Mastery Expectations For the Kindergarten Curriculum In Kindergarten, Everyday Mathematics focuses on procedures, concepts, and s in two critical areas: Representing and comparing whole numbers, initially with sets of objects. Describing shapes and space. Common Core Sections 1 through 3 Sections 4 and 5 Sections 6 and 7 Sections 8 and 9 K.CC.1 Count orally by ones to 19. Count orally by ones to 50. Count orally by ones to 80. Count to 100 by ones and by tens. Count orally by tens to 50. Count orally by tens to 80. K.CC.2 Count forward to 10 starting from numbers other than 1. Count forward to 50 starting from numbers other than 1. Count forward to 80 starting from numbers other than 1. Count forward to 100 beginning from numbers other than 1. K.CC.3 Read and write numbers from 0 to 10. Represent up to 10 objects with a written numeral. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. K.CC.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. or to promote long-term retention, s, generalization, and transfer). 1
Sections 1 through 3 Sections 4 and 5 Sections 6 and 7 Sections 8 and 9 K.CC.4c Understand that each successive number name refers to a quantity that is one larger. K.CC.5 Count arranged and scattered sets of up to 10 objects. Count out up to 10 objects. Count arranged sets of up to 20 objects. Count scattered sets of up to 10 objects. Count out up to 10 objects. 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.. K.CC.6 Compare the number objects in two groups using the terms more, fewer, and same. 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. K.CC.7 Compare two numbers between 1 and 10 presented as written numerals. K.OA.1 Represent endunknown addition and subtraction situations within 5 concretely (using objects, fingers, drawings, or acting out). Represent addition and subtraction concretely and verbally, but not yet symbolically. Represent addition concretely, verbally, and symbolically. Represent subtraction concretely and verbally, but not yet symbolically. Represent addition and subtraction concretely (e.g., with objects, fingers, mental images, drawings, sounds, acting out situations), verbally, and symbolically (with expressions or equations). or to promote long-term retention, s, generalization, and transfer). 2
Sections 1 through 3 Sections 4 and 5 Sections 6 and 7 Sections 8 and 9 K.OA.2 Solve end-unknown number stories involving addition and subtraction within 5 using direct modeling with fingers, counters, pictures, or acting out. Add and subtract within 5 using objects, drawings, or other concrete strategies. Solve simple number stories involving addition and subtraction using direct modeling. Add and subtract within 10 using objects, drawings, or other concrete strategies. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.. K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way in the context of manipulatives, dot patterns, and ten frames. Decompose numbers less than or equal to 10 into pairs in more than one way. Record decompositions with drawings. 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). K.OA.4 Find number pairs that add to 10. 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. K.OA.5 Develop strategies for addition and subtraction within 5. Develop strategies for addition and subtraction within 5. Fluently add and subtract within 5. or to promote long-term retention, s, generalization, and transfer). 3
Sections 1 through 3 Sections 4 and 5 Sections 6 and 7 Sections 8 and 9 K.NBT.1 Understand, compose, and decompose, numbers 11-19 as ten ones and some more ones concretely (e.g., with fingers or on a ten frame). Understand, compose, and decompose, numbers 11-19 as ten ones and some more ones concretely (e.g., with fingers or on a ten frame). 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 (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. K.MD.1 Describe the length and weight of objects using terms such as long, tall, short, heavy, and light. Describe various measurable attributes of objects. Describe several measurable attributes of a single object. Describe various measurable attributes of objects, including length, weight, and capacity. Describe several measurable attributes of a single object. K.MD.2 Directly compare objects by length and describe the comparisons using the terms longer and shorter. Directly compare objects by length and weight and describe the comparisons using terms such as longer, taller, shorter, heavier, and lighter. Directly compare objects by length and weight and describe the comparisons using terms such as longer, taller, shorter, heavier, and lighter. Directly compare various measurable attributes of objects, such as length, weight, and capacity, and describe the comparisons. K.MD.3 Sort objects into categories using obvious attributes, such as color or shape. Count up to 10 objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. K.G.1 Understand some positional terms. Identify 2-dimensional shapes in the environment. Understand many positional terms. Identify 2-dimensional and some 3-dimensional shapes in the environment. Use many positional terms. Describe objects in the environment using names of 2- and 3-dimensional shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. or to promote long-term retention, s, generalization, and transfer). 4
