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Core Content and Skills
Math Grade 3
2007-2008
BOE Approved 

Trading Stickers, Combining Coins  Content   Skills  The Base-Ten Number System: Understanding the equivalence of one group and the units that comprise it.   Recognizing and representing the place value of each digit in 2- and 3-digit numbers Using equivalencies among pennies, dimes, and dollars Finding different combinations of 100s, 10s, and 1s for a number and recognizing their equivalence (i.e. 1 hundred, 3 tens, and 7 ones equals 1 hundred, 2 tens, and 17 ones, or 13 tens and 7 ones) Recognizing and demonstrating the equivalence of one 100 to ten 10s and of one 10 to ten 1s Recognizing and using coin equivalencies   Computational Fluency: Adding and subtracting accurately and efficiently   Adding and subtracting multiples of 10 Solving addition problems with 2-digit numbers by using strategies that involve breaking numbers apart by place or adding one number in parts Solving addition problems with 2-digit numbers that involve more than 10 ones in the ones place and explaining the effect on the sum Finding the difference between a 2-digit number and 100 Adding pennies and dimes to sums up to $2.00 Learning/reviewing addition combinations up to 10 + 10 Using knowledge of place value to find pairs of 2-digit numbers that add to 100 or a number close to 100 Using known pairs of 2-digit numbers that add to 100 to find related pairs that add to 100 or a number close to 100 (for example, 20 + 80 = 100, so 22 + 78 = 100) Estimating the sums of 2-digit numbers by using knowledge of place value and known combinations Finding combinations of coins that equal $1.00

Surveys and Line Plots  Content   Skills  Data Analysis: Describing, summarizing, and comparing data   Describing and interpreting categorical data Using summaries such as almost all, very few, half, or more than half Using data to compare groups Describing the shape of ordered, numerical data: where data are spread out or concentrated, where there are few data, highest and lowest values, and outliers Developing arguments based on the data on a graph Describing what values are typical or atypical in a data set   Data Analysis: Representing data   Developing classifications to organize categorical data Organizing categorical data in different ways to answer different questions Representing categorical data by using a picture or graph Considering how well a data representation communicates to an audience Reading and interpreting a bar graph Reading a scale on a graph with intervals larger than 1 Using a line plot, bar graph, or other representation to represent ordered, numerical data Interpreting what the numbers and symbols on a line plot mean Developing a consistent scale to show where data are and are not concentrated Reading and interpreting a representation of ordered, numerical data   Data Analysis: Designing and carrying out a data investigation   Developing and revising a survey question Interpreting results of a data investigation   Linear Measurement: Measuring with standard units   Linear Measurement Measuring with standard units Measuring lengths longer than the measuring tool Understanding the relationship between feet and inches Combining feet and inches to get a total measurement Using correct notation to write a measurement in feet and inches

Collections and Travel Stories (Addition, Subtraction, and the Number Syste  Content   Skills  The Base-Ten Number System: Extending knowledge of the number system to 1,000   Reading, writing, and sequencing numbers to 1,000 Using place value to determine the size of any number to 1,000 Constructing 1,000 from groups of 100 Recognizing and representing the groups of 10s in 3-digit numbers Representing the structure of 3-digit numbers as being composed of 100s, 10s, and 1s Using the value of each place to make 2- and 3-digit numbers closest to 100   The Base-Ten Number System: Understanding the equivalence of one group and the discrete units that comprise it   Constructing 1,000 from groups of 100 Recognizing and representing the groups of 10s in 3-digit numbers Representing the structure of 3-digit numbers as being composed of 100s, 10s, and 1s Using the value of each place to make 2- and 3-digit numbers closest to 100   Computational Fluency: Adding and subtracting accurately and efficiently   Estimating the sums of 2- and 3-digit numbers using knowledge of place value and known combinations Finding pairs of numbers that add to 100 Finding the difference between 3-digit numbers Solving addition problems with 2- and 3-digit numbers (up to 400) by breaking numbers apart and recombining them Representing addition strategies Adding and subtracting multiples of 10 and 100 Developing strategies for solving addition problems by focusing on how each strategy starts Gaining fluency with subtraction facts related to addition combinations up to 10 + 10 Finding the difference between 2- and 3-digit numbers and 100 Using multiples of 100 as a landmark to solve subtraction problems Finding the difference between two numbers by either adding or subtracting Reasoning about how increasing or decreasing the numbers in a subtraction problem affects the difference Solving subtraction problems with 2- and 3-digit numbers (up to 300) using strategies that involve either subtracting one number in parts, adding up, or subtracting back   Whole-Number Operations: Understanding different types of subtraction problems   Solving subtraction problems that involve finding a missing part Visualizing and representing the action of a subtraction problem that involves finding a missing part Understanding comparison as the difference between two numbers Solving subtraction story problems that involve comparison Visualizing and representing the action of comparison problems Using number lines to represent solutions to comparison problems Solving subtraction problems that involve removal Visualizing and representing the action of removal problems

