Math Unit Template
El Rancho Unified School District
Topic/Main Idea:Solving linear equations and pairs of simultaneous linear equations. / CCSS: 8 Analyze and solve pairs of simultaneous linear equations.
- 8a. 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.
- 8b 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.
- 8c Solve real-world and mathematical problems leading to 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.
Objectives/Concept/Skill (DOK):1,2
- Understand that solutions to a system of two linear equations in two variables (Level 1)
- Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. (Level 2)
- Solve real-world and mathematical problems leading to two linear equations in two variables. (Level 2)
- Grade 6. EE.B.6 Expressions and Equations
- Grade 6. EE.B.7 Expressions and Equations
- Grade 7. EE.B3 Expressions and Equations
- Grade 7. EE.B4 Expressions and Equations
Performance Task/Activity (DOK): 3
DVD CLUB Problem
The DVD CLUB Problem involves students having to figure out through surveys and research the pricing of DVD’s for members and non-members. (Level 3) / Relevance/Rationale:
- Systems of Equations are used in practical problems in everyday life. They are used to determine when two people will have the same amount of money for the same amount of time, for example.
- This unit leads a foundation for developing systems of equations in three dimensions captured in Algebra 2 and Pre-Calculus.
SBAC Assessment Item References:
- Grade 8 Practice Test Questions #15 and #16
- Linear
- System of Equations
- Point of Intersection
- Solution, No Solution, or Infinitely Many Solutions
Textbook References (i.e., Homework Resources):
- Practice problems will be available in Algebra I Connections Chapter 4.
- Grid paper
- Rulers
- Calculators
Mathematical Practices
___X_ 1. Makes sense of problems and persevere in solving them. ____ 5. Use appropriate tools strategically. ____ 2. Reason abstractly and quantitatively. ____ 6. Attend to precision.
____ 3. Construct viable arguments and critique the reasoning of others. ____ 7. Look for and make use of structure.
___X_ 4. Model with Mathematics. ____ 8. Look for and express regularity in repeated reasoning.
Explanation:
- In solving a system, students will make sense of problems by explaining to themselves the meaning of the problem and looking for entry points to its solution. They will persevere in solving them.
- Students will model the mathematics as they analyze relationships mathematically to draw conclusions.
Lesson Topic: / LOL (Learning Objective with Language): / Resources (Instructional Strategies, Textbook References, etc.):
1. Connecting Linear Rules and
Graphs / “The Hills are Alive” problem. Students individually or in pairs will represent this problem with a system of equations. Solve the system and explain how its solution relates to the yodelers on the music trip. Students will need to represent this problem with a graph and identify how the solution to this problem appears on the graph. / “Tile Pattern Analysis”-Growth rate, rule, and graph.
Textbook: Algebra Connections Volume One Chapter 4, Pages 146-147, problems 4.18 – 4.20
2. Representation Web-Table,
Rule, Pattern, Graph / Students will check their connections by using pieces of information from different parts of the web (provided in book) by using pieces of information from different parts of the web to generate a complete pattern. Students will also work together as a team, and the more they listen to how other people see the connections and the more they share their own ideas, the more they will know at the end of the lesson. Each student will turn in their own paper at the end of this activity, showing four complete representations for each pattern by talking and agreeing that all explanations are correct. / “Team Challenge-Checking the Connections”
Textbook: Algebra Connections Volume One Chapter 4, Pages 152-153, problems 4.37 – 4.38
3. Graphing a Line Without an
Input/Output Table / Students will use an equation to create a graph without the intermediate step of creating an x-y table by graphing the following rules without first making a table for parts (a), and (b) (provided in their books ) by placing them on the same set of axes, as well as parts (c) and (d). Students will label each line with its equation, y-intercept (where it crosses the y-axis), and a growth triangle. / “Given various graphs to analyze in order to come up with how the pattern changes”
Textbook: Algebra Connections Volume One Chapter 4, Pages 156-157, problems 4.49 – 4.53
4. Writing Rules from Word
Problems / Students will analyze situations provided in their book on “Buying Bicycles” by using multiple tools that they have studied by using at least two different ways to find time (in weeks) when Latanya and George will have the same amount of money in their savings accounts. The students will also have to be prepared to share their methods with the class. / “Buying Bicycles”
Textbook: Algebra Connections Volume One Chapter 4, Pages 167-168, problems 4.76 – 4.79
5. Solving Systems Algebraically / Students will solve a system of equations algebraically by doing various problems to help them understand that graphing is not always convenient and accurate. / “Chubby Bunny” and “Changing Populations”
Textbook: Algebra Connections Volume One Chapter 4, Pages 169-171, problems 4.85 – 4.89