Created byDarren Kraft
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Combining Like Terms: Solve for the Unknown
Grade 8Math1 days
In this project, 8th-grade students will learn to solve linear equations by combining like terms and using inverse operations. They will participate in activities such as 'The Great Equation Race' and complete portfolio assignments like 'Term Detective,' 'Combine & Conquer,' 'Inverse Operation Invasion,' and 'Equation Solver' to master these concepts. A detailed rubric will assess their ability to identify like terms, simplify expressions, and solve equations, ensuring a comprehensive understanding of algebraic principles. Students will reflect on their learning, challenges, and strategies used throughout the project.Combining Like TermsInverse OperationsLinear EquationsAlgebraProblem-SolvingEquation SolvingMathematical Accuracy
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Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we use the principles of combining like terms and inverse operations to strategically isolate a variable and solve equations, ensuring the accuracy of our solutions?Essential Questions
Supporting questions that break down major concepts.- How can we simplify expressions by combining like terms?
- How do we isolate the variable to solve for its value?
- What operations can be used to solve equations?
- How can we check if our solution is correct?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to identify like terms in algebraic expressions.
- Students will be able to combine like terms to simplify algebraic expressions.
- Students will be able to use inverse operations to isolate a variable in an equation.
- Students will be able to solve linear equations with variables on one side.
- Students will be able to check the accuracy of their solutions by substitution.
Entry Events
Events that will be used to introduce the project to studentsThe Great Equation Race
Students compete in teams to solve equations and navigate a race course. The first team to correctly solve all equations and reach the finish line wins. This entry event encourages teamwork, problem-solving, and a competitive spirit.📚
Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Activity 1
Term Detective
Students identify and categorize like terms in various algebraic expressions.Steps
Here is some basic scaffolding to help students complete the activity.1. Review the definition of like terms (terms with the same variable raised to the same power).
2. Examine a series of algebraic expressions and underline like terms using different colors for each group of like terms.
3. Create a table organizing the identified like terms into categories (e.g., x terms, y terms, constant terms).
Final Product
What students will submit as the final product of the activityA completed table categorizing like terms with accurately identified groups of like terms.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Students will be able to identify like terms in algebraic expressions.Activity 2
Combine & Conquer
Students practice combining like terms to simplify algebraic expressions.Steps
Here is some basic scaffolding to help students complete the activity.1. Start with a set of algebraic expressions containing multiple like terms.
2. Combine like terms within each expression, showing each step of the simplification process.
3. Write the simplified expression as the final answer.
Final Product
What students will submit as the final product of the activityA worksheet or document showing the step-by-step simplification of algebraic expressions by combining like terms.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Students will be able to combine like terms to simplify algebraic expressions.Activity 3
Inverse Operation Invasion
Students use inverse operations to isolate variables in simple equations.Steps
Here is some basic scaffolding to help students complete the activity.1. Review the concept of inverse operations (addition/subtraction, multiplication/division).
2. Solve a series of one-step equations by applying the appropriate inverse operation to both sides.
3. Check the solution by substituting it back into the original equation.
Final Product
What students will submit as the final product of the activityA set of solved one-step equations with each step clearly shown and solutions checked for accuracy.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Students will be able to use inverse operations to isolate a variable in an equation.Activity 4
Equation Solver
Students solve linear equations with variables on one side.Steps
Here is some basic scaffolding to help students complete the activity.1. Solve multi-step equations with variables on one side of the equation.
2. Simplify both sides of the equation by combining like terms.
3. Isolate the variable using inverse operations.
4. Check the solution by substituting it back into the original equation.
Final Product
What students will submit as the final product of the activityA portfolio of solved linear equations, showing all steps and checked solutions.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goals: Students will be able to solve linear equations with variables on one side and Students will be able to check the accuracy of their solutions by substitution.🏆
Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolio8th Grade Mathematical Equations and Like Terms Rubric
Category 1
Identification of Like Terms
Assesses the ability to correctly identify and categorize like terms in algebraic expressions.Criterion 1
Recognition of Like Terms
Ability to accurately identify terms that share the same variable and exponent, categorizing them by type.
Exemplary
4 PointsIdentifies all groups of like terms accurately and categorizes them correctly in all given expressions.
Proficient
3 PointsCorrectly identifies most groups of like terms with minimal errors in categorization.
Developing
2 PointsIdentifies like terms inconsistently, with some errors in grouping and categorization.
Beginning
1 PointsStruggles to identify like terms, with multiple errors and misconceptions.
Category 2
Combining Like Terms
Evaluates the ability to simplify algebraic expressions by combining like terms accurately.Criterion 1
Simplification Process
Ability to combine like terms to simplify algebraic expressions, demonstrating understanding through clear steps.
Exemplary
4 PointsConsistently combines like terms with no errors, showing detailed steps of simplification in all expressions.
Proficient
3 PointsCombines like terms accurately in most cases, with clear documentation of steps.
Developing
2 PointsOccasionally combines like terms correctly, but often misses steps or includes errors.
Beginning
1 PointsFrequently combines like terms incorrectly, missing key steps in simplification.
Category 3
Use of Inverse Operations
Measures proficiency in using inverse operations to isolate a variable in equations.Criterion 1
Application of Inverse Operations
Ability to correctly use inverse operations to solve one-step equations and validate results by substitution.
Exemplary
4 PointsApplies inverse operations effectively with clear reasoning in all steps, checking solutions accurately.
Proficient
3 PointsUses inverse operations correctly and checks solutions in most instances.
Developing
2 PointsSometimes uses inverse operations correctly, with inconsistencies in verification.
Beginning
1 PointsStruggles with inverse operations, with frequent errors and unchecked work.
Category 4
Solving Multi-step Equations
Assesses ability to solve equations with multiple steps using strategic methods.Criterion 1
Equation Solving and Verification
Ability to solve multi-step linear equations by combining like terms and using inverse operations, ensuring solutions are checked through substitution.
Exemplary
4 PointsSolves multi-step equations with precision, verifying each step comprehensively and validating the final solution.
Proficient
3 PointsAccurately solves multi-step equations in most instances, demonstrating correct verification techniques.
Developing
2 PointsDisplays some accuracy in solving multi-step equations but makes frequent errors, often omitting verification.
Beginning
1 PointsSignificant errors in solving equations, with steps and verification largely incorrect or missing.
Reflection Prompts
End-of-project reflection questions to get students to think about their learningQuestion 1
Reflecting on the "Equation Solver" project, what was your most significant challenge when solving linear equations, and how did you overcome it?
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Question 2
On a scale of 1 to 5, how confident are you in your ability to solve linear equations with variables on one side, and what specific steps do you take to ensure the accuracy of your solutions?
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Question 3
In the "Combine & Conquer" activity, which strategy for combining like terms did you find most effective, and why?
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Question 4
How did the "Inverse Operation Invasion" activity help you understand the relationship between different operations, and how did you use this understanding in the "Equation Solver" project?
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Question 5
Which project, "Term Detective", "Combine & Conquer", "Inverse Operation Invasion", or "Equation Solver", do you feel best demonstrates your understanding of solving equations with variables on one side? Explain your choice.
Multiple choice
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Options
Term Detective
Combine & Conquer
Inverse Operation Invasion
Equation Solver