The Common Core in Kentucky

KY.5.OA Operations and Algebraic Thinking

• Write and interpret numerical expressions.

  • KY.5.OA.1 Use parentheses, brackets or braces in numerical expressions and evaluate expressions that include symbols.

    • Evaluate numerical expressions (5-O.5)
    • Evaluate numerical expressions with parentheses (5-O.6)
    • Identify mistakes involving the order of operations (5-O.8)
    • Evaluate numerical expressions with parentheses in different places (5-O.9)

  • KY.5.OA.2 Write simple expressions with numbers and interpret numerical expressions without evaluating them.

    • Write numerical expressions: one operation (5-O.3)
    • Write numerical expressions: two operations (5-O.4)

• Analyze patterns and relationships.

  • KY.5.OA.3 Generate numerical patterns for situations.

    • KY.5.OA.3.a Generate a rule for growing patterns, identifying the relationship between corresponding terms (x, y).

    • KY.5.OA.3.b Generate patterns using one or two given rules (x, y).

      • Use a rule to complete a number sequence (5-S.1)

    • KY.5.OA.3.c Use tables, ordered pairs and graphs to represent the relationship between the quantities.

      • Compare patterns (5-S.2)
      • Use a rule to complete a table and a graph (5-T.5)
      • Complete a table for a two-variable relationship (5-U.8)
      • Complete a table from a graph (5-U.9)
      • Graph a two-variable relationship (5-U.11)

KY.5.NBT Number and Operations in Base Ten

• Understand the place value system.

  • KY.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

    • Convert between standard and expanded form (5-A.1)
    • Place value (5-A.2)
    • Place values in decimal numbers (5-G.5)
    • Relationship between decimal place values (5-G.6)

  • KY.5.NBT.2 Multiply and divide by powers of 10.

    • KY.5.NBT.2.1 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10.

      • Multiplication patterns over increasing place values (5-C.3)
      • Multiply numbers ending in zeroes (5-C.4)
      • Multiply numbers ending in zeroes: word problems (5-C.5)

    • KY.5.NBT.2.2 Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

      • Multiply a whole number by a power of ten: with exponents (5-E.4)
      • Multiply a decimal by a power of ten: with exponents (5-E.5)
      • Divide by a power of ten: with exponents (5-E.6)
      • Multiply and divide by a power of ten: with exponents (5-E.7)
      • Multiply a decimal by a power of ten (5-I.3)
      • Multiply by 0.1 or 0.01 (5-I.4)
      • Multiply by a power of ten with decimals: find the missing number (5-I.5)
      • Divide by powers of ten (5-J.1)
      • Decimal division patterns over increasing place values (5-J.2)
      • Divide by a power of ten with decimals: find the missing number (5-J.3)
      • Divide by 0.1 or 0.01 (5-J.10)

    • KY.5.NBT.2.3 Use whole-number exponents to denote powers of 10.

      • Understanding powers of ten (5-E.1)
      • Evaluate powers of ten (5-E.2)
      • Write powers of ten with exponents (5-E.3)

  • KY.5.NBT.3 Read, write and compare decimals to thousandths.

    • KY.5.NBT.3.a Read and write decimals to thousandths using base-ten numerals, number names and expanded form.

      • What decimal number is illustrated? (5-G.1)
      • Understanding decimals expressed in words (5-G.4)
      • Convert decimals between standard and expanded form (5-G.7)
      • Compose and decompose decimals in multiple ways (5-G.8)
      • Convert decimals between standard and expanded form using fractions (5-G.21)

    • KY.5.NBT.3.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

      • Compare decimals using grids (5-G.12)
      • Compare decimals on number lines (5-G.13)
      • Compare decimal numbers (5-G.14)

  • KY.5.NBT.4 Use place value understanding to round decimals to any place.

    • Round decimals (5-G.10)
    • Estimate sums and differences of decimals using rounding (5-H.9)

• Perform operations with multi-digit whole numbers and with decimals to hundredths.

  • KY.5.NBT.5 Fluently multiply multi-digit whole numbers (not to exceed four-digit by two-digit multiplication) using an algorithm.

    • Multiply by 2-digit numbers: complete the missing steps (5-C.13)
    • Multiply 2-digit numbers by 2-digit numbers (5-C.14)
    • Multiply 2-digit numbers by 3-digit numbers (5-C.15)
    • Multiply by 2-digit numbers: word problems (5-C.17)
    • Multiply three or more numbers up to 2 digits each (5-C.18)

  • KY.5.NBT.6 Divide up to four-digit dividends by two-digit divisors.

