# Voyager Sopris Learning Vmath, Levels C-I, correlated to the South Carolina College- and Career-Ready Standards for Mathematics, Grades 2-8

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2 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: Module 4: Lesson 7: Reason both contextually and abstractly. Module 1: Lesson 7: Module 1: Lesson 10: Module 2: Lesson PL2: Use critical thinking skills to justify mathematical reasoning Module 1: Lesson 7: and critique the reasoning of others. Module 1: Lesson 10: Module 2: Lesson PL2: Module 3: Lesson PL2: Connect mathematical ideas and real-world situations through modeling. Page 2 of 35 Module 1: Lesson 2: Module 1: Lesson 4: Module 1: Lesson 5: Module 1: Lesson 6: Module 4: Lesson PL1: Module 4: Lesson PL 2: Module 2: Lesson PL1: Module 3: Lesson PL1: Use a variety of mathematical tools effectively and strategically. 6. Communicate mathematically and approach mathematical situations with precision. 7. Identify and utilize structure and patterns. Module 1: Lesson 1: Module 1: Lesson 2: Module 1: Lesson 3: Module 1: Lesson 10: Module 2: Lesson 7: Module 7: Lesson 8: Number Sense and Base Ten 2.NSBT.1 Understand place value through 999 by demonstrating that: a. 100 can be thought of as a bundle (group) of 10 tens called a hundred ; b. the hundreds digit in a three-digit number represents the number of hundreds, the tens digit represents the number of tens, and the ones digit represents the number of ones; c. three-digit numbers can be decomposed in multiple ways (e.g., 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.). 2.NSBT.2 Count by tens and hundreds to 1,000 starting with any number. 2.NSBT.3 Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form. 2.NSBT.4 Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <). 2.NSBT.5 Add and subtract fluently through 99 using knowledge of place value and properties of operations. Module 1: Lesson 6: Module 1: Lesson 6: Module 1: Lesson 3: Module 1: Lesson 4: Module 1: Lesson 5: Module 1: Lesson 6: Module 1: Lesson 7: Module 1: Lesson 5: Module 1: Lesson 6: Module 2: Lesson 1: Module 2: Lesson 2: Module 2: Lesson 3:

3 Grade 2 2.NSBT.6 Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations. 2.NSBT.7 Add and subtract through 999 using concrete models, drawings, and symbols which convey strategies connected to place value understanding. 2.NSBT.8 Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing. Algebraic Thinking and Operations 2.ATO.1 Solve one- and two-step real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts VMath, Level C Module 2: Lesson 4: Module 2: Lesson 5: Module 2: Lesson 6: Module 2: Lesson 9: Module 2: Lesson 10: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 7: Module 2: Lesson 1: Module 2: Lesson 2: Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: Module 2: Lesson 6: Module 2: Lesson 9: Module 2: Lesson 10: Module 2: Lesson 10: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 2: Lesson 1: Module 2: Lesson 2: Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: Module 2: Lesson 6: Module 2: Lesson 9: Module 2: Lesson 10: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 9: Module 3: Lesson 10: Module 2: Lesson 7: Module 3: Lesson 5: Module 3: Lesson 6: Page 3 of 35

4 Grade 2 of the whole, and as a comparison) through 99 with unknowns in all positions. 2.ATO.2 Demonstrate fluency with addition and related subtraction facts through ATO.3 Determine whether a number through 20 is odd or even using pairings of objects, counting by twos, or finding two equal addends to represent the number (e.g., = 6). 2.ATO.4 Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Geometry 2.G.1 Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. 2.G.2 Partition a rectangle into rows and columns of samesize squares to form an array and count to find the total number of parts. 2.G.3 Partition squares, rectangles and circles into two or four equal parts, and describe the parts using the words halves, fourths, a half of, and a fourth of. Understand that when partitioning a square, rectangle or circle into two or four equal parts, the parts become smaller as the number of parts increases. Measurement and Data Analysis 2.MDA.1 Select and use appropriate tools (e.g., rulers, yardsticks, meter sticks, measuring tapes) to measure the length of an object. 2.MDA.2 Measure the same object or distance using a standard unit of one length and then a standard unit of a different length and explain verbally and in writing how and why the measurements differ. 2.MDA.3 Estimate and measure length/distance in customary units (i.e., inch, foot, yard) and metric units (i.e., centimeter, meter). Page 4 of 35 Module 7: Lesson 7: Module 1: Lesson 4: Module 2: Lesson 8: VMath, Level C Module 5: Lesson 4: Module 5: Lesson 5: Module 5: Lesson 6: Module 5: Lesson 7: Module 5: Lesson 10: Module 3: Lesson 8: Module 5: Lesson 8: Module 5: Lesson 9: Module 7: Lesson 9: Module 7: Lesson 10: Module 3: Lesson 8: Module 5: Lesson 8: Module 5: Lesson 9: Module 7: Lesson 1: Module 7: Lesson 2: Module 7: Lesson 3: Module 7: Lesson 4: Module 7: Lesson 5: Module 7: Lesson 6: Module 7: Lesson 9: Module 7: Lesson 10: Module 4: Lesson 1: Module 4: Lesson 3: Module 4: Lesson 4: Module 4: Lesson 5: Module 4: Lesson PL2: Module 4: Lesson 3: MDA.4 Measure to determine how much longer one object Module 4: Lesson 2:

