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Curriculum Standards:


Compare benchmark fractions (¼, ⅓, ½, ⅔, ¾) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations. - 4.N.2.8
Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. - 4.N.2.7
Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money. - 4.N.2.6
Multiply a whole number by a fraction. - 5.NC.61
Represent a problem situation with a mathematical model. - 5.NC.60
Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. - 4.1.2.5
Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. - 4.1.2.3
Multiply two fractions. - 5.NC.65
Use models to multiply two fractions. - 5.NC.64
Multiply fractions and whole numbers. - 5.NC.63
Multiply a fraction by a whole number. - 5.NC.62
Subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.58
Use models to subtract mixed numbers. - 5.NC.57
Locate points on a coordinate grid. - 5.G.1
Add mixed numbers using equivalent fractions and a common denominator. - 5.NC.56
Graph points on a coordinate grid. - 5.G.2
Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. - 5.DS.A.2
Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. - 5.DS.A.1
Solve real-world problems by graphing points. - 5.G.3
Add mixed numbers using models. - 5.NC.55
Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.G.4
Classify triangles by their angles and sides. - 5.G.5
Classify quadrilaterals by their properties. - 5.G.6
Add and subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.59
Classify quadrilaterals using a hierarchy. - 5.G.7
Construct arguments about geometric figures. - 5.G.8
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. - NC.4.MD.3.c
Solve problems involving a fixed area and varying perimeters and a fixed perimeter and varying areas. - NC.4.MD.3.b
Find areas of rectilinear figures with known side lengths. - NC.4.MD.3.a
Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. - 5.NF.B.8
Analyze patterns and graph ordered pairs generated from number sequences. - 5.OA.8
Use multiplication to divide a whole number by a unit fraction. - 5.NC.72
Extend the concept of multiplication to multiply a fraction or whole number by a fraction. - 5.NF.B.7
Use tables to identify relationships between patterns. - 5.OA.7
Implement division of fractions to show quotients as fractions and mixed numbers. - 5.NC.71
Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. - 5.NF.B.6
Understand how fractions are related to division. - 5.NC.70
Make sense of problems and persevere in solving them. - 5.OA.9
Justify the reasonableness of a product when multiplying with fractions. - 5.NF.B.5
Interpret numerical expressions without evaluating them. - 5.OA.4
Solve multi-step problems involving division with unit fractions. - 5.NC.76
Estimate results of sums, differences and products with fractions and decimals to the thousandths. - 5.NF.B.4
Write simple expressions that show calculations with numbers. - 5.OA.3
Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths. - 5.GM.B.5
Use models to divide whole numbers and unit fractions. Check your answer using multiplication. - 5.NC.75
Understand the concept of volume and recognize that volume is measured in cubic units. - 5.GM.B.4
Use models to divide unit fractions by non-zero whole numbers. - 5.NC.74
Analyze numerical patterns. - 5.OA.6
Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. - 5.NC.73
Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.OA.5
Use previously learned knowledge to make sense of problems and persevere in solving them. - 5.NC.69
Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. - 5.GM.2.1
Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. - 5.NC.68
Evaluate expressions with parentheses, brackets, and braces. - 5.OA.2
Use models, equations, and previously learned strategies to multiply mixed numbers. - 5.NC.67
Use the order of operations to evaluate expressions. - 5.OA.1
Find the area of a rectangle using fractions and diagrams. - 5.NC.66
Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. - 4.1.1.3
Use an understanding of place value to multiply a number by 10, 100 and 1000. - 4.1.1.2
Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines). - 4.N.2.1
Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. - 4.OA.12
Use multiplication to find multiples of a given number. - 4.OA.10
Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. - 4.N.2.4
Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g., ¾ = ¼ + ¼ + ¼). - 4.N.2.3
Generate a shape pattern that follows a given rule and predict a shape in the pattern. - 4.OA.13
Use benchmark fractions (0, ¼, ⅓, ½, ⅔, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols. - 4.N.2.2
Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. - 4.1.1.6
Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 4.1.1.5
Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. - 4.1.1.4
Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. - 5.NC.77
Convert metric units of length. - 5.MD.10
Convert metric units of mass. - 5.MD.12
Convert metric units of capacity. - 5.MD.11
Critique the reasoning of others using understanding of line plots and fractions. - 5.MD.18
Solve problems using data in a line plot. - 5.MD.17
Define a first quadrant Cartesian coordinate system. - 5.GM.C.6
Be precise when solving measurement problems. - 5.MD.14
Plot and interpret points in the first quadrant of the Cartesian coordinate plane. - 5.GM.C.7
Solve real-world problems with measurement conversions. - 5.MD.13
Organize and display data in a line plot. - 5.MD.16
Read and analyze line plots. - 5.MD.15
Compare and order fractions and or decimals to the thousandths place using the symbols >, = or <, and justify the solution. - 5.NF.A.3
