Hampton School District
Math Competencies and Standards for Grade 5
OPERATIONS AND ALGEBRAIC THINKING
▪ Analyze patterns and relationships.
▪ Evaluate expressions with parentheses, brackets, or braces.
▪ Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
▪ Generate two numerical patterns using two given rules. Ex. 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.
▪ Identify apparent relationships between corresponding terms in two numerical patterns when given rules. Ex. observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
▪ Interpret numerical expressions without evaluating them. Ex. recognize that 3×(18932+921) is three times as large as 18932+921, without having to calculate the indicated sum or product
▪ Use parentheses, brackets, or braces in numerical expressions.
▪ Write and interpret numerical expressions.
▪ Write simple expressions that record calculations with numbers.
NUMBER AND OPERATIONS IN BASE TEN
▪ 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.
▪ Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols.
▪ Explain patterns in the number of zeros of the product when multiplying a number by powers of 10.
▪ Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
▪ 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.
▪ Fluently multiply multi-digit whole numbers using the standard algorithm.
▪ Illustrate and explain the division calculation by using equations, rectangular arrays, and/or area models.
▪ Perform operations with multi-digit whole numbers and with decimals to hundredths.
▪ 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).
▪ Read, write, and compare decimals to thousandths.
▪ 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.
▪ Relate the strategy used to add, subtract, multiply, and divide decimals to hundredths to a written method and explain the reasoning used.
▪ Understand the place value system. Use place value understanding to round decimals to any place.
▪ Use whole number exponents to denote powers of 10.
NUMBER AND OPERATIONS – FRACTIONS
▪ Add and subtract fractions with unlike denominators (including mixed numbers).
▪ Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
▪ Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
▪ Compute quotients of a whole number by a unit fraction. Ex. Use the relationship between multiplication and division to explain that 4÷(1/5)=20 because 20×(1/5)=4.
▪ 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.
▪ Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
▪ Interpret division of a unit fraction by a non-zero whole number and compute such quotients. Ex. Use the relationship between multiplication and division to explain (1/3)÷4=1/12 because (1/12)×4=1/3.
▪ 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. Ex. use a visual fraction model to show (2/3)×4=8/3, and create a story context for this equation.
▪ Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
▪ Solve real world problems involving multiplication of fractions and mixed numbers.
▪ Solve real-world problems involving division of unit fractions by whole numbers and division of whole numbers by unit fractions. Ex. 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?
▪ Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
▪ 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. Ex. 3/4 is the result of dividing 3 by 4,
noting that 3/4 multiplied by 4 equals 3, and when 3 wholes are shared equally among 4 people each person has 3/4.
▪ Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Ex. recognize an incorrect result 2/5+1/2=3/7,
▪ Use equivalent fractions as a strategy to add and subtract fractions.
MEASUREMENT AND DATA
▪ 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.
▪ 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.
▪ 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.
▪ 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.
▪ Convert like measurement units within a given measurement system.
▪ 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.
▪ 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.
▪ Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
▪ Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
▪ Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
▪ Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
▪ Recognize volume as additive.
▪ Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
▪ Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
▪ Represent and interpret data.
▪ Represent three-fold whole-number products as volumes, e.g., to represent the associative property of multiplication.
▪ Use operations on fractions to solve problems involving information presented in line plots. Ex. different measurements of liquid in identical beakers, how much liquid would each beaker contain if the total amount in all the beakers was redistributed equally.
▪ Classify two-dimensional figures in a hierarchy based on properties.
▪ Classify two-dimensional figures into categories based on their properties.
▪ Graph points on the coordinate plane to solve real-world and mathematical problems.
▪ In coordinates, 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).
▪ Interpret coordinate values of points in the context of a real world situation.
▪ Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane.
▪ Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Ex.. all rectangles have four right angles, squares are rectangles, so all squares have four right angles.
▪ 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, by using an ordered pair of numbers (coordinates).
Hampton School District
Math Competencies and Standards for Grade 5
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