## 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?

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.

## Discriminant

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.

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## 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.