Convert decimals to fractions and fractions to decimals. - 5.NF.A.2
Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. - 4.MD.8
Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. - 4.N.1.2
Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). - 4.N.1.6
Read and interpret data using line plots. - 4.MD.1
Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. - 5.GM.3.4
Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. - 4.N.1.5
Recognize and use the relationship between inches, feet, and yards to measure and compare objects. - 5.GM.3.3
Solve problems involving line plots and fractions. - 4.MD.3
Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. - 4.N.1.3
Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. - 5.NC.21
Use models and strategies to solve word problems. - 5.NC.20
Use prior math knowledge and equations or bar diagrams to solve problems. - 5.NC.14
Add and subtract decimals. - 5.NC.13
Subtract decimals to the hundredths using the standard algorithm. - 5.NC.12
Add decimals to the hundredths using the standard algorithm. - 5.NC.11
Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. - 5.NC.18
Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products. - 5.NC.17
Use rounding and compatible numbers to estimate products. - 5.NC.16
Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. - 5.NC.15
Represent problems using equations with a letter standing for the unknown quantity. - NC.4.OA.3.c
Use estimation strategies to assess reasonableness of answers. - NC.4.OA.3.a
Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. - 5.NC.19
Create an input/output chart or table to represent or extend a numerical pattern. - 4.A.1.1
Create growth patterns involving geometric shapes and define the single operation rule of the pattern. - 4.A.1.3
Use place-value patterns and mental math to find quotients. - 5.NC.32
Use previously learned concepts and skills to represent and solve problems. - 5.NC.31
Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. - NC.5.NBT.3.b
Multiply decimals using the standard algorithm for multiplication and multiplication strategies. - 5.NC.30
Write decimals using base-ten numerals, number names, and expanded form. - NC.5.NBT.3.a
Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number. - 5.NC.25
Use models to represent multiplying a decimal and a whole number. - 5.NC.24
Use rounding and compatible numbers to estimate the product of a decimal and a whole number. - 5.NC.23
Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. - 5.NC.22
Use number sense and reasoning to place the decimal point in a product. - 5.NC.29
Use properties to multiply decimals. - 5.NC.28
Multiply decimals using partial products and models. - 5.NC.27
Use grids to model decimals and find the product of a decimal and a decimal. - 5.NC.26
The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. - 5.1
The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. - 5.4
The student will simplify whole number numerical expressions using the order of operations. - 5.7
Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions by: - NC.4.NF.2
Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. - NC.4.NF.1
Generate two numerical patterns using two given rules. - NC.5.OA.3
Use the standard algorithm for division to divide decimals by a whole number. - 5.NC.43
Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: - NC.5.OA.2
Use models to help find quotients in problems involving decimals. - 5.NC.42
Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. - 5.NC.41
Use mental math and place-value patterns to divide a decimal by a power of 10. - 5.NC.40
Find the quotient when the divisor is a multiple of 10. - 5.NC.36
Solve division problems using partial quotients. - 5.NC.35
Add numbers to one million with and without regrouping using the standard algorithm. - 4.NC.8
Use models to find quotients. - 5.NC.34
Use place value and an algorithm to subtract whole numbers. - 4.NC.9
Use compatible numbers and place-value patterns to estimate quotients. - 5.NC.33
Make sense of problems and keep working. - 5.NC.39
Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors. - 5.NC.38
Decide where to place the first digit of the quotient when dividing whole numbers. - 5.NC.37
Determine whether a given whole number is a multiple of a given one-digit number. - NC.4.OA.4.b
Recognize that a whole number is a multiple of each of its factors. - NC.4.OA.4.a
Recognize the relationship between adjacent digits in a multi-digit number. - 4.NC.2
Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. - NC.4.NF.7
Use decimal notation to represent fractions. - NC.4.NF.6
Use place value to round multi-digit numbers. - 4.NC.4
Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. - NC.4.NF.3
Analyze and describe the properties of prisms and pyramids. - 5.GM.A.3
Solve problems with area and perimeter. - NC.4.MD.3
Classify figures in a hierarchy based on properties. - 5.GM.A.2
Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. - NC.4.MD.2
Understand that attributes belonging to a category of figures also belong to all subcategories. - 5.GM.A.1
Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true. - 4.A.2.1
Determine whether a survey question will yield categorical or numerical data. - NC.4.MD.4.c
Know relative sizes of measurement units. Solve problems involving metric measurement. - NC.4.MD.1
Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers. Use real-world situations to represent number sentences and vice versa. - 4.A.2.2
Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. - NC.4.MD.4.b
Collect data by asking a question that yields numerical data. - NC.4.MD.4.a
Determine if the number is prime or composite. - NC.4.OA.4.c
Find common denominators for fractions with unlike denominators. - 5.NC.50
