Organization: Pearson Product Name: envisionmath2.0 Common Core Grade 5 2016 v1-2 Product Version: 1 Source: IMS Online Validator Profile: 1.2.0 Identifier: realize-f18c67cf-fb9d-302f-b802-88bea9c8fce4 Timestamp: Tuesday, November 26, 2019 02:00 PM EST Status: VALID! Conformant: true ----- VALID! ----- Resource Validation Results The document is valid. ----- VALID! ----- Schema Location Results Schema locations are valid. ----- VALID! ----- Schema Validation Results The document is valid. ----- VALID! ----- Schematron Validation Results The document is valid. Curriculum Standards: Add up to four two-digit numbers using strategies based on place value and properties of operations. - 1C1DA20C-7053-11DF-8EBF-BE719DFF4B22 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. - 1CFA5CEC-7053-11DF-8EBF-BE719DFF4B22 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. - 6A679C90-6EC0-11DF-AB2D-366B9DFF4B22 Attend to precision. - A647016E-6F89-11DF-BAEE-EA329DFF4B22 Classify two-dimensional figures in a hierarchy based on properties. - 1E0D090E-7053-11DF-8EBF-BE719DFF4B22 Add or subtract within 1000, and justify the solution. - 1C21468C-7053-11DF-8EBF-BE719DFF4B22 Describe the denominator as the number of pieces that make the whole. - 1CAEC8AE-7053-11DF-8EBF-BE719DFF4B22 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. - 1CCE490E-7053-11DF-8EBF-BE719DFF4B22 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. - 1DFD3DDA-7053-11DF-8EBF-BE719DFF4B22 An angle that turns through n one-degree angles is said to have an angle measure of n degrees. - 1D8A5E46-7053-11DF-8EBF-BE719DFF4B22 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. For example, 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). - 1D5EB11A-7053-11DF-8EBF-BE719DFF4B22 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. - 1D593CDA-7053-11DF-8EBF-BE719DFF4B22 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. - 1C2F57FE-7053-11DF-8EBF-BE719DFF4B22 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. - 1D8D6FD2-7053-11DF-8EBF-BE719DFF4B22 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. - 1C9077BE-7053-11DF-8EBF-BE719DFF4B22 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. - 1BD4F4C6-7053-11DF-8EBF-BE719DFF4B22 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. - 1C4ECCBA-7053-11DF-8EBF-BE719DFF4B22 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. - 1D94061C-7053-11DF-8EBF-BE719DFF4B22 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, e.g., by using visual fraction models and equations to represent the problem. For example, 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? - 1D64E8DC-7053-11DF-8EBF-BE719DFF4B22 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. - 1D2C094A-7053-11DF-8EBF-BE719DFF4B22 Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a) /(n × b) to the effect of multiplying a/b by 1. - 1DD9F0F0-7053-11DF-8EBF-BE719DFF4B22 Fluently multiply multi-digit whole numbers using the standard algorithm. - 1DBF3422-7053-11DF-8EBF-BE719DFF4B22 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. - 1C2BFE2E-7053-11DF-8EBF-BE719DFF4B22 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. - 6A602AFA-6EC0-11DF-AB2D-366B9DFF4B22 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 within 100 on a number line diagram. - 1C344980-7053-11DF-8EBF-BE719DFF4B22 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). - 1CF419FE-7053-11DF-8EBF-BE719DFF4B22 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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . - 1DC7693A-7053-11DF-8EBF-BE719DFF4B22 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. - 1D78FB56-7053-11DF-8EBF-BE719DFF4B22 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. - 1CAA2D6C-7053-11DF-8EBF-BE719DFF4B22 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . - 1DCAB7DE-7053-11DF-8EBF-BE719DFF4B22 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. - 1BE46B0E-7053-11DF-8EBF-BE719DFF4B22 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - 1DF7BF18-7053-11DF-8EBF-BE719DFF4B22 Explain why addition and subtraction strategies work, using place value and the properties of operations. - 1C22EFFA-7053-11DF-8EBF-BE719DFF4B22 Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. - 1D41C53C-7053-11DF-8EBF-BE719DFF4B22 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. - 1D40416C-7053-11DF-8EBF-BE719DFF4B22 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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. - 1CCB1324-7053-11DF-8EBF-BE719DFF4B22 Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - 1DECFD94-7053-11DF-8EBF-BE719DFF4B22 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - 1E03D00A-7053-11DF-8EBF-BE719DFF4B22 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole number units. - 1C426BAA-7053-11DF-8EBF-BE719DFF4B22 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. - 1C461F20-7053-11DF-8EBF-BE719DFF4B22 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 = ? - 1C71E10A-7053-11DF-8EBF-BE719DFF4B22 Solve multistep 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. - 1D2F3E58-7053-11DF-8EBF-BE719DFF4B22 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation 'add 8 and 7, then multiply by 