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Product Name: enVisionmath2.0 Custom Grade 4 Virginia
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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
Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. - 4.1.2.6
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
Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. - 4.1.2.4
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 fractions and whole numbers. - 5.NC.63
Round decimals to the nearest tenth. - 4.1.2.7
Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids. - NC.3.G.1.b
Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals. - NC.3.G.1.a
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
Extend the concept of multiplication to multiply a fraction or whole number by a fraction. - 5.NF.B.7
Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. - 5.NF.B.6
Understand the concept of volume and recognize that volume is measured in cubic units. - 5.GM.B.4
Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. - 5.NC.73
Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. - 3.4.1.1
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
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
Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. - 4.OA.11
Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. - 4.OA.12
Write and solve two-step problems involving variables using any of the four operations. - 3.RA.D.9
Use multiplication to find multiples of a given number. - 4.OA.10
Represent tenths and hundredths with concrete models, making connections between fractions and decimals. - 4.N.2.5
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
Solve problems by using patterns. - 4.OA.14
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). - M.3.3
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). - M.3.1
Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). - M.3.6
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
Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. - M.3.7
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
Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. - M.3.5
Solve two-step word problems using the four operations, 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. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). - M.3.8
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). - M.3.9
Understand that parts of a whole can be expressed as fractions and or decimals. - 5.NF.A.1
The student will read and interpret data represented in pictographs and bar graphs. - 3.15b
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 customary units of length and convert from a larger unit to a smaller unit. - 4.MD.5
Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. - 4.MD.6
Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. - 4.MD.7
Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. - 4.MD.8
Recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit. - 4.MD.9
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
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
Represent data using line plots and interpret data in line plots to solve problems. - 4.MD.2
Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. - 4.N.1.4
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 using an understanding of line plots. - 4.MD.4
Measure distances around objects. - 3.3.2.3
Find the perimeter of a polygon by adding the lengths of the sides. - 3.3.2.2
Represent problems using equations with a letter standing for the unknown quantity. - NC.4.OA.3.c
Interpret remainders in word problems. - NC.4.OA.3.b
Use estimation strategies to assess reasonableness of answers. - NC.4.OA.3.a
Create an input/output chart or table to represent or extend a numerical pattern. - 4.A.1.1
Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. - NC.3.MD.2.c
Create growth patterns involving geometric shapes and define the single operation rule of the pattern. - 4.A.1.3
Solve problems involving perimeters of polygons. - 3.GM.D.15
Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. - NC.3.MD.2.b
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
Write decimals using base-ten numerals, number names, and expanded form. - NC.5.NBT.3.a
Use rounding and compatible numbers to estimate the product of a decimal and a whole number. - 5.NC.23
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. - M.3.12
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. - M.3.11
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.13
Use place value understanding to round whole numbers to the nearest 10 or 100. - M.3.10
Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. - 3.3.1.2
Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. - 3.3.1.1
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
Know relationships among units of time. - 3.3.3.2
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
Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. - 3.3.3.1
Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). - M.3.16
Use the given sides of a polygon and the known perimeter to find the unknown side length. - 3.MD.23
Find the perimeter of different polygons with common shapes. - 3.MD.22
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). - M.3.18
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. - M.3.17
Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. - 3.A.2.2
Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. - 3.A.2.1
Round greater whole numbers to estimate sums and differences. - 4.NC.7
Add numbers to one million with and without regrouping using the standard algorithm. - 4.NC.8
Use place value and an algorithm to subtract whole numbers. - 4.NC.9
Determine whether a given whole number is a multiple of a given one-digit number. - NC.4.OA.4.b
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. - M.3.23
Recognize that a whole number is a multiple of each of its factors. - NC.4.OA.4.a
Solve word problems involving addition and subtraction to measure quantities of time. - 3.MD.15
