Maryland College and Career-Ready Standards 5th Grade Math Activities

MD.MA.5.OA. Operations and Algebraic Thinking (OA)

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

5.OA.A.1. Additional Standard: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.1.1. Ability to build on knowledge of order of operations to find the value of an expression without variables.

5.OA.A.2. Additional Standard: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2×(8+7). Recognize that 3×(18932+921) is three times as large as 18932+921, without having to calculate the indicated sum or product.

5.OA.A.2.1. Knowledge of the term “expressions” and the difference between this term and equation.

5.OA.A.2.3. Ability to write simple expressions without actually calculating them.

5.OA.A.2.4. Ability to apply their reasoning of the four operations and knowledge of place value to describe the relationship between numbers.

5.OA.A.2.5. This standard does not include variables, only numbers and operational signs.

5.OA.A.2.6. Ability to apply their understanding of four operations and grouping symbols to write expressions.

5.OA.B. Analyze patterns and relationships.

5.OA.B.3. Additional Standard: 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.

5.OA.B.3.1. Ability to generate and analyze patterns (4.OA.C.5).

5.OA.B.3.2. Knowledge that corresponding terms are used to create ordered pairs.

5.OA.B.3.3. Ability to apply knowledge of the coordinate system. Graphing points in the first quadrant of a coordinate plane (5.G.A.1 and 2).

MD.MA.5.NBT. Number and Operations in Base Ten (NBT)

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

5.NBT.A.1. Major Standard: 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.

5.NBT.A.1.1. Ability to identify place value of individual digits in a multi-digit whole number (4.NBT.A.1 and 2).

5.NBT.A.1.2. Ability to describe the relationship between decimal fractions and decimal notation (4.NBT.C.5, 6, 7) – grade 4 to hundredths, grade 5 to thousandths.

5.NBT.A.1.3. Ability to identify and describe the integration of decimal fractions into place value system.

5.NBT.A.1.4. Ability to reason about the magnitude of whole numbers, decimals, and decimal fractions (Identify which digit is 10 times, 100 times, or 1/10, 1/100, etc. of another digit).

5.NBT.A.2. Major Standard: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

5.NBT.A.2.1. Knowledge of exponents with powers of 10.

5.NBT.A.2.2. Knowledge of when dividing by powers of 10, the exponent above the 10 indicates how many places the decimal point is moving (how many times we are dividing by 10, the number because ten time smaller). When dividing by 10, the decimal point moves to the left.

5.NBT.A.3a. Major Standard: Read, write, and compare decimals to thousandths (builds on grade 4 work to hundredths) – Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347.392 = 3x100+4x10+7x1+3x(1/10)+9x(1/100)+2x(1/1000).

5.NBT.A.3a.1. See the skills and knowledge that are stated in the standard.

5.NBT.A.3b. Major Standard: Read, write, and compare decimals to thousandths (builds on grade 4 work to hundredths) – Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons (builds on work from 4.NBT.C.7 and 5.NBT.A.2).

5.NBT.A.3b.1. See the skills and knowledge that are stated in the standard.

5.NBT.A.4. Major Standard: Use place value understanding to round decimals to any place.

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

5.NBT.B.4. Major Standard: Use place value understanding to round decimals to any place.

5.NBT.B.4.1. Ability to reason and explain the answers to a problem that requires rounding using knowledge of place value and number sense.

5.NBT.B.4.2. Ability to identify two possible answers and use understanding of place value to compare the given number to the possible answers to round to any place.

5.NBT.B.5. Major Standard: Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.5.1. Accurate recall of single digit multiplication facts.

5.NBT.B.5.2. Select and use accurate and efficient methods to compute such as mental math, properties of multiplication, decomposing/composing numbers, (as they transition to the standard algorithm).

5.NBT.B.5.3. Ability to apply an understanding of place value and multiplying multi-digit numbers.

5.NBT.B.5.4. Ability to use the standard algorithm and recognize the importance of place value.

5.NBT.B.6. Major Standard: 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.