Sections 1 through 3 Sections 4 and 5 Sections 6 and 7 Sections 8 and 9 K.G.2 Identify and name some triangles, circles, and rectangles (including squares) in different sizes and orientations. Identify and name triangles, circles, and rectangles (including squares) in different sizes and orientations. Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ). Correctly name shapes regardless of their orientations or overall size. K.G.3 Identifies shapes as 2-dimensional or 3-dimensional Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ). K.G.4 Describe the numbers of sides and vertices of triangles, circles, and rectangles (including squares) in different sizes and orientations. Analyze and describe attributes of triangles, circles, and rectangles (including squares) in different sizes and orientations. Compare attributes of 2-dimensional shapes Analyze and describe attributes of basic 2-dimensional and 3-dimensional shapes in different sizes and orientations. Compare attributes of 2-dimensional shapes. Analyze and compare 2- and 3-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). K.G.5 Draw recognizable circles, triangles, squares, and other rectangles. Draw circles, triangles, squares, and other rectangles. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6 Compose shapes from other shapes with the support of puzzle outlines or other structured guidance. Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? or to promote long-term retention, s, generalization, and transfer). 5
Mastery Expectations For the First Grade Curriculum In First Grade, Everyday Mathematics focuses on procedures, concepts, and s in four critical areas: Understanding addition, subtraction, and strategies within 20. Understanding whole number relationships and place value, including grouping by tens and ones. Understanding linear measurement as iterating length units. Composing and decomposing geometric shapes and reasoning about the attributes of shapes. Common Core Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.OA.1 Solve parts-and-total number stories within 10. Solve and write number models for parts-andtotal, change, and comparison number stories within 10. 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. 1.OA.2 Solve number stories with three addends by first finding a combination of 10 or a double from two of the addends. 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. or to promote long-term retention, s, generalization, and transfer). 1
Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.OA.3 Explain what the turnaround rule means. Recognize that a fact and a turnaround fact have the same sum. Add three numbers by first finding a combination of 10 or a double from two of the addends. Apply properties of operations as strategies to add and subtract.2 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.) 1.OA.4 Understand that some addition strategies can be used to solve subtraction problems. For example, think What do I need to add to 7 in order to get 10? Understand that a difference can be found with both subtraction and addition. Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8. 1.OA.5 Use counting on a number line or number grid to solve addition and subtraction problems. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.6 Add and subtract on the number line to solve simple number stories and extend number patterns. Add and subtract within 10, including fluently solving addition and subtraction doubles and combinations of 10. Use think addition, counting up, and counting back strategies to solve subtraction facts. 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). or to promote long-term retention, s, generalization, and transfer). 2
Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.OA.7 Use an equal sign to write addition and subtraction number models. Explain the meaning of the equal sign and identify true and false number sentences containing addition and subtraction facts within 10. 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. 1.OA.8 Find the unknown number of hops between two numbers. 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 = _.. 1.NBT.1 Use skip counting to add and subtract on the number line. Extend number patterns within 100. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.2 Identify the two-digit number represented by base-10 blocks. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:. 1.NBT.2a Exchange 1 ten for 10 ones. 10 can be thought of as a bundle of ten ones called a ten.. or to promote long-term retention, s, generalization, and transfer). 3
Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.NBT.2b Identify the teen number represented by base-10 blocks. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.. 1.NBT.2c Identify the multiple of 10 represented by base-10 blocks. 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). 1.NBT.3 Compare the value of two numbers (<20). Use >, =, and < to record comparisons of numbers. Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1.NBT.4 Add a two-digit and a one-digit number using tools. Add within 100 using tools. 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. 1.NBT.5 Given a two-digit number, find 10 more and 10 less than the number using any tool Given a two-digit number, find 10 more or 10 less than the number using a tool only if needed. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. or to promote long-term retention, s, generalization, and transfer). 4
Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.NBT.6 Find the difference between two-digit multiples of 10 using tools. Subtract two-digit multiples of 10 from other two-digit multiples of 10 using tools. 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. 1.MD.1 Identify the shortest and longest out of two or three objects. Order three objects by length. Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.2 Measure a path with base-10 cubes. 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. 1.MD.3 Show time to the hour on an analog clock with both the hour and minute hands. Tell and write time in hours and half-hours using analog and digital clocks. or to promote long-term retention, s, generalization, and transfer). 5
Units 1 through 3 Units 4 and 5 Units 6 and 7 Units 8 and 9 1.MD.4 Organize data in a tally chart. Answer simple questions about a tally chart. Organize data in a tally chart. Answer simple questions about a tally chart or bar graph. Organize data in a tally chart or bar graph. Answer simple questions about a tally chart or bar graph. 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. 1.G.1 Draw shapes. Build shapes with a specified number of sides. Name defining attributes of 2-dimensional shapes. 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. 1.G.2 Combine pattern blocks to make designs; combine base-10 blocks to build structures. Compose a new twodimensional shape from two two-dimensional shapes; compose shapes with base-10 blocks. Using two twodimensional shapes, compose two different two-dimensional shapes. Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or threedimensional 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. 1.G.3 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. or to promote long-term retention, s, generalization, and transfer). 6
Mastery Expectations For the Second Grade Curriculum In Second Grade, Everyday Mathematics focuses on procedures, concepts, and s in four critical areas: Understanding of base-10 notation. Building fluency with addition and subtraction. Using standard units of measure. Describing and analyzing shapes. Common Core Units 7 through 9 2.OA.1 Write an addition number story that matches a picture, write a number model to represent the story, and solve the story. Add and subtract within 20 to solve onestep word problems involving situations of adding to, taking from, putting together, and taking apart by using drawings or equations to represent the problem. Add and subtract within 100 to solve one-step word problems involving situations of adding to, taking from, putting together, and taking apart, e.g. by using drawings or equations to represent the problem. Use addition and subtraction within 100 to solve one- and twostep 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. 2.OA.2 Know doubles and combinations-of-10 facts. Know doubles and combinations-of-10 facts; know +/- 0 and +/-1 facts. Know doubles and combinations-often facts, and apply strategies to solve all addition and subtraction facts. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3 Determine whether a group of objects (up to 20) has an even or odd number of members with the aid of manipulatives. 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. or to promote long-term retention, s, generalization, and transfer). 1
Units 7 through 9 2.OA.4 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. 2.NBT.1 Understand that the 2-digits of a 2-digit number represent amounts of tens and ones. Understand that three nonzero digits of a 3-digit number represent amounts of hundreds, tens, and ones. 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: 2.NBT.1a Demonstrate an understanding of exchanging 10 and 1s using manipulatives. Represent 3-digit numbers that are multiples of 100 using base-10 blocks. Understand that 100 can be thought of as a bundle of ten tens called a hundred. 2.NBT.1b Understand that the numbers 10, 20..... 90 refer to some tens and no ones. Represent 3-digit numbers that are multiples of 100 using base-10 blocks. Understand that 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). 2.NBT.2 Count by 1s to at least 120; skip count by 5s using a calculator; and skip count by10s to at least 200. Count by 1s within 500; skip count by 5s and 10s past 200; count by 100 to 900. Count within 1000; skip-count by 5s, 10s, and 100s. or to promote long-term retention, s, generalization, and transfer). 2
Units 7 through 9 2.NBT.3 Read and write numbers to at least 120 using base-10 numerals and numbers to 10 using number names. Read and write numbers to at least 600 using base-10 numerals. Read and write numbers to 20 using number names. Read and write numbers in expanded form to 99 without manipulatives. Read and write numbers in expanded form to 999 using base-10 blocks. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.4 Compare two 3-digit numbers with nonzero digits based on meanings of the hundreds, tens, and ones digits, using <, >, and = symbols to record the results of comparisons. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 2.NBT.5 Add and subtract within 100 using a number grid, a number line, or counters. Add within 100 using a number grid, number line, or counters, and use the inverse relationship between addition and subtraction to write fact families and solve addition and subtraction facts. Add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, with or without tools. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6 Add up to four twodigit numbers using strategies based on place value and properties of operations. or to promote long-term retention, s, generalization, and transfer). 3
