Algebra 2 Course Lesson 4 Solving Linear Equations
Created: Feb 24, Updated: Mar 7, Lesson 1: Solving two step equations with fractional answers - moving into forming and solving equations with algebraic perimeter. Lesson 3: Solving linear equations with two unknowns - moving into forming and solving linear equations with shapes. Lesson 4: Solving all of the above with fractions. ABCD assessments, a main activity and an more challenging task to be used as a plenary.
Read more. Report a problem. View more. How can I re-use this? Worry free guarantee. Solving Linear Equations 4 Lessons no rating 0 customer reviews. Share Email Post. Lesson 1: Solving two step equations with fractional answers - moving into forming and solving equations with algebraic perimeter Lesson 2: Solving linear equations involving fractions - moving into a peer assessment activity Lesson 3: Solving linear equations with two unknowns - moving into forming and solving linear equations with shapes Lesson 4: Solving all of the above with fractions.
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Linear Equations Lesson
Other resources by this author. Popular paid resources. Updated resources.Part of my class routine is a do now at the beginning of every class. Students walk into class and pick up the packet for the day.
They get to work quickly on the problems. Often, I create do nows that have problems that connect to the task that students will be working on that day.
For this lesson I want students to start thinking about the concept of equality and reviewing algebra vocabulary. I ask for a volunteer to read number 1a. How did you find your answer? A common mistake is that students put 7 in the blank because they see 15 as the answer to the expression on the left.
I want students to understand that the equal sign indicates that the expressions on both sides of the equal sign must equal the same value when you simplify them. I ask for students to share out answers and strategies for b and c. I ask for a student to read 2 and share an answer choice that does not match the description. After the Do Now, I have a student read the objectives for the day. I tell students that they will again be solving one and two-step algebraic equations and creating equivalent expressions.
I have a volunteer read the shopping problem. Before students start working, I ask a student to make a reasonable estimate of about how much one pair of jeans will cost. I ask another student whether or not that estimate is reasonable. I have students work independently for a few minutes to answer the problem and write the equation.
I walk around and monitor student progress. I ask for a student to share how much one pair of jeans cost. How did you figure that out? Why did you do that? Did anyone solve this problem differently? I will call on students to share out their equations and post them on the board. Some possibilities are I want to address this misunderstanding before we move on. I introduce the concept of an equation having to parts that are balanced or equal. I connect this to their work on 1 on the do now and to the idea of a balance where there are two items that weigh the same amount.
By using the bag of money instead of a variable and coins, students can connect more easily with the concept of finding the value of the unknown. We work through together on page 4. Students can usually quickly identify the number of coins in the bag in these examples. Students work on number on page 5 independently for a couple of minutes. I monitor student progress and look at the equations students are writing.
If students are struggling with the equations I put four possible equations up for that problem 2 correct and 2 incorrect. I tell students to brainstorm with their partner which of the equations match what is going on in the problem. Students share out ideas and we identify the correct equations and add to them if students have other ideas. A volunteer reads the definition of equivalent expressions and the examples. Together we work through problem 1 and 2 together.
It is using a variable, but it is still repeated addition.Linear equations are equations involving only one variable, like x or y, and they do not involve anything complicated like powers, square roots, or anything like that. Some people think that since linear equations are the simplest equations that students encounter, they are the easiest to learn.
But nothing could be further from the truth. Linear equations are hard to learn and their reputation is well deserved. The reason for this is that linear equations are the first opportunity to practice operating with equations and develop equation solving skills. So if you are frustrated with linear equations, you are most likely not stupid and in a good company.
This easy word problem captures the essense of all linear equations. Whenever you are stuck with some linear equation, just remember Bob and his apples.
How do you solve it? Let us write the solution in words, so that you would not be bothered with mathematical forms. All you need to know is your arithmetics. First of all, have Bob eat the three apples from his pocket.
How many apples would be left? If you still remember arithmetics, since he had 33 apples and ate 3, he would have apples left, that is, 30 apples would be left in sacks. I hope that you now feel that you are making progress. What you know is that you have three equal sacks, which altogether have 30 apples. How many apples are in each sack? As should be apparent, you have to split 30 into three equal parts, that is divide 10 by 3.
The result is This means that each sack has 10 apples. Here's your answer! Now let's go back to our friend Bob and his apples. Let's try to rewrite the problem in form of an equation. As you can see, the first thing you do in problems like that is to write an equation. This equation simply restates the problem, but in mathematical language instead of English.
Because in the old times ink was expensive, mathematicians did not like to write long names like "apples", so they use letter x or some other letters instead of "apples" and such.
Linear Equations Teacher Resources
To solve equations like this, you have to get rid of whatever surrounds x.Username: Password: Register in one easy step! Reset your password if you forgot it. Algebra: Equations Section. Solvers Solvers. Lessons Lessons. Answers archive Answers. I will start with the following example.
The left side of the equation is an expression, which is to the left of the equal sign. The right side of the equation is an expression, which is to the right of the equal sign. Terms containing variable x are called variable terms ; terms containing the numbers only are called constant termsor simply constants. The equation under consideration is called a linear equationbecause its both sides are linear polynomials.
The solution of an equation is such a value of the variable x that turns the equation into a valid equality when this value is substituted to both sides.
I am explaining below how to solve this linear equation, in other words, how to find the unknown value of the variable x. The first step you should do is to simplify both sides of the equation by collecting the common terms containing variable x and the common constant terms separately at each side of the equation. Let us do it. Thus, now the left side is 7x - Making similar calculations at the right side of the equation, you will get the right side 4x - 4.
