{
  "summary": {
    "standards": 395,
    "skills": 314,
    "facets": 529,
    "templatesPresent": 171,
    "lessonsPresent": 97,
    "booksPresent": 6,
    "bookLinkedTemplates": 102,
    "publicationRecords": 0,
    "generatedArtifacts": 0,
    "testedArtifacts": 0,
    "independentlyReviewedArtifacts": 0,
    "publishedArtifacts": 0,
    "fullyCoveredSkills": 0,
    "fullyCoveredStandards": 0
  },
  "curriculum": {
    "skills": 314,
    "standards": 395,
    "numberedStandards": 385,
    "highSchoolStandards": 156,
    "advancedHighSchoolStandards": 43,
    "domainReferences": 10,
    "mappedStandards": 390,
    "plannedSkills": 314,
    "implementedSkills": 0,
    "verifiedSkills": 0,
    "facets": 529
  },
  "bands": [
    {
      "band": "K–2",
      "templates": [
        {
          "id": "shifted-ruler-length",
          "title": "Measure from a shifted start",
          "skillId": "ruler-measurement",
          "description": "Read a whole-unit interval from a nonzero ruler position.",
          "version": 1,
          "gradeBand": "K–2",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "count-objects",
          "version": 1,
          "title": "Count objects",
          "skillId": "count-to-20",
          "gradeBand": "K–2",
          "description": "Count up to ten objects."
        },
        {
          "id": "add-within-20",
          "version": 1,
          "title": "Add within twenty",
          "skillId": "addition-within-20",
          "gradeBand": "K–2",
          "description": "Add two nonnegative whole numbers with a sum at most twenty."
        },
        {
          "id": "subtract-within-20",
          "version": 1,
          "title": "Subtract within twenty",
          "skillId": "subtraction-within-20",
          "gradeBand": "K–2",
          "description": "Subtract without a negative result."
        },
        {
          "id": "place-value-digit",
          "version": 1,
          "title": "Value of a digit",
          "skillId": "hundreds-place-value",
          "gradeBand": "K–2",
          "description": "Find the value represented by a digit in a three-digit number."
        },
        {
          "id": "bar-chart-total",
          "version": 1,
          "title": "Total from a bar chart",
          "skillId": "picture-bar-graphs",
          "gradeBand": "K–2",
          "description": "Add three category counts from a labeled bar chart."
        },
        {
          "id": "bar-chart-difference",
          "version": 1,
          "title": "Compare chart categories",
          "skillId": "picture-bar-graphs",
          "gradeBand": "K–2",
          "description": "Find how many more items one category contains than another."
        },
        {
          "id": "join-within-10",
          "title": "Join two small groups",
          "skillId": "addition-within-10",
          "description": "Model joining within ten with a ten-frame.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "take-away-within-10",
          "title": "Take some away",
          "skillId": "subtraction-within-10",
          "description": "Find a remainder in a removal story within ten.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "number-bond-missing",
          "title": "Find the other part",
          "skillId": "number-bonds",
          "description": "Complete a two-part decomposition of a number through ten.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "ten-frame-complement",
          "title": "Fill a ten-frame",
          "skillId": "make-ten",
          "description": "Find the empty places needed to complete ten.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "teen-frame-compose",
          "title": "One ten and extra ones",
          "skillId": "teen-place-value",
          "description": "Compose eleven through nineteen from ten ones and extras.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "unknown-addend-story",
          "title": "Find what was added",
          "skillId": "missing-addend",
          "description": "Recover an unknown change from a start and total within twenty.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "missing-start-story",
          "title": "Find the starting amount",
          "skillId": "addition-stories",
          "description": "Recover a starting amount from a removal and remaining amount.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "balanced-addition",
          "title": "Make both sides equal",
          "skillId": "equality",
          "description": "Find a missing number in an equation with arithmetic on both sides.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "three-addend-story",
          "title": "Combine three groups",
          "skillId": "three-addends",
          "description": "Add three quantities with a total at most twenty.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "make-ten-remainder",
          "title": "Split an addend to make ten",
          "skillId": "addition-within-20",
          "description": "Find the part of an addend left after completing a ten.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "subtract-through-ten",
          "title": "Split a subtraction at ten",
          "skillId": "subtraction-within-20",
          "description": "Find the amount still to subtract after reaching ten.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "tens-ones-model",
          "title": "Read tens and ones",
          "skillId": "tens-and-ones",
          "description": "Compose a two-digit number from ten rods and unit squares.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "ten-more-or-less",
          "title": "Change one ten",
          "skillId": "ten-more-less",
          "description": "Find ten more or ten less without recounting ones.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "add-ones-regroup",
          "title": "Make a new ten",
          "skillId": "add-two-digit",
          "description": "Add a one-digit number to a two-digit number by regrouping ones.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "subtract-whole-tens",
          "title": "Subtract bundles of ten",
          "skillId": "ten-more-less",
          "description": "Subtract whole tens with a nonnegative result.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "hundreds-model",
          "title": "Read hundreds tens and ones",
          "skillId": "hundreds-place-value",
          "description": "Compose a three-digit number including zero-place cases.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "expanded-form-missing",