5 Grade 2 is than another, using standard length units. 2.MDA.5 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,, and represent whole-number sums and differences through 99 on a number line diagram. 2.MDA.6 Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m. 2.MDA.7 Solve real-world/story problems involving dollar bills using the \$ symbol or involving quarters, dimes, nickels, and pennies using the symbol. 2.MDA.8 Generate data by measuring objects in whole unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units. 2.MDA.9 Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a singleunit scale. 2.MDA.10 Draw conclusions from t-charts, object graphs, picture graphs, and bar graphs. Module 4: Lesson 6: Module 6: Lesson 1: Module 5: Lesson 1: Module 5: Lesson 2: Module 5: Lesson 3: Module 6: Lesson 10: Module 4: Lesson 9: Module 4: Lesson 10: Module 6: Lesson 5: Module 6: Lesson 6: VMath, Level C Page 5 of 35

6 VMath, Level D Grade 3 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 2: Lesson PL1: Module 5: Lesson PL1: Module 3: Lesson 15: Module 5: Lesson 10: Reason both contextually and abstractly. Module 5: Lesson PL2: Module 7: Lesson PL1: Module 7: Lesson PL2: Use critical thinking skills to justify mathematical reasoning Module 6: Lesson PL2: and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations Module 6: Lesson 2: through modeling. 5. Use a variety of mathematical tools effectively and Module 2: Lesson PL2: strategically. Module 1: Lesson 3: Module 7: Lesson LP2: Communicate mathematically and approach mathematical Module 3: Lesson PL1: situations with precision. Module 3: Lesson PL2: Identify and utilize structure and patterns. Module 1: Lesson 1: Module 1: Lesson 3: Module 4: Lesson 4: Number Sense and Base Ten 3.NSBT.1 Use place value understanding to round whole numbers to the nearest 10 or NSBT.2 Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations. 3.NSBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10 90, using knowledge of place value and properties of operations. 3.NSBT.4 Read and write numbers through 999,999 in standard form and equations in expanded form. 3.NSBT.5 Compare and order numbers through 999,999 and represent the comparison using the symbols >, =, or <. Page 6 of 35 Module 2: Lesson 8: Module 2: Lesson 9: Module 3: Lesson 7: Module 3: Lesson 14: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 5: Module 3: Lesson 6: Module 3: Lesson 8: Module 3: Lesson 9: Module 3: Lesson 10: Module 3: Lesson 11: Module 3: Lesson 12: Module 3: Lesson 13: Module 3: Lesson 15: Module 4: Lesson 13: Module 1: Lesson 5: Module 1: Lesson 6: Module 1: Lesson 7: Module 2: Lesson 2: Module 2: Lesson 6: Module 2: Lesson 7:

7 Grade 3 3.NSF.1 Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers. a. A fraction 1 (called a unit fraction) is the quantity formed by one part when a whole is partitioned into equal parts; b. A fraction is the quantity formed by parts of size 1; Module 6: Lesson 1: Module 6: Lesson 2: Module 6: Lesson 1: Module 6: Lesson 2: Module 6: Lesson 8: VMath, Level D c. A fraction is a number that can be represented on a number line based on counts of a unit fraction; d. A fraction can be represented using set, area, and linear Module 6: Lesson 2: models. Module 6: Lesson 3: Number Fractions 3.NSF.2 Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: a. two fractions are equal if they are the same size, based on Module 6: Lesson 6: the same whole, or at the same point on a number line; b. fraction equivalence can be represented using set, area, Module 6: Lesson 5: and linear models; Module 6: Lesson 6: c. whole numbers can be written as fractions (e.g., 4= 41 and 1= 44); d. fractions with the same numerator or same denominator Module 2: Lesson 6: can be compared by reasoning about their size based on the same whole. 3.NSF.3 Develop an understanding of mixed numbers (i.e., denominators 2, 3, 4, 6, 8, 10) as iterations of unit fractions on a number line. Algebraic Thinking and Operations 3.ATO.1 Use concrete objects, drawings and symbols to Module 4: Lesson PL2: represent multiplication facts of two single-digit whole Module 4: Lesson 10: numbers and explain the relationship between the factors (i.e., 0 10) and the product. 3.ATO.2 Use concrete objects, drawings and symbols to Module 5: Lesson PL2: represent division without remainders and explain the relationship among the whole number quotient (i.e., 0 10), divisor (i.e., 0 10), and dividend. 3.ATO.3 Solve real-world problems involving equal groups, Module 5: Lesson 9: area/array, and number line models using basic multiplication Module 6: Lesson PL1: and related division facts. Represent the problem situation using an equation with a symbol for the unknown. 3.ATO.4 Determine the unknown whole number in a Module 5: Lesson 8: multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. 3.ATO.5 Apply properties of operations (i.e., Commutative Module 4: Lesson 11: Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply Page 7 of 35

