Curriculum Map

Every skill, Pre-K to 8th grade

22 topics. 273 free guides and references. See what your child should learn at each stage — and find the articles to help you teach it.

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Number & Operations

Building from counting to multi-step computation

Counting

Pre-K–2nd

The foundation everything else builds on — understanding that numbers represent real quantities.

  • Rote counting to 100 and beyond
  • One-to-one correspondence with objects
  • Counting on and counting back
  • Skip counting by 2s, 5s, and 10s
Grade ExpectationsHands-On LearningSkip CountingNumber RecognitionCounting BasicsCounting Strategies

Starts with physical objects and finger counting, then moves to number lines and hundred charts so the concept sticks before the symbols arrive.

8 articles

Addition

Pre-K–4th

From combining groups of blocks to multi-digit mental math — addition is the first operation kids own.

  • Adding within 10 using manipulatives
  • Number bonds and fact families
  • Adding with regrouping (carrying)
  • Multi-digit addition strategies
  • Mental math shortcuts (doubles, make-a-ten)
Developmental ReadinessGrade ExpectationsRegroupingFact FamiliesNumber BondsMulti-Digit OperationsMental MathEarly AdditionReview StrategiesCounting StrategiesFact FluencyHomeschool Tips

Builds number bonds first so kids see the relationship between parts and wholes, then layers in standard algorithms once the reasoning is solid.

17 articles

Subtraction

Pre-K–3rd

More than "take away" — subtraction teaches kids to think about differences, missing parts, and comparison.

  • Subtracting within 10 and 20
  • Take-away vs. comparison models
  • Regrouping (borrowing) across place values
  • Multi-digit subtraction
  • Checking answers with addition
Developmental ReadinessGrade ExpectationsRegroupingFact FamiliesEarly SubtractionMulti-Digit OperationsMental MathLearning GapsHomeschool TipsRetention

Uses part-whole bar models so children understand subtraction as finding a missing part, not just removing objects.

12 articles

Multiplication

K–6th

Equal groups, arrays, and area models give kids three different ways to see why multiplication works.

  • Equal groups and repeated addition
  • Array and area models
  • Times-table fluency (through 12×12)
  • Multi-digit multiplication
  • Properties: commutative, associative, distributive
Grade ExpectationsCommon PitfallsPropertiesArea ModelEqual Groups & ArraysFact FamiliesTools & ResourcesLearning HabitsLearning GapsMulti-Digit MultiplicationSkip CountingFraction OperationsTimes Tables & FluencyPowers of TenFactors & MultiplesReview StrategiesFact FluencyReadinessMastery LearningPractice MethodsConceptual Understanding

Starts with visual models (arrays, equal groups) before memorization so kids build conceptual understanding first, then practice for speed.

26 articles

Division

1st–5th

The flip side of multiplication — sharing equally, grouping, and eventually long division with confidence.

  • Equal sharing and grouping
  • Relating division to multiplication
  • Division with and without remainders
  • Long division with multi-digit dividends
  • Interpreting remainders in context
Fact FamiliesLong DivisionEarly DivisionFraction OperationsHomeschool Tips

Teaches division as the inverse of multiplication from day one, so kids always have a strategy to fall back on when they get stuck.

6 articles

Fractions, Decimals & Ratios

Understanding parts, proportions, and relationships

Fractions

2nd–5th

The topic more parents worry about than any other — fractions become intuitive when kids build them from equal parts.

  • Identifying and naming unit fractions
  • Equivalent fractions and simplifying
  • Comparing and ordering fractions
  • Adding and subtracting with unlike denominators
  • Multiplying and dividing fractions
Grade ExpectationsMixed NumbersIntroduction to FractionsCommon DenominatorsConceptual UnderstandingLearning GapsMath AnxietyHands-On LearningFraction OperationsFraction RepresentationsFraction Word ProblemsEquivalent FractionsComparing FractionsReal-World MathCommon Struggles

Grounds every concept in fraction bars and number lines before introducing procedures, so kids understand why you need a common denominator.

19 articles

Decimals

3rd–5th

Decimals are just fractions in disguise — kids who understand place value transition to decimals naturally.

  • Reading and writing decimals to thousandths
  • Connecting decimals to fractions
  • Comparing and rounding decimals
  • Adding and subtracting decimals
  • Multiplying and dividing decimals
Introduction to DecimalsDecimal Place ValueDecimal Operations

Ties every decimal lesson back to place value and fraction equivalents so kids never see decimals as a separate, disconnected topic.

4 articles

Percents

5th–7th

Percents connect fractions and decimals to everyday life — discounts, tips, grades, and statistics all use them.

  • Understanding percent as "per hundred"
  • Converting between fractions, decimals, and percents
  • Finding a percentage of a number
  • Percent increase and decrease
  • Solving real-world percent problems
Percent BasicsPercent ApplicationsReal-World Math

Uses hundred-grids and real-life scenarios (sales tax, batting averages) so percents feel practical, not abstract.

