Lesson 1
Learning goal(s)
Students will be able analyze and solve linear equations and pairs of simultaneous linear equations by a graphical method
Evidence and assessment of learning (informal assessment, student self‐assessment, formal assessment)
The assessment usually conjures up the ability of a student to solve algebra equations. Now starting with some numbers if we begin to multiply a particular number by 10 and then divide it by 16 we get 20. So, the equation which gets to be formed is: 6x + 16 = 20.
Most teachers have a perception that students can solve these equations more easily than the words problems.
In this particular lesson, the student needs to recognize the consistency between the slopes which is derived from the graph of the given equation. If a certain graph is observed to be inconsistent, he or she should rectify his error. The student needs to acquire two factors,fluency as well as interpret the slope of the equation from the given function.
How does lesson link to prior learning and/or build on previous lesson to develop deep learning of content?
We have already learned several ways of graphing a linear equation in the form of slope intercept. We can utilize these slopes as well as y‐intercept or else derive the two intercepts and connect them with the help of a straight line.
Learning activities
(what students do)
Include, where appropriate, how you and your students will use educational technology.
Before starting off with this lesson teachers can inform the students how they can use Desmos to graph the intercepts and thus perform smart work rather than hard work.
They can also be instructed to use graphical calculators to complete the lessons more swiftly and efficiently.
Instructional strategies
(what you do, key questions, and grouping)
If there is a single equation we need to assume a certain value and check the consistency
If there are two equations we can solve both the equations and find the two intercepts.
We can utilize these slopes as well as y‐intercept or else derive the two intercepts, plot them in the graph and connect them with the help of a straight line.
ELD and ALD
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Adaptations/accommodations for students with specific learning needs
Student should try to exchange information and ideas through conversations and oral
communication.
Listen actively in the class and ask or answer to the teacher’s questions concerning what was actually heard.
Students should read closely and focus on explaining the interpretations and ideas from the reading.
They should compose or write some literary as well as informational texts
At the completion of Lesson 1: Based on what you learned as a result of teaching this lesson, what changes, if any, will you make to the next lesson?
Lesson 2
Learning goal(s)
Students will be able to analyze and solve linear equations and pairs of simultaneous linear equations by Substitution method.
Evidence and assessment of learning (informal assessment, student self‐assessment, formal assessment)
Substitution methods will help the students in solving linear equations for one variable at a time and then substitute them in another equation to find the other variable.
Students should also be provided with incorrect equations and the equations should be framed and labeled correctly so that it doesn’t confuse the student.
They should be allowed to discuss the equations and review them finding a reason why they are not correct. The students should be able to explain the steps which they implemented to determine the strategies
How does lesson link to prior learning and/or build on previous lesson to develop deep learning of content?
We have learnt to compare both the strategies that are used in solving the linear equations.
Providing the student with incorrect equation can help him determine the difference between correct and incorrect intercepts. It is necessary to encourage students to critically think about the different methods as well as steps they are implementing.
Learning activities
(what students do)
Include, where appropriate, how you and your students will use educational technology.
Technology can help a student to think critically and develop their skills by solving complex equations by the means of desmos.
Instructional strategies
(what you do)
Student has to follow the given steps:
Solving one equation first for one variable.
Using Step 1 in order to substitute the expression in another equation and thus solve for another variable.
Taking the help of Step 2, we need to substitute the value, into the original equation and thus solve in order to derive the value of the variable in Step 1.
ELD and ALD
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Adaptations/accommodations for students with specific learning needs
Student should try to exchange information and ideas through conversations and oral
communication.
Listen actively in the class and ask or answer to the teacher’s questions concerning what was actually heard.
Students should read closely and focus on explaining the interpretations and ideas from the reading.
They should compose or write some literary as well as informational texts
At the completion of Lesson 2: Based on what you learned as a result of teaching this lesson,what changes, if any, will you make to the next lesson?
Lesson 3
Learning goal(s)
Students will be able to analyze and solve linear equations and pairs of simultaneous linear equations by Elimination method.
Evidence and assessment of learning (informal assessment, student self‐assessment, formal assessment)
One variable can be eliminated by adding or subtracting both the equations. Thus, we can find the value of the remaining variable. The two same variables get eliminated from the different equations and both the terms should be equal.
When initially commencing group activities and model “how to work with a partner to discuss potential strategies, how to label the steps of each strategy, and how to explain the similarities and differences observed between strategies”.
How does lesson link to prior learning and/or build on previous lesson to develop deep learning of content?
The student either working in pairs or groups need to explain all steps of all the strategies that are implemented and also label the differences as well as identical equations to show that they are well accustomed with the tasks.
Learning activities
(what students do)
Include, where appropriate, how you and your students will use educational technology.
Same as substitution methods, Technology can help a student to think critically and develop their skills by solving complex equations by the means of graphical calculators or Intergraph.
Instructional strategies
(what you do)
Students need to add or subtract the equations in order to eliminate a variable.
Student need to solve the resultant equation for deriving another equation.
Then the value needs to be substituted into the original equation in order to derive the value of the eliminated variable.
ELD and ALD
Students need to solve real world as well as mathematical problems for two linear equations in two variables. “For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair”.
Adaptations/accommodations for students with specific learning needs
Student should try to exchange information and ideas through conversations and oral
communication.
Listen actively in the class and ask or answer to the teacher’s questions concerning what was actually heard.
Students should read closely and focus on explaining the interpretations and ideas from the reading.
They should compose or write some literary as well as informational texts.
At the completion of Lesson 3: Based on what you learned as a result of teaching this lesson, what changes, if any, will you make to the next lesson?