          "title": "Complete expanded form",
          "skillId": "hundreds-place-value",
          "description": "Find a missing place-value amount in an expanded equation.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "exchange-base-ten",
          "title": "Exchange equal units",
          "skillId": "hundreds-place-value",
          "description": "Regroup ten ones or ten tens while preserving value.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "add-several-two-digit",
          "title": "Add several groups",
          "skillId": "multiple-addends",
          "description": "Combine three or four two-digit quantities.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "add-with-regrouping",
          "title": "Regroup a three-digit sum",
          "skillId": "regroup-hundreds",
          "description": "Add within one thousand with a required ones-to-tens exchange.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "subtract-with-regrouping",
          "title": "Exchange to subtract",
          "skillId": "regroup-hundreds",
          "description": "Subtract within one thousand including borrowing across a zero tens place.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "skip-count-missing",
          "title": "Find the next count",
          "skillId": "skip-counting",
          "description": "Continue a count by fives tens or hundreds within one thousand.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "two-step-change",
          "title": "Follow two changes",
          "skillId": "two-step-stories",
          "description": "Solve a join-then-remove story within one hundred.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "continue-count-to-120",
          "title": "Continue counting",
          "skillId": "tens-and-ones",
          "description": "Continue by ones from any supported starting point through 120.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "small-array-total",
          "title": "Count a unit array",
          "skillId": "arrays",
          "description": "Count unit squares in arrays no larger than five rows by five columns.",
          "version": 1,
          "gradeBand": "K–2"
        },
        {
          "id": "pairing-leftover",
          "title": "Pair the counters",
          "skillId": "odd-and-even",
          "description": "Find whether zero or one counter remains after pairing a quantity through twenty.",
          "version": 1,
          "gradeBand": "K–2"
        }
      ]
    },
    {
      "band": "3–5",
      "templates": [
        {
          "id": "fractional-ruler-length",
          "title": "Read the spaces between marks",
          "skillId": "ruler-measurement",
          "description": "Read an exact half- or quarter-unit distance.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "rectangle-border-length",
          "title": "Follow the whole border",
          "skillId": "perimeter",
          "description": "Find the complete perimeter of a rectangle.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "rectangle-missing-border-side",
          "title": "Find a missing side from the border",
          "skillId": "perimeter",
          "description": "Recover a rectangle side from perimeter and one perpendicular side.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "rectangle-missing-area-side",
          "title": "Find the missing factor",
          "skillId": "area-perimeter-models",
          "description": "Recover a rectangle side from area and one perpendicular side.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "border-or-cover-unit",
          "title": "Choose the right kind of unit",
          "skillId": "area-perimeter-models",
          "description": "Distinguish boundary length from surface coverage.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "same-area-border-choice",
          "title": "Same area, different border",
          "skillId": "area-perimeter-models",
          "description": "Compare perimeters of two rectangles with equal area.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "same-border-area-choice",
          "title": "Same border, different area",
          "skillId": "area-perimeter-models",
          "description": "Compare areas of two rectangles with equal perimeter.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "metric-length-rename",
          "title": "Rename with smaller units",
          "skillId": "unit-conversion",
          "description": "Convert a whole count of a larger metric length unit to a smaller unit.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "metric-length-reverse",
          "title": "Rename with larger units",
          "skillId": "measurement-conversions",
          "description": "Convert a whole count of smaller metric units to an exact larger-unit value.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "mixed-length-total",
          "title": "Bring lengths to one unit",
          "skillId": "measurement-conversions",
          "description": "Add lengths expressed in meters and centimeters.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "mixed-unit-border",
          "title": "One unit around the border",
          "skillId": "measurement-conversions",
          "description": "Convert perpendicular rectangle sides to one unit before finding perimeter.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredFigureCapability": "measurement-models-v1"
        },
        {
          "id": "rectangle-two-constraints-choice",
          "title": "Meet both design conditions",
          "skillId": "area-perimeter-models",
          "description": "Choose a positive whole-number rectangle meeting area and perimeter constraints.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "rectangle-existence-choice",
          "title": "Can the design exist?",
          "skillId": "area-perimeter-models",
          "description": "Decide whether given area and perimeter allow positive whole-number sides.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "whole-pack-ribbon-choice",
          "title": "Compare what you must buy",
          "skillId": "multistep-whole-stories",
          "description": "Compare total costs under whole-pack and divisible-length purchase rules.",
          "version": 1,
          "gradeBand": "3–5",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "multiply-facts",
          "version": 1,
          "title": "Multiplication facts",
          "skillId": "multiplication-facts",
          "gradeBand": "3–5",
          "description": "Multiply whole numbers from two through twelve."