2?' as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. - 1DA33B6E-7053-11DF-8EBF-BE719DFF4B22 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. - 1D6C8830-7053-11DF-8EBF-BE719DFF4B22 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? - 1C3BC548-7053-11DF-8EBF-BE719DFF4B22 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. - 1DA19174-7053-11DF-8EBF-BE719DFF4B22 Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. - 1CE680E6-7053-11DF-8EBF-BE719DFF4B22 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. - 1DF5B920-7053-11DF-8EBF-BE719DFF4B22 Look for and express regularity in repeated reasoning. - A6497ED0-6F89-11DF-BAEE-EA329DFF4B22 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a 'hundred.' - 1BFEE3E4-7053-11DF-8EBF-BE719DFF4B22 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. - 1CFDC6B6-7053-11DF-8EBF-BE719DFF4B22 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. - 1CBB7252-7053-11DF-8EBF-BE719DFF4B22 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - 1D537C0A-7053-11DF-8EBF-BE719DFF4B22 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, e.g., by using a visual model. - 1D6F45FC-7053-11DF-8EBF-BE719DFF4B22 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. - 1C273042-7053-11DF-8EBF-BE719DFF4B22 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). - 1C04AC98-7053-11DF-8EBF-BE719DFF4B22 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. For example, 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.) - 1D61B090-7053-11DF-8EBF-BE719DFF4B22 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. - 1BDADC38-7053-11DF-8EBF-BE719DFF4B22 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions, e.g.,1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. - 1CB4FD64-7053-11DF-8EBF-BE719DFF4B22 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. - 1C5052C4-7053-11DF-8EBF-BE719DFF4B22 Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - 1DD8D468-7053-11DF-8EBF-BE719DFF4B22 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. - 1E096CC2-7053-11DF-8EBF-BE719DFF4B22 Describe the numerator as representing the number of pieces being considered. - 1CAD407E-7053-11DF-8EBF-BE719DFF4B22 Tell and write time to the nearest minute and 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. - 1CC31A8E-7053-11DF-8EBF-BE719DFF4B22 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). - 1DB65B40-7053-11DF-8EBF-BE719DFF4B22 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1 ; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. - 1CB74646-7053-11DF-8EBF-BE719DFF4B22 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. - 1DD6625A-7053-11DF-8EBF-BE719DFF4B22 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. - 1CB3397A-7053-11DF-8EBF-BE719DFF4B22 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? - 1DD01CA6-7053-11DF-8EBF-BE719DFF4B22 Use place value understanding to round whole numbers to the nearest 10 or 100. - 1C9F81E6-7053-11DF-8EBF-BE719DFF4B22 Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. - 1DB21288-7053-11DF-8EBF-BE719DFF4B22 Understand that 100 can be thought of as 10 tens – called a “hundred”. - 1C084592-7053-11DF-8EBF-BE719DFF4B22 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. - 1D470AC4-7053-11DF-8EBF-BE719DFF4B22 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. - 1D3D00EC-7053-11DF-8EBF-BE719DFF4B22 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. - 1DFA6114-7053-11DF-8EBF-BE719DFF4B22 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - 1DEA1322-7053-11DF-8EBF-BE719DFF4B22 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; 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. For example, 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), ... - 1D7521F2-7053-11DF-8EBF-BE719DFF4B22 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. - 1DB89338-7053-11DF-8EBF-BE719DFF4B22 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. - 1C28D5BE-7053-11DF-8EBF-BE719DFF4B22 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. - 1C69E356-7053-11DF-8EBF-BE719DFF4B22 Understand a fraction a/b with a > 1 as a sum of 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. Justify decompositions, e.g., by using a visual fraction model. Examples: 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. - 1D552AF0-7053-11DF-8EBF-BE719DFF4B22 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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. - 1D822EC4-7053-11DF-8EBF-BE719DFF4B22 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 1D45D410-7053-11DF-8EBF-BE719DFF4B22 Fluently add and subtract within 5. - 6A628052-6EC0-11DF-AB2D-366B9DFF4B22 Construct viable arguments and critique the reasoning of others. - A6430F50-6F89-11DF-BAEE-EA329DFF4B22 Fluently add and subtract multi-digit whole numbers using the standard algorithm. - 1D4438DA-7053-11DF-8EBF-BE719DFF4B22 Read and write numbers to 1000 using number names, base-ten numerals and expanded form. - 1C0EB29C-7053-11DF-8EBF-BE719DFF4B22 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. - 1C92E49A-7053-11DF-8EBF-BE719DFF4B22 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, distinguishing multiplicative comparison from additive comparison. - 1D2D9580-7053-11DF-8EBF-BE719DFF4B22 