3 articles

Ratios

5th–8th

Ratios and proportional reasoning unlock middle-school math — from recipes to map scales to unit rates.

  • Writing and interpreting ratios
  • Equivalent ratios and ratio tables
  • Unit rates and rate comparison
  • Solving proportions
  • Scaling and proportional relationships
Grade ExpectationsRatio BasicsProportionsUnit RatesScale & ProportionRatios & Proportions

Starts with concrete comparisons kids already make (recipe doubling, mixing paint) and formalizes the math from there.

6 articles

Number Sense & Problem Solving

Flexible thinking with numbers and real-world applications

Place Value

K–5th

Place value is the operating system of our number system — every computation skill depends on it.

  • Understanding ones, tens, and hundreds
  • Reading and writing numbers in expanded form
  • Comparing and ordering multi-digit numbers
  • Rounding to the nearest 10, 100, and 1,000
  • Place value through millions and decimals
Grade ExpectationsPlace Value BasicsExpanded FormHomeschool TipsAssessment HelpHands-On LearningRoundingDecimal Place ValuePowers of TenComparing NumbersEmotional SupportLearning GapsLearning ProgressionCommon Pitfalls

Uses base-ten blocks and place-value charts so kids physically see how 10 ones become 1 ten — the big idea that makes regrouping click.

18 articles

Number Sense

Pre-K–8th

Number sense is the intuition that lets kids estimate, check their work, and know when an answer "feels wrong."

  • Composing and decomposing numbers flexibly
  • Estimating and checking reasonableness
  • Mental math strategies
  • Understanding number lines and benchmarks
  • Recognizing number relationships and patterns
Developmental ReadinessSpecial NeedsGrade ExpectationsCommon PitfallsWhen to Get HelpNumber Sense OverviewIntegersPrime NumbersNumber LinesHomeschool TipsLearning StylesAssessment HelpTools & ResourcesDigital LearningLearning HabitsMath AnxietyConceptual UnderstandingEmotional SupportRoundingPatternsIrrational NumbersFraction RepresentationsFactors & MultiplesEstimationSchedulingCurriculum ReviewsMastery LearningPractice MethodsLearning ProgressionRetention

Builds through number talks, estimation routines, and mental math games — daily low-stakes practice that develops mathematical intuition.

45 articles

Word Problems

2nd–5th

Word problems are where math meets the real world — kids learn to read a situation, choose a strategy, and solve.

  • Identifying which operation a problem requires
  • Drawing models and diagrams to represent problems
  • Solving multi-step problems
  • Writing equations from word descriptions
  • Checking answers for reasonableness
Special NeedsLearning StylesProblem-Solving StrategiesReading ComprehensionFraction Word ProblemsReview StrategiesAssessment Help

Teaches a read-draw-solve routine: understand the story first, sketch a model, then pick the math — so kids stop guessing which operation to use.

8 articles

Geometry & Measurement

Shapes, space, and units of measure

Algebra & Advanced Topics

Patterns, variables, and higher-level reasoning

Algebra

2nd–8th

Algebra starts way before x and y — it begins with patterns, missing numbers, and "what goes in the box?"

  • Extending and creating patterns
  • Understanding variables as unknowns
  • Writing and evaluating expressions
  • Solving one- and two-step equations
  • Graphing on the coordinate plane
Special NeedsGrade ExpectationsOrder of OperationsPropertiesLinear EquationsInequalitiesVariables & EquationsFunctionsSystems of EquationsProperties of OperationsNegative NumbersFunctions & PatternsCoordinate Plane

Introduces algebraic thinking through pattern recognition and balance-scale models years before formal equation solving.

21 articles

Exponents

5th–8th

Repeated multiplication, powers of 10, and scientific notation — the tools kids need for upper-level math and science.

  • Understanding exponents as repeated multiplication
  • Powers of 10 and place-value connections
  • Evaluating expressions with exponents
  • Order of operations (PEMDAS) with exponents
  • Introduction to scientific notation
Special NeedsScientific NotationExponent BasicsSquare RootsIrrational Numbers

Connects exponents to the place-value system kids already know, making powers of 10 the bridge to this new notation.

7 articles

Data & Probability

1st–7th

Collecting, organizing, and interpreting data teaches kids to ask good questions and support answers with evidence.

  • Collecting and organizing data in tally charts and tables
  • Reading and creating bar graphs, line plots, and circle graphs
  • Calculating mean, median, mode, and range
  • Describing probability with words and numbers
  • Drawing conclusions from data sets
ProbabilityStatisticsGraphs & ChartsData Collection

Kids gather their own data from surveys and experiments first, then learn to graph and analyze — so statistics feels like detective work.

7 articles

Phonics & Decoding

Letter recognition through multisyllabic word attack

Vocabulary & Word Knowledge

Building word power from early vocabulary through academic language

Reading Fluency

From choppy word-by-word reading to smooth, expressive performance

Reading Comprehension

Understanding, analyzing, and engaging with text

Literary Analysis & Critical Reading

Author's craft, rhetoric, and synthesis across texts

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