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Algebra 1 Foundations

A middle-school Algebra 1 foundations path for variables, equations, inequalities, linear relationships, systems, exponents, and clear mathematical explanation.

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Middle school grades 7-8 / Algebra 1 readiness / NY Next Generation Math

Algebra 1 Foundations

A middle-school Algebra 1 foundations path for variables, equations, inequalities, linear relationships, systems, exponents, and clear mathematical explanation.

5 units400 checked answers5 units, 10-16 weeks Algebra 1 cycle
Outcomes
  • Translate contexts into expressions, equations, tables, and graphs.
  • Solve linear equations and inequalities with checks that prove the answer works.
  • Explain slope, intercepts, and systems using evidence from representations.

Study links

AlgebraMathematics Guidance & ResourcesNYS P-12 Learning Standards by Content AreaAlgebra curriculumFlexBook textbooks and concepts
Source index

Unit sequence

Start at unit 1. Move forward only after the checks are clean.

  1. 01

    Variables, expressions, and one-step structure

    80 checks
    • Represent unknowns with variables and expressions.
    • Use properties to simplify expressions without changing meaning.

    Practice: Translate five word contexts into expressions and label the quantity each variable represents.

    Open practice checks
    Sequenced original practice checks

    Move in order: foundation, transfer, analysis, timed readiness, then metacognitive repair.

    6 shown / 80 checked answers
    Exercise path
    Foundation: 25Developing: 25Proficient: 24Advanced: 6

    Start the next sequenced check: #1 Expression. Do not jump ahead until this one is correct.

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1ExpressionFluencyfoundationNext

    Set 2: simplify 6x + 7x.

    #2EquationFluencydeveloping

    Set 2: solve 6x + 8 = 26.

    #3ExpressionFluencyfoundation

    Set 1: simplify 5x + 2x.

    #4EquationFluencydeveloping

    Set 1: solve 5x + 3 = 18.

    #5InequalityConceptdeveloping

    Set 1: solve x + 5 > 9. Give the boundary value.

    #6SlopeApplicationdeveloping

    Set 1: a line rises 15 and runs 5. What is the slope?

  2. 02

    Equations, inequalities, and checks

    80 checks
    • Solve one-step, two-step, and multi-step equations.
    • Graph and interpret inequalities in context.

    Practice: Solve a mixed equation set and verify every answer in the original statement.

    Open practice checks
    Sequenced original practice checks

    Move in order: foundation, transfer, analysis, timed readiness, then metacognitive repair.

    6 shown / 80 checked answers
    Exercise path
    Developing: 25Proficient: 24Advanced: 6Foundation: 25

    Start the next sequenced check: #1 Proportion. Do not jump ahead until this one is correct.

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1ProportionApplicationdevelopingNext

    Set 3: solve 8/6 = x/24.

    #2Table ruleApplicationproficient

    Set 3: a table follows y = 4x + 8. What is y when x = 7?

    #3InequalityConceptdeveloping

    Set 1: solve x + 6 > 10. Give the boundary value.

    #4SlopeApplicationdeveloping

    Set 1: a line rises 24 and runs 6. What is the slope?

    #5Function meaningAnalysisproficient

    Set 2: in y = 4x + 3, what does 4 represent?

    #6Assessment checkExam Readinessadvanced

    Set 2: if x = 4, check 7x = 28. What is the left side?

  3. 03

    Linear tables, graphs, slope, and intercepts

    80 checks
    • Connect rate of change and initial value across tables, graphs, equations, and stories.
    • Interpret slope and intercepts using units.

    Practice: Compare two linear models and write which has the greater rate of change with graph evidence.

    Open practice checks
    Sequenced original practice checks

    Move in order: foundation, transfer, analysis, timed readiness, then metacognitive repair.

    6 shown / 80 checked answers
    Exercise path
    Foundation: 25Proficient: 24Developing: 25Advanced: 6

    Start the next sequenced check: #1 Linear value. Do not jump ahead until this one is correct.

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1Linear valueApplicationfoundationNext

    Set 5: for y = 5x + 5, find y when x = 11.

    #2SystemAnalysisproficient

    Set 5: solve x + y = 28 and x - y = 6. What is x?

    #3Linear valueApplicationfoundation

    Set 1: for y = 5x + 6, find y when x = 7.

    #4SystemAnalysisproficient

    Set 1: solve x + y = 21 and x - y = 7. What is x?

    #5Slope interceptConceptfoundation

    Set 4: which equation has slope 5 and y-intercept 2?

    #6ExponentFluencyproficient

    Set 4: simplify x^13 / x^3.

  4. 04

    Systems and word-problem modeling

    80 checks
    • Solve simple systems by graphing, substitution, or elimination.
    • Use systems to model comparisons and break-even situations.

    Practice: Write and solve a system from a school event or pricing situation, then check the solution in words.

    Open practice checks
    Sequenced original practice checks

    Move in order: foundation, transfer, analysis, timed readiness, then metacognitive repair.

    6 shown / 80 checked answers
    Exercise path
    Foundation: 25Developing: 25Proficient: 24Advanced: 6

    Start the next sequenced check: #1 Expression. Do not jump ahead until this one is correct.

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1ExpressionFluencyfoundationNext

    Set 7: simplify 14x + 4x.

    #2EquationFluencydeveloping

    Set 7: solve 14x + 5 = 47.

    #3Slope interceptConceptfoundation

    Set 1: which equation has slope 3 and y-intercept 8?

    #4ExponentFluencyproficient

    Set 1: simplify x^10 / x^2.

    #5InequalityConceptdeveloping

    Set 6: solve x + 13 > 21. Give the boundary value.

    #6SlopeApplicationdeveloping

    Set 6: a line rises 39 and runs 13. What is the slope?

  5. 05

    Exponents, quadratics preview, and assessment explanation

    80 checks
    • Use exponent rules and identify common nonlinear patterns.
    • Write assessment-ready explanations with claim, work, and verification.

    Practice: Revise a weak algebra response into a complete explanation and name the next practice target.

    Open practice checks
    Sequenced original practice checks

    Move in order: foundation, transfer, analysis, timed readiness, then metacognitive repair.

    6 shown / 80 checked answers
    Exercise path
    Developing: 25Proficient: 24Advanced: 6Foundation: 25

    Start the next sequenced check: #1 Proportion. Do not jump ahead until this one is correct.

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1ProportionApplicationdevelopingNext

    Set 8: solve 16/3 = x/12.

    #2Table ruleApplicationproficient

    Set 8: a table follows y = 4x + 16. What is y when x = 4?

    #3ProportionApplicationdeveloping

    Set 1: solve 9/3 = x/12.

    #4Table ruleApplicationproficient

    Set 1: a table follows y = 4x + 9. What is y when x = 4?

    #5Function meaningAnalysisproficient

    Set 7: in y = 4x + 7, what does 4 represent?

    #6Assessment checkExam Readinessadvanced

    Set 7: if x = 4, check 15x = 60. What is the left side?

Algebra 1 Foundations curriculum · PeerTutor