5.NBT.B.6.2. Ability to use a variety of strategies to find whole number quotients such as, relationship between multiplication and division, properties of operations, place value, etc.

5.NBT.B.6.3. Ability to apply place value understanding to multiplying and dividing multi-digit numbers.

5.NBT.B.6.4. Ability to explain calculations by using equations or models.

5.NBT.B.6.6. Limits up to four-digit and two-digit divisors, can include remainders.

5.NBT.B.7. Major Standard: Add, subtract, multiply, and divide 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.

5.NBT.B.7.1. Ability to use concrete models and pictorial representations to perform operations with decimals to hundredths.

5.NBT.B.7.2. Ability to recognize that the product is not always larger than its factors.

5.NBT.B.7.3. Ability to recognize that the quotient is not always smaller than the dividend.

5.NBT.B.7.4. Ability to write numerical expressions or equations to represent the problem and solution.

5.NBT.B.7.5. Ability to reason and explain how the models, pictures, or strategies were used to solve the problem.

MD.MA.5.NF. Number and Operations – Fractions (NF)

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

5.NF.A.1. Major Standard: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

5.NF.A.1.1. Knowledge of understanding of addition and subtraction of fractions with like denominators and unit fractions from grade 4 (4.NF.B.3.a-d).

5.NF.A.1.3. Ability to create equivalent fractions for each addend by using the identity property (standard algorithm).

5.NF.A.2. Major Standard: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.

5.NF.A.2.1. Knowledge of understanding addition and subtraction of fractions as joining and separating parts referring to the same whole (4.NF.A.3a).

5.NF.A.2.2. Ability to add and subtract fractions with unlike denominators by using visual fraction models or equations (5.NF.A.1).

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

5.NF.B.3. Major Standard: 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, 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?

5.NF.B.3.1. Ability to recognize that a fraction is a representation of division.

5.NF.B.3.2. Relate division of whole numbers to division of fractions.

5.NF.B.4a. Major Standard: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction – Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q÷b. For example, use a visual fraction model to show (2/3)x4 = 8/3, and create a story context for this equation. Do the same with (2/3)x(4/5) = 8?15. (In general, (a/b)x(c/d) = ac/bd.)

5.NF.B.4a.1. Ability to apply knowledge of multiplication of a whole numbers to multiplying fractions by a whole number as repeated addition of a unit fraction using fraction models and then equations (4.NF.B.4c).

5.NF.B.4a.3. Ability to multiply a fraction times a fraction using fraction models and then equations.

5.NF.B.4a.4. Ability to create a story context to multiply a fraction by a fraction.

5.NF.B.4b. Major Standard: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction – Find the area of a rectangle with fractional side lengths by tiling it with unit 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.

5.NF.B.4b.1. Knowledge of unit fractions to multiply all fractions (4.NF.B.3a, b).

5.NF.B.5a. Major Standard: Interpret multiplication as scaling (resizing) by: 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.

5.NF.B.5a.2. Ability to reason abstractly about the magnitude of products with fractions.

5.NF.B.5a.3. For example: 5x3 is 5 times as big as 3 (grade 4); Grade 5 – 1/2 x 3 is half the size of 3.

5.NF.B.5b. Major Standard: Interpret multiplication as scaling (resizing) by: Explaining why multiplying a given number by a fraction greater than one 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 x a)/(n x b) to the effect of multiplying (a/b) by 1.

5.NF.B.5b.1. Ability to understand the differences in results when multiplying whole numbers and when multiplying fractions (when multiplying a fraction greater than 1, the number increases and when multiplying by a fraction less than 1, the number decreases).

5.NF.B.5b.2. Ability to explore the concepts in this standard while doing work on 5.NF.B.4a.

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

5.NF.B.6.2. Solve a variety of problems using multiplication of fractions. Include problems involving fraction by a whole number, fraction by a fraction, fraction by a mixed number, and mixed number by a mixed number.

5.NF.B.7c. Major Standard: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients – 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?

5.NF.B.7c.1. Knowledge of the relationship between multiplication and division (4.NBT.B.6., 5.NF.B.7a and 7b).