    • KY.5.NBT.6.a Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using...

      • KY.5.NBT.6.a.1 strategies based on place value

        • Divide numbers ending in zeroes (5-D.7)
        • Divide numbers ending in zeroes: word problems (5-D.8)
        • Divide by 2-digit numbers using models (5-D.12)
        • Divide by 2-digit numbers using partial quotients (5-D.13)
        • Divide 2-digit and 3-digit numbers by 2-digit numbers (5-D.14)
        • Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems (5-D.15)
        • Divide 4-digit numbers by 2-digit numbers (5-D.16)
        • Divide 4-digit numbers by 2-digit numbers: word problems (5-D.17)
        • Multi-step word problems: multiplicative comparison (5-D.19)

      • KY.5.NBT.6.a.2 the properties of operations

      • KY.5.NBT.6.a.3 the relationship between multiplication and division

        • Relate multiplication and division (5-D.20)
        • Choose numbers with a particular quotient (5-D.22)

    • KY.5.NBT.6.b Illustrate and explain the calculation by using equations, rectangular arrays and/or area models.

      • Divide by 2-digit numbers using models (5-D.12)

  • KY.5.NBT.7 Operations with decimals to hundredths.

    • KY.5.NBT.7.a Add, subtract, multiply and divide decimals to hundredths using…

      • KY.5.NBT.7.a.1 concrete models or drawings

        • Add decimal numbers using blocks (5-H.1)
        • Subtract decimal numbers using blocks (5-H.)
        • Multiply a decimal by a one-digit whole number using blocks (5-I.6)
        • Multiply a decimal by a two-digit whole number using area models (5-I.9)
        • Complete the decimal multiplication sentence using grids (5-I.13)
        • Multiply decimals using grids (5-I.14)
        • Divide decimals using blocks: complete the equation (5-J.4)
        • Divide decimals using area models: complete the equation (5-J.5)

      • KY.5.NBT.7.a.2 strategies based on place value

        • Add decimal numbers (5-H.2)
        • Subtract decimal numbers (5-H.3)
        • Add and subtract decimal numbers (5-H.4)
        • Add and subtract decimals: word problems (5-H.5)
        • Multiply a decimal by a one-digit whole number using the distributive property (5-I.7)
        • Multiply a decimal by a one-digit whole number (5-I.8)
        • Multiply a decimal by a multi-digit whole number (5-I.10)
        • Multiply decimals and whole numbers: word problems (5-I.11)
        • Multiply two decimals: where does the decimal point go? (5-I.15)
        • Multiply two decimals: products up to hundredths (5-I.16)
        • Multiply two decimals: products up to thousandths (5-I.17)
        • Division with decimal quotients (5-J.6)
        • Division with decimal quotients and rounding (5-J.7)
        • Division with decimal quotients: word problems (5-J.8)
        • Divide by decimals without adding zeroes (5-J.11)
        • Divide by decimals (5-J.12)
        • Add, subtract, multiply, and divide decimals (5-O.11)
        • Add, subtract, multiply, and divide decimals: word problems (5-O.12)
        • Add and subtract money amounts (5-R.1)
        • Add and subtract money: word problems (5-R.2)
        • Multiply money amounts: word problems (5-R.5)
        • Divide money amounts: word problems (5-R.8)
        • Unit prices (5-R.10)

      • KY.5.NBT.7.a.3 properties of operations

        • Multiply three or more numbers, one of which is a decimal (5-I.12)

      • KY.5.NBT.7.a.4 the relationship between addition and subtraction

        • Choose decimals with a particular sum or difference (5-H.6)
        • Complete the decimal addition or subtraction sentence (5-H.7)

    • KY.5.NBT.7.b Relate the strategy to a written method and explain the reasoning used.

KY.5.NF Number and Operations–Fractions

• Use equivalent fractions as a strategy to add and subtract fractions.

