Algebra 1, Part 2

Multiplying polynomials is an important skill in algebra that helps us combine and expand expressions with variables and coefficients. It allows us to solve equations, simplify expressions, and explore mathematical relationships. One useful method for multiplying polynomials is using rectangles.

This method breaks down the multiplication process into simpler steps using rectangles. It helps us understand the concepts visually before using symbols and formulas.

In this module we will explore the various ways that algebraic situations are represented.  We will make the connections between a situation (tile pattern), table, equation (rule) and a graph.

Diamond Problems are an excellent way of practicing addition, subtraction, multiplication, and division of positive and negative integers, decimals and fractions. They have the added benefit of preparing students for factoring binomials in algebra. 

Algebra tiles are special tools that help us understand math problems in a hands-on way. They are like small blocks or tiles that represent different parts of a math equation.

There are different types of tiles. Some tiles represent regular numbers, like 1 or 2, and others represent letters that stand for unknown numbers, like "x". We can also find tiles that represent squares of numbers, which are like multiplying a number by itself.

Using these tiles, we can see how different parts of an equation fit together. We can arrange them to show how addition, subtraction, multiplication, and division work. For example, if we want to solve an equation or simplify an expression, we can move the tiles around and see how they change. This helps us understand what is happening in the math problem.

In Module 5, we will practice a strategy to help us solve a wide range of word problems.  Guess and Check challenges us to use our number sense to arise at an accurate solution in a logical and easy-to-understand way.

Proportions often arise when solving problems in Geometry. You will be asked to determine if a given proportion is true or what values for the variables contained within the proportion will make it true. Proportion are most easily solved by "cross-multiplying", and solving the resulting equation, whether it be linear or quadratic. Let's watch the video to examine what you may be asked to do and how to do it. 

Solving multi-step equations involves a series of steps to determine the value of the variable(s) in an equation that contains multiple operations. The goal is to isolate the variable on one side of the equation and find its numerical value.

In this module we take a look at how to graph linear equations given point-slope form or slope intercept form.

Evaluating expressions refers to the process of finding the numerical value of a mathematical expression by substituting given values for the variables and performing the necessary operations. An expression is a combination of numbers, variables, and mathematical symbols, such as addition, subtraction, multiplication, division, and exponentiation.

To simplify a fraction means to express it in its simplest or most reduced form. It involves reducing the numerator and denominator to their smallest possible values by dividing both of them by their greatest common divisor (GCD).

Sometimes we are given two linear equations, and we are asked to determine the point (if any) where the lines described meet, i.e cross one another; we called this the intersection point. There are three popular methods for doing this. They are: (a) substitution, (b) elimination and (c) graphing. In this module we examine the first of these - substitution.

With substitution, you solve one of the equations for one of the variables, and then substitute that quantity into the remaining equation. Let's watch the video to examine the method more closely.

Solving a system using linear elimination involves multiplying each equation by conveniently selected differing constants so that a variable will be eliminated when the equations are added or subtracted. Once a variable is eliminated, we solve for the remaining variable. Let's watch the video to examine the method more closely.

Solving a system via graphing involves plotting the lines on the Cartesian Plane using a calculator and using the Intersect feature to determine where (if at all) the lines have a common point, i.e. they cross (intersect) each other at that point. Let's watch the video to examine the method more closely.