Perimeter, Angles, and Area (2-D Geometry and Measurement)  Content   Skills  Linear Measurement: Measuring with standard units   Reviewing the length of units of measure (inch, foot, yard, centimeter, and meter) Establishing measurement benchmarks Using U.S. standard and metric units to accurately measure length Recognizing and explaining possible sources of measurement error   Linear Measurement: Understanding and finding perimeter   Understanding perimeter as the measure around the outside edges of a 2-dimensional figure Finding perimeter using standard units Creating different shapes with the same perimeter Finding the perimeter of an irregular shape   Area Measurement: Understanding and finding area   Understanding that area is measured in square units Understanding that when measuring area, the space being measured must be completely covered with no gaps or overlaps Using squares and triangles to make shapes with an area of four square units Examining the relationship between the area of squares and triangles Understanding that shapes with the same area can look different Finding the area of partially covered rectangles Finding the area of an irregular shape Designing a shape for a given area Finding area by counting or calculating whole and partial square units   Features of Shape: Describing and classifying 2-dimensional figures   Determining the geometric moves needed (slides, flips, turns) to prove or disprove congruence between two shapes Identifying the attributes of triangles: three sides, three vertices, and three angles Identifying the attributes of quadrilaterals: four sides, four vertices, and four angles Comparing the properties of squares and rectangles   Features of Shape: Describing and measuring angles   Recognizing right angles Identifying a right angle as having a measure of 90 degrees Understanding angle size as the degree of turn Comparing the sizes of angles

Equal Groups (Multiplication and Division)  Content   Skills  Whole-Number Operations: Understanding the meaning of multiplcation   Understanding multiplication as combining equal groups Writing and solving multiplication problems in context Identifying the number of groups, the number in each group, and the product in a multiplication situation Understanding the relationship among skip counting, repeated addition, and multiplication Using and understanding multiplication notation   Whole-Number Operations: Reasoning about numbers and their factors and multiples   Finding the multiples of the numbers 2, 3, 4, 5, 6, and 10 by skip counting Describing and comparing characteristics of the multiples of a number Understanding that doubling (or halving) one factor in a multiplication expression doubles (or halves) the product   Whole-Number Operations: Understanding and working with an array model of multiplication   Using arrays to model multiplication situations Using arrays to find factors of 2-digit numbers up to 50 Using arrays to identify characteristics of numbers, including prime and square numbers Using arrays to find a product by skip counting by one of its dimensions Breaking an array into parts to find the product represented by the array   Computational Fluency: Learning the multiplication combinations with products up to 50 fluently   Using known multiplication combinations to determine the product of more difficult combinations Identifying and learning multiplication combinations not yet known   Whole-Number Operations: Developing strategies for division based on understanding the inverse relationship between multiplication and division   Understanding division as the splitting of a quantity into equal groups Using the inverse relationship between multiplication and division to solve problems Using multiplication combinations to solve division problems Using and understanding division notation Writing and solving division problems in context

Stories, Tables, and Graphs (Patterns, Functions, and Change)  Content   Skills  Measuring Temperature: Understanding temperature and measuring with standard units   Reading and interpreting positive and negative temperatures on a thermometer and on a line graph Associating temperatures with particular activities or clothing   Using Tables and Graphs: Using graphs to represent change   Describing the overall shape of a line graph—increasing, decreasing, staying the same Finding the difference between values on a line graph, including the difference between a positive and negative value Associating a story with its corresponding graph Plotting points on a graph to represent a situation in which one quantity is changing in relation to another Identifying points on a graph with corresponding values in a table and interpreting the numerical information in terms of the situation the graph represents Comparing situations by describing differences in their graphs   Using Tables and Graphs: Using tables to represent change   Using tables to represent the relationship between two quantities in a situation with a constant rate of change interpreting numbers in a table in terms of the situation they represent Comparing situations by describing differences in the tables that represent them   Linear Change: Describing and representing a constant rate of change   Describing the relationship between two quantities in a situation with a constant rate of change Creating a representation for a situation with a constant rate of change Comparing different representations that show the same situation Making rules that relate one variable to the other in situations with a constant rate of change Connecting the steps of a general method or rule to the parts of the situation they represent   Number Sequences: Constructing, describing, and extending number sequences with constant increments   Identifying the unit of a repeating pattern Associating counting numbers with elements of a pattern Determining the element of an ABC pattern associated with a particular counting number Describing and extending a number sequence with a constant increment (e.g., 3, 6, 9, . . . or 2, 5, 8, . . .) Identifying numbers that are multiples of three, or one less or one more than a multiple of 3