8 VMath, Level D Grade 3 and divide and explain the reasoning. 3.ATO.6 Understand division as a missing factor problem. Module 5: Lesson 8: ATO.7 Demonstrate fluency with basic multiplication and Module 4: Lesson 5: related division facts of products and dividends through 100. Module 4: Lesson 6: Module 4: Lesson 7: Module 4: Lesson 8: Module 4: Lesson 9: Module 5: Lesson 3: Module 5: Lesson 4: Module 5: Lesson 5: Module 5: Lesson 7: ATO.8 Solve two-step real-world problems using addition, Module 5: Lesson 10: subtraction, multiplication and division of whole numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity. 3.ATO.9 Identify a rule for an arithmetic pattern (e.g., Module 1: Lesson 1: patterns in the addition table or multiplication table). Module 4: Lesson 4: Geometry 3.G.1 Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 3.G.2 Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction. Recognize that equal parts of identical wholes need not have the same shape. 3.G.3 Use a right angle as a benchmark to identify and sketch acute and obtuse angles. 3.G.4 Identify a three-dimensional shape (i.e., right rectangular prism, right triangular prism, pyramid) based on a given two-dimensional net and explain the relationship between the shape and the net. Measurement and Data Analysis 3.MDA.1 Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes. 3.MDA.2 Estimate and measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (ml, L) to the nearest whole unit. 3.MDA.3 Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a Page 8 of 35 Module 7: Lesson 11: Module 7: Lesson 12: Module 7: Lesson 13: Module 6: Lesson 1: Module 7: Lesson 5: Module 7: Lesson 7: Module 7: Lesson 2: Module 7: Lesson 3:

9 VMath, Level D Grade 3 scaled bar graph to represent the data. 3.MDA.4 Generate data by measuring length to the nearest Module 7: Lesson PL2: inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units. 3.MDA.5 Understand the concept of area measurement. a. Recognize area as an attribute of plane figures; Module 7: Lesson 15: b. Measure area by building arrays and counting standard supports: standard: unit squares; Module 7: Lesson 15: c. Determine the area of a rectilinear polygon and relate to supports: standard: multiplication and addition. Module 7: Lesson 15: MDA.6 Solve real-world and mathematical problems involving perimeters of polygons, including finding the Module 7: Lesson 14: perimeter given the side lengths, finding an unknown side Module 7: Lesson 15: length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Page 9 of 35

10 VMath, Level E Grade 4 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 15: Module 7: Lesson 15: Reason both contextually and abstractly. Module 1: Lesson 6: Module 2: Lesson LP2: Use critical thinking skills to justify mathematical reasoning Module 3: Lesson PL1: and critique the reasoning of others. Module 4: Lesson PL2: Connect mathematical ideas and real-world situations Module 1: Lesson 6: through modeling. Module 1: Lesson 9: Module 2: Lesson 1: Module 2: Lesson 8: Use a variety of mathematical tools effectively and strategically. 6. Communicate mathematically and approach mathematical situations with precision. Page 10 of 35 Module 1: Lesson 6: Module 2: Lesson 8: Module 5: Lesson PL1: 230 Module 5: Lesson PL2: 231 Module 6: Lesson PL1: Module 6: Lesson PL2: Module 7: Lesson PL1: Module 7: Lesson PL2: Identify and utilize structure and patterns. Module 4: Lesson 5: Module 3: Lesson 3: Number Sense and Base Ten 4.NSBT.1 Understand that, in a multi-digit whole number, a Module 1: Lesson 2: digit represents ten times what the same digit represents in the place to its right. 4.NSBT.2 Recognize math periods and number patterns Module 1: Lesson 2: within each period to read and write in standard form large numbers through 999,999, NSBT.3 Use rounding as one form of estimation and round Module 1: Lesson 9: whole numbers to any given place value. Module 1: Lesson 10: NSBT.4 Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm. 4.NSBT.5 Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations. 4.NSBT.6 Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Number Sense and Operations Fractions Module 2: Lesson 2: Module 2: Lesson 3: Module 2: Lesson 6: Module 2: Lesson 7: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 5: Module 3: Lesson 6: Module 3: Lesson 14: Module 3: Lesson 15: Module 3: Lesson 10: Module 3: Lesson 11: Module 3: Lesson 13:

11 VMath, Level E Grade 4 4.NSF.1 Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, Module 4: Lesson 6: , 10, 12, 25, 100),, is equivalent to a fraction, Module 4: Lesson 7: , 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. 4.NSF.2 Compare two given fractions (i.e., denominators 2, 3, Module 4: Lesson 9: , 5, 6, 8, 10, 12, 25, 100) by creating common denominators Module 4: Lesson 10: or numerators, or by comparing to a benchmark fraction such as 12 and represent the comparison using the symbols >, =, or <. 4.NSF.3 Develop an understanding of addition and Module 5: Lesson 9: subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, Module 5: Lesson 10: , 25, 100) based on unit fractions. Module 5: Lesson 11: a. Compose and decompose a fraction in more than one way, Module 4: Lesson 5: recording each composition and decomposition as an addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; Module 5: Lesson 12: c. Solve real-world problems involving addition and Module 5: Lesson 9: subtraction of fractions referring to the same whole and Module 5: Lesson 10: having like denominators. Module 5: Lesson 11: Module 5: Lesson 12: NSF.4 Apply and extend an understanding of multiplication by multiplying a whole number and a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). a. Understand a fraction as a multiple of 1; b. Understand a multiple of as a multiple of 1, and use this understanding to multiply a fraction by a whole number; c. Solve real-world problems involving multiplication of a fraction by a whole number (i.e., use visual fraction models and equations to represent the problem). 4.NSF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and NSF.6 Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction. 4.NSF.7 Compare and order decimal numbers to hundredths, and justify using concrete and visual models. Algebraic Thinking and Operations 4.ATO.1 Interpret a multiplication equation as a comparison (e.g. interpret 35 = 5x7 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. Page 11 of 35 Module 5: Lesson 15: Module 5: Lesson 15: supports standard: Module 4: Lesson 7: Module 5: Lesson 13: Module 5: Lesson 3: Module 3: Lesson PL1:

12 Grade 4 4.ATO.2 Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups unknown). 4.ATO.3 Solve multi-step, real-world problems using the four operations. Represent the problem using an equation with a variable as the unknown quantity. 4.ATO.4 Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range and determine whether the whole number is prime or composite. 4.ATO.5 Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence. Geometry 4.G.1 Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these in two-dimensional figures. 4.G.2 Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines. 4.G.3 Recognize right triangles as a category, and identify right triangles. 4.G.4 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 linesymmetric figures and draw lines of symmetry. Measurement and Data Analysis 4.MDA.1 Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, ml, L) from a larger to a smaller unit. 4.MDA.2 Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations. 4.MDA.3 Apply the area and perimeter formulas for rectangles. 4.MDA.4 Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot. 4.MDA.5 Understand the relationship of an angle measurement to a circle. Page 12 of 35 Module 7: Lesson 10: VMath, Level E Module 2: Lesson 10: Module 7: Lesson 10: Module 4: Lesson PL1: Module 4: Lesson 2: supports standard: Module 7: Lesson 11: Module 6: Lesson PL1: Module 6: Lesson PL2: Module 6: Lesson 1: 301 Module 6: Lesson 7: Module 6: Lesson 6: supports standard: Module 6: Lesson PL2: Module 6: Lesson 1: 301 Module 6: Lesson 4: Module 6: Lesson 7: Module 6: Lesson 9: Module 6: Lesson 10: Module 7: Lesson 6: Module 5: Lesson 8: Module 7: Lesson 2: Module 7: Lesson 3: Module 7: Lesson 7: supports standard: Module 7: Lesson PL1: Module 7: Lesson 14: 401 Module 6: Lesson 7:

13 Grade 4 4.MDA.6 Measure and draw angles in whole number degrees using a protractor. 4.MDA.7 Solve addition and subtraction problems to find unknown angles in real-world and mathematical problems. 4.MDA.8 Determine the value of a collection of coins and bills greater than \$1.00. VMath, Level E Module 6: Lesson 1: 301 Module 6: Lesson 1: 301 Module 5: Lesson 8: Page 13 of 35