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. - 1D88BF6E-7053-11DF-8EBF-BE719DFF4B22 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. - 1D7A9FD8-7053-11DF-8EBF-BE719DFF4B22 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. - 1C0A9220-7053-11DF-8EBF-BE719DFF4B22 Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. - 1D0092F6-7053-11DF-8EBF-BE719DFF4B22 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. - 1DB01910-7053-11DF-8EBF-BE719DFF4B22 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, 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. - 1DE199F4-7053-11DF-8EBF-BE719DFF4B22 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and 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. - 1D129348-7053-11DF-8EBF-BE719DFF4B22 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 1/4 of the area of the shape. - 1D15A9E8-7053-11DF-8EBF-BE719DFF4B22 Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. - 1DDB862C-7053-11DF-8EBF-BE719DFF4B22 Model with mathematics. - A6446404-6F89-11DF-BAEE-EA329DFF4B22 Apply properties of operations as strategies to multiply and divide.2 Examples: 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.) - 1C7AACCC-7053-11DF-8EBF-BE719DFF4B22 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. - 1C1A5BD8-7053-11DF-8EBF-BE719DFF4B22 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. - 1CC5CF22-7053-11DF-8EBF-BE719DFF4B22 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. - 1D31F4AE-7053-11DF-8EBF-BE719DFF4B22 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3? and the starting number 0, and given the rule "Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. - 1DA8E6C2-7053-11DF-8EBF-BE719DFF4B22 Recognize and generate equivalent fractions. - 1D4DAAD2-7053-11DF-8EBF-BE719DFF4B22 Make sense of problems and persevere in solving them. - A630F7A2-6F89-11DF-BAEE-EA329DFF4B22 Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. - 1CF1F340-7053-11DF-8EBF-BE719DFF4B22 Look for and make use of structure. - A648672A-6F89-11DF-BAEE-EA329DFF4B22 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 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. - 1C8B79DA-7053-11DF-8EBF-BE719DFF4B22 Add up to four two-digit numbers. - 1C1FCA5A-7053-11DF-8EBF-BE719DFF4B22 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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. - 1D69D842-7053-11DF-8EBF-BE719DFF4B22 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 1DC0E6DC-7053-11DF-8EBF-BE719DFF4B22 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. - 1D4C574A-7053-11DF-8EBF-BE719DFF4B22 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. - 1D928580-7053-11DF-8EBF-BE719DFF4B22 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. - 1E05F22C-7053-11DF-8EBF-BE719DFF4B22 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. - 1D915D72-7053-11DF-8EBF-BE719DFF4B22 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems. - 1DFB949E-7053-11DF-8EBF-BE719DFF4B22 Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. - 6A5D645A-6EC0-11DF-AB2D-366B9DFF4B22 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. - 1C6EE16C-7053-11DF-8EBF-BE719DFF4B22 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). - 6A6114D8-6EC0-11DF-AB2D-366B9DFF4B22 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. For example, 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. - 1D350A5E-7053-11DF-8EBF-BE719DFF4B22 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. - 1D5B69BA-7053-11DF-8EBF-BE719DFF4B22 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. - 1C866120-7053-11DF-8EBF-BE719DFF4B22 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - 1DC286F4-7053-11DF-8EBF-BE719DFF4B22 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? - 1DE4813C-7053-11DF-8EBF-BE719DFF4B22 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. For example, 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. (In general, (a/b) × (c/d) = ac/bd.) - 1DD3A600-7053-11DF-8EBF-BE719DFF4B22 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. - 1D08C73C-7053-11DF-8EBF-BE719DFF4B22 Use place value understanding to round decimals to any place. - 1DBAA114-7053-11DF-8EBF-BE719DFF4B22 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. - 1D8BFE7C-7053-11DF-8EBF-BE719DFF4B22 Use appropriate tools strategically. - A645CA4C-6F89-11DF-BAEE-EA329DFF4B22 Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. - 1DDEC3E6-7053-11DF-8EBF-BE719DFF4B22 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. - 1C647CF4-7053-11DF-8EBF-BE719DFF4B22 Estimate lengths using units of inches, feet, centimeters, and meters. - 1C2A6244-7053-11DF-8EBF-BE719DFF4B22 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. - 1BE827A8-7053-11DF-8EBF-BE719DFF4B22 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. - 1C4D20EA-7053-11DF-8EBF-BE719DFF4B22 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. - 6A619174-6EC0-11DF-AB2D-366B9DFF4B22 Relate area to the operations of multiplication and addition. Recognize area as additive. 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. - 1D03EF28-7053-11DF-8EBF-BE719DFF4B22 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 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