        },
        {
          "id": "fraction-model",
          "version": 1,
          "title": "Read a fraction",
          "skillId": "fraction-model",
          "gradeBand": "3–5",
          "description": "Express a shaded part of one whole as a fraction."
        },
        {
          "id": "add-fractions",
          "version": 1,
          "title": "Add fractions",
          "skillId": "fraction-addition",
          "gradeBand": "3–5",
          "description": "Add two positive fractions with possibly different denominators."
        },
        {
          "id": "rectangle-area",
          "version": 1,
          "title": "Rectangle area",
          "skillId": "rectangle-area",
          "gradeBand": "3–5",
          "description": "Find area from perpendicular side lengths."
        },
        {
          "id": "divide-facts",
          "version": 1,
          "title": "Division facts",
          "skillId": "division-facts",
          "gradeBand": "3–5",
          "description": "Divide whole numbers into equal groups."
        },
        {
          "id": "decimal-addition",
          "version": 1,
          "title": "Add decimals",
          "skillId": "decimal-arithmetic",
          "gradeBand": "3–5",
          "description": "Add two amounts expressed in hundredths."
        },
        {
          "id": "compare-fractions",
          "version": 1,
          "title": "Compare fractions",
          "skillId": "fraction-comparison",
          "gradeBand": "3–5",
          "description": "Choose the larger of two distinct positive fractions."
        },
        {
          "id": "multiply-fractions",
          "version": 1,
          "title": "Multiply fractions",
          "skillId": "fraction-multiplication",
          "gradeBand": "3–5",
          "description": "Multiply two positive proper fractions."
        },
        {
          "id": "decimal-multiplication",
          "version": 1,
          "title": "Multiply decimals",
          "skillId": "decimal-arithmetic",
          "gradeBand": "3–5",
          "description": "Multiply two positive amounts expressed in tenths."
        },
        {
          "id": "operation-order",
          "version": 1,
          "title": "Order of operations",
          "skillId": "numerical-expressions",
          "gradeBand": "3–5",
          "description": "Evaluate an expression with parentheses, multiplication and addition."
        },
        {
          "id": "clock-elapsed-minutes",
          "version": 1,
          "title": "Elapsed minutes",
          "skillId": "elapsed-time",
          "gradeBand": "3–5",
          "description": "Find a duration up to two hours between times on the same morning."
        },
        {
          "id": "unit-piece-size",
          "title": "Size of one equal part",
          "skillId": "unit-fractions",
          "description": "Name one part of a whole partitioned into 2, 3, 4, 6, or 8 equal pieces.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-unit-count",
          "title": "Count fractional units",
          "skillId": "unit-fractions",
          "description": "Count shaded equal units, including quantities greater than one.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-line-position",
          "title": "Read a fraction location",
          "skillId": "fractions-number-line",
          "description": "Read a marked position on a zero-based rational number line through three wholes.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-whole-as-parts",
          "title": "Rename a whole in fractional units",
          "skillId": "equivalent-fractions",
          "description": "Find the numerator when a whole number is expressed using a specified denominator.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "equivalent-numerator",
          "title": "Rename with smaller pieces",
          "skillId": "fraction-equivalence",
          "description": "Find a missing numerator when both counts scale by an integer factor.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "equivalent-denominator",
          "title": "Rename with larger pieces",
          "skillId": "fraction-equivalence",
          "description": "Find a missing denominator when equal groups are collected.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "like-fraction-missing-part",
          "title": "Complete a fractional amount",
          "skillId": "like-fraction-addition",
          "description": "Find the missing addend with a shared denominator.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "like-fraction-difference",
          "title": "Remove like fractional units",
          "skillId": "like-fraction-addition",
          "description": "Subtract positive like-denominator amounts with a nonnegative result.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "mixed-to-improper-numerator",
          "title": "Count the parts in a mixed amount",
          "skillId": "mixed-numbers",
          "description": "Find the numerator of a mixed number renamed with its existing denominator.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "improper-whole-part",
          "title": "Find full wholes in an amount",
          "skillId": "mixed-numbers",
          "description": "Count complete wholes in a positive improper fraction.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "improper-fractional-part",
          "title": "Find the part beyond full wholes",
          "skillId": "mixed-numbers",
          "description": "Find the fractional remainder after removing complete wholes.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "mixed-fraction-difference",
          "title": "Subtract through a whole",
          "skillId": "mixed-numbers",