14 VMath, Level F Grade 5 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 5: Lesson PL2: 257 Module 6: Lesson 3: Reason both contextually and abstractly. Module 1: Lesson 10: Module 4: Lesson PL1: Module 4: Lesson PL2: Module 3: Lesson 15: Use critical thinking skills to justify mathematical reasoning Module 5: Lesson 9: and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations Module 1: Lesson 1: through modeling. Module 6: Lesson PL2: Module 7: Lesson PL1: Module 4: Lesson 12: Use a variety of mathematical tools effectively and strategically. 6. Communicate mathematically and approach mathematical situations with precision. Module 1: Lesson 1: Module 2: Lesson PL1: Module 7: Lesson 10: Module 3: Lesson PL2: Module 7: Lesson PL2: Module 6: Lesson 10: Identify and utilize structure and patterns. Module 3: Lesson PL1: Number Sense and Base Ten 5.NSBT.1 Understand that, in a multi-digit whole number, a Module 2: Lesson 3: digit in one place represents 10 times what the same digit Module 2: Lesson 4: represents in the place to its right, and represents 110 times Module 2: Lesson 5: what the same digit represents in the place to its left. 5.NSBT.2 Use whole number exponents to explain: a. patterns in the number of zeroes of the product when multiplying a number by powers of 10; b. patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: Module 3: Lesson 6: Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: Module 3: Lesson 6: NSBT.3 Read and write decimals in standard and expanded Module 1: Lesson 8: form. Compare two decimal numbers to the thousandths Module 2: Lesson 3: using the symbols >, =, or <. Module 2: Lesson 4: NSBT.4 Round decimals to any given place value within Module 2: Lesson 9: thousandths. Module 2: Lesson 10: NSBT.5 Fluently multiply multi-digit whole numbers using Module 3: Lesson 7: strategies to include a standard algorithm. 5.NSBT.6 Divide up to a four-digit dividend by a two-digit Module 3: Lesson 10: divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division. 5.NSBT.7 Add, subtract, multiply, and divide decimal numbers Module 3: Lesson 1: to hundredths using concrete area models and drawings. Module 3: Lesson 2: Page 14 of 35

15 Grade 5 Number Sense and Operations Fractions 5.NSF.1 Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line. 5.NSF.2 Solve real-world problems involving addition and subtraction of fractions with unlike denominators. 5.NSF.3 Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., = ). 5.NSF.4 Extend the concept of multiplication to multiply a fraction or whole number by a fraction. a. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths; b. Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product; c. Interpret multiplication in which both factors are fractions less than one and compute the product. 5.NSF.5 Justify the reasonableness of a product when multiplying with fractions. a. Estimate the size of the product based on the size of the two factors; Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 5: Module 3: Lesson 8: Module 3: Lesson 9: Module 3: Lesson 11: Module 3: Lesson 12: Module 4: Lesson 3: Module 4: Lesson 4: Module 4: Lesson 5: Module 4: Lesson 6: Module 4: Lesson 3: Module 4: Lesson 4: Module 4: Lesson 5: Module 4: Lesson 6: Module 4: Lesson 12: 235 Module 4: Lesson 11: Module 7: Lesson 8: Module 4: Lesson 10: 229 Module 4: Lesson 11: VMath, Level F supports standard: Module 3: Lesson 15: Module 4: Lesson 10: 229 Module 4: Lesson 11: b. Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number; c. Explain why multiplying a given number by a fraction less Module 4: Lesson 10: 229 than 1 results in a product smaller than the given number; Module 4: Lesson 11: d. Explain why multiplying the numerator and denominator Module 5: Lesson PL2: 257 by the same number has the same effect as multiplying the fraction by 1. 5.NSF.6 Solve real-world problems involving multiplication of Module 4: Lesson 15: a fraction by a fraction, improper fraction and a mixed number. 5.NSF.7 Extend the concept of division to divide unit fractions Module 4: Lesson 13: and whole numbers by using visual fraction models and Page 15 of 35

16 Grade 5 equations. a. Interpret division of a unit fraction by a non-zero whole number and compute the quotient; b. Interpret division of a whole number by a unit fraction and compute the quotient. 5.NSF.8 Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations. Algebraic Thinking and Operations 5.ATO.1 Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces). 5.ATO.2 Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases. 5.ATO.3 Investigate the relationship between two numerical patterns. a. Generate two numerical patterns given two rules and organize in tables; b. Translate the two numerical patterns into two sets of ordered pairs; c. Graph the two sets of ordered pairs on the same coordinate plane; d. Identify the relationship between the two numerical patterns. Page 16 of 35 Module 4: Lesson 13: Module 4: Lesson 14: Module 4: Lesson 15: Module 5: Lesson 2: Module 5: Lesson 3: Module 5: Lesson 6: Module 5: Lesson 5: Module 5: Lesson 10: VMath, Level F Module 6: Lesson 6: Module 6: Lesson 8: supports standard: Module 5: Lesson 5: Module 5: Lesson 10: Geometry 5.G.1 Define a coordinate system. supports standard: Module 7: Lesson 9: a. The x- and y- axes are perpendicular number lines that supports standard: intersect at 0 (the origin); Module 7: Lesson 9: b. Any point on the coordinate plane can be represented by supports standard: its coordinates; Module 7: Lesson 9: c. The first number in an ordered pair is the x-coordinate and supports standard: represents the horizontal distance from the origin; Module 7: Lesson 9: d. The second number in an ordered pair is the y-coordinate supports standard: and represents the vertical distance from the origin. Module 7: Lesson 9: G.2 Plot and interpret points in the first quadrant of the Module 7: Lesson 10: coordinate plane to represent real-world and mathematical situations. 5.G.3 Understand that attributes belonging to a category of supports standard: two-dimensional figures also belong to all subcategories of Module 7: Lesson 1: that category. Module 7: Lesson 2: G.4 Classify two-dimensional figures in a hierarchy based on Module 7: Lesson 1: their attributes. Measurement and Data Analysis 5.MDA.1 Convert measurements within a single system of Module 7: Lesson 3:

17 Grade 5 measurement: customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., mm, cm, m, km, g, kg, ml, L) from a larger to a smaller unit and a smaller to a larger unit. 5.MDA.2 Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot. 5.MDA.3 Understand the concept of volume measurement. a. Recognize volume as an attribute of right rectangular prisms; b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes; c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes. 5.MDA.4 Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation. Module 7: Lesson 4: Module 6: Lesson 9: 333 Module 7: Lesson 6: Module 7: Lesson 7: 371 supports standard: Module 7: Lesson 6: Module 7: Lesson 7: 371 supports standard: Module 7: Lesson 6: Module 7: Lesson 7: 371 Module 7: Lesson 6: Module 7: Lesson 8: VMath, Level F Page 17 of 35

18 VMath, Level G Grade 6 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 2: Lesson PL1: Module 5: Lesson 5: Reason both contextually and abstractly. Module 1: Lesson 4: Module 3: Lesson PL1: Use critical thinking skills to justify mathematical reasoning Module 1: Lesson 6: and critique the reasoning of others. 4. Connect mathematical ideas and real-world situations Module 1: Lesson 8: through modeling. Module 2: Lesson PL2: Module 3: Lesson PL2: Module 5: Lesson PL1: Use a variety of mathematical tools effectively and strategically. 6.NS.6 Extend the understanding of the number line to include all rational numbers and apply this concept to the Page 18 of 35 Module 6: Lesson PL1: Module 6: Lesson PL2: Module 7: Lesson PL2: Module 4: Lesson PL1: Communicate mathematically and approach mathematical situations with precision. 7. Identify and utilize structure and patterns. Module 1: Lesson 10: Module 4: Lesson PL1: Module 4: Lesson PL2: 187 Module 7: Lesson PL1: The Number System 6.NS.1 Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations). 6.NS.2 Fluently divide multi-digit whole numbers using a standard algorithmic approach. 6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach. 6.NS.4 Find common factors and multiples using two whole numbers. a. Compute the greatest common factor (GCF) of two numbers both less than or equal to 100. b. Compute the least common multiple (LCM) of two numbers both less than or equal to 12. c. Express sums of two whole numbers, each less than or equal to 100, using the distributive property to factor out a common factor of the original addends. 6.NS.5 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation. Module 3: Lesson 9: Module 3: Lesson 10: Module 1: Lesson 3: Module 1: Lesson 7: Module 1: Lesson 8: Module 1: Lesson 9: Module 2: Lesson 1: Module 2: Lesson 2: Module 2: Lesson 3: Module 2: Lesson 5: Module 2: Lesson 6: Module 2: Lesson 4: Module 2: Lesson 5: Module 2: Lesson 6: Module 4: Lesson 5: 199 Module 2: Lesson 7: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 5:

19 VMath, Level G Grade 6 coordinate plane. a. Understand the concept of opposite numbers, including zero, and their relative locations on the number line. Module 7: Lesson 10: b. Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the Module 7: Lesson 10: coordinate plane. c. Recognize when ordered pairs are reflections of each other on the coordinate plane across one axis, both axes, or the Module 7: Lesson 10: origin. d. Plot rational numbers on number lines and ordered pairs on coordinate planes. Module 7: Lesson 10: NS.7 Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers. a. Interpret statements using equal to (=) and not equal to ( ). b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. c. Use concepts of equality and inequality to write and to Module 4: Lesson 11: explain real-world and mathematical situations. d. Understand that absolute value represents a number s Module 2: Lesson 8: distance from zero on the number line and use the absolute Module 2: Lesson 9: value of a rational number to represent real-world situations. e. Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational Module 2: Lesson 8: numbers, understand that as the absolute value increases, Module 2: Lesson 9: the value of the negative number decreases. 6.NS.8 Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers. a. Plot points in all four quadrants to represent the problem. Module 7: Lesson 10: b. Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates. Module 7: Lesson 10: c. Relate finding the distance between two points in a coordinate plane to absolute value using a number line. Module 7: Lesson 10: NS.9 Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100. Page 19 of 35 Module 5: Lesson 7: Module 5: Lesson 8: Module 5: Lesson 9: Ratios and Proportional Relationships 6.RP.1 Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole. 6.RP.2 Investigate relationships between ratios and rates. Module 5: Lesson 2: Module 5: Lesson 3: a. Translate between multiple representations of ratios (i.e., Module 5: Lesson 2: ,:, to, visual models).