Read and write numbers in expanded form, with numerals, and using number names. - 4.NC.1
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. - M.3.25
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
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. - M.3.24
Recognize the relationship between adjacent digits in a multi-digit number. - 4.NC.2
Use place value to compare multi-digit numbers. - 4.NC.3
Use decimal notation to represent fractions. - NC.4.NF.6
Use pictures to help solve problems about mass and volume. - 3.MD.19
Use place value to round multi-digit numbers. - 4.NC.4
Use previously learned concepts and skills to construct arguments about place value. - 4.NC.5
Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. - NC.4.NF.3
Add and subtract whole numbers mentally using a variety of methods. - 4.NC.6
Solve problems with area and perimeter. - NC.4.MD.3
Analyze and describe the properties of prisms and pyramids. - 5.GM.A.3
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
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
Use estimation strategies to assess reasonableness of answers. - NC.3.NBT.2.a
Make a representation of data and interpret data in a frequency table, scaled bar graph, and/or line plot. - NC.4.MD.4.b
Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems. - NC.3.NBT.2.b
Collect data by asking a question that yields numerical data. - NC.4.MD.4.a
Use graphs to solve problems. - 3.MD.11
Use expanded form to decompose numbers and then find sums and differences. - NC.3.NBT.2.c
Determine if the number is prime or composite. - NC.4.OA.4.c
Find common denominators for fractions with unlike denominators. - 5.NC.50
Subtract fractions with unlike denominators. - 5.NC.52
Add fractions with unlike denominators using equivalent fractions with a common denominator. - 5.NC.51
Solve word problems involving addition and subtraction of time intervals that cross the hour. - NC.4.MD.8
Develop an understanding of angles and angle measurement. - NC.4.MD.6
The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. - 4.7
Represent and interpret data using whole numbers. - NC.4.MD.4
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
The student will solve practical problems related to elapsed time in hours and minutes within a 12-hour period. - 4.9
Decompose a rectangle into smaller rectangles to find the area of the original rectangle. - 3.GM.C.14
Multiply whole-number side lengths to solve problems involving the area of rectangles. - 3.GM.C.12
Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. - 3.GM.C.11
Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. - 3.A.1.1
Create a frequency table and/or line plot to display measurement data. - 4.DS.A.1
Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. - 5.NF.B.7b
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
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
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 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
Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. - NC.4.NBT.7
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
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
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. - M.4.16
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
Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. - M.4.24
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: - M.4.23
Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. - M.4.26
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). - M.4.25
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
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
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
Use place value to compare decimals through thousandths. - 5.NC.5
Read and write decimals through thousandths in different ways. - 5.NC.4
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
Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. - NC.4.MD.6.c
Classify quadrilaterals by lines and angles. - 4.G.3
Measure and sketch angles in whole-number degrees using a protractor. - NC.4.MD.6.b
Recognize and draw lines of symmetry. Identify line symmetric figures. - 4.G.4
Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. - NC.4.MD.6.a
Draw and identify perpendicular, parallel, and intersecting lines. - 4.G.1
Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. - NC.3.MD.3.b
Classify triangles by line segments and angles. - 4.G.2
Solve one and two-step “how many more” and “how many less” problems using information from these graphs. - NC.3.MD.3.c
Collect data by asking a question that yields data in up to four categories. - NC.3.MD.3.a
Draw figures that have line symmetry. - 4.G.5
Identify arithmetic patterns and explain the patterns using properties of operations. - 3.RA.E.11
Use understanding of two-dimensional shapes to critique the reasoning of others. - 4.G.6
Interpret products of whole numbers. - 3.RA.A.1
Use multiplication and division within 100 to solve problems. - 3.RA.A.4
Describe in words or drawings a problem that illustrates a multiplication or division situation. - 3.RA.A.3
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
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
Interpret patterns of multiplication on a hundreds board and/or multiplication table. - NC.3.OA.9
Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. - NC.3.OA.8
Represent, interpret, and solve one-step problems involving multiplication and division. - NC.3.OA.3
Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. - NC.3.OA.7
Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. - NC.3.OA.6
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
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
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
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
Add and subtract whole numbers up to and including 1,000. - NC.3.NBT.2
Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. - NC.3.NBT.3
Apply properties of operations as strategies to multiply and divide. - 3.RA.B.6