          "description": "Subtract mixed numbers with like denominators, requiring one whole to be regrouped.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "unlike-fraction-difference",
          "title": "Subtract using a shared unit",
          "skillId": "fraction-addition",
          "description": "Subtract distinct-denominator positive fractions with a nonnegative difference.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-distance-gap",
          "title": "Measure a fractional gap",
          "skillId": "fraction-addition",
          "description": "Find the distance between two marked rational positions on a common-unit line.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "whole-times-fraction",
          "title": "Several groups of a fraction",
          "skillId": "fraction-times-whole",
          "description": "Find the total of a whole number of equal fractional-liter portions.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "whole-sharing-fraction",
          "title": "Share whole quantities equally",
          "skillId": "fraction-as-division",
          "description": "Share a whole number of liters among a whole-number group, including improper shares.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "unit-fraction-share",
          "title": "Share one fractional unit",
          "skillId": "unit-fraction-division",
          "description": "Divide a unit fraction of a liter among a positive whole-number group.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "whole-unit-groups",
          "title": "Count unit-fraction groups",
          "skillId": "unit-fraction-division",
          "description": "Count unit-fraction-liter containers in a whole number of liters.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-of-quantity",
          "title": "Scale a whole amount",
          "skillId": "fraction-multiplication",
          "description": "Take a proper fraction of a positive whole-liter amount.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "fraction-equivalence-choice",
          "version": 1,
          "requiredResponseCapability": "single-choice-v1",
          "title": "Different pieces, same amount",
          "skillId": "fraction-equivalence",
          "gradeBand": "3–5",
          "description": "Select an equivalent name for a proper fraction among scaling and additive misconceptions."
        },
        {
          "id": "full-kits",
          "title": "Count complete kits",
          "skillId": "multistep-whole-stories",
          "description": "Count complete fixed-size kits from a whole-item stock, including exact division.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "seats-needed",
          "title": "Make room for everyone",
          "skillId": "multistep-whole-stories",
          "description": "Find the smallest whole number of vehicles with enough seats, including exact division.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "kit-leftovers",
          "title": "Find unused items",
          "skillId": "multistep-whole-stories",
          "description": "Count items left after making as many complete kits as possible.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "share-whole-items",
          "title": "Share equally among trays",
          "skillId": "division-meaning",
          "description": "Find items per share from a total and a given number of equal shares.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "measure-whole-pieces",
          "title": "Measure equal pieces",
          "skillId": "division-meaning",
          "description": "Count fixed-length pieces in an exactly divisible whole-centimeter length.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "equal-tray-total",
          "title": "Count equal trays",
          "skillId": "multiplication-meaning",
          "description": "Find a total from equal visible groups of items.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "unknown-group-size",
          "title": "Find the group size",
          "skillId": "missing-factor",
          "description": "Find an unknown factor from a group count and a total.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "unknown-dividend",
          "title": "Find the starting total",
          "skillId": "missing-factor",
          "description": "Find the unknown dividend in a whole-number division equation.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "split-array-part",
          "title": "Use one part of an array",
          "skillId": "operation-properties",
          "description": "Find a partial product represented by a disjoint row region of an array.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "nested-bag-total",
          "title": "Count groups inside groups",
          "skillId": "operation-properties",
          "description": "Find the total in crates containing equal bags of equal items.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "zero-one-groups",
          "title": "Use zero and one groups",
          "skillId": "multiplication-meaning",
          "description": "Find products when a group count or group size is zero or one.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "comparison-amount",
          "title": "Find a compared amount",
          "skillId": "multiplicative-comparison",
          "description": "Find a quantity described as a whole-number multiple of another.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "comparison-factor",
          "title": "Find how many times as many",
          "skillId": "multiplicative-comparison",
          "description": "Find the multiplicative comparison factor from two whole-number quantities.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "delivery-then-use",
          "title": "Combine deliveries and use some",