Estimate sums and differences of fractions and mixed numbers. - 5.NC.54
Write equivalent fractions to add and subtract fractions with unlike denominators. - 5.NC.53
Subtract fractions with unlike denominators. - 5.NC.52
Add fractions with unlike denominators using equivalent fractions with a common denominator. - 5.NC.51
Use the standard algorithm to divide decimals, annexing zeros as needed. - 5.NC.47
Use the standard algorithm and place-value patterns to divide a decimal by another decimal. - 5.NC.46
Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals. - 5.NC.45
Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts. - 5.GM.1.1
Use models to visualize the relationship between division and multiplication to divide decimals by a 2-digit whole number. - 5.NC.44
Estimate sums and differences of fractions by using the nearest half or whole number. - 5.NC.49
Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.NC.48
Solve word problems involving addition and subtraction of time intervals that cross the hour. - NC.4.MD.8
The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. - 4.7
Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins. - 4.N.3.1
Represent and interpret data using whole numbers. - NC.4.MD.4
The student will investigate and describe the concept of variable. - 5.19a
The student will write an equation to represent a given mathematical relationship, using a variable. - 5.19b
The student will use an expression with a variable to represent a given verbal expression involving one operation. - 5.19c
The student will create a problem situation based on a given equation, using a single variable and one operation. - 5.19d
Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. - 5.NF.B.7a
Calculate and interpret the product of two fractions less than one. - 5.NF.B.7c
Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. - 5.NF.B.7b
Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts. - NC.5.NF.3.a
Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. - M.4.13
Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. - NC.4.NBT.5
Model and interpret a fraction as the division of the numerator by the denominator. - NC.5.NF.3.b
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. - M.4.12
Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or - NC.4.NBT.6
Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. - NC.4.NBT.1
Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. - NC.4.NBT.2
Solve one-step word problems involving division of whole numbers leading to answers in the form of fractions and mixed numbers, with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, using area, length, and set models or equations. - NC.5.NF.3.c
Find whole-number quotients and remainders with up to four-digit dividends and one-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. - M.4.11
Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. - M.4.10
Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. - NC.4.NBT.4
Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). - M.4.17
Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) - M.4.19
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. - M.4.18
Solve problems involving addition and subtraction by using information presented in a data display. - 4.DS.A.2
Analyze the data in a frequency table, line plot, bar graph or picture graph. - 4.DS.A.3
Generate two numeric patterns given two rules. - 5.RA.A.1a
Graph numeric patterns on the Cartesian coordinate plane. - 5.RA.A.1c
Translate two numeric patterns into two sets of ordered pairs. - 5.RA.A.1b
Identify the relationship between two numeric patterns. - 5.RA.A.1d
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. - M.4.20
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). - M.4.22
Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) - M.4.21
Define the second number in an ordered pair as the vertical distance from the origin. - 5.GM.C.6d
Use rounding or compatible numbers to estimate sums and differences. - 5.NC.9
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. - M.4.28
Use properties of addition and strategies to solve problems mentally. - 5.NC.8
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. - M.4.27
Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. - NC.5.MD.1
Use place value to compare decimals through thousandths. - 5.NC.5
Read and write decimals through thousandths in different ways. - 5.NC.4
Represent and interpret data. - NC.5.MD.2
Use the structure of the decimal place-value system to solve problems involving patterns. - 5.NC.7
Round decimals to different places. - 5.NC.6
Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. - NC.5.MD.4
Use exponents to write powers of 10 and calculate products. - 5.NC.1
Represent the axes as scaled perpendicular number lines that both intersect at 0, the origin. - 5.GM.C.6a
Identify any point on the Cartesian coordinate plane by its ordered pair coordinates. - 5.GM.C.6b
Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals. - 5.NC.3
Define the first number in an ordered pair as the horizontal distance from the origin. - 5.GM.C.6c
Read and write whole numbers using standard form, expanded form, and number names. - 5.NC.2
Relate volume to the operations of multiplication and addition. - NC.5.MD.5
Estimate the size of the product based on the size of the two factors. - 5.NF.B.5a
Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. - 5.NF.B.5c
Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. - 5.NF.B.5b
Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1. - 5.NF.B.5d
Recognize and draw lines of symmetry. Identify line symmetric figures. - 4.G.4
Classify triangles by line segments and angles. - 4.G.2
