An important property of linear functions is that they grow by equal differences over equal intervals. In this task students prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope.

In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

This purpose of this task is for students to understand how to partition shapes into equal pieces. This task starts students with concrete representations of the shapes that they can fold and cut, so that later they will understand more abstract representations like diagrams and symbols. Part one provides students with opportunities to manipulate paper shapes, folding them to create equal parts.

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Discover the rules for keeping it balanced. Collect stars by playing the game!

This task helps students understand the meaning of the equal sign and to use it appropriately.

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

An interactive applet and associated web page that demonstrate the equation of a line in point-slope form. The user can move a slider that controls the slope, and can drag the point that defines the line. The graph changes accordingly and equation for the line is continuously recalculated with every slider and / or point move. The grid, axis pointers and coordinates can be turned on and off. The equation display can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the equation of a line in point - slope form, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

In this problem students must transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent.

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking. The Equivalent Ratios problem asks students to use the digits 1-9 to see how many ratios they can make that are equivalent to 2:3

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

Franklin works with Laverne to create a budget for a job painting a room, in this video segment from TV 411.

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

This lesson unit is intended to help teachers assess how well students are able to: estimate lengths of everyday objects; convert between decimal and scientific notation; and make comparisons of the size of numbers expressed in both decimal and scientific notation.

Harry estimates how long it will take him to get to the front of a long ticket line in this Cyberchase video segment.

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases. Random sampling (like mixing names in a hat and drawing out a sample) is not a new idea to most students, although the terminology is likely to be new.

Students estimate the storage capacity of CDs and DVDs by assessing diffraction patterns of green and red laser beams.