Check out these new bundles in my store.  

New Activity Sheets being added every day.

Almost every day I have been uploading new activity sheets for Algebra I.  

Here is a list of six activity sheets I have uploaded that deal with Solving Linear Equations.

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

Activity-Sheet-on-Solving-Two-Step-Equations

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

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

Activity-Sheet-on-Writing-Ratios-and-Solving-Proportions

Activity-Sheet-on-Solving-Literal-Equations

You can also purchase all six activity sheets in a bundled package at a reduced price.

A-Bundle-of-Activity-Sheets-on-Solving-Linear-Equations

Almost every day I add additional Activity Sheets for Algebra to my store Math-Through-Discovery-Llc.

These activity sheets can be used as the basis of a lesson, a homework assignment, or a worksheet.  Each sheet usually has 20 exercises.  Each Activity Sheet comes with a full set of solutions.

Three of the latest Activity Sheets include

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

This set of Related Rates Matching Cards is made up of

• eight related rate problems

• eight equations

• eight related rate equations

• eight solutions

Give each group of students 24 cards (eight related rate problems, eight equations, and eight related rate equations).  Students should read through the related rate problems and find the matching equation that could be used to solve the problems.  Then they should match the related rate equations that can be generated from the equation using implicit differentiation. 

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.

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

Related-Rates-Matching-Cards

If you have two solid that have identical bases and height but one is a prism and one is a pyramid, students will often look at the two shapes and say that the pyramid will fit in the prism exactly twice.  Most students don't even think it could be three times. 

I have filled a square prism and square pyramid with water and the students are shocked that the pyramid fits in three times.  They can't figure out how that can work.

With this product you can show the students how the three pyramids fit into the square prism.  After students have seen this model, they never forget that the pyramid fits in the prism three times. 

Build-a-Model-Volume-of-a-Square-Prism-and-Volume-of-a-Square-Pyramid

As you are thinking about starting the new year in AB Calculus, BC Calculus or just a regular Calculus class you might want to check out this product.  

These five lessons are designed to be used in five 40 minute periods to introduce students to the 5 main topics they will be studying for the next year.  

1. Instantaneous Rate of Change
2. Behavior of a Function
3. Definite Integrals
4. Using Formulas to find Definite Integrals
5. Limits

Each lesson is designed to use the graphing calculator to building understanding for the five topics graphically, numerically, analytically, and verbally. Each lesson is designed to be completed in one regular class period of 40-50 minutes.

A two question assignment is also included.

Answers to all activities are included.

This is a great way to begin a study of calculus.


Jet-Tour-of-Calculus-Five-Days-of-Lessons-Bundled

This is a really fun activity to do with students. You take a given picture (run two-sided), cut it apart into 9 or 16 pieces, distribute one piece to each student, and then give students directions to either enlarge the square they just received, reduce the square they have just received, or distort the square they have just received.

After they have completed their new square the students use the codes on the back of their original square to reconstruct the cartoon.

This activity really helps students understand how enlargements, reductions, and distortions are achieved.

You can display the original and the new image on the wall of your classroom.

Making-an-Enlargement-Reduction-or-Distortion-of-a-Cartoon

These two products were designed to be used by students in both AB and BC calculus classes to review all the concepts they have learned over the year.  But a recent purchaser wrote that

• I wanted to review Calculus. This was a great help! Thank you.

The product has had many positive reviews:

• Nice Review
• This is a great product!
• Great exam recap.
• I which I had found this a bit earlier in the year last year. My students love it, but wished they had it about a month earlier. I will be using it at the beginning of the second semester this coming year. Thanks !!!
• Kids felt that this really helped them focus their study for the AP Exam. Got them thinking about what they need to do for given problem situations.
• I am using this activity with my AP Calc AB class as we review for the AP exam. It has been very helpful in getting the students to really think about what they do when they see certain words. It brings the Calc AB concepts together in one activity, giving the students a great review sheet in the end.

AB-Calculus-Final-Review

BC-Calculus-Final-Review

This is a day 2 lesson-activity for AP Calculus.  In just 5 days you can introduce your calculus students to the five many concepts they will be learning about.  

What is in the lesson-activity?

This lesson is made up of an 40-50 minute activity and a 2-page homework assignment with 2 questions similar to those in the activity. Answers to all activities are included. 

How have I used it?   

