The Common Core in Illinois

5.NBT Number and Operations in Base Ten

• 5.NBT.A Understand the place value system.

  • 5.NBT.A.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.

    • Place value (5-A.2)
    • Place values in decimal numbers (5-G.5)
    • Relationship between decimal place values (5-G.6)

  • 5.NBT.A.2-2 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)

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

    • 5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

      • 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)
      • Convert decimals between standard and expanded form using fractions (5-G.21)

    • 5.NBT.A.3b 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)

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

    • Round decimals (5-G.10)

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

  • 5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard 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 2-digit numbers by larger numbers (5-C.16)
    • Multiply by 2-digit numbers: word problems (5-C.17)

  • 5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

    • 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)
    • Relate multiplication and division (5-D.20)

  • 5.NBT.B.7-1 Add two decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    • Add decimal numbers (5-H.2)

  • 5.NBT.B.7-2 Subtract two decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    • Subtract decimal numbers (5-H.3)

  • 5.NBT.B.7-3 Multiply tenths with tenths or tenths with hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    • Multiply a decimal by a one-digit whole number using blocks (5-I.6)
    • 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 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)
    • 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)

  • 5.NBT.B.7-4 Divide in problems involving tenths and/or hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    • Divide decimals using blocks: complete the equation (5-J.4)
    • Divide decimals using area models: complete the equation (5-J.5)
    • Division with decimal quotients (5-J.6)
    • Divide by decimals without adding zeroes (5-J.11)
    • Divide by decimals (5-J.12)

  • 5.NBT.B.A.Int.1 Demonstrate understanding of the place value system by combining or synthesizing knowledge and skills articulated in 5.NBT.A.

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

  • 5.NBT.B.Int.1 Perform exact or approximate multiplications and/or divisions that are best done mentally by applying concepts of place value, rather than by applying multi-digit algorithms or written strategies.

    • Divide numbers ending in zeroes (5-D.7)
    • Multiply a decimal by a power of ten (5-I.3)
    • Divide by powers of ten (5-J.1)
    • Decimal division patterns over increasing place values (5-J.2)

5.NF Number and Operations—Fractions

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

  • 5.NF.A.1-1 Add two fractions with unlike denominators, or subtract two fractions with unlike denominators, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad+bc)/bd.)

    • Add fractions with unlike denominators using models (5-L.6)
    • Add fractions with unlike denominators (5-L.8)
    • Subtract fractions with unlike denominators using models (5-L.9)
    • Subtract fractions with unlike denominators (5-L.11)

  • 5.NF.A.1-2 Add three fractions with no two denominators equal by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum of fractions with like denominators. For example, 1/2 + 1/3 + 1/4 = (3/6 + 2/6) + 1/4 = 5/6 + 1/4 = 10/12 + 3/12 = 13/12 or alternatively 1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12.

    • Add up to 4 fractions with denominators of 10 and 100 (5-L.7)
    • Add 3 or more fractions with unlike denominators (5-L.13)

  • 5.NF.A.1-3 Compute the result of adding two fractions and subtracting a third, where no two denominators are equal, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 1/2 + 1/3 − 1/4 or 7/8 − 1/3 + 1/2.

  • 5.NF.A.1-4 Add two mixed numbers with unlike denominators, expressing the result as a mixed number, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum with like denominators. For example, 3 1/2 + 2 2/3 = (3 + 2) + (1/2 + 2/3) = 5 + (3/6 + 4/6) = 5 + 7/6 = 5 + 1 + 1/6 = 6 1/6.

    • Add mixed numbers with unlike denominators (5-L.19)

  • 5.NF.A.1-5 Subtract two mixed numbers with unlike denominators, expressing the result as a mixed number, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent difference with like denominators.

    • Subtract mixed numbers with unlike denominators (5-L.20)

  • 5.NF.A.2-1 Solve word problems involving addition and subtraction of fractions referring to the same whole, in cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

    • 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 and subtract mixed numbers: word problems (5-L.21)

  • 5.NF.A.2-2 Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers to word problems involving addition and subtraction of fractions referring to the same whole in cases of unlike denominators. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

    • Estimate sums and differences of fractions using benchmarks (5-L.10)

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

  • 5.NF.B.3-1 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

    • Relate division and fractions (5-K.16)

  • 5.NF.B.3-2 Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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

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

    • 5.NF.B.4a-1 For a whole number q, 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

      • 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 I (5-M.15)

    • 5.NF.B.4a-2 For a fraction q, 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

      • Multiply two unit fractions using models (5-M.18)
      • Multiply two fractions using models (5-M.20)
      • Multiply two fractions (5-M.21)

    • 5.NF.B.4b-1 Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

      • Understand fraction multiplication and area (5-M.30)
      • Multiply fractions to find area (5-M.31)
      • Area of rectangles with fractions and mixed numbers (5-DD.6)

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

    • 5.NF.B.5a 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)

  • 5.NF.B.6-1 Solve real world problems involving multiplication of fractions, e.g., by using visual fraction models or equations to represent the problem.

    • Multiply fractions by whole numbers: word problems (5-M.13)
    • Multiply two fractions: word problems (5-M.22)

  • 5.NF.B.6-2 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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

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

    • 5.NF.B.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

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

    • 5.NF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

      • 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)

    • 5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

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

  • 5.NF.A.Int.1 Solve word problems involving knowledge and skills articulated in 5.NF.A.

    • Add 3 or more fractions: word problems (5-L.14)
    • Add and subtract fractions in recipes (5-L.22)

5.OA Operations and Algebraic Thinking

• 5.OA.A Write and interpret numerical expressions.

