Lesson Title: 8.EE.C.8b Solving Systems with Substitution
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 8
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical
Practices do you expect students to engage in during the lesson?
8.EE.C.8 Analyze and solve pairs of simultaneous linear equations.
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
solutions because 3x  2y cannot simultaneously be 5 and 6.
MP1:
MP2:
MP3:
MP4:
MP5:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students recall strategies used to solve the
baseball shop task. What did the strategies have in
common?
(Look for evidence of MP4.)
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
How can substitution be used to solve a scenario involving
system of equations? How does the substitution strategy
relate to representing a system algebraically?
(Look for evidence of MP7.)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Note: This lesson should follow the Baseball Shop Task or a similar investigation.
1. Discuss the lesson launch. Tell students that today we will be making connections between the problem-solving
strategies used in the baseball shop task and some algebraic strategies that can be used to solve problems
involving systems of equations. (Look for evidence of MP1, MP4, and MP7.)
2. Introduce the following scenario to students: At a local movie theater, you can buy two large sodas and a box of
popcorn for $11.00. If you only want one large soda and a box of popcorn, it will cost $8.00. How much does
the popcorn cost? Have students think-pair-share to solve the problem. Discuss strategies used to solve the
problem. How are these strategies similar to the strategies used in the baseball shop task? [Students should be
recognizing that in order to solve the problem, quantities are being substituted into the other scenario to help find
a solution. Substitution is a method of replacing quantities with equivalent quantities to help find a solution.]
(Look for evidence of MP3.)
3. Have students write equations to represent the scenario. [Note: This may be the first point in the lesson that
variables are introduced.] Sample equations: let x = cost of a large soda and y = cost of a box of popcorn.

 2x  y  11

 x  y  11

4. Now have students connect the algebraic representation with the strategy used. For example, if students said,
“Since one large soda and a box of popcorn is $8.00, then one additional soda must be $11.00-$8.00 or $3.00,”
then have students see that this is equivalent to:
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 8.EE.C.8b Solving Systems with Substitution
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 8
Start/end times: _________________________
x  (x  y)  11
x  8  11
x3
(Look for evidence of MP2, MP3, MP6, MP7, and MP8.)
5. Once the solution is verified with substitution, have students examine the problem graphically either by and or
with a graphing calculator (if this strategy has not already been discussed). Students should be verifying that the
solution to the system is the intersection point on the graphs. (Look for evidence of MP2, MP5, MP6, MP7, and
MP8.)
6. Have students complete the additional scenarios practice. This activity can be completed as stations around the
room or by assigning groups a task and having them jigsaw to discuss the different problems with other
classmates. (Look for evidence of MP1, MP4, MP5, MP6, and MP8.)
a. Becca and Samantha go out to lunch. Samantha’s meal cost $2.00 more than Becca’s. The total bill
came to $19.00. How much did each of the meals cost? [Solution: Becca’s meal cost $8.50 and
Samantha’s meal cost $10.50.]
b. If you order a Big Mac and medium fries from McDonald’s, the meal will be 920 calories. A Big Mac
has 160 more calories than the medium fries. How many calories are in each item? [Solution: A Big
Mac has 540 calories and the medium fries has 380 calories.]
c. To earn money over Spring Break, Devon mows lawns and washes cars for the neighbors. He charges
$15 for each lawn he mows and $10 for each car he washes. At the end of Spring Break, Devon mowed
three more lawns than cars he washed. He earned a total of $160 for his work. How many lawns did he
mow and how many cars did he wash? [He mowed 8 lawns and washed 5 cars.]
7. Have students share solutions and discuss closure questions. (Look for evidence of MP3.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will be able to use a substitution strategy to solve system of equations. Students will be able to connect the
strategy to algebraic representations. The teacher will be able to measure student understanding by monitoring class
discussions and group work on the scenario practice.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Key vocabulary: solution, intersection, slope, y-intercept, parallel
Connections: Students will need to connect to their prior understanding of the solution to systems of equation
represented as the intersection of the graphs.
Common Mistakes: If students are working with algebraic representations, it is important for students to clearly
define all variables used. If this is not done, students may mix up variables and substitute incorrectly.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Scenario list
Multiple representations graphic organizer (optional)
Access to manipulatives (Katie Kubes, graph paper,
etc.)
Markers (optional)
Graphing calculators
Have students create their own scenario that would require
substitution to solve. Students should also show work to
solve the scenario. (Look for evidence of MP1, MP2,
MP4, MP6, MP7, and MP8.)
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 8.EE.C.8b Solving Systems with Substitution
Course: Common Core Mathematics 8
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
How well do students understand how to use substitution to solve a system of equations?
Are students able to transfer scenarios into an algebraic representation?
How will I differentiate upcoming lessons to meet the needs of the various learners in my class?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.