          "skillId": "multi-operation-stories",
          "description": "Find remaining stock after equal deliveries and a known use.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "purchase-change",
          "title": "Find change after equal purchases",
          "skillId": "multi-operation-stories",
          "description": "Find whole-dollar change after buying several equally priced items.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "factor-partner",
          "title": "Find the other factor",
          "skillId": "factors-multiples",
          "description": "Complete one specified factor pair for a whole number through one hundred.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "tens-contribution",
          "title": "Find the tens partial product",
          "skillId": "whole-multiplication",
          "description": "Find the tens contribution in a two-digit by one-digit product.",
          "version": 1,
          "gradeBand": "3–5"
        },
        {
          "id": "neighbor-product-change",
          "title": "Compare neighboring products",
          "skillId": "arithmetic-patterns",
          "description": "Find the change when an equal-row array gains one row.",
          "version": 1,
          "gradeBand": "3–5"
        }
      ]
    },
    {
      "band": "6–8",
      "templates": [
        {
          "id": "negative-integer-power",
          "title": "Evaluate a negative power",
          "description": "Evaluate a nonzero rational base raised to a negative integer exponent.",
          "version": 1,
          "skillId": "exponent-laws",
          "gradeBand": "6–8"
        },
        {
          "id": "product-of-powers-exponent",
          "title": "Multiply powers with the same base",
          "description": "Combine integer exponents in a product with a shared nonzero base.",
          "version": 1,
          "skillId": "exponent-laws",
          "gradeBand": "6–8"
        },
        {
          "id": "quotient-of-powers-exponent",
          "title": "Divide powers with the same base",
          "description": "Combine integer exponents in a quotient with a shared nonzero base.",
          "version": 1,
          "skillId": "exponent-laws",
          "gradeBand": "6–8"
        },
        {
          "id": "power-of-power-exponent",
          "title": "Raise a power to a power",
          "description": "Combine nested integer powers of a nonzero base.",
          "version": 1,
          "skillId": "exponent-laws",
          "gradeBand": "6–8"
        },
        {
          "id": "median-data",
          "version": 1,
          "title": "Median of data",
          "skillId": "signed-data-summaries",
          "gradeBand": "6–8",
          "description": "Order a finite dataset and find its middle value or the mean of its two middle values."
        },
        {
          "id": "range-data",
          "version": 1,
          "title": "Range of data",
          "skillId": "signed-data-summaries",
          "gradeBand": "6–8",
          "description": "Find the distance between the greatest and least values in a finite dataset."
        },
        {
          "id": "interquartile-range-data",
          "version": 1,
          "title": "Interquartile range",
          "skillId": "signed-data-summaries",
          "gradeBand": "6–8",
          "description": "Find quartiles by the stated median-of-halves convention and subtract the lower quartile from the upper."
        },
        {
          "id": "right-triangle-missing-leg",
          "version": 1,
          "title": "Find a missing leg",
          "skillId": "pythagorean-theorem",
          "gradeBand": "6–8",
          "description": "Find either leg of an integer right triangle from its hypotenuse and other leg."
        },
        {
          "id": "pythagorean-converse",
          "version": 1,
          "title": "Recognize a right triangle from its sides",
          "skillId": "pythagorean-theorem",
          "gradeBand": "6–8",
          "description": "Use the Pythagorean theorem and its converse to decide whether three given triangle sides form a right triangle.",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "linear-equation",
          "version": 1,
          "title": "Solve a linear equation",
          "skillId": "linear-equations",
          "gradeBand": "6–8",
          "description": "Solve an equation with an integer solution."
        },
        {
          "id": "mean-data",
          "version": 1,
          "title": "Mean of a dataset",
          "skillId": "statistics-mean",
          "gradeBand": "6–8",
          "description": "Compute an exact mean of five observations."
        },
        {
          "id": "right-triangle",
          "version": 1,
          "title": "Pythagorean theorem",
          "skillId": "pythagorean-theorem",
          "gradeBand": "6–8",
          "description": "Find a hypotenuse from a scaled integer right triangle."
        },
        {
          "id": "divide-fractions",
          "version": 1,
          "title": "Divide fractions",
          "skillId": "fraction-division",
          "gradeBand": "6–8",
          "description": "Divide a positive fraction by another positive fraction."
        },
        {
          "id": "ratio-missing",
          "version": 1,
          "title": "Equivalent ratios",
          "skillId": "ratios",
          "gradeBand": "6–8",
          "description": "Scale a ratio to find a missing quantity."
        },
        {
          "id": "percent-of",
          "version": 1,
          "title": "Percent of a quantity",
          "skillId": "percentages",
          "gradeBand": "6–8",
          "description": "Find an exact percentage of a whole-number quantity."
