3rd Grade Standards Guide Table of Contents Content Page Number Overview to the Math Standards Guide 2-3 Geometry 4 Measurement & Data 4-6 Numbers & Operations Fractions 6-7 Numbers & Operations in Base Ten 7 Operations & Algebraic Thinking 8-9 1
Overview to the Math Standards Guide What is the Math Standards Guide? Teachers know the Common Core standard language is important, yet it can often be dense or confusing. The Math Standards Guide is designed to shed light on each Common Core standard, including the key parts of the standard and the aspect(s) of rigor (,, or ) to which each standard most appropriately aligns. How should I use the Math Standards Guide? Use the Standards Guide to deeply study the standards. We suggest using this document during annual and unit planning as it is designed to help you better understand the key components of each standard and see how standards fit together within their cluster and domain. What is different about the Math Standards Guide in 2015-16? We have revised this document, as we do every year, to best reflect our deepening knowledge of the Common Core. Standards are now aligned to aspects of rigor to give you a better understanding of which standards call for conceptual understanding of key concepts, speed and accuracy in calculations (procedural rigor), and/or to use math flexibly for applications in problem-solving contexts., supporting, and additional clusters are also noted. The revisions represent feedback from Achievement Network s assessment and coaching teams, Student Achievement Partners, and our schools. We suggest using this document differently than you may have used ANet s Objective Guides in the past. When planning, be sure to consider how the parts fit together, representing the breadth of the standard, as well as how the standards fit within the appropriate cluster and domain. It s important to note that fragmenting the standards may prevent you from recognizing the full scope and rigor of the standards, so avoid interpreting the parts of the standard as individual or daily objectives. 2
For example: Domain Cluster CC Standard CC Standard Language 4.NBT.A 4.NBT.1 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. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) 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. Recognize that 10 tens is 100, 10 hundreds is 1,000, so forth up to 1,000,000. Apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10. Number & Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 4.NBT.2 4.NBT.3 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.(4.nbt footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Read multi-digit Read whole the parts numbers individually using base-ten to better numerals, understand number names, the standard s & expanded requirements form but avoid treating them as discrete or daily objectives. Instead, consider how Write multi-digit the parts whole fit together, numbers using planning base-ten to ensure numerals, they number will all names, be addressed & expanded in your form lesson(s). Compare multi-digit numbers based on the meaning of the digits Standards each fit within a cluster and domain. Use the symbols, >, and = to compare two multidigit each numbers standard When planning, read the language of within the cluster to see how, together, they achieve the cluster-level requirements. Note that major, supporting, and additional emphases Round multi-digit are given at whole the cluster numbers level. to any place (with specific attention to thousands, ten thousands, Are there deeper connections across standards (or hundred thousands, and millions places as these are clusters) that can be made during instruction? Is there an new in Grade 4.) opportunity for supporting or additional standards to support the major work of the grade? 3
Geometry 3.G.A p Supporting Reason with shapes and their attributes. 3.G.A.1 3.G.A.2 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. 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. Understand that shared attributes can define a larger category Understand that shapes in different categories may share attributes Recognize rhombuses, rectangles, and squares as examples of quadrilaterals Draw examples of quadrilaterals that are not rhombuses, rectangles, and squares Partition shapes into parts with equal areas Express the area of each equal part as a unit fraction of the whole (with denominators of 2, 3, 4, 6, and 8) Write time to the nearest minute Tell time to the nearest minute Measurement & Data 3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.A.1 3.MD.A.2 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. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (3.MD.A.2 footnote: Excludes compound units such as cm^3 and finding the geometric volume of a container.) 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.(3.md.a.2 footnote: Excludes multiplicative comparison problems(problems involving notions of "times as much"; see CCSS Glossary, Table 2).), Solve word problems involving subtraction of time intervals in minutes Solve word problems involving addition of time intervals in minutes Represent word problems involving addition and subtraction of time intervals in minutes on a number line diagram Measure time intervals in minutes (within 60 minutes), including finding elapsed time Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units Measure and estimate liquid volumes using standard units of grams (g), kilograms (kg), and liters (l) Measure and estimate masses of objects using standard units of grams (g), kilograms (kg), and liters (l) Use drawings to represent one-step word problems involving masses or volumes 3.MD.B p Supporting Represent and interpret data. 3.MD.B.3 3.MD.B.4 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. 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. Draw a scaled bar graph to represent a data set with several categories Draw a scaled picture graph to represent a data set with several categories Solve one-step "how many more" and "how many less" problems using information presented in scaled bar graphs Solve two-step "how many more" and "how many less" problems using information presented in scaled bar graphs Generate measurement data (to the nearest fourth of an inch) by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a fractional line plot, where the horizontal scale is marked off in appropriate units - whole numbers, halves, or quarters 4
3.MD.C.5a 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. Understand units used to measure area Recognize area as an attribute of plane figures 3.MD.C.5b 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. Understand "a unit square" is a square with a side length of 1 unit Understand area is measured in square units Understand area is the number of square units needed to cover a plan figure without gaps or overlaps 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)., Recognize that the number of tiles along a side corresponds to the length of the side Measure area by counting unit square Measurement & Data 3.MD.C Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.7a 3.MD.C.7b 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. Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning., Tile a rectangle to find the area Show that the area found using the method above is the same as would be found by multiplying the side lengths Draw an area model to represent given dimensions Represent whole-number products as rectangular areas in mathematical reasoning (draw a rectangle from a given area) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of real world and mathematical problems Multiply side lengths to find areas of rectangles with whole-number side lengths 3.MD.C.7c 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. Use tiling to show that the area of a rectangle with 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 3.MD.C.7d 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., Recognize area as additive Decompose or compose composite regions into non-overlapping rectangles, find the area of each region Solve real world problems involving composite areas 5
