Unit Plan

EDCP 342A Unit planning

Eric Lou

Richmond Secondary School, Math 9

Topic of unit: Linear Relationship and Inequalities

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Linear relationship and inequalities is vital in multiple areas of science in secondary teaching. There are a lot of topics that need students to apply certain knowledge of linear relations since many relations learned in introduction of physics, chemistry and biology are linear. Students need this part of knowledge to be able to solve for answers in science equations and do approximations in some special cases in science. On the other hand, linear relationship is the foundation of further learning the concept of balancing and solving equations. That makes knowledge of this chapter vital to learning grade 9 and higher-level math courses, especially pre-calculus and calculus 12. I hope students can fully understand the value and meaning of linear relationship and be able to solve basic linear equations and inequalities. They should have the capability to identify the application of linear relations in real-life situations and solve for answers. Students should be intrinsically motivated when they find out this topic is applied to many aspects of their daily life. Thus, they would understand that linear relationship is not hard to learn also quite important.

(2) A mathematics project connected to this unit: Unit Project(group of no more than 4): Students need to find a pattern they observed in some places other than math classes and identify at least one linear relationship inside the pattern. The resource of the pattern can be anything other than math class. They are encouraged to find some patterns from real-life situations, video games, comic books, TV shows or anything. They will be given some examples as height of stairs, their own height from year to year, the “coins” they spend on reviving their characters from video games at different levels, the weight of iron man suits of different models, etc. After they decide what their topic is, they would need to do their own research on that topic to find numbers and list their resources. Then they need to identify a pattern inside those numbers and find all the linear relations they can find inside the pattern. The next step is to model at least one of the linear relations and use some examples to prove it is correct. Since the patterns are from “real” cases, students will also need to explain why they think the numbers have that linear relation. They need to write a formal project report in no more than 4 pages. They are welcomed to include graphs and pictures in their report. Then they need to prepare a 10-minute group presentation to the whole class. During the presentation, each group need to listen carefully and do a peer assessment for each other group. They will be given the assessing rubric at the beginning of this project and they will use this rubric to assess other groups’ projects. Their final mark of the unit project would be: 70% project report + 20% peer assessment from other groups + 10% how they assessed other groups

(3) Assessment and evaluation:  Check students’ reactions during the lesson to see if they understand the concepts and steps. Make some adjustments of pacing if necessary.  During the in-class practice, walk around the classroom to check on their individual working status and see if anyone need additional help on understanding or calculation. Check the homework of prior class for their completion and understanding. Check students’ project reports and their peer reviews to check their understanding of this unit and their ability to assess others’ projects. Mark their unit tests. Give back the unit tests and let students make corrections and hand those test back to teacher.

Lesson	Topic
1	Understanding Linear Equations
2	Solving Basic Equations
3	Removing Fractions, Decimals and Parentheses
4	Linear Inequalities
5	Adding and Subtracting Linear Inequalities
6	Multiplying Linear Inequalities
7	Applications of Linear Equations
8	Applications of Linear Inequalities
9	Unit Project Introduction and Work Block
10	Unit Review #1 and Work Block
11	Project Report
12	Unit Review #2 and Unit Test

Math 9 Understanding Linear Equations Lesson Plan

Subject: Math	Grade: 9	Date: Jan 29th, 2018	Duration: 80 min
Lesson Overview	•   The lesson will talk about linear relationship •   Students will learn what is a linear relationship and where can they find the application of that in real-life situations
Class Profile 2-2 2-3	•   Students have just finished a unit on polynomials, they have learned how to add/ subtract/ multiply/ divide polynomials. They have already done some problems of solving linear equations in their previous homework without know that. •   29 students, 16 male and 13 female •   23 students, 10 male and 13 female

Big Idea

•   The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

Curriculum Competencies

•   Apply multiple strategies to solve problems in both abstract and contextualized situations •   Visualize to explore mathematical concepts