        },
        {
          "id": "integer-addition",
          "version": 1,
          "title": "Add signed integers",
          "skillId": "signed-addition",
          "gradeBand": "6–8",
          "description": "Combine positive and negative integer changes."
        },
        {
          "id": "integer-power",
          "version": 1,
          "title": "Evaluate powers",
          "skillId": "integer-powers",
          "gradeBand": "6–8",
          "description": "Evaluate a whole-number base raised to a nonnegative integer exponent."
        },
        {
          "id": "line-slope",
          "version": 1,
          "title": "Slope through two points",
          "skillId": "slope",
          "gradeBand": "6–8",
          "description": "Find slope as change in y divided by change in x."
        },
        {
          "id": "simple-probability",
          "version": 1,
          "title": "Probability of one draw",
          "skillId": "probability",
          "gradeBand": "6–8",
          "description": "Find a probability from equally likely objects."
        },
        {
          "id": "arithmetic-term",
          "version": 1,
          "title": "Arithmetic sequences",
          "skillId": "arithmetic-sequences",
          "gradeBand": "6–8",
          "description": "Find a term given the first term and a common difference."
        },
        {
          "id": "unit-price",
          "version": 1,
          "title": "Proportional cost",
          "skillId": "proportional-relationships",
          "gradeBand": "6–8",
          "description": "Use a constant unit price to find a total cost."
        },
        {
          "id": "signed-fraction-sum",
          "title": "Add and subtract signed fractions",
          "description": "Add or subtract two signed fractions with different denominators.",
          "skillId": "signed-addition",
          "gradeBand": "6–8",
          "version": 1
        },
        {
          "id": "signed-fraction-product",
          "title": "Multiply and divide signed fractions",
          "description": "Multiply or divide two signed fractions and reduce the result.",
          "skillId": "signed-multiplication",
          "gradeBand": "6–8",
          "version": 1
        },
        {
          "id": "complex-fraction",
          "title": "Simplify a complex fraction",
          "description": "Simplify a fraction whose numerator and denominator contain fractions.",
          "skillId": "complex-fractions",
          "gradeBand": "6–8",
          "version": 1
        },
        {
          "id": "circle-circumference-coefficient",
          "title": "Circle circumference",
          "skillId": "circle-measurement",
          "description": "Find an exact circumference from a radius or diameter.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "circle-area-coefficient",
          "title": "Circle area",
          "skillId": "circle-measurement",
          "description": "Find an exact circle area from a radius or diameter.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "percent-change-rate",
          "title": "Find the percent change",
          "description": "Compare an increase or decrease with its original positive quantity, including changes in percentage-valued shares.",
          "version": 1,
          "skillId": "percent-change",
          "gradeBand": "6–8"
        },
        {
          "id": "percent-change-final",
          "title": "Apply a percent change",
          "description": "Find the final quantity after one exact percentage increase or decrease.",
          "version": 1,
          "skillId": "percent-change",
          "gradeBand": "6–8"
        },
        {
          "id": "percent-change-original",
          "title": "Recover the original quantity",
          "description": "Undo one percentage increase or decrease using its nonzero multiplier.",
          "version": 1,
          "skillId": "percent-change",
          "gradeBand": "6–8"
        },
        {
          "id": "affine-linear-inequality",
          "title": "Solve a linear inequality",
          "description": "Find an exact half-line solution set with signed rational coefficients and all four comparison signs.",
          "version": 1,
          "skillId": "linear-inequalities",
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "grouped-linear-inequality",
          "title": "Solve an inequality with grouped terms",
          "description": "Distribute, collect variable terms on both sides, and solve an inequality with an exact rational boundary.",
          "version": 1,
          "skillId": "linear-inequalities",
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "cancelled-linear-inequality",
          "title": "Classify an inequality after cancellation",
          "description": "Determine whether an inequality with cancelling variable terms holds for every real number or none.",
          "version": 1,
          "skillId": "linear-inequalities",
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "linear-system-pair",
          "title": "Solve for both coordinates",
          "description": "Find the exact ordered pair satisfying two linear equations, including fractional coordinates and axis-aligned lines.",
          "version": 1,
          "skillId": "linear-systems",
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "linear-system-solution-count",
          "title": "Count a linear system’s solutions",
          "description": "Distinguish one, no, and infinitely many shared ordered pairs in two linear equations.",
          "version": 1,
          "skillId": "linear-systems",
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "coordinate-point-reading",
          "version": 1,
          "title": "Read a coordinate",
          "skillId": "coordinate-four-quadrants",
          "gradeBand": "6–8",
          "description": "Read one coordinate of a labeled point on a unit grid."