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using b unit cubes is said to have a volume of b cubic units. - M.5.20b
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 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. - M.5.20a
Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. - M.5.16
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. (e.g., 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?) - M.5.13
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 (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). Instructional Note: In general, a/b + c/d = (ad + bc)/bd. - M.5.11
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators 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 (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). - M.5.12
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 related operations, relate the strategy to a written method and explain the reasoning used. - M.5.10
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., 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). - M.5.19
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. - M.5.18
Identify apparent relationships between corresponding terms. - NC.5.OA.3.a
Form ordered pairs consisting of corresponding terms from the two patterns. - NC.5.OA.3.b
Graph the ordered pairs on a coordinate plane. - NC.5.OA.3.c
Classify two-dimensional figures in a hierarchy based on properties. - M.5.26
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. - M.5.24
Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. - NC.5.NF.1.a
Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. - NC.5.NF.1.b
Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles). - M.5.25
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). - M.5.23
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - M.5.21
Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. - NC.5.NBT.7.b
Make sense of problems and persevere in solving them. - 5.MP.1
Add and subtract decimals to thousandths using models, drawings or strategies based on place value. - NC.5.NBT.7.a
Use estimation strategies to assess reasonableness of answers. - NC.5.NBT.7.d
Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. - NC.5.NBT.7.c
Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. - 5.GM.B.4b
Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. - 5.GM.B.4a
Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. - NC.5.G.1
Classify quadrilaterals into categories based on their properties. - NC.5.G.3
Parentheses, using the order of operations. - NC.5.OA.2.a
Commutative, associative and distributive properties. - NC.5.OA.2.b
Look for and make use of structure. - 5.MP.7
Attend to precision. - 5.MP.6
Look for and express regularity in repeated reasoning. - 5.MP.8
Construct viable arguments and critique the reasoning of others. - 5.MP.3
Reason abstractly and quantitatively. - 5.MP.2
Use appropriate tools strategically. - 5.MP.5
Model with mathematics. - 5.MP.4
Read, write, and compare decimals to thousandths. - NC.5.NBT.3
Explain the patterns in the place value system from one million to the thousandths place. - NC.5.NBT.1
Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. - NC.5.NBT.7
Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. - NC.5.NBT.6
Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. - NC.5.NBT.5
Classify quadrilaterals in a hierarchy based on properties. - NC.5.G.3.b
Explain that attributes belonging to a category of quadrilaterals also belong to all subcategories of that category. - NC.5.G.3.a
Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. - 5.2.1.1
The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. - 4.11
Find the unknown length or width of a rectangle using the known area or perimeter. - 4.MD.10
The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. - 4.15
The student will recognize and demonstrate the meaning of equality in an equation. - 4.16
Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods). - 5.N.3.2
Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data. - 5.N.3.3
Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. - 5.N.3.1
Interpret multiplication as scaling (resizing), by: 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. - M.5.15b
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. - M.5.15a
Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. - NC.4.NF.3.b
Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. - NC.4.NF.3.c
Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. - NC.4.NF.3.d
Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. - 4.RA.A.3
Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. - 4.RA.A.2
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 are areas of rectangles and represent fraction products as rectangular areas. - M.5.14b
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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. (e.g., 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.) Instructional Note: In general, (a/b) × (c/d) = ac/bd. - M.5.14a
Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. - 5.2.2.1
Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. - M.5.6b
Read, write, and compare decimals to thousandths. 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)). - M.5.6a
The student will classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles. - 5.13a
The student will investigate the sum of the interior angles in a triangle and determine an unknown angle measure. - 5.13b
The student will read, write, and identify the place and value of each digit in a nine-digit whole number. - 4.1a
Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. - 5.N.2.3
The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. - 4.1c
Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. - 5.N.2.4
Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. - 5.N.2.1
Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. - NC.4.G.2
Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. - 5.N.2.2
Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. - NC.4.G.3
Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems. - 5.A.1.1
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. (e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many1/3-cup servings are in 2 cups of raisins?) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. - M.5.17c
Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. - NC.4.NF.4.a
Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. - 5.A.1.2
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a whole number by a unit fraction and compute such quotients. (e.g., 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.) Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. - M.5.17b
Solve word problems involving multiplication of a fraction by a whole number. - NC.4.NF.4.b
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Instructional Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division, but division of a fraction by a fraction is not a requirement at this grade. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. (e.g., 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.) - M.5.17a
The student will identify and describe the diameter, radius, chord, and circumference of a circle. - 5.10
The student will solve practical problems related to elapsed time in hours and minutes within a 24-hour period. - 5.11
The student will classify and measure right, acute, obtuse, and straight angles. - 5.12
The student will recognize and apply transformations, such as translation, reflection, and rotation. - 5.14a
The student will determine the probability of an outcome by constructing a sample space or using the Fundamental (Basic) Counting Principle. - 5.15
The student will investigate and describe the results of combining and subdividing polygons. - 5.14b
Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. - 5.RA.C.5
The student will represent equivalent fractions. - 4.2b
Evaluate expressions and solve equations involving variables when values for the variables are given. - 5.2.3.3
Make sense of problems and persevere in solving them. - MP.1
Reason abstractly and quantitatively. - MP.2
Convert measurements in a larger unit in terms of a smaller unit. - 4.GM.C.6a
Look for and make use of structure. - MP.7
Look for and express regularity in repeated reasoning. - MP.8
Construct viable arguments and critique the reasoning of others. - MP.3
Model with mathematics. - MP.4
Use appropriate tools strategically. - MP.5
Attend to precision. - MP.6
Use models or rename fractions to compare. - 4.NC.47
The student will compare and order decimals. - 4.3c
Decompose a fraction or mixed number into a sum of fractions in more than one way. - 4.NC.50
The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. - 5.18
Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). - 5.A.2.1
The student, given a practical problem, will represent data in line plots and stem-and-leaf plots. - 5.16a
The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. - 5.16b
Convert customary units of length. - 5.MD.7
The student, given a practical problem, will compare data represented in a line plot with the same data represented in a stem-and-leaf plot. - 5.16c
Use previously learned knowledge about volumes to choose the appropriate tools to solve volume problems. - 5.MD.6
Convert Customary Units of weight. - 5.MD.9
Convert customary units of capacity. - 5.MD.8
Find the volume of prisms in different ways. - 5.MD.3
Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. - NC.5.NF.1
Find the volume of rectangular prisms using a formula. - 5.MD.2
Use models, prior knowledge of volumes, and previously learned strategies to solve word problems involving volume. - 5.MD.5
Use fractions to model and solve division problems. - NC.5.NF.3
Find the volume of a solid figure that is the combination of two or more rectangular prisms. - 5.MD.4
Find the volume of solid figures. - 5.MD.1
Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form. - 3.NBT.A.2
The student will estimate and determine sums, differences, and products of whole numbers. - 4.4b
The student will estimate and determine quotients of whole numbers, with and without remainders. - 4.4c
Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.41
The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. - 4.4d
Use a number line to locate and identify equivalent fractions. - 4.NC.43
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. - NC.5.NF.4
Use words or mathematical symbols to express a rule for a given pattern. - 4.RA.C.7
Generate a number pattern that follows a given rule. - 4.RA.C.6
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Recognize volume as additive and 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. - M.5.22c
Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.40
Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. - NC.5.NF.7
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. - M.5.22b
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 threefold whole-number products as volumes (e.g., to represent the associative property of multiplication). - M.5.22a
The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. - 4.4a
The student, given a practical context, will describe mean, median, and mode as measures of center. - 5.17a
The student, given a practical context, will describe mean as fair share. - 5.17b
The student, given a practical context, will describe the range of a set of data as a measure of spread. - 5.17c
