Objective
Solve real-world and mathematical problems using systems and any method of solution.
Common Core Standards
Core Standards
The core standards covered in this lesson
8.EE.C.8.B— 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.
Expressions and Equations
8.EE.C.8.B— 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.
8.EE.C.8.C— 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.
Expressions and Equations
8.EE.C.8.C— 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.
Foundational Standards
The foundational standards covered in this lesson
8.EE.C.7
Expressions and Equations
8.EE.C.7— Solve linear equations in one variable.
8.F.B.4
Functions
8.F.B.4— Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Look for and make use of structure in equations to determine an efficient method to solve a system of equations (MP.7).
- Write a system of equations to represent a situation and interpret the solution in context.
- Solve systems of equations using any strategy.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Lessons 10 and 11 bring the concepts of the unit together. This is a good opportunity for students to focus on targeted concepts or skills where they still need practice or development.
Fishtank Plus
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Problem 1
Which method—graphing, substitution, or elimination—would you choose to solve each system below? Explain your answer.
| System A | System B | System C |
$${y={2\over3}x-6}$$ $${y=-{x\over4}+2}$$ | $${1.5x-6.2y=18.3}$$ $${1.5x+6.2y=-4.8}$$ | $${x=3(y+1)}$$ $${2x+4y=-7}$$ |
Guiding Questions
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Problem 2
The sum of two numbers is 361, and the difference between the two numbers is 173. What are the two numbers?
Write a system of equations to represent the information above. Solve it using any method.
Guiding Questions
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References
EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29—Example 1
Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 3
A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend, but we know that the quinoa in the blend contains 16.2% protein and the corn in the blend contains 3.5% protein. Overall, each 57-gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one 57-gram serving of the pasta?
Guiding Questions
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References
Illustrative Mathematics Quinoa Pasta 1
Quinoa Pasta 1, accessed on March 12, 2017, 6:53 p.m., is licensed by Illustrative Mathematics under either theCC BY 4.0orCC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Modified by Fishtank Learning, Inc.
Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Problem 1
Small boxes contain Blu-ray disks and large boxes contain one gaming machine. Three boxes of gaming machines and a box of Blu-rays weigh 48 pounds. Three boxes of gaming machines and five boxes of Blu-rays weigh 72 pounds. How much does each box weigh?
References
EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29—Exit Ticket, Question #1
Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 2
A language arts test is worth 100 points. There is a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary questions worth 5 points each. How many of each type of question are there?
References
EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29—Exit Ticket, Question #2
Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Include a variety of problems for students to solve, with and without context, that may be efficiently solved with the three different strategies.
- Challenge: Two friends travelalong astraight path towards one another. One friend starts at mile marker 0 and runs 6miles per hour. The other friend starts at mile marker 12. If the two friends meet up at mile marker 8after 1 hour and 20 minutes, how fast was the second friend traveling?
- Kuta Software Free Algebra 1 Worksheets Solving Systems of Equations Word Problems
- 101Questions Basketball Shots
- Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics (6-8 Expressions and Equations)—Problems on page 13
- EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29—Exercises and Problem Set
Lesson 9
Lesson 11