        },
        {
          "id": "graphed-line-slope",
          "version": 1,
          "title": "Slope from a graph",
          "skillId": "slope",
          "gradeBand": "6–8",
          "description": "Find exact slope from two labeled lattice points."
        },
        {
          "id": "number-line-distance",
          "version": 1,
          "title": "Distance on a number line",
          "skillId": "absolute-value",
          "gradeBand": "6–8",
          "description": "Find the nonnegative distance between two signed integers."
        },
        {
          "id": "fraction-group-count",
          "title": "Count full and partial groups",
          "skillId": "fraction-division",
          "description": "Measure a rational total in fractional-liter container units, allowing partial groups.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "fraction-share-amount",
          "title": "Share a fractional total",
          "skillId": "fraction-division",
          "description": "Share a positive non-unit fractional-liter amount among a whole-number group.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "substitute-linear-expression",
          "title": "Put a value into a rule",
          "skillId": "variable-expressions",
          "description": "Evaluate a signed linear expression at an integer or half-integer input.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "distributive-expression-choice",
          "title": "Multiply into parentheses",
          "skillId": "expression-properties",
          "description": "Recognize an equivalent expansion of a signed grouped expression.",
          "version": 1,
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "combine-like-coefficient",
          "title": "Collect the x terms",
          "skillId": "linear-expressions",
          "description": "Find only the coefficient of x after combining like terms.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "grouped-linear-equation",
          "title": "Unwrap an equation",
          "skillId": "linear-equations",
          "description": "Solve a grouped linear equation with an exact rational result.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "negative-coefficient-equation",
          "title": "Undo a negative multiplier",
          "skillId": "linear-equations",
          "description": "Solve an equation with a negative coefficient.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "rational-coefficient-equation",
          "title": "Undo a fraction multiplier",
          "skillId": "linear-equations",
          "description": "Solve an equation whose x coefficient is a noninteger fraction.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "both-sides-linear-equation",
          "title": "Bring the unknowns together",
          "skillId": "linear-equations",
          "description": "Solve a unique-solution equation with variables on both sides.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "check-equation-candidate",
          "title": "Test a proposed answer",
          "skillId": "linear-equations",
          "description": "Select the correct substitution check of a proposed integer value.",
          "version": 1,
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "unequal-step-rate",
          "title": "Look past the step sizes",
          "skillId": "slope",
          "description": "Find a constant rate from linear observations with unequal input steps.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "recover-linear-intercept",
          "title": "Find the output at zero",
          "skillId": "linear-models",
          "description": "Recover a zero-input output from a stated rate and another observation.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "predict-linear-output",
          "title": "Extend a linear pattern",
          "skillId": "linear-models",
          "description": "Predict an output from two points under an explicit linear assumption.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "relation-function-choice",
          "title": "One input, one output?",
          "skillId": "function-notation",
          "description": "Identify a finite relation with exactly one output for each input.",
          "version": 1,
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "proportional-rule-choice",
          "title": "Find a proportional rule",
          "skillId": "proportional-relationships",
          "description": "Recognize a real-valued rule y=kx among affine rules with nonzero intercepts.",
          "version": 1,
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "shared-plan-input",
          "title": "Find when two plans meet",
          "skillId": "linear-systems",
          "description": "Find the nonnegative input where two affine cost rules agree.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "first-cheaper-whole-input",
          "title": "Find the first lower price",
          "skillId": "linear-models",
          "description": "Find the first whole input at which a fixed-fee plan is strictly cheaper.",
          "version": 1,
          "gradeBand": "6–8"
        },
        {
          "id": "distance-graph-meaning",
          "title": "Read a distance graph",
          "skillId": "qualitative-graphs",
          "description": "Interpret a level or falling distance-from-home segment without inferring a route or motion speed.",
          "version": 1,
          "gradeBand": "6–8",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "equation-solution-count",
          "version": 1,
          "requiredResponseCapability": "single-choice-v1",
          "title": "One, none, or every number?",
          "skillId": "linear-equations",
          "gradeBand": "6–8",
          "description": "Classify the solution set of a linear equation with positive integer coefficients on both sides."
        },
        {
          "id": "graph-equation-choice",
          "version": 1,
          "requiredResponseCapability": "single-choice-v1",
          "title": "Find the graph’s rule",
          "skillId": "linear-models",
          "gradeBand": "6–8",
          "description": "Match an increasing line with positive integer slope and intercept to its equation."
