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Core Content and Skills
Math Grade 4
2008-2009
BOE Approved 

Describing the Shape of the Data  Content   Skills  Data Analysis -Representing data Data Analysis - Describing, summarizing and comparing data Data Analysis Analyzing and interpreting data Data Analysis Designing and carrying out a data investigation Probability Describing the probability of an event   •organize numerical data to describe a data set • use a line plot to represent ordered numberical data • represent two sets of data in order to compare them • describe the shape of a data set : where the data are spread out or concentrated, what the highest and lowest values are, what the range is, and what the outliers are • describe what values are typical or atypical in a data set • determine the range of a data set • describe and interpret data that compare two groups • find the median of a data set • use medians to compare groups • consider what information a median does and does not provide • compare two sets of data using the shape and spread of the data • develop arguments based on data • draw conclusions based on data • record and keep track of data • consider how well a data representation communicates to an audience • develop and revise a survey question • associate the word probability with the likelihood of an event • arrange events along a line representing the range of certain to impossible • use numbers from 0 to1 as measures of probability • associate verbal descriptions of probability with numeric descriptions • compare the expected probability of an event with the actual results of repeated trials of that event     Fraction Cards and Decimal Squares  Content   Skills  Rational numbers - Understanding the meaning of fractions and decimal fractions Rational numbers - comparing the values of fractions and decimal fractions Computation with rational numbers - using representations to add rational numbers   • find fractional parts of a rectangular area • find fractional parts of a group • interpret the meaning of the numerator and denominator of a fraction • write, read and apply fraction notation • represent fractions greater than 1 • identify everyday uses of fractions and decimals • read and write tenths and hundreths • represent tenths and hundredths as part of an area • identify relationships between unit fractions when one denominator is a multiple of the other • compare the same fractional parts of different-sized wholes • identify equivalent fractions • order fractions and justify their order through reasoning about fraction equivalencies and relationships • represent fractions using a number line • compare fractions to the landmarks, 0, ½ , 1 and 2 • order decimals and justify their order through reasoning about representations and the meaning of the numbers • identify decimal and fraction equivalents • use representations to add fractions that sum to 1 • estimate sums of fractions • add fractions with the same and related denominators • estimate sums of decimal numbers • add decimal numbers that are multiples of 0.1 amnd 0.25 • use representations to combine tenths and hundreths

Factors, Multiples, and Arrays (Multiplication and  Content   Skills  Whole number operations - Understanding and working with an array model of multiplication Whole number operations - reasoning about numbers and their factors Computational Fluency - Fluency with multiplication combinations to 12x12   • use an array to model multiplication situations • break an array into parts to find the product represented by the array • use arrays to find factors of 2-digit numbers • identify features of numbers, including prime, square and composite numbers • find the multiples of a number by skip counting • determine whether one number is a factor or a multiple of another number • identify the factors of a given number • Identify all the factors of 100 • use known multiplication combinations to find related combinations for a given product • use representations to show that a factor of a number is also a factor of its multiples • identify and learn multiplication combinations not yet known fluently • use known multiplication combinations to determine the products of more difficult combinations

Multiple Towers and Division Stories (Multiplicati  Content   Skills  Computational Fluency -Solving Multiplication Problems with 2-digit numbers Whole number operations - Understanding and using the relationship between multiplication and divison to solve division problems Whole number operations - Reasoning about numbers and their factors Whole number operations - Representing the meaning of multiplication and division   • develop strategies for multiplying that involve breaking apart numbers • review multiplication combinations 12x12 • multiplying multiples of 10 • solve division story problems • use and interpret division notation • solve division problems by making groups of the divisor • use known multiplication combinations to solve division problems • understand the effect of myltiplying by a multiple of 10 • find multiples of 2-digit numbers • describe a sequence of multiples in order to predict other multiples • determine the effect on the product when a factor is doubled or halved • represent a multiplication or division problem with pictures, diagrams or models • use arrays to model multiplication • make sense of remainders interms of the problem context • create a story problem to represent a division expression • compare visual representations of multiplication situations

Size, Shape and Symmetry (2-D Geometry and Measure  Content   Skills  Linear Measurement - Measuring with standard units Features of a shape - describing and classifying 2-dimensional figures Area Measurement - Finding and understanding area   • review the lengths of units of measure (inches, feet yards, centimeters, meters) • use U.S. standard and metric units to accurately measure length • estimate lengths based on common units (inches, feet yards, centimeters, meters) • determine when estimates or exact measurements are needed • find perimeter using standard measurement • recognize and explain possible sources of measurement error • compare different paths that have the same length • define polygons as closed figures with line segments as sides and vertices • classify polygons by attribute, including number of sides, length of sides, and size of angles • combine polygons to make new polygons • recognize numbers of sides as a descriptor of various polygons • develop vocabulary to describe attributes and properties of quadrilaterals • understand the relationship between squares and rectangles • find the area of symmetrical designs • understand that the larger the unit of area, the smaller the number of units needed to measure the area • divide irregular polygons into two shapes that have equal area • find the area of polygons by decomposing shapes • find the area of polygons using square units • find the area of rectangles • find the area of triangles in relation to the area of rectangles