Behavior of Functions was designed to have students think about how the behavior of a function is changing.  This lessons has the students study the behavior of four functions they have seen since Algebra 2.  I encourage students to see if they can make a sketch without a graphing calculator, but then I also encourage they them to use their graphing calculator to build a window that matches the given graph and then make a sketch from their calculator.  (Notice these windows are not standard windows - a skill students must use on the AP test.)  After creating the four graphs, students are asked to draw a tangent line on each graph at x = 1 and use their graphs to approximate the slope of the tangent line.  Students are asked to describe how the behavior of the function at x = 1 on each graph.  Depending on the slope students could say the graph is increasing, decreasing or neither and relate that to the slope of their tangent line. 

This is a one day lesson-activity that is part of a larger package known as a Jet Tour of Calculus.  

The Jet Tour of Calculus is a set of five one-day lessons, where students are introduced to the five main topics of Calculus,  AB Calculus, and BC Calculus.   The titles of the five lessons are  

1. Instantaneous Rate of Change

2. Behavior of a Function

3. Definite Integrals

4. Using Formulas to find Definite Integrals

5. Limits

The five lessons can be purchased separately or in a bundle.  

Each lesson is designed to engage students in using their graphing calculator to building understanding for the five topics graphically, numerically, analytically, and verbally.  The concept of the five topics is emphasized but the notation does not need to be emphasized since you will be returning to each of these topics to study them further. Upon completion of the five lessons students gain a strong understanding of what they will be studying in the year of calculus that is ahead for them.

The product is for sale at https://www.teacherspayteachers.com/Product/Behavior-of-Functions-Day-2-of-a-Jet-Tour-of-Calculus-1406541 

This is a one day lesson that is part of a larger package known as a Jet Tour of Calculus.

The Jet Tour of Calculus is a set of 5 one day lessons, where students are introduced to the five main topics of Calculus,  AB Calculus, and BC Calculus.   The five lessons are:

1. Instantaneous Rate of Change
2. Behavior of a Function
3. Definite Integrals
4. Using Formulas to find Definite Integrals
5. Limits

The five lessons can be purchased separately or in a bundle.

Using Instantaneous Rate of Change:

The lesson can be used several different ways.  You can first separate the students into groups or pairs and have them work through a question about the height of a rocket.  Then bring the class back together for a discussion about what the tables of values are describing about the various average rates of change.  Or you can guide the students through the questions as a class, allowing them to use their graphing calculators to complete the tables.

This first lesson, Instantaneous Rate of Change, introduces the concept that average rates of change can lead to finding the instantaneous rate of change on any function by making the change in x smaller and smaller.  The first real world problem is focused around studying the height of a homemade rocket after it fired from a platform 400 feet above the ground at an initial speed of 300 ft/sec.    Students are asked to make a sketch of a possible graph for the height of the rocket as a function of time.  Then students are presented with a possible equation for the height of the rocket as a function of time, which they are asked to use their graphing calculators to find the graph.  Students are then challenged to think if they can find the instantaneous rate of change of the rocket at exactly 1 second after it was fired from the platform.

Using four different sets of table values, students notice they can approximate the instantaneous rate of change of the rocket at 1 second after the rocket is fired, by making decrease from the change from 0.1 to 0.01 to 0.001 to 0.0001 to 0.000001 to 0.0000001.  Then students are challenged to use similar tables to approximate the instantaneous rate of change at the rate at time when the rocket is at the same height it was at 1 second?  Students notice that the two approximations are opposite of each other because at the first time the rocket is rising and at the second time the rocket is falling.

This lesson is made up of an 40-50 minute activity and a 2-page homework assignment with 2 questions similar to those in the activity. Answers to all activities are included.

Each lesson is designed to engage students in using their graphing calculator to building understanding for the five topics graphically, numerically, analytically, and verbally.  The concepts of the five topics are emphasized but the notation does not need to be emphasized since you will be returning to each of these topics to study them further. Upon completion of the five lessons students gain a strong understanding of what they will be studying in the year of calculus that is ahead for them.

Comment from a buyer:  I liked this lesson,so I returned to buy the set of all 5-lessons.

Another buyer stated that they enjoyed using the five day jet tour because it is a great foundation for their students.

These 24 task cards can be used to review the concepts for the PARRC exam.  This set comes with a full set of answers/solutions and sheets of QR codes that students can use to self check their answers.  The QR codes are printed on separate cards so the teacher is in control as to when a student has access to the codes.  Check these out in my store at Teachers Pay Teachers.  https://www.teacherspayteachers.com/Product/High-School-Geometry-Task-Cards-3729926 

Congruent-Triangles-Task-Card-Bundle

This set of task cards has recently been updated and now includes two identical sets of cards.  One set has the QR codes on the card and the other set of identical questions have no QR codes.  An activity can be made that includes some QR codes and other cards that do not have QR codes.  Full solutions are included for all cards.