Fair Shares (Fractions)  Content   Skills  Rational Numbers: Understanding the meaning of fractions (halves, fourths, eighths, thirds, sixths)and decimal fractions (0.50, 0.25) as equal parts of a whole (an object, an area, a set of objects)   Finding equal parts of a whole and naming them with fractions • Dividing an area into equal part Naming fractional parts with unit fractions (1/2, 1/3, 1/4, etc.) Ordering unit fractions Demonstrating that different-shaped pieces that are the same fraction of the same area have equal areas Naming fractional parts with fractions that have numerators greater than 1 (3/4, 2/3, 3/6, etc) Dividing a group into equal parts and naming the parts with fractions Identifying equivalent fractional parts Using fraction notation to record equivalencies (e.g., 3/6 = 1/2, 1/2 = 2/4) Using mixed numbers to represent quantities greater than 1 Identifying equivalent fractions and decimals for values involving halves and fourths (e.g., 1/2 = 0.50, 1/4 = 0.25, 2 1/2 = 2.5 ) Reading, writing, and interpreting the meaning of the decimal numbers 0.50, 0.25, and numbers greater than 1 with these decimal portions, such as 2.5 and 2.25   Rational Numbers: Using representations to combine fractions (halves, fourths, eighths, thirds, and sixths)   Using representations to combine fractions that sum to 1 (eg., 1/4 + 3/4 = 1, 1/3 + 1/3 +1/3 =1, 1/2 + 1/4 + 1/4 = 1) Using representations to combine fractions to equal other fractions (1/2 = 1/3 + 1/6) Fraction sense is based on the development of visual images of equivalent fractions, especially relationships among halves, fourths, and eighths and among halves, thirds, and sixths. Using understanding of these equivalents in the contexts of rectangular “brownies,” pattern blocks, and groups of things, students find combinations of fractions that are equivalent to a whole or to another fraction (e.g., 1/2 + 2/6 + 1/6 = 1, 1/3 + 1/6 = 1/2).

How Many Hundreds? How Many Miles? (Addition, Subtraction, and the Number S  Content   Skills  Computational Fluency: Adding and subtracting accurately and efficiently.   Combining hundreds to numbers above 1,000 Subtracting from multiples of 100 Adding multiples of 10 and 100 to, and subtracting them from 3-digit numbers Estimating answers to subtraction problems with 3-digit numbers Using the relationship of numbers in a subtraction expression to multiples of 100 to solve subtraction problems Solving addition problems with 3-digit numbers Finding the multiples of numbers Estimating and solving addition problems with sums greater than 1,000 Solving addition and subtraction problems in the context of money (dollars, cents) Solving addition problems with more than 2 addends Estimating which of two sums is greater Knowing and using subtraction problems related to the addition combinations to 10 + 10 (the subtraction facts - e.g., 8 - 5, 13 - 9) with fluency Solving addition and subtraction problems with more than one step Determining combinations of addends for a given sum   Whole-Number Operations: Describing, analyzing, and comparing strategies for adding and subtracting whole numbers   Using story contexts and representations to support explanations about how changing a number in a subtraction problem affects the difference (e.g., 200 - 75 = 125 and 200 - 78 = 122) Solving addition problems by changing the numbers to create an equivalent problem that is easier to solve Using story contexts and representations to support explanations about equivalent addition expressions (e.g., 88 + 105 = 90 + 103) Identifying addition strategies by focusing on how each strategy starts Solving subtraction problems that involve comparison, removal, or finding a missing part Subtracting 3-digit numbers by using strategies that involve either subtracting one number in parts, adding up, or subtracting back Representing solutions to subtraction problems with number lines, 1,000 charts, and/or story contexts Subtracting by using strategies that involve changing one number to make a problem that is easier to solve

Solids and Boxes (3-D Geometry and Measurement)  Content   Skills  Features of Shape: Describing properties of 3-dimensional shapes   Describing the components and properties of different classes of solids such as polyhedra (3-D shapes having only flat surfaces, such as prisms and pyramids) and nonpolyhedra (such as cones and cylinders) Distinguishing between polyhedra and nonpolyhedra Distinguishing between prisms and pyramids Identifying the components of polyhedra (faces, edges, and vertices) and how they come together to form the whole Visualizing and building polyhedra by using knowledge of their components (faces, edges, and vertices) and how they come together to form the whole   Features of Shape: Translating between 2-dimensional and 3-dimensional shapes   Determining the number and shapes of the faces of cubes and other rectangular prisms and how they come together to form the whole Designing patterns that make open boxes for a cube Designing patterns that make open boxes for 2-cube rectangular prisms Determining the number and shapes of the faces of a triangular pyramid and how they come together to form the whole Designing patterns that make nets for triangular pyramids Communicating about spatial relationships Decomposing images of 3-D shapes and then recombining them to make a given structure   Volume: Structuring rectangular prisms and determining their volume   Determining the number of cubes that will fit in the box made by a given pattern Designing patterns for boxes that will hold a given number of cubes Seeing that the cubes filling a rectangular prism can be decomposed into congruent layers