  • KY.5.NF.1 Efficiently add and subtract fractions with unlike denominators (including mixed numbers) by…

    • KY.5.NF.1.1 using reasoning strategies, such as counting up on a number line or creating visual fraction models

      • Add fractions with unlike denominators using models (5-L.6)
      • Subtract fractions with unlike denominators using models (5-L.9)

    • KY.5.NF.1.2 finding common denominators

      • Add up to 4 fractions with denominators of 10 and 100 (5-L.7)
      • Add fractions with unlike denominators (5-L.8)
      • Subtract fractions with unlike denominators (5-L.11)
      • Add 3 or more fractions with unlike denominators (5-L.13)
      • Complete addition and subtraction sentences with fractions (5-L.16)
      • Add mixed numbers with unlike denominators (5-L.19)
      • Subtract mixed numbers with unlike denominators (5-L.20)
      • Complete addition and subtraction sentences with mixed numbers (5-L.23)

  • KY.5.NF.2 Solve word problems involving addition and subtraction of fractions.

    • KY.5.NF.2.a Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

      • Add and subtract fractions with like denominators: word problems (5-L.4)
      • Add and subtract fractions with unlike denominators: word problems (5-L.12)
      • Add 3 or more fractions: word problems (5-L.14)
      • Add and subtract mixed numbers: word problems (5-L.21)
      • Add and subtract fractions in recipes (5-L.22)

    • KY.5.NF.2.b Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

      • Estimate sums and differences of fractions using benchmarks (5-L.10)
      • Inequalities with addition and subtraction of fractions (5-L.17)
      • Estimate sums and differences of mixed numbers (5-L.18)

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

  • KY.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem.

    • Fractions of a whole: word problems (5-K.2)
    • Relate division and fractions (5-K.16)
    • Understand fractions as division: word problems (5-K.17)

  • KY.5.NF.4 Apply and extend previous understanding of multiplication to multiply a fraction or whole number by a fraction.

    • KY.5.NF.4.a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

      • Multiply fractions by whole numbers using arrays (5-M.5)
      • Multiply fractions by whole numbers I (5-M.11)
      • Multiply fractions by whole numbers II (5-M.12)
      • Multiply fractions by whole numbers: input/output tables (5-M.14)
      • Fractions of a number: model and multiply (5-M.)
      • Fractions of a number I (5-M.15)
      • Fractions of a number: word problems (5-M.16)
      • Fractions of a number II (5-M.17)
      • Multiply two unit fractions using models (5-M.18)
      • Multiply two fractions using models (5-M.20)
      • Multiply two fractions (5-M.21)
      • Multiply a mixed number by a whole number (5-M.36)
      • Multiply a mixed number by a fraction (5-M.37)
      • Multiply two mixed numbers (5-M.38)

    • KY.5.NF.4.b Find the area of a rectangle with fractional side lengths by tiling it with squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.

      • Multiply two unit fractions using models (5-M.18)
      • Multiply two fractions using models: fill in the missing factor (5-M.19)
      • Multiply two fractions using models (5-M.20)
      • Understand fraction multiplication and area (5-M.30)
      • Multiply fractions to find area (5-M.31)
      • Area of rectangles with fractions (5-DD.)
      • Area of rectangles with fractions and mixed numbers (5-DD.6)
      • Area and perimeter: word problems (5-DD.12)

  • KY.5.NF.5 Interpret multiplication as scaling (resizing), by:

    • KY.5.NF.5.a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

      • Scaling whole numbers by fractions (5-M.24)
      • Scaling fractions by fractions (5-M.25)
      • Scaling mixed numbers by fractions (5-M.26)

    • KY.5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

      • Multiply two fractions using models (5-M.20)
      • Scaling whole numbers by fractions: justify your answer (5-M.23)

  • KY.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.

    • Multiply fractions by whole numbers: word problems (5-M.13)
    • Multiply two fractions: word problems (5-M.22)
    • Multiplication with mixed numbers: word problems (5-M.40)
    • Multiply fractions and mixed numbers in recipes (5-M.41)

  • KY.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

    • KY.5.NF.7.a Interpret division of a unit fraction by a non-zero whole number and compute such quotients.

      • Divide unit fractions by whole numbers using models (5-N.1)
      • Divide unit fractions by whole numbers (5-N.2)

    • KY.5.NF.7.b Interpret division of a whole number by a unit fraction and compute such quotients.

      • Divide whole numbers by unit fractions using models (5-N.3)
      • Divide whole numbers by unit fractions (5-N.4)
      • Divide unit fractions and whole numbers using area models (5-N.5)

    • KY.5.NF.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.

      • Divide unit fractions and whole numbers: word problems (5-N.7)

KY.5.MD Measurement and Data

• Convert like measurement units within a given measurement system.

  • KY.5.MD.1 Convert among different size measurement units (mass, weight, liquid volume, length, time) within one system of units (metric system, U.S. standard system and time).