The student will create equations to represent equivalent mathematical relationships. - 3.17
Read, write, and compare decimals to thousandths. - NC.5.NBT.3
Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. - NC.5.NBT.7
Solve one- and two-step problems using information presented in bar and/or picture graphs. - 3.DS.A.2
Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. - 3.DS.A.1
Demonstrate fluency with products within 100. - 3.RA.C.8
Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. - 3.RA.C.7
The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. - 3.1b
Find the measure of an angle that turns through a fraction of a circle. - 4.MD.13
Recognize and draw lines, rays, and angles with different measures. - 4.MD.12
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
Be precise when solving measurement problems. - 4.MD.11
The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. - 4.12
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
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. - M.4.23a
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
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through b one-degree angles is said to have an angle measure of b degrees. - M.4.23b
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - NC.4.NF.3.a
The student will represent fractions and mixed numbers with models and symbols. - 3.2b
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
The student will name and write fractions and mixed numbers represented by a model. - 3.2a
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 problems involving addition and subtraction of minutes. - 3.GM.B.6
Estimate time intervals in minutes. - 3.GM.B.5
Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. - 3.GM.B.8
Measure or estimate length, liquid volume and weight of objects. - 3.GM.B.7
Tell and write time to the nearest minute. - 3.GM.B.4
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
Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. - 3.GM.2.8
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
Develop and use formulas to determine the area of rectangles. 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. - 3.GM.2.2
Use appropriate tools, such as a protractor and ruler, to solve problems. - 4.MD.17
The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. - 3.3b
Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations. - 3.GM.2.1
Use addition and subtraction to solve problems with unknown angle measures. - 4.MD.16
The student will estimate and determine the sum or difference of two whole numbers. - 3.3a
Use a protractor to measure and draw angles. - 4.MD.15
Use known angle measures to measure unknown angles. - 4.MD.14
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
Use number lines to join equal groups. - 3.OA.2
Use arrays as one way to think about and understand multiplication. - 3.OA.3
Understand and use the Commutative Property of Multiplication. - 3.OA.4
Draw diagrams and write equations to solve two-step problems involving addition and subtraction of whole numbers. - 3.OA.37
The student will read, write, and identify the place and value of each digit in a nine-digit whole number. - 4.1a
The student will compare and order whole numbers expressed through millions. - 4.1b
Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. - 3.OA.39
The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. - 4.1c
Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. - 5.N.2.3
Solve multiplication and division problems that involve different strategies and representations. - 3.OA.33
Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. - 5.N.2.4
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 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
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
Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. - NC.4.G.1
The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. - 3.4d
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
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
The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. - 3.4c
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 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
The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. - 3.4b
The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. - 3.4a
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - NC.3.MD.7.a
Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. - 3.GM.A.1
Know from memory all products with factors up to and including 10. - NC.3.OA.7.a
Illustrate and explain using the relationship between multiplication and division. - NC.3.OA.7.b
Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. - 3.GM.A.3
Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. - 3.GM.A.2
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. - NC.3.MD.7.b
Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. - 5.RA.C.5
The student will compare and order fractions and mixed numbers, with and without models. - 4.2a
The student will represent equivalent fractions. - 4.2b
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
Use fraction strips and number lines to add fractions. - 4.NC.49
Use benchmarks, area models, and number lines to compare fractions. - 4.NC.46
Construct viable arguments and critique the reasoning of others. - MP.3
Model with mathematics. - MP.4
Use division to find equivalent fractions. - 4.NC.45
Use appropriate tools strategically. - MP.5
Construct arguments about fractions. - 4.NC.48
Use models or rename fractions to compare. - 4.NC.47
Attend to precision. - MP.6
The student will read, write, represent, and identify decimals expressed through thousandths. - 4.3a
Solve problems involving separating parts of the same whole by subtracting fractions. - 4.NC.53
The student will round decimals to the nearest whole number. - 4.3b
Use tools such as fraction strips, area models, and number lines to subtract fractions. - 4.NC.52
The student will compare and order decimals. - 4.3c