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	•   Briefly myself and the experience I had when I was learning this unit. Tell students that I’ve also had some problems while I was learning these concepts. So, it is normal for them to be confused at first. But they can feel free to ask me any questions they have and improve their understanding on this unit. •   Review the content of last class. Show 6 equations on the projector (or write them on the whiteboard if technology fails) and let students identify if they are true or false. There are three true equations, one false equation and two equations that are neither true or false because there are variables in them. After they have answers, let them explain why. For the equations that students are not sure true or false, give students two numbers to replace the variables then let them decide whether the equations are true or not. And introduce the topic of today’s class: understanding linear equations. •   After introducing the topic, let the students form groups of no more than 4 people (2 tables). Give each group a K-W-L-Q chart. Let the students discuss what they already know and what they want to know about the topic (K and W). After 3 minutes of discussion, each group will write the thoughts on their chart. Walk around and observe their discussion. •   Let students volunteer and write down some Ks from their group discussions on the whiteboard. Talk about the things they have written down on the whiteboard and make some corrections (if any). •   Then let them share things they want to know the most and try to make sure to cover those parts in the lesson. If that is not practical, try to include those things in next lesson.	15 min
2.	Addition Principle	•   Give students the set of notes and algebra tiles. •   Let students take a look at the first 3 pairs of linear equations. They are equivalent equations for each pair that can be transformed by using addition. Let them talk about what they have noticed and share their ideas with their neighbours. •   Don’t give them answers. Let the students try to model those expressions using algebra tiles, see if the answers matches what they’ve noticed. •   Introduce the addition principle: for any real numbers a, b and c: a = b implies that a + c = b + c •   Lead the class to solve the first two questions using the addition principle, make sure to go over every step and every detail. Explain your thoughts for each step. Keep paying attention to students reactions to see if you need to repeat some of the steps one more time. •   Take a volunteer to do the next question on whiteboard to check their understanding. •   Give them five minutes to work on the forth and fifth question.	20 min
3	Multiplication Principle	•   Let students take a look at the next 3 pairs of linear equations. They are equivalent equations for each pair that can be transformed by using multiplication. Let them talk about what they have noticed and share their ideas with their neighbours. •   Don’t give them answers. Let students plug in same number for the variables in those equations and check if they had the correct ideas. •   Introduce the multiplication principle: for any real numbers a, b and c: a = b implies that a * c = b * c •   Lead the class to solve the first two questions using the multiplication principle, make sure to go over every step and every detail. Explain your thoughts for each step. Keep paying attention to students reactions to see if you need to repeat some of the steps one more time. •   Take a volunteer to do the next question on whiteboard to check their understanding. •   Give them five minutes to work on the next two questions.	20 min
4.	Algebra Tiles and Applications	•  Solve the next two linear equations using algebra tiles •  Let students solve two questions using algebra tiles •  Then tell students to clean up and put the algebra tiles back in the box. •   Show students some applications of linear equations in addition, subtraction, multiplication and division. •  Then let the students work on the rest of the questions on that page or exercise 6.1. Check their homework from last class and answer questions if they have any. Then work around and check how they are doing. Explain certain steps if someone is confused.	15 min
5.	Closure	•   Ask the students to go back to their groups to finish their K-W-L-Q charts: have a quick discussion for 3 minutes and write down what they have learned in this class and what questions do they still have for this topic. •   Let them share the things they have on those charts and try to answer the questions they still have. •   Assign exercise 6.1 and the rest of questions on notes as homework. Tell them I will check their homework for completion next class.	10min

Materials and Equipment Needed for this Lesson

•   Notes •   KWLQ charts •   Slides •   Projector •   Markers •   White Board

Assessment/Evaluation of Students’ Learning

•   Check students’ reactions during the lesson to see if they understand the concepts and steps. Make adjustments of pacing if necessary. •   During the in-class practice, walk around the classroom to check on their individual working status and see if anyone need additional help on understanding and calculation. •  Collect their KWLQ charts to see if they still have any questions •  Check the homework next class for their completion

Math 9 Applications of Linear Equations Lesson Plan

Subject: Math	Grade: 9	Date: Feb 14th, 2018	Duration: 80 min
Lesson Overview	•   The lesson will talk about application of linear equations •   They will learn about patterns of number that have linear relations
Class Profile 2-2 2-3	•   Students have learned linear equations and inequality •   29 students, 16 male and 13 female •   23 students, 10 male and 13 female

Big Idea

•   The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

Curriculum Competencies

•   Apply multiple strategies to solve problems in both abstract and contextualized situations •   Visualize to explore mathematical concepts