Measurement & Data 3.MD.D o Additional Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.D.8 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., Find the missing side length of a figure, including finding the side length of a regular polygon where the perimeter is given Find the perimeter of a figure, given all side lengths Solve real-world problems involving all of the above skills Differentiate between perimeter and area; recognize that figures can have the same area and different perimeters, and vice versa 3.NF.A.1 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 footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) Understand a fraction 1/b (unit fraction) as the quantity formed by 1 part when a whole is partitioned into b equal parts (where b is 2, 3, 4, 6, or 8) Understand a fraction a/b as the quantity formed by a parts of size 1/b (where b is 2, 3, 4, 6, or 8) Number & Operations - Fractions 3.NF.A Develop understanding of fractions as numbers. 3.NF.A.2a 3.NF.A.2b 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 footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) 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.(3.nf footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) Recognize that each part has size 1/b Recognize that the endpoint of the part based at 0 locates the number 1/b on the number line (Recognize that 1/b is the part starting at 0) Represent a fraction 1/b (unit fraction) on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts (where b is 2, 3, 4, 6, or 8) Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0 3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.(3.nf footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) Understand two fractions as equivalent (equal) if they are the same point on a number line (with denominators 2, 3, 4, 6, and 8) Understand two fractions as equivalent (equal) if they are the same size (with denominators 2, 3, 4, 6, and 8) 6
3.NF.A.3b 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 footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) Recognize simple equivalent fractions (with denominators 2, 3, 4, 6, and 8) Generate simple equivalent fractions (with denominators 2, 3, 4, 6, and 8) Explain why the fractions are equivalent, e.g., by using a visual fraction model Number & Operations - Fractions 3.NF.A (cont'd) Develop understanding of fractions as numbers. 3.NF.A.3c 3.NF.A.3d 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.(3.nf footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) 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.nf footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) Express whole numbers as fractions Recognize fractions that are equivalent to whole numbers (e.g. by recognizing they are the same point on the number line) Understand that fractions that have the same numerator the one with the larger denominator is smaller, by reasoning, for example, that in order for more (identical) pieces to make the same whole, the pieces must be smaller Understand that fractions that have the same denominator, the underlying unit fractions are the same size, so the fraction with the greater numerator is greater because it is made of more unit fractions 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 Justify comparisons (e.g., by using a visual fraction model) Number & Operations in Base Ten 3.NBT.A o Additional Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.A.1 3.NBT.A.2 3.NBT.A.3 Use place value understanding to round whole numbers to the nearest 10 or 100. (3.NBT footnote: A range of algorithms may be used.) 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. (3.NBT footnote: A range of algorithms may be used.) 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.NBT footnote: A range of algorithms may be used.),,, Use place value understanding to round whole numbers to the nearest 10 Use place value understanding to round whole numbers to the nearest 100 Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction Focus on methods that generalize readily to larger numbers so that these methods can be extended to 1,000,000 in 4th grade Fluently add and subtract within 1000 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations 7
Distinguish between the number of groups and the size of groups 3.OA.A.1 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. Interpret products of whole-number as the total number of objects in n groups of n objects each Represent a situation with a multiplication expression; represent a multiplication expression with a situation 3.OA.A 3.OA.A.2 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. Interpret whole-number quotients as the number of groups when a set number of objects are partitioned Interpret whole-number quotients as the number of objects in each group when partitioned into equal groups Represent a situation with a division expression; represent a division expression with a situation Represent and solve problems involving multiplication and division. 3.OA.A.3 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. (3.OA.A.3 footnote: See CCSS Glossary, Table 2.) Use multiplication within 100 (up to 10 x 10) to solve word problems in situations involving equal groups, arrays, and measurement quantities (including area) Use division within 100 (up to 10 x 10) to solve word problems in situations involving equal groups, arrays, and measurement quantities (including area) Use drawings to represent multiplication and division problems Operations & Algebraic Thinking Use equations with a symbol for the unknown number to represent multiplication and division problems 3.OA.A.4 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? = 48, 5 = 3, 6 6 =?. Determine the unknown whole number, in any place, in a division equation relating three whole numbers Determine the unknown whole number, in any place, in a multiplication equation relating three whole number 3.OA.B 3.OA.B.5 Apply properties of operations as strategies to multiply and 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.B.5 footnote: Students need not use formal terms for these properties.) Apply associative property of multiplication as strategies to multiply Apply commutative property of multiplication as strategies to multiply Apply distributive property as strategies to multiply and divide Understand properties of multiplication and the relationship between multiplication and division. 3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Understand the number of objects being partitioned (dividend) as equivalent to the product of number of groups and number of objects in each group Understand the dividend represents the product of the divisor and quotient Understand division as the inverse of multiplication and vice versa Represent a division problem as an equivalent multiplication problem with an unknown factor 8
Fluently divide within 100 (up to 10 x 10) 3.OA.C Multiply and divide within 100. 3.OA.C.7 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. Fluently multiply within 100 (up to 10 x 10) Use strategies such as the relationship between multiplication and division to multiply and divide within 100 Use properties of operations to multiply and divide within 100 Know from memory all products of two one-digit numbers Operations & Algebraic Thinking 3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.D.8 3.OA.D.9 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.D.8 footnote: This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 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., Determine if an answer is reasonable using mental computation and estimation strategies including rounding Explain if an answer is reasonable using mental computation and estimation strategies including rounding Represent a two-step word problem using equations with a letter standing for the unknown quantity Use addition and subtraction within 1,000, and multiplication and division within 100 to solve two step real- world problems Identify arithmetic patterns Identify arithmetic patterns in an addition or multiplication table Explain arithmetic patterns using properties of operations 9