# MATHEMATICS Grade 4 Standard: Number, Number Sense and Operations. Organizing Topic Benchmark Indicator Number and Number Systems

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1 Standard: Number, Number Sense and Operations A. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals. 2. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths. Meaning of Operations Meaning of Operations B. Recognize and generate equivalent representations for whole numbers, fractions and decimals. C. Represent commonly used fractions and mixed numbers using words and physical models. D. Use models, points of reference and equivalent terms of commonly used fractions to judge the size of fractions and to compare, describe and order them. E. Recognize and classify numbers as prime or composite and list factors. F. Count money and make change using both coins and paper bills. G. Model and use commutative and associative properties for addition and multiplication. H. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication. 3. Round whole numbers to a given place value. 1. Identify and generate equivalent forms of fractions and decimals. For example: a. Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., ½, 5/10, five tenths, 0.5, shaded rectangles with half, and five tenths. b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form. 5. Use models and points of reference to compare commonly used fractions. 4. Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite. 8. Solve problems involving counting money and making change, using both coins and paper bills.

2 Standard: Number, Number Sense and Operations I. Demonstrate fluency in multiplication facts with factors 14. Demonstrate fluency in adding and subtracting whole through 10 and corresponding divisions. numbers and in multiplying and dividing whole numbers J. Estimate the results of whole number computations using a variety of strategies and judge the reasonableness. K. Analyze and solve multi-step problems involving addition, subtraction, multiplication, and division of whole numbers. by 1- and 2-digit numbers and multiples of ten. 9. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 6. Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as: 5 X 47 = 5 X X 7 = = Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money. L. Use a variety of methods and appropriate tools (e.g., mental math, paper and pencil, calculators) for computing with whole numbers. 12. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem. 11. Develop and explain strategies for performing computations mentally. 13. Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator. 14. Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.

3 Standard: Number, Number Sense and Operations M. Add and subtract commonly used fractions with like denominators and decimals using models and paper and pencil. 9. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 10. Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators.

4 Standard: Use Techniques and Tools Use Techniques and Tools A. Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature using: Object of uniform size U.S. customary units (e.g., mile, square, inch, cubic) inch, degree, Fahrenheit, and other units as appropriate) Metric units (e.g., millimeter, kilometer, square cm, kilogram, cubic cm, degree, Celsius and other units as appropriate) B. Know what the number of units is inversely related to the size of the unit for any item being measured. C. Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates. D. Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature. 3. Identify and select appropriate units to measure: a. Perimeter string or links (inches or centimeters). b. Area- tiles (square inches or square centimeters). c. Volume cubes (cubic inches or cubic centimeters). 1. Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher. 5. Make simple unit conversions within a measurement system (e.g., inches to feet, kilograms to grams, quarts to gallons). 2. Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object. 4. Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume. 6. Write, solve and verify solutions to multi-step problems involving measurement. E. Tell time to the nearest minute.

5 Standard: Geometry and Spatial Sense Characteristics and A. Provide rationale for groupings and comparisons of twodimensional 2. Describe, classify, compare and model two- and three- Properties figures and three-dimensional objects. dimensional objects using their attributes. 3. Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. Spatial Relationships Transformations and Symmetry Characteristics and Properties Characteristics and Properties Characteristics and Properties B. Describe and identify points, lines and planes in the environment. C. Describe and identify intersecting, parallel and perpendicular lines or segments in the environment. D. Identify and draw right, obtuse, acute and straight angles. 4. Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles). 5. Describe points, lines and planes, and identify models in the environment. 1. Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines. E. Use attributes to describe, classify, and sketch plane 2. Describe, classify, compare and model two- and threedimensional objects using their attributes. figures and build solid objects. F. Develop definitions of classes of shapes. 2. Describe, classify, compare and model two- and threedimensional objects using their attributes. 3. Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. Spatial Relationships 4. Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles). G. Find and name locations in coordinate systems. 6. Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points (x, y).

6 Standard: Geometry and Spatial Sense Transformations H. Identify and describe line and rotational symmetry in twodimensional and Symmetry shapes and designs. Transformations I. Describe, identify and model reflections, rotations and Indicator moved to 3 rd grade and Symmetry translations, using physical materials. Transformations J. Describe a motion of series of transformations that show Indicator moved to 3 rd grade and Symmetry two shapes are congruent. Visualization and Geometric Models K. Write, solve and verify solutions to multi-step problems involving geometry and spatial sense. 8. Use geometric models to solve problems in other areas of mathematics, such as number (multiplication and division) and measurement (area, perimeter, and border).

7 Standard: Patterns, Functions and Algebra Use Patterns, Relations and Functions A. Analyze and extend patterns, and describe the rule in words. 2. Represent and analyze patterns and functions using words, tables and graphs. Use Patterns, Relations and Functions Use Algebraic Representation Use Algebraic Representation Use Algebraic Representation Use Algebraic Representation Analyze Change B. Use patterns to make predictions, identify relationships, and solve problems. 1. Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications. C. Write and solve open sentences and explain strategies. 5. Represent mathematical relationships with equations or inequalities. D. Represent an unknown quantity as a variable using a 2. Represent and analyze patterns and functions using symbol, including letters. words, tables and graphs. E. Use variables to create and solve equations representing 4. Use rules and variables to describe patterns and other problem situations. relationships. F. Construct and use a table of values to solve problems 3. Construct a table of values to solve problems associated associated with mathematical relationships. with a mathematical relationship. G. Describe how change in one variable affects the value of a related variable. 6. Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases.

8 Standard: Data Analysis & Probability Data Collection A. Gather and organize data from surveys and classroom 1. Create a plan for collecting data for a specific purpose. experiments including data collected over a period of time. Data Collection B. Read and interpret tables, charts, graphs (bar, picture, line, line plot) and timelines as sources of information, identify main idea, draw conclusions, and make predictions. 2. Represent and interpret data using tables, bar graphs, line plots and line graphs. 5. Propose and explain interpretations and predictions based Data Collection Data Collection C. Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and simple Venn Diagrams. D. Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; (e.g., each = 10 bicycles or the intervals on an axis are multiples of 10). on data displayed in tables, charts and graphs. 2. Represent and interpret data using tables, bar graphs, line plots and line graphs. 3. Interpret and construct Venn Diagrams to sort and describe data. 4. Compare different representations of the same data to evaluate how well each representation show important aspects of the data, and identify appropriate ways to display the data. 4. Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data. Statistical Methods E. Describe data using mode, median, and range. 6. Describe the characteristics of a set of data based on a graphical representation, such as range of the data, clumps of data, and holes in the data. 7. Identify the median of a set of data and describe what it indicates about the data. 8. Use range, median and mode to make comparisons among related sets of data.

9 Standard: Data Analysis & Probability Probability F. Conduct simple probability experiment and draw conclusions about the likelihood of possible outcomes. 9. Conduct simple probability experiments and draw conclusions from the results (e.g., rolling number cubes or drawing marbles from a bag). 10. Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles. 11. Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain). Probability Probability G. Identify and represent possible outcomes, such as arrangements of a set of up to 4 members and possible combinations from several sets, each containing 2 or 3 members. H. Use the set of possible outcomes to describe and predict events. 12. Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g., impossible, unlikely, equal, likely, certain. 13. List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts, and 2 pairs of shoes. 10. Represent the likelihood of possible outcomes for chance situations (e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles). 11. Relate the concepts of impossible and certain-to-happen events to the numerical values of 1 (impossible) and 1 (certain).

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