The student, given a practical context, will determine the mean, median, mode, and range of a set of data. - 5.17d
Use fractions or decimals to solve word problems involving money. - 4.NC.68
Multiply or divide to solve problems involving a multiplicative comparison. - 4.RA.A.1
The student will represent and identify equivalencies among fractions and decimals, with and without models. - 5.2a
The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. - 4.5c
The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. - 5.2b
Use area and length models to multiply two fractions, with the denominators 2, 3, 4. - NC.5.NF.4.a
Reasoning about their size and using area and length models. - NC.4.NF.2.a
Using benchmark fractions 0, ½, and a whole. - NC.4.NF.2.b
Comparing common numerator or common denominators. - NC.4.NF.2.c
Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number. - NC.5.NF.4.b
Solve one-step word problems involving multiplication of fractions using models to develop the algorithm. - NC.5.NF.4.c
The student will add and subtract fractions and mixed numbers having like and unlike denominators. - 4.5b
Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. - 4.3.3.2
Use equivalent fractions and properties of operations to add mixed numbers with like denominators. - 4.NC.57
The student will identify and describe the characteristics of even and odd numbers. - 5.3b
Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. - 4.RA.B.4
Use the four operations to solve problems involving time. - 4.NC.63
Calculate and interpret the quotient of a whole number by a unit fraction. - 5.NF.B.8b
Compare decimals by reasoning about their size. - 4.NC.66
Calculate and interpret the quotient of a unit fraction by a non-zero whole number. - 5.NF.B.8a
Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. - 4.4.1.1
Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. - 4.NF.C.12
Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. - 4.RA.B.5
Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. - 4.NF.C.11
The student will add and subtract with decimals. - 4.6a
The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. - 4.6b
The student will identify and describe the characteristics of prime and composite numbers. - 5.3a
Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. - 4.3.1.1
Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data. - 5.4.1.2
Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a “leveling out” of data. - 5.4.1.1
Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. - 5.NBT.A.1
Classify two-dimensional shapes by their sides and/or angles. - 4.GM.A.2
Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. - 5.NBT.A.2
Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left. - 5.NBT.A.3
Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. - 4.3.2.4
Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. - 4.3.2.3
Explain patterns in products and quotients when numbers are multiplied by 1,000, 100, 10, 0.1, and 0.01 and/or divided by 10 and 100. - NC.5.NBT.1.b
Explain 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. - NC.5.NBT.1.a
Construct lines of symmetry for a two-dimensional figure. - 4.GM.A.3
The student will estimate and determine the product and quotient of two numbers involving decimals. - 5.5a
The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. - 5.5b
Develop and use the formulas V = ℓwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. - 5.3.2.4
Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. - 5.3.2.1
Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. - 5.3.2.3
Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. - 5.3.2.2
Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. - 4.NC.30
Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. - 5.NBT.A.8
Evaluate the value of powers of 10 and understand the relationship to the place value system. - 5.NBT.A.4
The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. - 5.6a
Round numbers from billions to thousandths place. - 5.NBT.A.5
The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. - 5.6b
Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. - 5.NBT.A.6
Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. - 5.NBT.A.7
Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. - 4.2.2.1
Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. - 4.NF.B.6
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. - 4.NF.B.7
Find the volume of a 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. - NC.5.MD.5.a
Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. - 4.NC.19
Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. - 4.NF.B.4
Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. - 4.NC.18
Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. - 4.NF.B.5
Model sums and differences of decimals. - 5.NC.10
Find volume of solid figures with one-digit dimensions composed of two non-overlapping rectangular prisms. - NC.5.MD.5.c
Build understanding of the volume formula for rectangular prisms with whole-number edge lengths in the context of solving problems. - NC.5.MD.5.b
Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.1.1.4
Estimate solutions to arithmetic problems in order to assess the reasonableness of results. - 5.1.1.3
Solve problems involving multiplication of a fraction by a whole number. - 4.NF.B.8
Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. - NC.4.OA.1
Solve two-step word problems involving the four operations with whole numbers. - NC.4.OA.3
Generate and analyze a number or shape pattern that follows a given rule. - NC.4.OA.5
Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. - M.4.1
Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. - M.4.2