Use the Distributive Property to break apart unknown facts with 4 as a factor. - 3.OA.16
Use number lines and benchmark fractions to estimate fraction sums and differences. - 4.NC.55
The student will given a model, write the decimal and fraction equivalents. - 4.3d
Count forward or backward on a number line to add or subtract. - 4.NC.54
Gain fluency in multiplication when multiplying by 0 or 1. - 3.OA.10
Solve problems involving joining parts of the same whole by adding fractions. - 4.NC.51
Decompose a fraction or mixed number into a sum of fractions in more than one way. - 4.NC.50
Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions. - 3.N.3.3
Describe the numerator as representing the number of pieces being considered. - 3.NF.A.2a
Construct fractions using length, set, and area models. - 3.N.3.2
Use mental math to subtract. - 3.NC.5
Use place value and a number line to round numbers. - 3.NC.3
Read and write fractions with words and symbols. - 3.N.3.1
Round whole numbers to the nearest 10 or 100. - 3.NBT.A.1
Use partial quotients and place-value understandings to divide with greater dividends. - 4.NC.39
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
Use partial quotients to divide. - 4.NC.38
Use a multiplication table to find the missing factor in a division problem. - 3.OA.30
Use rounding or compatible numbers to estimate a sum. - 3.NC.6
Use place-value patterns and division facts to estimate quotients for 4-digit dividends. - 4.NC.35
Use compatible numbers to estimate quotients. - 4.NC.34
Multiply whole numbers by multiples of 10 in the range 10-90. - 3.NBT.A.4
Demonstrate fluency with addition and subtraction within 1000. - 3.NBT.A.3
Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. - 4.NC.37
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
Describe the denominator as the number of pieces that make the whole. - 3.NF.A.2b
Solve division problems and interpret remainders. - 4.NC.36
The student will estimate and determine sums, differences, and products of whole numbers. - 4.4b
Use area models to recognize and generate equivalent fractions. - 4.NC.42
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 multiplication to find equivalent fractions. - 4.NC.44
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
Use multiplication facts to divide. - 3.OA.22
Generate a number pattern that follows a given rule. - 4.RA.C.6
Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.40
Use multiplication facts to find related division facts. - 3.OA.23
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
The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. - 4.4a
Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. - 3.RA.D.10
Multiply or divide to solve problems involving a multiplicative comparison. - 4.RA.A.1
Use fractions or decimals to solve word problems involving money. - 4.NC.68
Add fractions with denominators of 10 and 100 by using equivalent fractions. - 4.NC.67
Use the structure of the place-value system for decimals to solve problems. - 4.NC.69
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
The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. - 3.8a
Reason with two-dimensional shapes and their attributes. - NC.3.G.1
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
Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. - 3.N.2.8
Recognize the relationship between multiplication and division to represent and solve real-world problems. - 3.N.2.7
The student will determine common multiples and factors, including least common multiple and greatest common factor. - 4.5a
The student will add and subtract fractions and mixed numbers having like and unlike denominators. - 4.5b
Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. - 3.N.2.4
Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. - 3.N.2.3
Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. - 3.N.2.6
Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. - 3.N.2.5
Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. - 4.3.3.2
Demonstrate fluency of multiplication facts with factors up to 10. - 3.N.2.2
Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. - 3.N.2.1
Identify quadrilaterals and use attributes to describe them. - 3.G.1
Use equivalent fractions and properties of operations to add mixed numbers with like denominators. - 4.NC.57
Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. - 3.NF.A.1
Use models and equivalent fractions to add and subtract mixed numbers. - 4.NC.56
Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. - 3.NF.A.2
Use a model to understand a fraction as a multiple of a unit fraction. - 4.NC.59
Represent fractions on a number line. - 3.NF.A.3
Use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers with like denominators. - 4.NC.58
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
Relate fractions and decimals with denominators of 10 to 100. - 4.NC.64
Use the four operations to solve problems involving time. - 4.NC.63
Compare decimals by reasoning about their size. - 4.NC.66
Calculate and interpret the quotient of a whole number by a unit fraction. - 5.NF.B.8b
The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. - 3.9b
Locate and describe fractions and decimals on number lines. - 4.NC.65
Calculate and interpret the quotient of a unit fraction by a non-zero whole number. - 5.NF.B.8a
Classify shapes according to their attributes. - 3.G.2
Use models to multiply fractions by whole numbers. - 4.NC.60
Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. - 4.NF.C.12
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
Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. - 4.NC.62
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
Use symbols and equations to multiply a fraction by a whole number. - 4.NC.61
Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. - 4.NF.C.11
Understand that fractions and decimals are equivalent representations of the same quantity. - 4.NF.C.10
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
Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools. - 3.GM.3.2
Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. - NC.3.MD.5
Represent and interpret scaled picture and bar graphs: - NC.3.MD.3
Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. - 3.2.2.1
Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. - 3.2.2.2
Relate area to the operations of multiplication and addition. - NC.3.MD.7
Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. - NC.3.MD.8
Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations. - 4.NC.11
Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. - NC.3.NF.3.a
Use number sense and regrouping to subtract across zeros. - 4.NC.10
Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. - NC.3.MD.1
The student will compare two different representations of the same data (e.g., a set of data displayed on a chart and a bar graph, a chart and a line graph, or a pictograph and a bar graph). - 4.14c
Solve problems involving customary measurement. - NC.3.MD.2
The student will collect, organize, and represent data in bar graphs and line graphs. - 4.14a
The student will interpret data represented in bar graphs and line graphs. - 4.14b
Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. - 4.3.1.1
Interpret the factors as representing the number of equal groups and the number of objects in each group. - NC.3.OA.1.a
Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties. - NC.3.OA.1.b
Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. - 4.GM.A.1
Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (e.g., Given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14b
Classify two-dimensional shapes by their sides and/or angles. - 4.GM.A.2
Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (e.g., Given that b parts is 4 parts, then 1/b represents 1/4. Students partition the number line into fourths and locate 1/4 on the number line.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14a
Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. - 5.NBT.A.1
Reason abstractly and quantitatively. - PS.2
Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. - 5.NBT.A.2
Make sense of problems and persevere in solving them. - PS.1
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
Compare angles according to size. Classify angles as acute, right and obtuse. - 4.3.2.2
Measure angles in geometric figures and real-world objects with a protractor or angle ruler. - 4.3.2.1
Look for and express regularity in repeated reasoning. - PS.8
Look for and make use of structure. - PS.7
Model with mathematics. - PS.4
Construct viable arguments and critique the reasoning of others. - PS.3
Construct lines of symmetry for a two-dimensional figure. - 4.GM.A.3
Attend to precision. - PS.6
Use appropriate tools strategically. - PS.5
Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. - 4.GM.1.1
Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. - 4.GM.1.2
The student will represent probability as a number between 0 and 1, inclusive. - 4.13b
Use decimal notation for fractions with denominators of 10 or 100. - 4.NF.C.9
The student will create a model or practical problem to represent a given probability. - 4.13c
The student will determine the likelihood of an outcome of a simple event. - 4.13a
The student will estimate and measure length and describe the result in U.S. Customary and metric units. - 4.8a
The student will estimate and measure weight/mass and describe the result in U.S. Customary and metric units. - 4.8b
The student will estimate and determine the product and quotient of two numbers involving decimals. - 5.5a
The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. - 4.8c
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
The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. - 4.8d
Understand the whole is partitioned into equal parts. - 3.NF.A.3b
Use different strategies to find products when one factor is a multiple of 10. - 3.NC.19
Understand the whole is the interval from 0 to 1. - 3.NF.A.3a
Make sense of problems and persevere in solving them. - 4.MP.1
Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. - 4.NC.28
Reason abstractly and quantitatively. - 4.MP.2
Use the Distributive Property and an area model to multiply two 2-digit numbers. - 4.NC.27
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
Construct viable arguments and critique the reasoning of others. - 4.MP.3
Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. - 4.NC.29
Model with mathematics. - 4.MP.4
Use appropriate tools strategically. - 4.MP.5
Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. - 4.NC.24
Use models and properties of operations to multiply 2-digit numbers by multiples of ten. - 4.NC.23
Attend to precision. - 4.MP.6
Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. - 4.NC.26
Look for and make use of structure. - 4.MP.7
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
Look for and express regularity in repeated reasoning. - 4.MP.8
Understand a fraction represents the endpoint of the length a given number of partitions from 0. - 3.NF.A.3c
Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. - 4.NC.25
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 models and algorithms to solve 2-digit by 2-digit multiplication problems. - 4.NC.31
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
Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. - 4.NC.33
Make sense of problems and persevere in solving them. - 4.NC.32
Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor. - NC.3.OA.2.b
Use a fraction to represent multiple copies of a unit fraction. - 3.NC.22
Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. - 3.1.3.1
Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group. - NC.3.OA.2.a
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
Represent fractions on a number line. - 3.NC.24
Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. - 4.3.1.2
Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. - 4.NF.B.6
Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.17
Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.16