The first step is done. The second step is to collect terms containing variable x in one side of the equation and make the other side of the equation free of variable terms. Subtract 4x from both sides. Collect common terms. Very good, now the term with the variable xwhich is 3x in this case, is in the left side and there are no terms with the x at the right side. The second step is done. The third step is to collect all the constant terms in the right side and make the left side free of constants.
Add 10 to both sides.Linear equations are the simplest equations that you'll deal with. You've probably already solved linear equations; you just didn't know it. Back in your early years, when you were learning addition, your teacher probably gave you worksheets to complete that had exercises like the following:. Once you'd learned your addition facts well enough, you knew that you had to put a " 2 " inside the box. Solving One-Step Equations.
Solving equations works in much the same way, but now we have to figure out what goes into the xinstead of what goes into the box. However, since we're older now than when we were filling in boxes, the equations can also be much more complicated, and therefore the methods we'll use to solve the equations will be a bit more advanced.
In general, to solve an equation for a given variable, we need to "undo" whatever has been done to the variable. We do this in order to get the variable by itself; in technical terms, we are "isolating" the variable. This results in the equation being rearranged to say " variable equals some number ", where some number is the answer they're looking for.
For instance:. The variable is the letter x. To solve this equation, I need to get the x by itself; that is, I need to get x on one side of the "equals" sign, and some number on the other side. Since I want just x on the one side, this means that I don't like the "plus six" that's currently on the same side as the x. Since the 6 is added to the xI need to subtract this 6 to get rid of it. That is, I will need to subtract a 6 from the x in order to "undo" their having added a 6 to it.
No matter what kind of equation we're dealing with — linear or otherwise — whatever we do to the one side of the equation, we must do the exact same thing to the other side of the equation. Equations are like toddlers in this respect:. We have to be totally, totally fair to the two sides, or unhappiness will ensue! Probably the best way to keep track of this subtraction of the 6 from both sides is to format your work this way:.
The above image is animated on the "live" page. What you see here is that I've subtracted 6 from both sides, drawn a horizontal "equals" bar underneath the entire equation, and then added down.
On the left-hand side LHS of the equation, this gives me:. The same "undo" procedure works for equations in which the variable has been paired with a subtraction. The variable is on the left-hand side LHS of the equation, and it's paired with a "subtract three". Since I want to get x by itself, I don't like the " 3 " that's currently subtracted from it.
The opposite of subtraction is addition, so I'll undo the "subtract 3 " by adding 3 to both sides of the equation, and then adding down to simplify to get my answer:. You may be instructed to "check your solutions", at least in the early stages of learning how to solve equations. To do this "checking", you need only plug your answer into the original equation, and make sure that you end up with a true statement.
This is, after all, the definition of the solution to an equation; namely, the solution is any value, or set of values [for more complicated equations, later on], which makes the original equation a true statement. So, to check my solution to the above equation, you'd plug " —2 " in place of the x in left-hand side LHS of the original equation, and check that this simplifies to give the original value for the right-hand side RHS of the equation:.
Because each side of the original equation now evaluates to the exact same thing, this confirms that the solution is indeed correct. This time, the variable is on the right-hand side RHS of the equation.Students will answer three clicker questions on Flipchart - p.
Solving Linear Equations
Preparation: To access the video linked below you will need an account on the SAS curriculum pathways website. Just follow the video link below and you can create a free account from that page. Before students begin their work today, I am going to help them to activate their prior knowledge of solving systems of equations by showing them a quick video.
I like how this video describes solving systems of equations in such a concise way. It also gives students a great side-by-side graphical and algebraic view of each solution as it proceeds. Draw a sketch of two graphs to justify your answer. My goal for this section of the lesson is for students to complete one 4-way Problem where they model a solution in three different ways. I sequenced them so that A is the easiest and D is the most difficult. I am going to place 1 copy of each problem at every table teams of 3 per table.
The students can work together to choose which problem each of them will work on. I place two restrictions on the activity: a two people at the same table cannot work on the same problem and b calculators should not be used. But, each student will be responsible for solving one of the four problems. As I monitor the classroom, I will encourage students to explain how they know that all four representations model the same solution.
At the end of the period, students will take a 5 question clicker quiz independently. This will help me to know which students may need extra assistance. Empty Layer. Home Professional Learning. Professional Learning. Learn more about. Sign Up Log In. SWBAT solve a system of non-linear equations both algebraically and graphically.
Big Idea Students model their solutions to non-linear systems in multiple ways. Lesson Author. Grade Level. Precalculus and Calculus. Construct a viable argument to justify a solution method. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP6 Attend to precision. MP7 Look for and make use of structure. Warm-up: Clicker Questions 3 minutes. Video: Solving Systems of Equations 10 minutes.
Narrative: Before students begin their work today, I am going to help them to activate their prior knowledge of solving systems of equations by showing them a quick video. Student worksheets - non-linear systems 4-way models. Closure: Clicker Quiz 10 minutes.
Flipchart - non-linear system of equations p. Previous Lesson.Lesson Topic. IM Lesson. Khan Academy Support Videos.
Khan Academy Online Practice. Class Notes. Lesson 1 — Number Puzzles. Lesson 1. Morgan 8. Lesson 2 — Keeping the Equation Balanced. Lesson 2. Lesson 3 —Balanced Moves. Lesson 3. Intro to Equations with variables on both sides. Equations with variables on both sides. Lesson 4 — More Balanced Moves. Lesson 4. Equations with parentheses. Lesson 5 — Solving Any Linear Equation. Lesson 5. Lesson 6 — Strategic Solving.