Units 7 through 9 2.NBT.7 Add and subtract within 100 using base-10 blocks, number grids and number lines. Add and subtract within 100 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; understand that in adding or subtracting 2-digit numbers, one adds or subtracts tens and tens, ones and ones.; understand that sometimes it is necessary to compose and decompose tens. Add and subtract within 100 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; understand that in adding or subtracting 3-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones.; understand that sometimes it is necessary to compose and decompose hundreds. Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8 Mentally add 10 and subtract 10 from a 2-digit number. Mentally add 10 to and subtract 10 from a given number 100-900. Mentally add and subtract 100 to a given number that is a multiple of 100 to 900. Mentally add 10 or 100 to a given number 100 900, and mentally subtract 10 or 100 from a given number 100 900. 2.NBT.9 Understand addition as putting together and subtraction as taking apart. Explain addition and subtraction fact strategies such as Making-10, Near Doubles, Turn-Around Rule for Addition, Think Addition, Counting Up, and Counting Back. Explain why addition and subtraction strategies work using place value. Explain why addition and subtraction strategies work, using place value and the properties of operations. 2.MD.1 Select an appropriate tool to measure inches and centimeters. Measure the length of an object by selecting and using appropriate tools to measure inches and centimeters. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. or to promote long-term retention, s, generalization, and transfer). 4
Units 7 through 9 2.MD.2 Measure the length of an object twice, using inches and centimeters for the two measurements. Measure the length of an object twice, using inches and centimeters for the two measurements and describe how the two measurements relate to the size of the unit. 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. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another by lining up both objects and measuring the part that does not overlap in inches and centimeters. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units using drawings. 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. 2.MD.6 Represent numbers from 1 through 10 as lengths from 0 on a number line. Represent numbers from 0 to 20 as lengths on a number line. Represent whole-number sums and differences within 20 on a number line. Represent whole numbers as lengths from 0 on a number line. Represent sums within 100 on an number line. 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. or to promote long-term retention, s, generalization, and transfer). 5
Units 7 through 9 2.MD.7 Tell and write time using analog and digital clocks to the nearest half hour. Draw events that typically occur in the A.M. and P.M. hours. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 Solve word problems involving dimes and pennies. Solve word problems involving a single type of coin (either quarters, dimes, nickels, or pennies); use symbol appropriately. Solve word problems involving quarters, dimes, nickels, and pennies to show exact change up to $; use symbol appropriately. 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? 2.MD.9 Generate measurements by measuring lengths of objects to the nearest inch, centimeter, or foot. 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 wholenumber units. 2.MD.10 Draw a picture graph to represent data from a tally chart. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple puttogether, take-apart, and compare problems using information presented in a bar graph. or to promote long-term retention, s, generalization, and transfer). 6
Units 7 through 9 2.G.1 Recognize 3- and 4-sided shapes. Recognize 3- and 4-sided shapes. Draw 3-, 4-, 5-, and 6-sided shapes; sort shapes and identify common attributes. 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. 2.G.2 Use same-size square tiles to partition a rectangle into rows and columns and count to find the total number of them. Use same-size square tiles to partition a rectangle into rows and columns and count to find the total number of them. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 2.G.3 Partition shapes into two equal parts and describe the shares using the words halves and half of. Partition shapes into two equal parts and describe the shares using the words halves and half of. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a 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. or to promote long-term retention, s, generalization, and transfer). 7
Mastery Expectations For the Third Grade Curriculum In Third Grade, Everyday Mathematics focuses on procedures, concepts, and s in four critical areas: Understanding of multiplication and division and strategies within 100. Understanding of fractions, especially unit fractions. Understanding of the structure of rectangular arrays and of area. Describing and analyzing two-dimensional shapes. Common Core Units 7 through 9 3.OA.1 Represent multiplication as equal groups with concrete objects and drawings. Represent multiplication as equal groups with arrays. Interpret multiplication in terms of equal groups. For example, describe a context in which a total number of objects can be expressed as 5 7. 3.OA.2 Equally share groups of concrete objects. Represent equal shares with drawings. Represent equal shares with drawings and number models. Interpret division in terms of equal shares or equal groups. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8. 3.OA.3 Use skip counting, repeated addition, or multiplication to solve number stories involving equal groups. Use multiplication or division to solve number stories involving equal groups or equal shares. Use multiplication and division to solve number stories. Model number stories involving multiplication. Use multiplication and division to solve number stories. Model number stories involving multiplication and division. or to promote long-term retention, s, generalization, and transfer). 1
