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PEMDAS & Number Sense

A middle-school math foundations track for order of operations, integer sense, fractions, decimals, ratios, percents, and clean equation setup before algebra work begins.

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Middle school grades 6-8 / arithmetic fluency / pre-algebra readiness

PEMDAS & Number Sense

A middle-school math foundations track for order of operations, integer sense, fractions, decimals, ratios, percents, and clean equation setup before algebra work begins.

5 units400 checked answers5 units, 8-12 weeks foundations cycle
Outcomes
  • Use order of operations accurately instead of guessing from left to right.
  • Repair number-sense gaps with integers, fractions, decimals, ratios, and percents.
  • Show checks and error corrections so tutors can see the exact misconception.

Study links

ArithmeticPre-algebraMathematics Guidance & ResourcesNYS P-12 Learning Standards by Content AreaPrealgebra 2eFlexBook textbooks and concepts
Source index

Unit sequence

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

  1. 01

    Order of operations and expression reading

    80 checks
    • Apply parentheses, exponents, multiplication, division, addition, and subtraction in the correct order.
    • Read an expression before calculating so the operation structure is clear.

    Practice: Solve a mixed PEMDAS set, then annotate the first operation and final check for each problem.

    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: 38Developing: 24Proficient: 12Advanced: 6

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

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1PEMDASFluencyfoundationNext

    Set 2: evaluate 6 + 7 * 3.

    #2PEMDASFluencyfoundation

    Set 2: evaluate (6 + 8) * 3.

    #3PEMDASFluencyfoundation

    Set 1: evaluate 5 + 2 * 3.

    #4PEMDASFluencyfoundation

    Set 1: evaluate (5 + 3) * 3.

    #5IntegersFluencydeveloping

    Set 1: compute -5 - 4 + 3.

    #6FractionsFluencydeveloping

    Set 1: compute 5/15 + 5/15. Give the fraction.

  2. 02

    Integer operations and rational-number sense

    80 checks
    • Add, subtract, multiply, and divide positive and negative numbers.
    • Use number lines and sign reasoning to catch arithmetic errors.

    Practice: Explain three integer-operation mistakes and rewrite each solution with a sign check.

    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
    Proficient: 12Foundation: 38Developing: 24Advanced: 6

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

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1SubstitutionApplicationproficientNext

    Set 3: if x = 6, evaluate 2x + 8.

    #2Inverse checkFluencyfoundation

    Set 3: 56 / 7 = ?

    #3IntegersFluencydeveloping

    Set 1: compute -6 - 4 + 4.

    #4FractionsFluencydeveloping

    Set 1: compute 6/24 + 5/24. Give the fraction.

    #5Order trapConceptfoundation

    Set 2: what is the first operation in 7 + 3 * (4 + 1)?

    #6Mixed reviewExam Readinessadvanced

    Set 2: compute 28 - 4^2.

  3. 03

    Fractions, decimals, and percents

    80 checks
    • Convert between fractions, decimals, and percents with meaning.
    • Compare rational numbers using benchmarks and equivalent forms.

    Practice: Build a conversion table from a school-data context and defend which representation is easiest to use.

    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: 38Developing: 24Proficient: 12Advanced: 6

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

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1DecimalsFluencyfoundationNext

    Set 5: compute 1.1 + 0.5.

    #2PercentApplicationdeveloping

    Set 5: what is 30% of 220?

    #3DecimalsFluencyfoundation

    Set 1: compute 0.7 + 0.6.

    #4PercentApplicationdeveloping

    Set 1: what is 35% of 140?

    #5Ratio tableApplicationdeveloping

    Set 4: if 10 notebooks cost $50, how much do 2 notebooks cost?

    #6ComparisonAnalysisproficient

    Set 4: which fraction is larger?

  4. 04

    Ratios, rates, and proportional reasoning

    80 checks
    • Use ratio tables, unit rates, and double number lines.
    • Identify proportional and non-proportional relationships.

    Practice: Model one rate problem with a table, equation, and sentence explaining the unit rate.

    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: 38Developing: 24Proficient: 12Advanced: 6

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

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1PEMDASFluencyfoundationNext

    Set 7: evaluate 14 + 4 * 3.

    #2PEMDASFluencyfoundation

    Set 7: evaluate (14 + 5) * 3.

    #3Ratio tableApplicationdeveloping

    Set 1: if 8 notebooks cost $24, how much do 8 notebooks cost?

    #4ComparisonAnalysisproficient

    Set 1: which fraction is larger?

    #5IntegersFluencydeveloping

    Set 6: compute -13 - 8 + 3.

    #6FractionsFluencydeveloping

    Set 6: compute 13/39 + 2/39. Give the fraction.

  5. 05

    Foundations error log and tutor handoff

    80 checks
    • Check arithmetic by substitution, estimation, and inverse operations.
    • Turn repeated errors into a focused tutoring target.

    Practice: Create an error log for ten missed problems and write the next two tutoring priorities.

    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
    Proficient: 12Foundation: 38Advanced: 6Developing: 24

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

    Learning analysis
    0/80
    Tried
    0
    Correct
    0%
    Mastery

    Weakest facet: Concept

    #1SubstitutionApplicationproficientNext

    Set 8: if x = 3, evaluate 2x + 16.

    #2Inverse checkFluencyfoundation

    Set 8: 64 / 4 = ?

    #3SubstitutionApplicationproficient

    Set 1: if x = 3, evaluate 2x + 9.

    #4Inverse checkFluencyfoundation

    Set 1: 36 / 4 = ?

    #5Order trapConceptfoundation

    Set 7: what is the first operation in 15 + 7 * (4 + 1)?

    #6Mixed reviewExam Readinessadvanced

    Set 7: compute 120 - 4^2.

PEMDAS & Number Sense curriculum · PeerTutor