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up + “Boring” application of linear equations	•   Review the content of last class. Show 3 linear equations on the projector (or write them on the whiteboard if technology fails) and let students solve those equations. •   And introduce the topic of today’s class: application of linear equations •   Show them two word problems on application of linear equations and give them 5 minutes to work on them •   They can check with their neighbors to see if they have the same answer when they are finished •   Solve the two questions in front •   Ask students if this is too boring for them and introduce our special topic today : arithmetic sequence	25 min
2.	Application of inequalities (arithmetic sequence)	•   Give students the set of notes. What is an arithmetic sequence (a, d, and n)? What is a finite arithmetic sequence? (2, 5, 8, 11) (Use examples from warm-up) What is an infinite arithmetic sequence? (3, 6, 9, 12, 15...) It is harder to locate a specific term in an infinite sequence by counting them. What should we do? ---- Find a general formula! Given t1=a, t2, and t3: Generate a formula for t2 and t3 in terms of a(t1) and d Predict what t4 and t5 will be Predict what t10 will be Find a formula for tn (let students guess first) Tn = t1 + (n - 1)d                      = tn-1 + d ·       Note that it is a linear function(link to previous lessons if possible) Special Cases: If the given terms are not adjacent, how do we find a and d? Example: Given T2, T5, T7	25 min
3.	Activity	Arithmetic sequence activity: Students pair up Part I On a sheet of paper, list two sets of uncompleted sequences with the first, second, and fourth terms (with positive common difference that is a whole number) Exchange their sequences with another group Find the third and fifth terms of the given arithmetic sequence Find a, d, and the formula for Tn Part II Make two more sequences on another sheet of paper. This time they need to have a negative common difference or a common difference that is not a whole number Exchange their sequences with other groups and solve for the same things	40 min
4.	Closure	•   Assign exercise 6.6 as homework. Tell them I will check their homework for completion next class. •   Let students work on the homework for the last 15 minutes of class.	15min

Materials and Equipment Needed for this Lesson

•   Notes •   Slides •   Projector •   Markers •   White Board

Assessment/Evaluation of Students’ Learning

•   Check students’ reactions during the lesson to see if they understand the concepts and steps. •   Check the sequences they have to see if their understanding is limited •   Check the homework next class for their completion

Math 9 Applications of Linear Inequalities Lesson Plan

Subject: Math	Grade: 9	Date: Feb 16th, 2018	Duration: 80 min
Lesson Overview	•  The lesson will talk about application of linear inequalities •   They will play a scavenger hunt on graphing inequalities
Class Profile 2-2 2-3	•  Students have learned how to graph a linear inequality •   29 students, 16 male and 13 female •   23 students, 10 male and 13 female

Big Idea

•   The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

Curriculum Competencies

•   Apply multiple strategies to solve problems in both abstract and contextualized situations •   Visualize to explore mathematical concepts

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	•   Review the content of last class. Show 3 inequalities on the projector (or write them on the whiteboard if technology fails) and let students solve those equations. •   Then let students graph those inequalities on their own graphing paper. •   And introduce the topic of today’s class: application of linear inequalities	10 min
2.	Application of inequalities	•   Give students the set of notes. •   There are two images of flags on that note. •  Identify the linear equation of each line on the flag and let students identify the inequalities behind coloring the flags •  They can have a discussion on how to use inequality to draw these flags •  Divide students into groups of no more than 4 people. They will have 15 minutes to draw one flag they really like (it can be a national flag, a flag from a game or any other flags as long as it is appropriate). •   They need to have some equations and inequalities to explain the process of drawing the flag. They can also explain what do the shapes represent.	25 min
3.	Scavenger Hunt	•   Objective: To practice graphing linear inequalities given in standard form. Vertical and horizontal lines included. •   Print 20 stations and scatter around the room (and in the hallway if possible but not too far). •   Distribute the recording worksheet to each student, then place students in groups of 2-3 and assign a random starting problem. Students scan the QR code on the card to reveal the problem. •   They must convert to slope-intercept form, graph, and shade the inequality. Their graph will lead them to the next problem. •   They will continue until they have looped through all 20 stations. •   When they finish, they can show teacher the recording sheet that is finished. And the first three student who finish the game will get a price.	35 min
4.	Closure	•   Assign exercise 6.7 (unit review) as homework. Tell them I will check their homework for completion next class. •   Let students work on the homework for the last 10 minutes of class.	10min

Materials and Equipment Needed for this Lesson

•   Notes •   Slides •   Projector •   Markers •   White Board

Assessment/Evaluation of Students’ Learning

•  Check students’ reactions during the lesson to see if they understand the concepts and steps. •  Check their flag project to see if they understand how to graph inequalities •   Check the homework next class for their completion