Units 7 through 9 3.OA.4 Use fact triangles to generate fact families. Determine the unknown product or factor in multiplication and division equations involving 1s, 2s, 5s, and 10s facts. Determine the unknown product or factor in multiplication and division equations involving square products, and 0s, 1s, 2s, 3s, 5s, 9s, and 10s facts. Determine the unknown in multiplication and division equations. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =?. 3.OA.5 Illustrate the turn-around rule (Commutative Property of Multiplication) with arrays and facts. Use strategies such as adding/subtracting a group, near squares, and doubling to multiply and divide. Apply properties of operations to multiply or divide. 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.) 3.OA.6 Use multiplication to determine the unknown factor in division equations involving 1s, 2s, 5s, and 10s facts. Use multiplication to determine the unknown factor in division equations involving 1s, 2s, 5s, 10s, square products, and 0s, 3s, and 9s facts. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. 3.OA.7 Know all products of one-digit numbers 1, 2, 5, and 10. Know all square products of one-digit numbers. Know all products of one-digit numbers 0, 1, 2, 3, 5, 9, and 10. 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. or to promote long-term retention, s, generalization, and transfer). 2
Units 7 through 9 3.OA.8 Use drawings, diagrams, and estimates to explain why answers to number stories involving addition and subtraction are reasonable. Use pictures, words, or numbers to solve 2-step number stories involving addition and subtraction. Use mental computation and estimation strategies, including rounding, to determine whether answers to addition and subtraction problems are reasonable. Represent problems using equations with a? standing for the unknown quantity. Solve 2-step number stories using two of the four operations. 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. 3.OA.9 Use the multiplication table to help identify whether products of 2 even factors, 2 odd factors, and 1 even and 1 odd factor are even or odd. Use doubling as a strategy to solve multiplication facts. 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. 3.NBT.1 Use open number lines to round 2-digit numbers to the nearest 10 and 3-digit numbers to the nearest 100. Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2 Add and subtract within 1000 using tools along with strategies based on place value and/or the relationship between addition and subtraction. Add and subtract within 1000 using partial-sums addition, and countingup and expand-and-trade subtraction, or other strategies. Fluently add within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction; fluently subtract within 1000 using counting up, expand and trade, trade first, or other strategies. 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. or to promote long-term retention, s, generalization, and transfer). 3
Units 7 through 9 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10 90 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. 3.NF.1 Identify and represent given unit (1//b) and nonunit (a//b) fractions using pictures, words, and fraction circles. 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. 3.NF.2; 3NF.2a Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NF.2; 3NF.2b Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. or to promote long-term retention, s, generalization, and transfer). 4
Units 7 through 9 3.NF.3; 3.NF.3a Use fraction circle pieces to determine that equivalent fractions are the same size. 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. 3.NF.3; 3.NF.3b Use fraction circle pieces to generate simple equivalent fractions 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. 3.NF.3; 3.NF.3c 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. or to promote long-term retention, s, generalization, and transfer). 5
Units 7 through 9 3.NF.3; 3.NF.3d Use tools, such as fraction circle pieces, to justify the conclusions of fraction comparisons. 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. 3.MD.1 Tell and write time to the nearest 5 minutes. Use an open number line or other tools to add time intervals in minutes. Use open number lines, toolkit clocks, or other strategies to solve problems and number stories involving 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. 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. 3.MD.2 Estimate the mass of objects by comparing benchmark masses to the masses of various items. Use addition and subtraction to solve one-step number stories about mass. 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 onestep 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. or to promote long-term retention, s, generalization, and transfer). 6