        }
      ]
    },
    {
      "band": "9–12",
      "templates": [
        {
          "id": "quadratic-vertex",
          "version": 1,
          "title": "Quadratic minimum",
          "skillId": "quadratic-minimum",
          "gradeBand": "9–12",
          "description": "Find the minimum value of a quadratic in vertex form."
        },
        {
          "id": "geometric-sequence",
          "version": 1,
          "title": "Geometric sequences",
          "skillId": "geometric-sequences",
          "gradeBand": "9–12",
          "description": "Find a term of a geometric sequence from its first term and ratio."
        },
        {
          "id": "logarithm-integer",
          "version": 1,
          "title": "Logarithms",
          "skillId": "logarithms",
          "gradeBand": "9–12",
          "description": "Evaluate a logarithm whose argument is an integer power of its base."
        },
        {
          "id": "linear-system-x",
          "version": 1,
          "title": "Solve a linear system",
          "skillId": "linear-systems",
          "gradeBand": "9–12",
          "description": "Find x in a system with a unique integer solution."
        },
        {
          "id": "function-evaluation",
          "version": 1,
          "title": "Evaluate a function",
          "skillId": "function-evaluation",
          "gradeBand": "9–12",
          "description": "Evaluate a quadratic expression at an integer input."
        },
        {
          "id": "quadratic-factored-solutions",
          "title": "Solve a factored quadratic",
          "skillId": "quadratic-equations",
          "description": "Find every real solution of a quadratic written as a product of linear factors.",
          "version": 1,
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "quadratic-expanded-solutions",
          "title": "Solve a quadratic by factoring",
          "skillId": "quadratic-equations",
          "description": "Factor an expanded quadratic and identify its complete real solution set.",
          "version": 1,
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "quadratic-real-solution-count",
          "title": "Count real quadratic solutions",
          "skillId": "quadratic-formula",
          "description": "Use the discriminant to count distinct real solutions without calculating the roots.",
          "version": 1,
          "gradeBand": "9–12"
        },
        {
          "id": "polynomial-addition",
          "title": "Add polynomials",
          "description": "Combine like terms in a sum of polynomials.",
          "skillId": "polynomial-arithmetic",
          "version": 1,
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "polynomial-subtraction",
          "title": "Subtract polynomials",
          "description": "Distribute a subtraction sign and combine like terms.",
          "skillId": "polynomial-arithmetic",
          "version": 1,
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "polynomial-multiplication",
          "title": "Multiply polynomials",
          "description": "Distribute every term and combine like terms in a polynomial product.",
          "skillId": "polynomial-arithmetic",
          "version": 1,
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1"
        },
        {
          "id": "simplify-square-root",
          "title": "Simplify a square root",
          "description": "Extract square factors and give an exact square-root expression.",
          "skillId": "rational-exponents",
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1",
          "version": 1
        },
        {
          "id": "combine-square-roots",
          "title": "Add and subtract square roots",
          "description": "Simplify radical terms, then combine terms with the same radical part.",
          "skillId": "rational-exponents",
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1",
          "version": 1
        },
        {
          "id": "multiply-square-roots",
          "title": "Multiply square roots",
          "description": "Multiply signed coefficients and nonnegative radicands, then simplify.",
          "skillId": "rational-exponents",
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1",
          "version": 1
        },
        {
          "id": "rationalize-radical-denominator",
          "title": "Rationalize a denominator",
          "description": "Remove a square root from a single-term denominator using an equivalent fraction.",
          "skillId": "rational-exponents",
          "gradeBand": "9–12",
          "requiredResponseCapability": "single-choice-v1",
          "version": 1
        },
        {
          "id": "rational-power",
          "title": "Evaluate a fractional power",
          "description": "Evaluate a positive rational base raised to a fractional exponent.",
          "skillId": "rational-exponents",
          "gradeBand": "9–12",
          "version": 1
        },
        {
          "id": "arc-length-coefficient",
          "title": "Arc length",
          "skillId": "arc-sector-measure",
          "description": "Find an exact arc length from a radius or diameter and a central angle in degrees.",
          "version": 1,
          "gradeBand": "9–12"
        },
        {
          "id": "sector-area-coefficient",
          "title": "Sector area",
          "skillId": "arc-sector-measure",
          "description": "Find an exact sector area from a radius or diameter and a central angle in degrees.",
          "version": 1,
          "gradeBand": "9–12"
        }
      ]
    }
  ],
  "skillsWithProblems": 94,
  "source": "AMP curriculum and content audit",
  "limitations": [
    "Catalog presence does not prove efficacy, publication, or full standards coverage.",
    "Selected skills only; not complete K–12 or SAT coverage."
  ]
}