This activity sheet, containing twenty exercises, focuses on the concept that to graph a line you need to locate two points that are solutions to the equation, graph them, and draw the line. 

The three forms for a linear equation are described:  Standard form, Slope-Intercept form, and Point-Slope form.  But all three approaches emphasize the same point:  let's locate two points so we know where the line is. 

• We can do it through replacing x with zero and y with zero and solving for two points
• We can do it through making an x-y table to find two points
• We can do it through the y-intercept and using slope to find a second point

All three forms are approached with the same strategy of locating two points on the line.  Once two points are located, the position of the line is determined. 

This activity sheet has three sets of questions:
· Given an equation, locate the graph of the line on a coordinate axis.  Students are not instructed as to which method they should use.  The general strategy is to use any method to find two points that are solutions to the equation.
· Given four equations and four graphs, students must match which graph corresponds with which graph.
· Given an equation and a point, students must describe if the point is a solution to the equation two different ways:  by graphing and by substitution.


Solutions for all exercises are included.

Activity-Sheet-on-Graphing-Linear-Equations

This activity sheet, containing 20 exercises, focuses on solving equations that have variables on both sides of the equation.  It should follow lessons where students have solved one-step, two-step, and multi-step equations. 

The activity sheet begins with some guidelines for students to follow as the approach this new type of equations.

• Students are recommended to perform all distributive properties so each side on the equation only has terms that are either variables or constants.
• If the equations only have terms that contain variables or constants begin by trying to collect the variables on one side and the constants on the other side.
• Most students find it easier to work with an equation by avoiding negatives.  Although this isn’t totally possible, we can minimize the number of negative signs by moving the term that represents the small of two quantities.
• Students are reminded that when solving more complex equations they may run into an equation where no solutions are possible or all solutions are possible.

To help the students understand each guideline, examples are included for each recommendation. 
The activity sheet has
• Twelve exercises that resemble those in the guidelines,
• Six slightly more challenged equations with variables on both sides of the equation,
• One geometry-related problem where students have to write and solve their own equation with variables on both sides of the equation, and
• One challenging problem that deals with variables on both sides of the equal sign.

A set of solutions for all exercises is included. 

Activity-Sheet-on-Solving-Equations-with-Variables-on-Both-Sides

The activity sheet contains 20 questions that can be used as the basis of a lesson or for a classwork or homework sheet on solving multi-step equations.

The emphasis is to use the distributive property and/or combine like terms to simplify the equation to a two-step equations of the form ax+b =c. 

The activity sheet has
• four equations where students combine like terms first,
• four problems where they use the distributive property first,
• four equations where they will use a reciprocal to simplify the equation,
• three equations where they can choose their method of solving,
• one exercise where they must discover where the error was made by a student in solving a multi-step equation,
• two more challenging multi-step equations to solve,  and
• two exercises where students write an multi-step equation for a perimeter problem. 

A complete set of solutions is included

Activity-Sheet-on-Solving-Multi-Step-Equations

This activity sheet has 20 conceptually based questions on solving one-step equations.

Five one-step equations are included: x + a =b, x - a = b, ax = b, x/a = b, and x^2 = a.

The emphasis is on understanding what the meaning of the equation is and then reasoning the solution based on what the equation is describing.

For example: If a student had the equation x + -2 = 8, they would first understand that the equation is saying that some number added to negative two will be positive eight.  Students think about that statement and reason that x must be ten since 10 + -2 = 8.

After solving several equations of each type, students are asked to observe their results to discover that they could have used the opposite operation to help them find the solution.

Solving one-step equations this way should improve their skills at solving one-step equations when they see them later as the result of solving two or more step equations.

A complete set of answers is included.

Activity-Sheet-on-Solving-One-Step-Equations

This set of Volume Matching Cards is made up of

• Eight Volume Problems

• Eight Graphs of the Region

• Eight Definite Integrals

• Eight Solutions

In the set of eight problems there are four cards where the volume is created by
revolving a region about a line and four cards where the volume is formed on a
region and all the cross sections perpendicular to the x-axis have a common shape.

Give each group of students 24 cards (eight volume problems, eight graphs, and eight definite integrals). Students should read the volume problem and find the matching graph that could be used to solve the problem. For each pair of problems and graphs they should then find the matching definite integral.

Students should then solve each of the eight problems. When they have solved the eight problems, distribute the eight solution cards so they can confirm their
solutions as they match their problem, graph, integral and solution cards.

This is a great activity if you are reviewing for a unit test on related rates or preparing for the final exam or for the AP exam.  It is appropriate for both AB and BC
Calculus classes.

 Volume-Matching-Cards-for-Calculus

This is a great way for students to review their knowledge of finding bounded area in Calculus.

This set of Bounded Area Matching Cards is made up of

• Eight Bounded Area Problems

• Eight Riemann Graphs

• Eight Definite Integrals

• Eight Solutions

Give each group of students 24 cards (eight bounded area problems, eight graphs, and eight definite integrals).  Students should read the bounded area problem and find the matching graph that could be used to solve the problem.  For each pair of problems and graphs they should then find the matching definite integral. 

Students should then solve each of the eight problems.  When they have solved the eight problems, distribute the eight solution cards so they can confirm their solutions as they match their problem, graph, integral and solution cards.

This is a great activity if you are reviewing for a unit test on related rates or preparing for the final exam or for the AP exam.  It is appropriate for both AB and BC Calculus classes.

Bounded-Area-Matching-Cards