Units 7 through 9 3.MD.3 Use information in a given scaled bar graph to solve one-step how many more and how many less problems. Represent a data set with several categories on a given scaled bar graph and use the information presented in the graph to solve onestep how many more and how many less problems. 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. 3.MD.4 Measure lengths to the nearest inch using rulers marked with whole and half inches. Measure lengths to the nearest half-inch using rulers marked with wholes, halves, and fourths of an inch. Represent length data on a line plot where the horizontal scale is marked off in whole numbers and halves. Measure lengths to the nearest half-inch using rulers marked with wholes, halves, and fourths of an inch. Represent length data on a line plot where the horizontal scale is marked off in whole numbers and halves. 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. 3.MD.5; 3.MD.5a Recognize area as an attribute of plane figures. 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. 3.MD.5; 3.MD.5b Recognize area as an attribute of plane figures. 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. or to promote long-term retention, s, generalization, and transfer). 7
Units 7 through 9 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7; 3.MD.7a Find the area of a rectangle with whole number side lengths by tiling it. 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. 3.MD.7; 3.MD.7b Multiply side lengths to find areas of rectangles. 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 wholenumber products as rectangular areas in mathematical reasoning. 3.MD.7; 3.MD.7c Explain how a given area model, fully labeled, with a side length decomposed into 2 addends can be used to solve a multiplication problem. Relate area to the operations of multiplication and addition. 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. or to promote long-term retention, s, generalization, and transfer). 8
Units 7 through 9 3.MD.7; 3.MD.7d 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 nonoverlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve problems involving perimeters of polygons. Distinguish between area and perimeter. 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. 3.G.1 Understand that shapes in different categories may share attributes that can define a larger category. Recognize specified subcategories of quadrilaterals. 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. or to promote long-term retention, s, generalization, and transfer). 9
Units 7 through 9 3.G.2 Partition rectangles into parts with equal areas. 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. or to promote long-term retention, s, generalization, and transfer). 10
Mastery Expectations For the Fourth Grade Curriculum In Fourth Grade, Everyday Mathematics focuses on procedures, concepts, and s in three critical areas: Understanding and fluency with multi-digit multiplication, and understanding of dividing to find quotients with multi-digit dividends. Understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers. Understanding that geometric figures can be analyzed and classified based on their properties. Common Core Units 7 and 8 4.OA.1 Recognize comparison situations that are multiplicative. Interpret a multiplication equation as a multiplicative comparison and represent statements of multiplicative comparisons as multiplication equations. (Does not address division.) 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. 4.OA.2 Identify a number story as additive or multiplicative and explain how they know. Solve multiplicative comparison number stories using multiplication. 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. or to promote long-term retention, s, generalization, and transfer). 1
Units 7 and 8 4.OA.3 Solve addition and subtraction multistep number stories. Articulate a plan for solving addition and subtraction multistep number stories. Assess the reasonableness of answers to addition and subtraction multistep number stories by comparing them to an estimate. Make sense of multistep number stories involving addition, subtraction and multiplication. Articulate a plan for solving addition, subtraction and multiplication multistep number stories. Assess the reasonableness of answers to addition, subtraction and multiplication multistep number stories by comparing them to an estimate. Solve multistep addition, subtraction and multiplication number stories. Model addition, subtraction and multiplication equations, using a letter for the unknown. Assess the reasonableness of answers to addition, subtraction and multiplication multistep number stories by comparing them to an estimate. 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. 4.OA.4 Identify more than one factor pair for composite numbers less than 40. Write multiples of a 1-digit number. Identify prime and composite numbers less than 40. 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. or to promote long-term retention, s, generalization, and transfer). 2
Units 7 and 8 4.OA.5 Apply an addition, subtraction, multiplication, or division rule to a What s My Rule? table and extend simple shape patterns. Predict the features of the next number or shape. Apply an addition, subtraction, multiplication, or division rule to a What s My Rule? table and extend simple shape patterns. Identify simple number or shape patterns that were not explicit in the original rule. Apply an addition, subtraction, multiplication, or division rule to a What s My Rule? table and extend simple shape patterns. Identify simple number or shape patterns that were not explicit in the original rule. 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. 4.NBT.1 Recognize the relationships between place values that are up to 100 times as large as another place. 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. or to promote long-term retention, s, generalization, and transfer). 3