Linear Targets Reference Chart
Algebra 1 Progression Guide Unit 2: Linear Equations & Inequalities
Targets 1–3 of 6
Solving Linear Equations: Learning Targets
Student 'I can' benchmarks, observable success criteria, and verification standards
Name: _________________
Period: ____
1 Level 1 • Foundations
One-Step Equations & Properties of Equality
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can isolate a variable in a one-step equation using inverse operations and verify my solution through substitution."
Measurable Success Criteria
- • Identify inverse operations: State the applied operation and apply its exact opposite to maintain equality on both sides.
- • Reciprocals & negatives: Solve equations with fractional/negative coefficients (e.g., \(-\frac{2}{3}x = 10\)) by multiplying by \(-\frac{3}{2}\).
- • Verification check: Substitute computed value into original equation to prove \(\text{LHS} = \text{RHS}\).
Exemplar Check
\(-\frac{3}{4}x = 15\)
\(x = 15 \cdot \left(-\frac{4}{3}\right)\)
\(x = -20\)
Check: \(-\frac{3}{4}(-20) = 15 \checkmark\)
2 Level 2 • Operations Order
Two-Step Equations & Grouping Structures
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can reverse the order of operations (SADMEP) to isolate the variable term before isolating the variable itself."
Measurable Success Criteria
- • Sequence operations systematically: Undo addition/subtraction constant terms first, then undo multiplication/division coefficients.
- • Manage leading negatives: Accurately process equations like \(12 - 4x = 28\), recognizing that the sign in front of the term belongs to it.
- • Grouped fraction division: Multiply first when the entire numerator is grouped, as in \(\frac{x + 5}{4} = 6\).
Exemplar Check
\(14 - 3x = 29\)
\(-3x = 15\) (-14)
\(x = -5\) (/ -3)
Check: \(14 - 3(-5) = 29 \checkmark\)
3 Level 3 • Expression Simplification
Distributive Property & Combining Like Terms
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can fully simplify each side of an equation before moving terms across the equal sign."
Measurable Success Criteria
- • Distribute signs accurately: Multiply through parentheses correctly, especially with negative multipliers (e.g., \(-(x - 6) = -x + 6\)).
- • Combine like terms on the same side: Add variable coefficients and constant terms on one side without performing inverse operations yet.
- • Vertical alignment: Write equivalent equations step-by-step keeping the equal sign aligned vertically to trace logic.
Exemplar Check
\(4(2x - 3) - 5x = 9\)
\(8x - 12 - 5x = 9\)
\(3x - 12 = 9 \implies\) \(x = 7\)
Check: \(4(11) - 35 = 9 \checkmark\)
Scoring Rubric: 1 = Beginning • 2 = Developing • 3 = Proficient (Target) • 4 = Mastery / Extension
Page 1 of 2 • Foundational & Multi-Step Operations
Algebra 1 Progression Guide Unit 2: Linear Equations & Inequalities
Targets 4–6 of 6
Advanced Linear Solving & Reasoning
Balancing both sides, classifying solution types, and real-world application
Page 2 of 2
4 Level 4 • Structural Relocation
Equations with Variables on Both Sides
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can gather all variable terms onto one side and all constants onto the other to solve equations with variables on both sides."
Measurable Success Criteria
- • Strategic side selection: Subtract/add the variable term with smaller coefficient to keep positive values and prevent sign slips.
- • Simultaneous balance: Correctly use Addition/Subtraction Properties to eliminate variable terms from one side.
- • Full expression distribution: Simplify expressions on both sides completely before attempting to collect variables.
Exemplar Check
\(5x - 7 = 2x + 8\)
\(3x - 7 = 8\) (-2x)
\(3x = 15 \implies\) \(x = 5\)
Check: \(5(5)-7 = 18 = 2(5)+8 \checkmark\)
5 Level 5 • Solution Categorization
Classifying Solutions: One, None, or Infinitely Many
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can recognize whether an equation results in a single point solution, a false contradiction (no solution), or an identity (infinitely many solutions)."
One Solution \(x = a\)
Coefficients of \(x\) are different.
\(3x + 2 = 5x - 6\)
\(x = 4\) (1 exact root)
No Solution \(\emptyset\)
Same coefficients, different constants.
\(2x + 7 = 2x - 3\)
\(7 = -3\) (False! Parallel)
Infinite Solutions \(\mathbb{R}\) Identity
Identical coefficients & constants.
\(3(x + 2) = 3x + 6\)
\(6 = 6\) (True \(\forall x\))
6 Level 6 • Contextual Synthesis
Real-World Modeling & Contextual Solutions
Mastery: 1: Novice 2: Dev 3: Proficient
Target Statement: "I can define variables, translate verbal scenarios into linear equations, solve them, and assess whether the result makes sense in context."
Measurable Success Criteria
- • Define variables with units: Write explicit definitions (e.g., "Let \(m =\) number of miles driven").
- • Translate rate and initial value: Match key phrases ("per month", "flat fee", "equal cost") into algebraic structures like \(ax + b = c\) or \(ax + b = cx + d\).
- • Contextual validity check: Check reasonableness (e.g., fractional people or negative elapsed time indicate an error).
Exemplar Check
Scenario: Plan A: $40 + $2/GB; Plan B: $25 + $5/GB.
\(40 + 2g = 25 + 5g \implies g = 5\)
Answer: Equal cost at 5 gigabytes ($50).
Unit Goal: Achieve Proficient (Level 3+) on all 6 Learning Targets before the summative assessment.
Target Verification Date: _________________
Scale: 1 = Beginning | 2 = Developing | 3 = Proficient (Standard Met) | 4 = Advanced / Extended
Page 2 of 2 • Advanced Structural Reasoning & Applications
