Cereal Bars

Solve a system of equations to determine the units of ingredients needed to make a cereal bar.

Don’t Push It

Use a Computer Based Laboratory (CBL) device to investigate how the gas pressure changes with the volume.

It’s Getting Darker

Use a Computer Based Laboratory (CBL) device to investigate how the intensity of light changes with the distance from a light source such as a bulb or a flashlight.

Chill Out

Use a Computer Based Laboratory (CBL) device to investigate what happens to the temperature of a cup of hot water while time is passing.

Bouncing Ball

Use a Computer Based Laboratory (CBL) device to investigate the motion of a bouncing ball.

Taking Classes

Given certain parameters, how many possible students can take math and English, science and English, and math and science?

Mystery Number

What is the mystery number that fits the description?

Palindrome Odometer

Determine how fast a bus was traveling during two hours of time.

Paper Folding

Determine the thickness of folded paper.

Phone Tree

Determine the structure of a telephone tree used by eighth graders in Jefferson County who offered to help when the river flooded their town.

Going to the Movies

Predict the cost of the movie tickets.

Library Fines

Help Minerva sort out her charges from the school library.

Sales Options

Which salary option should Mrs. Lee, the top salesperson in the company, take?

Double Dollars

What is the fewest number of years until an investment doubles in value?

Judy’s Gift

How much money did Judy give Dave?

Double Trouble

Find a number that fits the description.

Family Math

How old are a mother and son?

Largest Combination

Find the largest possible value of a given expression.

Summing to 100

Use the numbers from the given list no more than once to obtain a sum of 100.

Number Machine

What will the machine give me if I put in 100?

Bouncing Ball

How many times does the special bouncing ball hit the ground?

Nails in a Pail

Determine how much a pail and nails weigh.

Integer Function

Find the smallest integer for which an expression results in an integer.

Unknown Distance

Determine the distance between two points.

Choosing Salaries

Your principal wants to hire you to work for her for ten days. Determine which way would you earn the most money.

Lucky Find

How much money did Karen have before she found the $2?

Collecting Baseball Cards

On what day will Mike have exactly 100 baseball cards?

The Game Show

Determine what each question is worth on a television game show.

The Gonzalez Family

How old is each of the Gonzalez children?

Legs and Seats

How many more legs than seats are in the leftover Seats ‘R’ Us factory inventory?

Formulaic Properties

Find values of x, y, and z, so that a given expression equals 18.

How Did We Do?

In a mathematics contest, how many of your team’s answers were incorrect and how many problems were unanswered?

Counting Coins

How many coins does Kate have?

Walking Rates

Determine the distance and time required for Amel to overtake Bonne, Amel’s younger brother.

The Frog Race

Two frogs have a race. Determine which frog wins the race.

Piggy Savings

When will Parneshia’s bank have twice as much money as John’s?

Three Daughters

Determine the age of each daughter.

Reciprocal Sums

Given the sum of two positive integers, determine the smallest possible sum of their reciprocals.

Remainders and Factors

Determine the relationship of a group of positive integers that has 2 common divisors.

Symbolic Algebra

Determine which algebraic expression is greater.

Keith’s Pocket

How much money did Keith originally have in his pocket?

Units of Speed

Find an equation that will compare speed units of miles per hour to kilometers per hour.

Population Changes

Generate a function that will describe the population of your state vs. time.

Pricing Pizzas

What type of function (linear, quadratic, or exponential) would you create to describe the cost of the pizza vs. the number of toppings?

Comparing Temperatures

Use data to derive an equation that relates Celsius to Fahrenheit, Celsius to Kelvin, and Kelvin to Fahrenheit.

Altered State

Make a false equation correct by alternating the “punctuation” on the left side of the equation.

Piano Frequency

Is the given relation comparing key position and frequency actually a function?

Heron’s Area

Explore the world of Heron triangles – triangles with sides of integral length and integral area.

The Life of a Natural Number

Determine the behavior of natural numbers given that even and odd numbers act differently.

Shifting Parabolas

Examine graphs of y=x2 + bx + 6, where b is any real number.

Sliding Graph

Examine the graphs of 2x + 3y = A.

Forming a Square

Find four equations whose graphs are oblique (slanted) lines that will intersect to form the vertices of a square.


How can the discriminant help you determine how many times the graph will cross the x-axis?

Reciprocal Functions

Describe any patterns you find when comparing a function to its reciprocal function.

Absolute Value Functions and Transformations

Describe how the graph of an absolute value function changes when you modify a, b, and c.

Exponential Functions

When is a function in the form y=abx increasing or decreasing?

Using Roots to Generate an Equation

Find an equation of a parabola given the point(s) where it crosses the x-axis.

Symmetry of Polynomial Functions

Describe the symmetry of a function.

Fundamental Theorem of Algebra

What is the largest number of times a function can cross the x-axis? How about the smallest number of times?

Minimum Criteria

Given a set number of points on the coordinate plane, how many lines or parabolas can you make through these points?

Ending the Maximum

Find a shortcut to find the x-coordinate of the maximum or minimum of a parabola.

Does 0=0?

What happens when two equations in the form y = mx + b are set equal to each other?

Triangle from a Line

The line Ax + By = C will form a triangle with the x and y axis for what values of A, B, and C?

Changing Intercepts

Discover what happens to the graph when you vary the values for n and b in the equation g(n) = n2 + b.

Zero Coefficients

In the equation Ax + By = C, what happens when A or B or C is zero?

Fractional Forms of Repeating Decimals

Use a system of equations to determine the fractional form of a repeating decimal.

Crossing Curves

Find where a given linear function crosses a given quadratic function.

In Between

Find a number such that its square is between two given numbers.

Input Equals Output

Find two functions so that the input of one is always equal to the output of the other.

Solutions in a System

What is the largest number of solutions possible in a given system of equations?

Swapping Coordinates

What happens when you switch the x and y coordinates of a function?

Catching Up in Savings

How many years will it take Sally to have as much money as Judy?

Composite Functions

Determine the composite function of two distinct functions.

Burglar Alarm

Determine how much money a company should charge for a burglar alarm system.

Unusual Property


Varied Slopes and Intercepts

Discover what happens to the graph when you vary the values for m and b in the equation y = mx + b.

Twice Reflected over Parallel Lines

Find an equation that relates the distance between points reflected over parallel lines.

Twice Reflected over Intersecting Lines

Find an equation which relates the angles formed by intersecting lines and points reflected over these lines.

Segments on Secant

Find an equation that relates segments on a secant.

Area of a Kite

Find an equation that relates the area of a kite to its diagonals.

Edges, Face, Vertex

Find an equation that relates the number of edges to the number of faces and the number of vertices in three-dimensional objects.

Intersecting Chords

Find an equation to relate chords of a circle.

Distance to a Point in a Rectangle

Find an equation that relates segments inside a rectangle.