MD.MA.5.MD. Measurement and Data (MD)

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

5.MD.A.1. Supporting Standard: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real-world problems.

5.MD.A.1.1. Ability to convert measurements within the same measurement system (Metric and Customary) (4.MD.A.1).

5.MD.A.1.2. Ability to distinguish between and select the appropriate units for length, mass, and volume (4.MD.A.1).

5.MD.A.1.3. Knowledge of the relationships between the units of measurement in both metric and customary systems.

5.MD.A.1.4. Ability to use appropriate measuring tools for both systems (yardsticks/meter sticks, rulers (metric and customary), Measuring cups, etc.

5.MD.A.1.5. Ability to convert measurements found within the context of multi-step, real world word problems (4.MD.A.2).

5.MD.A.1.6. Ability to use knowledge of base ten system to converting metric measurements for length, mass, and volume.

5.MD.B. Represent and interpret data.

5.MD.B.2. Supporting Standard: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); Use operations for this grade to solve problems involving information presented 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 (4.MD.B.4).

5.MD.B.2.2. Ability to use equivalent fractions to add and subtract fractions (5.NF.A.1 and 2).

5.MD.B.2.3. Ability to apply knowledge of multiplication and division to multiply and divide fractions based on the line plot data.

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

5.MD.C.3. Major Standard: Recognize volume as an attribute of solid figures and understand concepts of volume measurement: A) A cube with side lengths 1 unit, called a “unit cube”, is said to have “one cubic unit” of volume, and can be used to measure volume; 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.

5.MD.C.3.1. Ability to understand that volume introduces a third dimension to figures.

5.MD.C.3.2. Ability to understand the differences in liquid volume and solid volume. Liquid volume (4.MD.A.2) fills the three dimension space of a container and takes the shape of the container. Solid volume fills the space of a three-dimensional container by packing the container with solid units.

5.MD.C.3.3. Knowledge that solid units are composed of 1 unit by 1 unit by 1. It called a cubic unit and it is the standard measure for finding volume.

5.MD.C.3.4. Ability to find the total volume of a solid figure by packing a solid figure with cubic inches or centimeters, without gaps or overlaps, and then counting the cubic units to find the total volume (Does not ‘fill’ a container randomly with cubic units).

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

5.MD.C.4.1. Ability to pack unit cubes without gaps or overlaps into right rectangular prisms and count the cubes to determine the volume.

5.MD.C.4.2. Understand that the volume of a right rectangular prism can be found by first packing the container with cubes to making rows to create layers (an array of rows and columns that pack the container without gaps or overlaps).

5.MD.C.5a. Major Standard: Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume – 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 three-fold whole-number products as volumes, e.g., to represent the associative property of multiplication.

5.MD.C.5a.1. Apply multiplicative reasoning to determine volume, looking for and making use of previously learned structure for finding volume using unit cubes in iterated layers. Use multiplication to find the area of the base of the container (length and width = 1 layer) and multiply the resulting area by the number of layers (height).

5.MD.C.5a.2. Ability to understand the height of the prism tells how many layers will fit in the prism.

5.MD.C.5a.3. Ability to represent three fold whole-number product as volume to represent the associative property (Volume is a derived attribute once length is specified; it can be computed as the product of three length measurements or as the product of one area and one length).

5.MD.C.5b. Major Standard: Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume – 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.

5.MD.C.5b.3. Ability to find the volume of a figure with an unknown dimension.

MD.MA.5.G. Geometry (G)

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

5.G.A.1. Additional Standard: 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).

5.G.A.1.1. See the skills and knowledge that are stated in the standard.

5.G.A.2. Additional Standard: Represent real-world 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.

5.G.A.2.1. See the skills and knowledge that are stated in the standard.

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

5.G.B.3. Additional Standard: 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.

5.G.B.3.1. Knowledge of classifying two dimensional figures; see relationships among the attributes of two-dimensional figures.

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

5.G.B.4.1. See the skills and knowledge that are stated in the standard.