Solving Systems by Substitution
10 min
Narrative
This activity uses pictures to set up the idea of solving systems by substitution. Students may be familiar with this type of problem in which a small detail change is important to solving the system. No such trick is given in this problem, but the idea can be addressed if students bring it up.
While several valid strategies exist, focus attention on solving for the value of each picture and using that value to find additional values for other pictures. This primes student thinking for using substitution to solve systems of linear equations.
Launch
Student Task
Find the value of the last line. Be prepared to explain your reasoning.
Sample Response
6. Sample reasoning: The star is worth 3 because 3 of them add up to 9, and 39=3. The sun is worth 2 because 2 stars are worth 6, and the solution to 6−x=4 is x=2. The rocket is worth 5 because we know the sun is worth 2, so 2 rockets must be worth 10, and 210=5. The last line is 6 because 3−2+5=6.
Activity Synthesis (Teacher Notes)
Ask a group to share their strategy to get started, and stop them when they offer the value of one of the symbols. Ask another group how they used that information to get the value of another symbol. Continue selecting groups until the value of each symbol is known and the value of the last line is shared.
If it does not come up in the discussion of the strategies, point out that the first three equations could be written as a system.
⎩⎨⎧3x=92x−y=42z+y=12
The solution to this system is x=3,y=2,z=5 and can be found by solving each equation from the first to the third, using known information.
Standards
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- HSA-REI.C.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
15 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Solving Systems by Substitution
10 min
Narrative
This activity uses pictures to set up the idea of solving systems by substitution. Students may be familiar with this type of problem in which a small detail change is important to solving the system. No such trick is given in this problem, but the idea can be addressed if students bring it up.
While several valid strategies exist, focus attention on solving for the value of each picture and using that value to find additional values for other pictures. This primes student thinking for using substitution to solve systems of linear equations.
Launch
Student Task
Find the value of the last line. Be prepared to explain your reasoning.
Sample Response
6. Sample reasoning: The star is worth 3 because 3 of them add up to 9, and 39=3. The sun is worth 2 because 2 stars are worth 6, and the solution to 6−x=4 is x=2. The rocket is worth 5 because we know the sun is worth 2, so 2 rockets must be worth 10, and 210=5. The last line is 6 because 3−2+5=6.
Activity Synthesis (Teacher Notes)
Ask a group to share their strategy to get started, and stop them when they offer the value of one of the symbols. Ask another group how they used that information to get the value of another symbol. Continue selecting groups until the value of each symbol is known and the value of the last line is shared.
If it does not come up in the discussion of the strategies, point out that the first three equations could be written as a system.
⎩⎨⎧3x=92x−y=42z+y=12
The solution to this system is x=3,y=2,z=5 and can be found by solving each equation from the first to the third, using known information.
Standards
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- A-REI.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- HSA-REI.C.6·Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.