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) - M.4.5
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). - M.4.6
Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. - M.4.3
Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. - M.4.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm. - M.4.9
Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. - 5.1.1.2
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. - M.4.7
Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. - 5.1.1.1
Use place value understanding to round multi-digit whole numbers to any place. - M.4.8
Estimate solutions to division problems in order to assess the reasonableness of results. - 5.N.1.1
Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.N.1.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). - M.4.15c
Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. - 5.N.1.2
Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. - 5.N.1.3
Solve multi-step problems that require measurement conversions. - 5.GM.D.9
Demonstrate fluency with addition and subtraction of whole numbers. - 4.NBT.A.5
Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. - 4.2.2.2
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. - 4.NBT.A.6
The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. - 5.8a
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. - 4.NBT.A.7
The student will differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. - 5.8b
Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. - NC.4.MD.1.b
Convert measurements of capacity, length and weight within a given measurement system. - 5.GM.D.8
Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. - 4.2.1.1
Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. - NC.4.MD.1.a
Make and interpret a representation of data using a line graph. - NC.5.MD.2.b
Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. - 4.GM.C.7
Collect data by asking a question that yields data that changes over time. - NC.5.MD.2.a
Apply the area and perimeter formulas for rectangles to solve problems. - 4.GM.C.8
Determine whether a survey question will yield categorical or numerical data, or data that changes over time. - NC.5.MD.2.c
Know relative sizes of measurement units within one system of units. - 4.GM.C.6
Compare two fractions using the symbols >, = or <, and justify the solution. - 4.NF.A.3
Explain and/or illustrate why two fractions are equivalent. - 4.NF.A.1
Recognize and generate equivalent fractions. - 4.NF.A.2
Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. - 5.1.2.3
Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. - 5.1.2.2
Round numbers to the nearest 0.1, 0.01 and 0.001. - 5.1.2.5
Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. - 5.1.2.4
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. - M.4.14c
Write, evaluate and interpret numeric expressions using the order of operations. - 5.RA.B.3
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). - M.4.14b
Translate written expressions into algebraic expressions. - 5.RA.B.4
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. - M.4.14d
The student will given the equivalent measure of one unit, identify equivalent measurements within the metric system. - 5.9a
The student will solve practical problems involving length, mass, and liquid volume using metric units. - 5.9b
Solve problems involving the conversion of one measure of time to another. - 4.GM.3.2
Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot. - 4.D.1.3
Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. - M.5.1
Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. - 4.D.1.1
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. - M.5.4
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. Use whole-number exponents to denote powers of 10. - M.5.5
Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., 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.) - M.5.2
Investigate the relationship between two numeric patterns. - 5.RA.A.1
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. (e.g., 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.) - M.5.3
Write a rule to describe or explain a given numeric pattern. - 5.RA.A.2
Fluently multiply multi-digit whole numbers using the standard algorithm. - M.5.8
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. - M.5.9
Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. - 5.1.2.1
Use place value understanding to round decimals to any place. - M.5.7
Represent tenths and hundredths with models, making connections between fractions and decimals. - NC.4.NF.6.c
Express, model and explain the equivalence between fractions with denominators of 10 and 100. - NC.4.NF.6.a
Round multi-digit whole numbers to any place. - 4.NBT.A.1
Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. - 4.NBT.A.2
Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. - 4.NBT.A.4
Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments. - 5.D.1.2
Model addition and subtraction of fractions and decimals using a variety of representations. - 5.1.3.2
Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. - 5.1.3.1
Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. - 5.1.3.4
Estimate sums and differences of decimals and fractions to assess the reasonableness of results. - 5.1.3.3
Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. - 4.1.2.2
Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. - 4.1.2.1
Solve two-step problems by finding and solving the hidden question first. - 4.OA.3
Use multiplication to find all the factor pairs for a whole number. - 4.OA.7
Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. - 5.2.1.2




List of all Files Validated:


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