Size, Shape and Symmetry continued  Content   Skills  Linear Measurement - Measuring with standard units Features of a shape - describing and classifying 2-dimensional figures Area Measurement - Finding and understanding area   • review the lengths of units of measure (inches, feet yards, centimeters, meters) • use U.S. standard and metric units to accurately measure length • estimate lengths based on common units (inches, feet yards, centimeters, meters) • determine when estimates or exact measurements are needed • find perimeter using standard measurement • recognize and explain possible sources of measurement error • compare different paths that have the same length • define polygons as closed figures with line segments as sides and vertices • classify polygons by attribute, including number of sides, length of sides, and size of angles • combine polygons to make new polygons • recognize numbers of sides as a descriptor of various polygons • develop vocabulary to describe attributes and properties of quadrilaterals • understand the relationship between squares and rectangles • find the area of symmetrical designs • understand that the larger the unit of area, the smaller the number of units needed to measure the area • divide irregular polygons into two shapes that have equal area • find the area of polygons by decomposing shapes • find the area of polygons using square units • find the area of rectangles • find the area of triangles in relation to the area of rectangles

Landmarks and Large Numbers (Addition, Subtraction  Content   Skills  The base-ten number system -Extending knowledge of the number system to 10,000 Computational Fluency -Adding and subtracting accurately and efficiently Whole number operations -Describing, analyzing, and comparing strategies for adding and subtracting whole numbers Whole number operations - Understanding the different types of subtraction problems   • read write and sequence numbers to 1,000 and 10,000 • understand the structure of 10,000 and its equivalence to one thousand 10s, one hundred 100s and ten 1,000s • recognize the place value of digits in large numbers • add and subtract multiples of 10, 100 and 1,000 • use multiples of 10 and 100 to find the difference between any 3-digit number and 1,000 • add 3- and 4-digit numbers • use clear and concise notation for recording addition and subtraction strategies • find combinations of 3-digit numbers that add to 1,000 • solve subtraction problems by breaking numbers apart • solve multistep addition and subtraction problems • combine positive and negative numbers • represent addition and subtraction on a number line • identify, describe, and compare addition and subtraction strategies by focusing on how each strategy starts • develop arguments about why two addition expressions are equivalent • use story contexts and representations to support explanations about equivalent addition expressions • understand the meaning of the steps and notation of the U.S. algorithm for addition • develop arguments about how the differences represented by two subtraction expressions are related • use story contexts and representations to support explanations about related subtraction expressions • understand the action of subtraction problems • represent subtraction situations

Landmarks and Large Numbers, continued  Content   Skills  The base-ten number system -Extending knowledge of the number system to 10,000 Computational Fluency -Adding and subtracting accurately and efficiently Whole number operations -Describing, analyzing, and comparing strategies for adding and subtracting whole numbers Whole number operations - Understanding the different types of subtraction problems   • read write and sequence numbers to 1,000 and 10,000 • understand the structure of 10,000 and its equivalence to one thousand 10s, one hundred 100s and ten 1,000s • recognize the place value of digits in large numbers • add and subtract multiples of 10, 100 and 1,000 • use multiples of 10 and 100 to find the difference between any 3-digit number and 1,000 • add 3- and 4-digit numbers • use clear and concise notation for recording addition and subtraction strategies • find combinations of 3-digit numbers that add to 1,000 • solve subtraction problems by breaking numbers apart • solve multistep addition and subtraction problems • combine positive and negative numbers • represent addition and subtraction on a number line • identify, describe, and compare addition and subtraction strategies by focusing on how each strategy starts • develop arguments about why two addition expressions are equivalent • use story contexts and representations to support explanations about equivalent addition expressions • understand the meaning of the steps and notation of the U.S. algorithm for addition • develop arguments about how the differences represented by two subtraction expressions are related • use story contexts and representations to support explanations about related subtraction expressions • understand the action of subtraction problems • represent subtraction situations

Fraction Cards and Decimal Squares (Fractions and  Content   Skills  Rational numbers - Understanding the meaning of fractions and decimal fractions Rational numbers - comparing the values of fractions and decimal fractions Computation with rational numbers - using representations to add rational numbers   • find fractional parts of a rectangular area • find fractional parts of a group • interpret the meaning of the numerator and denominator of a fraction • write, read and apply fraction notation • represent fractions greater than 1 • identify everyday uses of fractions and decimals • read and write tenths and hundreths • represent tenths and hundredths as part of an area • identify relationships between unit fractions when one denominator is a multiple of the other • compare the same fractional parts of different-sized wholes • identify equivalent fractions • order fractions and justify their order through reasoning about fraction equivalencies and relationships • represent fractions using a number line • compare fractions to the landmarks, 0, ½ , 1 and 2 • order decimals and justify their order through reasoning about representations and the meaning of the numbers • identify decimal and fraction equivalents • use representations to add fractions that sum to 1 • estimate sums of fractions • add fractions with the same and related denominators • estimate sums of decimal numbers • add decimal numbers that are multiples of 0.1 amnd 0.25 • use representations to combine tenths and hundreths

