From the apple on your desk and the coffee cup in your hand, to the cabinets along the classroom wall, basic three-dimensional shapes are found everywhere in the world around us. Introduce young mathematicians to the these common figures...

What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...

Have scholars show what they know with a 20-page assessment aligned to the California State Standards. The test covers concepts such as large and whole numbers, all four mathematical operations, fractions, decimals, geometric figures,...

Investigate dilations to learn more about them. The second segment in a series of 16 provides a discussion of properties of dilations by going through examples. The problem set provides opportunities for scholars to construct dilations.

An upper-level treatment of what is often presented as a basic concept (the right angle of an inscribed circle on the diameter), this activity really elevates the mathematical thought of the learner! Expected to develop formulas...

Sharpen your pencil and grab a ruler, it's time to draw some quadrilaterals! Given the definition of a parallelogram, rectangle, and rhombus, learners draw examples and nonexamples of each figure. The three definitions are...

Challenge the class to devise a method to determine the dimensions of a rectangle inscribed in another rectangle. Pupils make connections between functions and geometry as they examine the area and perimeter of a square or...

Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...

Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...

Parallelograms are pairs of triangles all the way around. Pupils measure to determine the area and perimeter of a parallelogram. They then find the area of the tirangles formed by drawing a diagonal of the parallelogram and compare their...

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

Pupils analyze a pattern of conference tables to determine the number of tables needed and the number of people that can be seated for a given size. Individuals develop general formulas for the two growing number patterns and...

The class braids irrational numbers, Pythagoras, and perimeter together. The mini-assessment requires scholars to use irrational numbers and the Pythagorean Theorem to find perimeters of rugs. The rugs are rectangular, triangular,...

Use the handout as guided or independent practice in drawing a reflection of a rectangle over a line. Three rectangles are provided for practice in addition to a critical thinking question.

To take the longest path, go around—or was that go over? Class members measure scale drawings of a cylindrical vase to find the height and diameter. They calculate the actual height and circumference and determine which is larger.  

It's all about lines when going around. Pupils graph the relationship between the length of a side of a square and its perimeter. Class members explain the origin in context of the side length and perimeter. They compare the graph to the...

Graph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...

Pupils design a fence for a backyard pool. Scholars develop a fence design based on given constraints, determine the amount of material they need, and calculate the cost of the project. 

Prompt scholars to complete a magic square using only variables. Then they can attempt to solve a numerical magic square using algebra. 

Take flight with a fun activity focused on graphing data on a coordinate plane. As learners study the data for Granny's hot-air balloon trip, including the time of day and the distance of the balloon from the ground, they practice...

Let's paint the town equal parts yellow and violet, or simply brown. Pupils calculate the amount of blue and red paint needed to make six quarts of brown paint. Individuals then explain how they determined the percentage of the brown...

Many problems in life have more than one possible solution, and the same is true for advanced mathematics. Scholars solve seven problems that all have at least two solutions. Then three higher-level thinking questions challenge them to...

Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a...

When told to describe a line, do your pupils list its color, length, and which side is high or low? Use a worksheet that engages scholars to properly label line graphs. It then requests two applied reasoning answers.