    • Convert time units (5-X.1)
    • Add and subtract mixed time units (5-X.2)
    • Compare and convert customary units of length (5-Y.2)
    • Compare and convert customary units of weight (5-Y.3)
    • Compare and convert customary units of volume (5-Y.4)
    • Compare and convert customary units (5-Y.5)
    • Conversion tables - customary units (5-Y.6)
    • Compare customary units by multiplying (5-Y.7)
    • Convert customary units involving fractions (5-Y.8)
    • Convert mixed customary units (5-Y.9)
    • Add and subtract mixed customary units (5-Y.10)
    • Multi-step problems with customary unit conversions (5-Y.11)
    • Compare and convert metric units of length (5-Y.13)
    • Compare and convert metric units of weight (5-Y.14)
    • Compare and convert metric units of volume (5-Y.15)
    • Compare and convert metric units (5-Y.16)
    • Convert metric units involving decimals (5-Y.17)
    • Conversion tables - metric units (5-Y.18)
    • Convert metric mixed units (5-Y.19)
    • Add and subtract metric mixed units (5-Y.20)
    • Multi-step problems with metric unit conversions (5-Y.21)
    • Multi-step problems with customary or metric unit conversions (5-Y.22)

• Understand and apply the statistics process.

  • KY.5.MD.2 Identify and gather data for statistical questions focused on both categorical and numerical data. Select an appropriate data display (bar graph, pictograph, dot plot). Make observations from the graph about the questions posed.

    • Interpret bar graphs (5-V.4)
    • Interpret bar graphs: multi-step problems (5-V.5)
    • Create bar graphs (5-V.6)
    • Interpret pictographs (5-V.7)
    • Create pictographs (5-V.8)
    • Interpret line plots (5-V.9)
    • Create line plots (5-V.10)
    • Create and interpret line plots with fractions (5-V.11)
    • Choose the best type of graph (5)

• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

  • KY.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

    • KY.5.MD.3.a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume and can be used to measure volume.

      • Volume of rectangular prisms made of unit cubes (5-DD.13)

    • KY.5.MD.3.b A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

      • Volume of rectangular prisms made of unit cubes (5-DD.13)

  • KY.5.MD.4 Measure volumes by counting unit cubic cm, cubic in, cubic ft. and improvised units.

    • Volume of rectangular prisms made of unit cubes (5-DD.13)

  • KY.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

    • KY.5.MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes.

      • Volume of rectangular prisms made of unit cubes (5-DD.13)
      • Relationship between volume and the area of the base: word problems (5-DD.17)

    • KY.5.MD.5.b Apply the formulas V =l × w × h and V = b × h for rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

      • Volume of cubes and rectangular prisms (5-DD.15)
      • Volume of cubes and rectangular prisms: word problems (5-DD.18)
      • Compare volumes and dimensions of rectangular prisms: word problems (5-DD.19)

    • KY.5.MD.5.c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

      • Volume of compound figures (5-DD.16)

KY.5.G Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems.

  • KY.5.G.1 Use a pair perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second.

    • Describe the coordinate plane (5-T.1)
    • Objects on a coordinate plane (5-T.2)

  • KY.5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

    • Graph points on a coordinate plane (5-T.3)
    • Graph points from a table (5-T.4)
    • Coordinate planes as maps (5-T.7)
    • Follow directions on a coordinate plane (5-T.8)

• Classify two-dimensional figures into categories based on their properties.

  • KY.5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

    • Parallel sides in quadrilaterals (5-AA.4)
    • Identify parallelograms (5-AA.5)
    • Identify rectangles (5-AA.7)
    • Identify rhombuses (5-AA.8)
    • Classify quadrilaterals (5-AA.9)
    • Identify the relationships between quadrilaterals (5-AA.11)
    • Describe relationships among quadrilaterals (5-AA.12)

  • KY.5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

    • Is it a polygon? (5-Z.1)
    • Regular and irregular polygons (5-Z.3)
    • Sort polygons into Venn diagrams (5-Z.9)
    • Acute, obtuse, and right triangles (5-AA.1)
    • Scalene, isosceles, and equilateral triangles (5-AA.2)
    • Classify triangles (5-AA.3)
    • Identify parallelograms (5-AA.5)
    • Identify rectangles (5-AA.7)
    • Identify rhombuses (5-AA.8)
    • Classify quadrilaterals (5-AA.9)