Organization: Pearson
Product Name: envisionMath2.0 Common Core Grade 1 2016 v1-2
Product Version: 1




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Identifier: realize-6a5c77bd-ef57-3ad7-909b-7c5c89a0e8ba
Timestamp:  Tuesday, November 26, 2019 01:11 PM EST
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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
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). - A65A4396-6F89-11DF-BAEE-EA329DFF4B22
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
Add or subtract within 1000, and justify the solution. - 1C21468C-7053-11DF-8EBF-BE719DFF4B22
Classify two-dimensional figures in a hierarchy based on properties. - 1E0D090E-7053-11DF-8EBF-BE719DFF4B22
Compare two numbers between 1 and 10 presented as written numerals. - 6A5EC4A8-6EC0-11DF-AB2D-366B9DFF4B22
Describe the denominator as the number of pieces that make the whole. - 1CAEC8AE-7053-11DF-8EBF-BE719DFF4B22
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. - A6644EF4-6F89-11DF-BAEE-EA329DFF4B22
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
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
Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" - 6A6BCF36-6EC0-11DF-AB2D-366B9DFF4B22
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
Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. - 6A66B26C-6EC0-11DF-AB2D-366B9DFF4B22
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
Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a 'ten.' - A662DBBE-6F89-11DF-BAEE-EA329DFF4B22
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
Fluently multiply multi-digit whole numbers using the standard algorithm. - 1DBF3422-7053-11DF-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
Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). - 6A69EBDA-6EC0-11DF-AB2D-366B9DFF4B22
Understand the following as special cases: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). - A663CE8E-6F89-11DF-BAEE-EA329DFF4B22
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
Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”. - A66048CC-6F89-11DF-BAEE-EA329DFF4B22
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
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
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
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 word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. - A6560772-6F89-11DF-BAEE-EA329DFF4B22
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
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). - A65B50C4-6F89-11DF-BAEE-EA329DFF4B22
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
Count to 100 by ones and by tens. - 6A59A66C-6EC0-11DF-AB2D-366B9DFF4B22
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
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
Understand the following as special cases: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. - A66356FC-6F89-11DF-BAEE-EA329DFF4B22
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
Understand that the two digits of a two-digit number represent amounts of tens and ones. - A661A6CC-6F89-11DF-BAEE-EA329DFF4B22
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
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?. - A65D81F0-6F89-11DF-BAEE-EA329DFF4B22
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 the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. - A65C6E3C-6F89-11DF-BAEE-EA329DFF4B22
Correctly name shapes regardless of their orientations or overall size. - 6A69772C-6EC0-11DF-AB2D-366B9DFF4B22
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. - A665D116-6F89-11DF-BAEE-EA329DFF4B22
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
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
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
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
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. - A66BE8BC-6F89-11DF-BAEE-EA329DFF4B22
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. - 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
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. - A654C16E-6F89-11DF-BAEE-EA329DFF4B22
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
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
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
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
Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. - A66A68DE-6F89-11DF-BAEE-EA329DFF4B22
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
Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. - 1DB01910-7053-11DF-8EBF-BE719DFF4B22
Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. - 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
Model with mathematics. - A6446404-6F89-11DF-BAEE-EA329DFF4B22
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - 1DDB862C-7053-11DF-8EBF-BE719DFF4B22
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
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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. - A66659B0-6F89-11DF-BAEE-EA329DFF4B22
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
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. - 6A609FC6-6EC0-11DF-AB2D-366B9DFF4B22
Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) - A657F942-6F89-11DF-BAEE-EA329DFF4B22
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
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
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
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
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. - 6A5E4F1E-6EC0-11DF-AB2D-366B9DFF4B22
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
Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. - 6A64D640-6EC0-11DF-AB2D-366B9DFF4B22
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
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). - 6A6ADFB8-6EC0-11DF-AB2D-366B9DFF4B22
Order three objects by length; compare the lengths of two objects indirectly by using a third object. - A667E604-6F89-11DF-BAEE-EA329DFF4B22
Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. - A658F1E4-6F89-11DF-BAEE-EA329DFF4B22
Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. - A6686BD8-6F89-11DF-BAEE-EA329DFF4B22
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. - A6654E08-6F89-11DF-BAEE-EA329DFF4B22
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
Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. - 6A663DDC-6EC0-11DF-AB2D-366B9DFF4B22
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
Calculate and interpret the product of two fractions less than one. - 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
Evaluate the value of powers of 10 and understand the relationship to the place value system. - 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
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. - A66CE028-6F89-11DF-BAEE-EA329DFF4B22
Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. - 1DDEC3E6-7053-11DF-8EBF-BE719DFF4B22
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter- circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. - A66C63D2-6F89-11DF-BAEE-EA329DFF4B22
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
Tell and write time in hours and half-hours using analog and digital clocks. - A6696704-6F89-11DF-BAEE-EA329DFF4B22
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. - 1DF382F4-7053-11DF-8EBF-BE719DFF4B22
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. - 1CA1FF34-7053-11DF-8EBF-BE719DFF4B22
Tell and write time from analog and digital clocks to the nearest five minutes, using A.M. and P.M. - 1C393E2C-7053-11DF-8EBF-BE719DFF4B22
Demonstrate fluency with addition and subtraction within 1000. - 1CA3F7D0-7053-11DF-8EBF-BE719DFF4B22
Reason abstractly and quantitatively. - A6424534-6F89-11DF-BAEE-EA329DFF4B22




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