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. - 4.NF.B.7
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 the standard algorithm to multiply 4-digit numbers by 1-digit numbers. - 4.NC.19
Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. - 4.NC.18
Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. - NC.3.NF.2
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
Use rounding to estimate products and check if answers are reasonable. - 4.NC.13
Model sums and differences of decimals. - 5.NC.10
Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies - 4.NC.12
Use place value and properties of operations to multiply mentally. - 4.NC.15
Use the Distributive Property to multiply larger numbers. - 4.NC.14
Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. - 4.NC.20
Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. - 4.NC.22
Use previously-learned concepts and skills to represent and solve problems. - 4.NC.21
Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; - NC.3.NF.1
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
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
Use place value understanding to round multi-digit whole numbers to any place. - M.4.8
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). - M.4.15b
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). - M.4.15a
Represent and identify unit fractions using area and length models. - NC.3.NF.1.b
Explain that a unit fraction is one of those parts. - NC.3.NF.1.a
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
Demonstrate fluency with addition and subtraction of whole numbers. - 4.NBT.A.5
Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.a
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
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
Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. - 3.1.2.1
Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.b
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 identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. - 4.10a
Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. - 3.1.2.2
The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. - 5.8a
The student will identify and describe intersecting, parallel, and perpendicular lines. - 4.10b
Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. - 3.1.2.3
Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. - 3.D.1.2
Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. - 3.1.3.3
Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. - M.3.22b
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
Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - M.3.22a
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
Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. - 4.GM.C.7
Apply the area and perimeter formulas for rectangles to solve problems. - 4.GM.C.8
Relate area to the operations of multiplication and addition. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. - M.3.22d
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
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - M.4.14a
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
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
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
Add 3-digit numbers using the standard algorithm. - 3.NC.11
Determine elapsed time. - 4.GM.3.1
Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. - 3.D.1.1
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
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
Use areas of rectangles to find the area of irregular shapes. - 3.MD.6
Use unit squares and multiplication to find the areas of squares and rectangles. - 3.MD.4
Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. - 5.1.2.1
Use graphs to compare and interpret data. - 3.MD.8
Represent tenths and hundredths with models, making connections between fractions and decimals. - NC.4.NF.6.c
Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0. - NC.3.NF.2.b
Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. - NC.3.NF.2.a
Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks. - 3.1.1.1
Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. - 3.1.1.2
Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. - 3.1.1.4
Express, model and explain the equivalence between fractions with denominators of 10 and 100. - NC.4.NF.6.a
Use equivalent fractions to add two fractions with denominators of 10 or 100. - NC.4.NF.6.b
Solve real-world and mathematical problems involving multiplication and division, including both 'how many in each group' and 'how many groups' division problems. - 3.1.2.4
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
Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. - 3.1.2.5
Interpret comparisons as multiplication or addition equations. - 4.OA.1
Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. - 4.NBT.A.3
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
Identify and estimate angles and their measure. - 4.GM.B.4
Draw and measure angles in whole-number degrees using a protractor. - 4.GM.B.5
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
Measure angles in geometric figures and real-world objects with a protractor or angle ruler. - 4.GM.2.1
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 and division to compare two quantities. - 4.OA.2
Make sense of a multi-step problem and keep working until it is solved. - 4.OA.5
Solve multi-step problems by finding and solving hidden questions first. - 4.OA.4
Use multiplication to find all the factor pairs for a whole number. - 4.OA.7
Choose an appropriate instrument and measure the length of an object to the nearest whole centimeter or quarter-inch. - 4.GM.2.4
Use arrays to find the factors of a given whole number. - 4.OA.6
Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric). - 4.GM.2.5
Use factors to determine whether a whole number greater than 1 is prime or composite. - 4.OA.9
Use repeated reasoning to generalize how to solve problems that are similar. - 4.OA.8




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