  • 5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these 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)

  • 5.OA.A.2-1 Write simple expressions that record calculations with numbers. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7).

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

  • 5.OA.A.2-2 Interpret numerical expressions without evaluating them. For example, recognize that 3 × (18932 + 921) is three times as large as 18932 + 921 without having to calculate the indicated sum or product.

• 5.OA.B Analyze patterns and relationships.

  • 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

    • Compare patterns (5-S.2)
    • 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)

5.MD Measurement and Data

• 5.MD.A Convert like measurement units within a given measurement system.

  • 5.MD.A.1-1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m).

    • Compare and convert customary units (5-Y.5)
    • Conversion tables - customary units (5-Y.6)
    • Convert customary units involving fractions (5-Y.8)
    • Compare and convert metric units (5-Y.16)
    • Convert metric units involving decimals (5-Y.17)
    • Conversion tables - metric units (5-Y.18)

  • 5.MD.A.1-2 Solve multi-step, real world problems requiring conversion among different-sized standard measurement units within a given measurement system.

    • Multi-step problems with customary unit conversions (5-Y.11)
    • Multi-step problems with metric unit conversions (5-Y.21)
    • Multi-step problems with customary or metric unit conversions (5-Y.22)

• 5.MD.B Represent and interpret data.

  • 5.MD.B.2-2 Use operations on fractions for this grade (knowledge and skills articulated in 5.NF) to solve problems involving information in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

    • Create and interpret line plots with fractions (5-V.11)

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

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

    • 5.MD.C.3a 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)

    • 5.MD.C.3b 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)

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

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

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

    • 5.MD.C.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right 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)

    • 5.MD.C.5c 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 irregular figures made of unit cubes (5-DD.14)

5.G Geometry

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

  • 5.G.A.1 Use a pair of 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 axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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

  • 5.G.A.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)

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

  • 5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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

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

    • Regular and irregular polygons (5-Z.3)
    • Sort polygons into Venn diagrams (5-Z.9)
    • Classify triangles (5-AA.3)
    • Classify quadrilaterals (5-AA.9)

5.C Reasoning

• 5.C.1-1 Base explanations/reasoning on place value and/or understanding of operations. Content Scope: Knowledge and skills articulated in 5.NBT.6

  • Divide numbers ending in zeroes (5-D.7)
  • Divide numbers ending in zeroes: word problems (5-D.8)
  • Divide by 2-digit numbers using partial quotients (5-D.13)

• 5.C.1-2 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 5.NBT.7

  • Add, subtract, multiply, and divide decimals (5-O.11)

• 5.C.1-3 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 5.MD.5a

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

• 5.C.2-1 Base explanations/reasoning on the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 5.NBT.6

  • Multi-step word problems: multiplicative comparison (5-D.19)
  • Relate multiplication and division (5-D.20)
  • Choose numbers with a particular quotient (5-D.22)

• 5.C.2-2 Base explanations/reasoning on the relationship between addition and subtraction or the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 5.NBT.7

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

• 5.C.2-3 Base explanations/reasoning on the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 5.NF.3, 5.NF.4a

• 5.C.2-4 Base explanations/reasoning on the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 5.NF.7

• 5.C.3 Reason about the place value system itself. Content Scope: Knowledge and skills articulated in 5.NBT.A

  • Place value (5-A.2)
  • Place values in decimal numbers (5-G.5)
  • Relationship between decimal place values (5-G.6)

• 5.C.4-1 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 5.NF.2

  • Add and subtract fractions with unlike denominators: word problems (5-L.12)
  • Add and subtract mixed numbers: word problems (5-L.21)

• 5.C.4-2 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 5.NF.4b

  • Multiply two unit fractions using models (5-M.18)
  • Multiply two fractions using models (5-M.20)
  • Understand fraction multiplication and area (5-M.30)
  • Multiply fractions to find area (5-M.31)

• 5.C.4-3 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 5.NBT.6

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

• 5.C.4-4 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 5.NBT.7

  • 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)

• 5.C.5-1 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 5.NF.2

  • Add and subtract fractions with like denominators: word problems (5-L.4)

• 5.C.5-2 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 5.NF.4a

  • Multiply unit fractions by whole numbers using number lines (5-M.1)
  • Multiply fractions by whole numbers using number lines (5-M.6)

• 5.C.5-3 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 5.NF.7a, 5.NF.7b

  • Divide unit fractions by whole numbers (5-N.2)
  • Divide whole numbers by unit fractions (5-N.4)

• 5.C.6 Base explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 5.MD.C

  • Volume of rectangular prisms made of unit cubes (5-DD.13)
  • Volume of irregular figures made of unit cubes (5-DD.14)

• 5.C.7-1 Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 5.NF.5b

  • Scaling whole numbers by fractions: justify your answer (5-M.23)

• 5.C.7-2 Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 5.NF.2

• 5.C.7-3 Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 5.NF.1

• 5.C.7-4 Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 4.NBT, 4.NF.A, 4.NF.B

• 5.C.8-2 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 5.MD.5c

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

5.D Modeling

• 5.D.1 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 5, requiring application of knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements.

  • Multi-step word problems: multiplicative comparison (5-D.19)
  • Multi-step word problems (5-P.3)

• 5.D.2 Solve multi-step contextual problems with degree of difficulty appropriate to Grade 5, requiring application of knowledge and skills articulated in 4.OA, 4.NBT, 4.NF, 4.MD

  • Multi-step word problems involving remainders (5-P.4)
  • Multi-step problems with customary unit conversions (5-Y.11)
  • Multi-step problems with metric unit conversions (5-Y.21)
  • Multi-step problems with customary or metric unit conversions (5-Y.22)