math through discovery

Thursday, March 7, 2019


Are you wondering how to teach Calculus students are slope fields?
Are you wondering what a slope field is?
Are you looking for some classroom materials to use to teach slope fields?
Does your textbook lack much information on slope fields?

Then you will probably want to check out this bundle or any of the seven individual products included in the bundle.

https://www.teacherspayteachers.com/Product/Slope-Field-Bundle-3145676




Many new teachers and experienced teachers are looking for ideas for teaching the concept of multiplying monomials and binomials or factoring polynomials.  I have created 12 lessons on these concepts.  Each lesson includes an explanation of the technique being studied and a set of problems for the students to complete based upon the explanation.  The idea presented in the explanation could become part of the teacher's presentation of the topic.  Or the teacher can hand the explanation to the students and have them study it explanation on their own.  Each lesson comes with a complete set of answers. 

The rectangular box method is used to complete the multiplication of binomials.  After students become comfortable with multiplying binomials, students are challenged with trying to find two binomials that multiply together to make a trinomial.  Students are encourage to try to use the rectangular box method in reverse.  As students work with the rectangular box they discover that they need to take the middle term of the trinomial and split it into two monomials.  Students look for four greatest common factors and then confirm that the two binomials they have found do multiply together to make the trinomial. 

These 12 lessons can be purchased separately or at a reduced price at a bundle. 

The 12 lessons are
1.Multiplying Monomials
2.Multiplying Monomials and Binomials
3.Multiplying General Binomials with Leading Coefficients of 1
4.Multiplying Binomials with Leading Coefficients of 1
5.Looking for Patterns When Multiplying Binomials with Leading Coefficients of 1
6.Multiplying Binomials with Leading Coefficients Not Equal to 1
7.Multiplying Special Binomials
8.Practice Multiplying Binomials
9.Reverse Multiplying (Factoring) Polynomials with Leading Coefficients of 1
10. Reverse Multiplying (Factoring) Polynomials with Leading Coefficients Other than 1
11. Factoring by Grouping
12. Factoring into Monomials and Binomials












https://www.teacherspayteachers.com/Product/12-Bundled-Lessons-on-Multiplying-and-Factoring-2463600

Wednesday, October 10, 2018

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.















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







Thursday, October 4, 2018

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


Sunday, September 16, 2018


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

Wednesday, September 12, 2018



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