class sets off on an open-ended investigation that really gives some...

Potty humor is always a big hit with the school-age crowd, and potty algebra takes this topic to a whole new level. Here the class develops a model that connects the dimensions (radii, paper thickness, and length of paper) of a...

Explore the mathematics of the paper snowflake! During the five lessons progressing in complexity from K through 12, pupils use spatial geometry to make predictions. Scholars consider a folded piece of paper with shapes cut out....

Somewhat of a puzzle, this problem gets pre-algebra preteens to write an expression representing a seating chart using triangle-shaped tables. This single task is an applicable lesson for meeting sixth grade Common Core math standards....

A video presentation shows duck-shaped soap that has a $1, $5, $10, $20, or $50 bill in its center. Learners consider different population distribution of the bills to determine a reasonable price for the duck. 

If cubism were a religion, would you follow it? Lower-level tasks focus primarily on counting the number cubes in a structure and relating the number to surface area. As learners progress to higher-level tasks, isometric drawings and...

Score some problems all related to soccer balls. The first few problems focus on pattern blocks to see relationships between figures. More advanced problems focus on actual soccer balls, the patterns on the balls, and their volumes and...

Two-axis rotations ... twice the fun as one-axis rotations! The last installment of a five-part module teaches scholars how to conduct two-axis rotations. They create isometric drawings before and after the rotations.

Develop an understanding of algebraic sequences through an exploration of patterns. Five leveled problems target grade levels from elementary through high school. Each problem asks young mathematicians to recognize a geometric pattern....

With minimal setup and maximum freedom, young geometers are encouraged to think outside the box on a seemingly simple application problem. Though the task seems simple, measuring a given paper clip and finding how many 10 meters can...

Use the alphabet as a tool for teaching your class about geometric figures. Break apart capital letters into line segments and arcs. Classify angles as right, acute, or obtuse. Identify parallel and perpendicular lines. An excellent...