How Many Packages? How Many Groups? (Multiplicatio  Content   Skills  Computational Fluency - Solving multiplication problems with 2-digit numbers Whole Number Operations - Understanding division as making groups of the divisor   • estimate solutions to 2-digit multiplication problems • multiply multiples of 10 • solve 2-digit multiplication problems by breaking a problem into smaller parts and combining the subproducts • solve 2-digit multiplication problems by changing one factor to create an easier problem • solve division problems by breaking the problem into parts • use multiples of 10 to solve division problems • use the relationship between multiplication and divison to solve division problems

How Many Packages? How Many Groups? continued  Content   Skills  Computational Fluency - Solving multiplication problems with 2-digit numbers Whole Number Operations - Understanding division as making groups of the divisor   • estimate solutions to 2-digit multiplication problems • multiply multiples of 10 • solve 2-digit multiplication problems by breaking a problem into smaller parts and combining the subproducts • solve 2-digit multiplication problems by changing one factor to create an easier problem • solve division problems by breaking the problem into parts • use multiples of 10 to solve division problems • use the relationship between multiplication and divison to solve division problems     Penny Jars and Plant Growth (Patterns, Functions,  Content   Skills  Using tables and graphs - Using graphs to represent change Using tables and graphs - Using tables to represent change Linear Change - Describing and representing a constant rate of change   • interpret the points and shape of a graph in terms of the situation the graph represents • find the difference between two values on a line graph • discriminate between features of a graph that represent quantity and those that represent changes in quantity • identify points in a graph with corresponding values in a table and interpret the numerical information in terms of the situation the graph represents • plot points on a coordinate grid to represent a situation in which one quantity is changing in relation to another • compare situations by describing the differences in their graphs • describe the relative steepness of graphs or parts of graphs in terms of different rates of change • compare tables, graphs, and situations of constant change with those of nonconstant change • use tables to represent the relationship between two quantities in a situation of constant change • interpreting numbers in a table in terms of the situation they represent • find the value of one quantity in a situation of constant change, given the value of the other • create a representation for a situation of constant change • describe the relationship between two quantities in a situation of constant change, taking into account a beginning amount and a constant increase • writing an arithmetic expression for finding the value of one quantity in terms of the other in a situation of constant change • making rules that relate one variable to another in situations of constant change • using symbolic letter notation to represent the value of one variable in terms of another

Penny Jars and Plant Growth, continued  Content   Skills  Using tables and graphs - Using graphs to represent change Using tables and graphs - Using tables to represent change Linear Change - Describing and representing a constant rate of change   • interpret the points and shape of a graph in terms of the situation the graph represents • find the difference between two values on a line graph • discriminate between features of a graph that represent quantity and those that represent changes in quantity • identify points in a graph with corresponding values in a table and interpret the numerical information in terms of the situation the graph represents • plot points on a coordinate grid to represent a situation in which one quantity is changing in relation to another • compare situations by describing the differences in their graphs • describe the relative steepness of graphs or parts of graphs in terms of different rates of change • compare tables, graphs, and situations of constant change with those of nonconstant change • use tables to represent the relationship between two quantities in a situation of constant change • interpreting numbers in a table in terms of the situation they represent • find the value of one quantity in a situation of constant change, given the value of the other • create a representation for a situation of constant change • describe the relationship between two quantities in a situation of constant change, taking into account a beginning amount and a constant increase • writing an arithmetic expression for finding the value of one quantity in terms of the other in a situation of constant change • making rules that relate one variable to another in situations of constant change • using symbolic letter notation to represent the value of one variable in terms of another

Moving Between Solids and Silhouettes  Content   Skills  Features of a shape - describing properties of 3-dimensional shapes Features of a shape - translating between 2-dimensional and 3-dimensional shapes Volume - structuring rectangular prisms and determining their volume   • describe attributes of geometric shapes • name geometric solids • understand how 3-D solids project silhouettes with 2-D shapes • decompose images of 3-D shapes and then recombine them to make a given structure • visualize that 3-D figures look like from different perspectives • recognize how components of 3-D cube buildings come together to form the whole building • draw silhouettes of 3-D cube buildings from different perspectives • integrate different silhouettes of an object, noth fo form a mental model and to build the whole object • see that cubes filling a rectangular prism can be decomposed into congruent layers • find the volume of cube buildings • design pattern for boxes that hold a given number of cubes • develop a strategy for determining the volume of a rectangular prism • find the number of cubes that will fit into the box made by a given pattern • double the number of cubes for a given box and consider how that changes the dimensions of the original box