20 Grade 6 b. Recognize that a rate is a type of ratio involving two different units. Module 5: Lesson 3: c. Convert from rates to unit rates. Module 5: Lesson 3: RP.3 Apply the concepts of ratios and rates to solve realworld and mathematical problems. a. Create a table consisting of equivalent ratios and plot the results on the coordinate plane. b. Use multiple representations, including tape diagrams, tables, double number lines, and equations, to find missing values of equivalent ratios. Module 5: Lesson 4: Module 7: Lesson 10: Module 5: Lesson 4: Module 7: Lesson 10: c. Use two tables to compare related ratios. Module 5: Lesson 2: VMath, Level G d. Apply concepts of unit rate to solve problems, including unit pricing and constant speed. e. Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages. f. Solve one-step problems involving ratios and unit rates (e.g., dimensional analysis). Expressions, Equations, and Inequalities 6.EEI.1 Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations. 6.EEI.2 Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers. a. Translate between algebraic expressions and verbal phrases that include variables. b. Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor. c. Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers. 6.EEI.3 Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions. 6.EEI.4 Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent. 6.EEI.5 Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. 6.EEI.6 Write expressions using variables to represent quantities in real-world and mathematical situations. Module 5: Lesson 5: Module 5: Lesson 3: Module 5: Lesson 2: Module 5: Lesson 3: Module 4: Lesson PL2: 187 Module 4: Lesson 3: Module 4: Lesson 1: Module 4: Lesson 1: Module 4: Lesson 3: Module 4: Lesson 4: 198 Module 4: Lesson 5: 199 Module 4: Lesson 5: 199 Module 4: Lesson 5: 199 Module 4: Lesson 5: 199 Module 4: Lesson 11: Module 4: Lesson 2: Module 4: Lesson 3: Page 20 of 35

21 Grade 6 Understand the meaning of the variable in the context of the situation. 6.EEI.7 Write and solve one-step linear equations in one variable involving nonnegative rational numbers for realworld and mathematical situations. 6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations. a. Write an inequality of the form > or < and graph the solution set on a number line. Page 21 of 35 VMath, Level G Module 4: Lesson 6: Module 4: Lesson 10: Module 4: Lesson 7: Module 4: Lesson 8: Module 4: Lesson 10: Module 4: Lesson 13: Module 4: Lesson 14: Module 4: Lesson 15: Module 4: Lesson 11: Module 4: Lesson 12: b. Recognize that inequalities have infinitely many solutions. Module 4: Lesson 11: EEI.9 Investigate multiple representations of relationships in real-world and mathematical situations. a. Write an equation that models a relationship between Module 4: Lesson 9: independent and dependent variables. b. Analyze the relationship between independent and Module 4: Lesson 10: dependent variables using graphs and tables. c. Translate among graphs, tables, and equations. Module 4: Lesson 10: Geometry 6.GM.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.GM.2 Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (=h, = h) are the same for whole or fractional edge lengths. Apply these formulas to solve realworld and mathematical problems. 6.GM.3 Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations. a. Given coordinates of the vertices, draw a polygon in the coordinate plane. b. Find the length of an edge if the vertices have the same x- coordinates or same y-coordinates. 6.GM.4 Unfold three-dimensional figures into twodimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problems. Module 6: Lesson 1: Module 6: Lesson 2: Module 6: Lesson 3: Module 6: Lesson 5: Module 6: Lesson 6: Module 6: Lesson 7: Module 6: Lesson 8: supports standard: Module 7: Lesson 10: supports standard: Module 7: Lesson 10: supports standard: Module 7: Lesson 10: Data Analysis and Statistics 6.DS.1 Differentiate between statistical and non-statistical questions. 6.DS.2 Use center (mean, median, mode), spread (range, Module 7: Lesson 1:

22 Grade 6 interquartile range, mean absolute value), and shape (symmetrical, skewed left, skewed right) to describe the distribution of a set of data collected to answer a statistical question. 6.DS.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.DS.4 Select and create an appropriate display for numerical data, including dot plots, histograms, and box plots. 6.DS.5 Describe numerical data sets in relation to their realworld context. a. State the sample size. b. Describe the qualitative aspects of the data (e.g., how it was measured, units of measurement). Module 7: Lesson 1: Module 7: Lesson 1: Module 7: Lesson 3: Module 7: Lesson 6: Module 7: Lesson 7: Module 7: Lesson 8: Module 7: Lesson 9: Module 7: Lesson 1: Module 7: Lesson 2: Module 7: Lesson 3: c. Give measures of center (median, mean). Module 7: Lesson 6: Module 7: Lesson 7: Module 7: Lesson 8: d. Find measures of variability (interquartile range, mean absolute deviation) using a number line. e. Describe the overall pattern (shape) of the distribution. f. Justify the choices for measure of center and measure of variability based on the shape of the distribution. g. Describe the impact that inserting or deleting a data point has on the measures of center (median, mean) for a data set. VMath, Level G Gizmos: Mean, Median, and Mode Page 22 of 35

23 VMath, Level H Grade 7 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 4: Lesson PL1: Module 4: Lesson PL2: Module 6: Lesson 15: Reason both contextually and abstractly. Module 1: Lesson 8: Module 3: Lesson PL1: Module 3: Lesson PL2: 127 Module 7: Lesson PL1: Use critical thinking skills to justify mathematical reasoning Module 7: Lesson 9: and critique the reasoning of others. Module 7: Lesson 10: Connect mathematical ideas and real-world situations Module 1: Lesson 1: through modeling. Module 1: Lesson 4: Use a variety of mathematical tools effectively and Module 6: Lesson PL1: strategically. Module 6: Lesson PL2: Communicate mathematically and approach mathematical Module 5: Lesson PL1: situations with precision. Module 5: Lesson PL2: Identify and utilize structure and patterns. Module 2: Lesson PL2: The Number System 7.NS.1 Extend prior knowledge of operations with positive Module 2: Lesson PL2: rational numbers to add and to subtract all rational numbers Module 2: Lesson 4: and represent the sum or difference on a number line. Module 2: Lesson 8: Module 2: Lesson 9: Module 2: Lesson 10: a. Understand that the additive inverse of a number is its Module 2: Lesson 2: opposite and their sum is equal to zero. b. Understand that the sum of two rational numbers (+) represents a distance from p on the number line equal to q where the direction is indicated by the sign of q. c. Translate between the subtraction of rational numbers and addition using the additive inverse, =+( ). d. Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference. e. Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers. Module 2: Lesson 4: Module 2: Lesson 7: 105 Module 2: Lesson 9: Module 2: Lesson 10: Module 2: Lesson PL2: Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: 100 Module 2: Lesson 6: Module 2: Lesson 7: 105 Module 2: Lesson 8: Module 2: Lesson 9: Module 2: Lesson 10: NS.2 Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. a. Understand that the multiplicative inverse of a number is Module 3: Lesson 1: its reciprocal and their product is equal to one. Page 23 of 35

24 VMath, Level H Grade 7 b. Understand sign rules for multiplying rational numbers. Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 9: Module 3: Lesson 10: c. Understand sign rules for dividing rational numbers and Module 3: Lesson 4: that a quotient of integers (with a non-zero divisor) is a Module 3: Lesson 5: rational number. Module 3: Lesson 6: 148 Module 3: Lesson 7: 149 Module 3: Lesson 8: d. Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers. e. Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat. 7.NS.3 Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems. 7.NS.4 Understand and apply the concepts of comparing and ordering to rational numbers. a. Interpret statements using less than (<), greater than (>), less than or equal to ( ), greater than or equal to ( ), and equal to (=) as relative locations on the number line. b. Use concepts of equality and inequality to write and explain real-world and mathematical situations. 7.NS.5 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions. Ratios and Proportional Relationships 7.RP.1 Compute unit rates, including those involving complex fractions, with like or different units. 7.RP.2 Identify and model proportional relationships given Page 24 of 35 Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 3: Module 3: Lesson 4: Module 3: Lesson 5: Module 3: Lesson 6: 148 Module 3: Lesson 7: 149 Module 3: Lesson 8: Module 3: Lesson 9: Module 3: Lesson 10: Module 2: Lesson PL1: supports standard: Module 2: Lesson 3: Module 2: Lesson 4: Module 2: Lesson 5: 100 Module 2: Lesson 6: Module 2: Lesson 7: 105 Module 2: Lesson 8: Module 2: Lesson 9: Module 2: Lesson 10: Module 3: Lesson PL1: Module 3: Lesson PL1: Module 4: Lesson 9: Module 4: Lesson 10: Module 3: Lesson 1: Module 3: Lesson 2: Module 3: Lesson 10: Module 5: Lesson PL2:

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