Outcome: PR 8.2
Model and solve problems using linear equations of the form:
- ax = b
- x/a = b, a ≠ 0
- ax + b = c
- x/a + b = c, a ≠ 0
- a(x + b) = c
concretely, pictorially, and symbolically, where a, b, and c are integers.
Indicators:
- Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman).
- Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically.
- Discuss the importance of the preservation of equality when solving equations.
- Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution.
- Generalize and apply symbolic strategies for solving linear equations.
- Identify, explain, and correct errors in a given solution of a linear equation.
- Demonstrate the application of the distributive property in the solving of linear equations (e.g., 2(x + 3); 2x + 6 = 5)
- Explain why some linear relations (e.g., x/a = b, a ≠ 0 and x/a + b = c, a ≠ 0) have a given restriction and provide an example of a situation in which such a restriction would be necessary.
- Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem.
- Explain the algebra behind a particular algebra puzzle such as this puzzle written for 2008:
- Pick the number of times a week that you would like to go out to eat (more than once but less than 10).
- Multiply this number by 2 (just to be bold).
- Add 5.
- Multiply it by 50.
- If you have already had your birthday this year add 1758. If you have not, add 1757.
- Now subtract the four digit year that you were born.
- You should have a three digit number. The first digit of this was your original number. The next two numbers are your age.
Level / Scale / Descriptor / Indicators / Student-Friendly Language
Pre-Requisite Knowledge /
- Students who are not able to be independently successful with level 1 questions will be given an E.
1 / B - Beginning
There is a partial understanding of some of the simpler details and processes.
Prior knowledge is understood. /
- Knowledge and Comprehension
- Students who are successful with level 1 questions or those who are successful with level 1 or 2 questions with assistance will be given a B.
- Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman).
- Discuss the importance of the preservation of equality when solving equations.
I can explain why it is important to preserve equality in equations (if you add two to one side of an equation, you must add two to the other side).
2 / A – Approaching
No major errors or omissions regarding the simpler details or processes, but assistance may be required with the complex processes. /
- Applying and Analysing
- Students who are able to be successful with level 1 and level 2 questions, or those who are successful with higher-level questions with assistance, will be given an A.
- Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically.
- Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution.
- Generalize and apply symbolic strategies for solving linear equations.
- Identify, explain, and correct errors in a given solution of a linear equation.
I understand what it means to solve an equation and I can check to see if a solution is correct using algebra-tiles, diagrams, or by substitution (putting the solution in for the variable to see if it works).
I can generalize strategies that I use with algebra-tiles (or virtual manipulatives) as algebra rules.
I can find and correct errors in solutions of linear equations.
3 / M – Meeting
No major errors or omissions regarding any of the information and/or processes that were explicitly taught.
This is the target level for proficiency. /
- Evaluating and Creating
- Students who are independently successful with level 3 or level 4 questions are given an M.
- Demonstrate the application of the distributive property in the solving of linear equations (e.g., 2(x + 3); 2x + 6 = 5)
- Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem.
- Pick the number of times a week that you would like to go out to eat (more than once but less than 10).
- Multiply this number by 2 (just to be bold).
- Add 5.
- Multiply it by 50.
- If you have already had your birthday this year add 1758. If you have not, add 1757.
- Now subtract the four digit year that you were born.
- You should have a three digit number. The first digit of this was your original number. The next two numbers are your age.
I can use linear equations to solve word problems. I can explain what the solution to the linear equation means in the context of the problem.
I can use algebra to explain some number puzzles.
4 / In addition to level 3 performance, in-depth inferences and applications go beyond what was explicitly taught. /
- Students successful at level 4 will receive supplementary comments specific to their achievement in addition to the M.
I can solve linear equations that involve fractions and decimals.
Meeting / I can write word problems to represent complex linear equations.
I can solve linear equations that involve fractions and decimals.
Approaching / I can solve linear equations using the distributive property (like 3(x+2) = 9).
I can use linear equations to solve word problems. I can explain what the solution to the linear equation means in the context of the problem.
I can use algebra to explain some number puzzles.
Beginning / I can use algebra-tiles (or other manipulatives) to model and solve linear equations.
I understand what it means to solve an equation and I can check to see if a solution is correct using algebra-tiles, diagrams, or by substitution (putting the solution in for the variable to see if it works).
I can generalize strategies that I use with algebra-tiles (or virtual manipulatives) as algebra rules.
I can find and correct errors in solutions of linear equations.
I can find examples of situations that can be modeled by linear equations (ex/ the cost of downloading x songs from iTunes)
I can explain why it is important to preserve equality in equations (if you add two to one side of an equation, you must add two to the other side).
Student-Friendly Rubric
Outcome: PR 8.2
Model and solve problems using linear equations of the form:
- ax = b
- x/a = b, a ≠ 0
- ax + b = c
- x/a + b = c, a ≠ 0
- a(x + b) = c
concretely, pictorially, and symbolically, where a, b, and c are integers.