# Everyday Mathematics GOALS

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2 38 Assessment Handbook Content Strand: NUMBER AND NUMERATION cont. Program Goal: Understand the Meanings, Uses, and Representations of Numbers cont. Meanings and uses of fractions manipulatives to model half of a region or a collection; describe the model. manipulatives and drawings to model halves, thirds, and fourths as equal parts of a region or a collection; describe the model. Goal 3. Use manipulatives and drawings to model fractions as equal parts of a region or a collection; describe the models and name the fractions. Goal 2. Read, write, and model fractions; solve fractional parts of a region or a collection; describe strategies used. Goal 2. Read, write, and model fractions; solve fractional parts of a region or a collection; describe and explain strategies used; given a fractional part of a region or a collection, identify the unit whole. Goal 2. Solve percents and discounts; describe and explain strategies used; identify the unit whole in situations involving fractions. Goal 2. Solve percents and discounts; explain strategies used; identify the unit whole in situations involving fractions, decimals, and percents. Number theory Goal 5. Use manipulatives to identify and model odd and even numbers. Goal 4. Recognize numbers as odd or even. Goal 3. Find multiples of 2, 5, and 10. Goal 3. Find multiples of whole numbers less than 10; identify prime and composite numbers; find whole-number factors of numbers. Goal 3. Identify prime and composite numbers; factor numbers; find prime factorizations. Goal 3. Use GCFs, LCMs, and divisibility rules to manipulate fractions. Program Goal: Understand Equivalent Names for Numbers Equivalent names for whole numbers Goal 5. Use drawings, and expressions involving addition and subtraction of 1-digit numbers to give equivalent names for whole numbers up to 20. Goal 6. Use drawings, tally marks, and expressions involving addition and subtraction of 1- or 2-digit numbers to give equivalent names for whole numbers up to 100. Goal 5. Use tally marks, arrays, and expressions involving addition and subtraction to give equivalent names for whole numbers. expressions involving one or more of the basic four arithmetic operations to give equivalent names for whole numbers. expressions involving one or more of the basic four arithmetic operations and grouping symbols to give equivalent names for whole numbers. expressions involving one or more of the basic four arithmetic operations, grouping symbols, and exponents to give equivalent names for whole numbers; convert between base-10, exponential, and repeated-factor notations. Goal 4. Apply the order of operations to expressions to give equivalent names for rational numbers. Copyright Wright Group/McGraw-Hill

3 Copyright Wright Group/McGraw-Hill Content Strand: NUMBER AND NUMERATION cont. Program Goal: Understand Equivalent Names for Numbers cont. Equivalent names for fractions, decimals, and percents Goal 6. Use manipulatives and drawings to model equivalent names for 1_ 2. Goal 5. Use manipulatives and drawings to find and represent equivalent names for fractions; use manipulatives to generate equivalent fractions. Goal 5. Use expressions to find and represent equivalent names for fractions and decimals; use and explain a multiplication rule to find equivalent fractions; rename fourths, fifths, tenths, and hundredths as decimals and percents. Goal 5. Use expressions to find and represent equivalent names for fractions, decimals, and percents; use and explain division rules to find equivalent fractions and fractions in simplest form; convert between fractions and mixed numbers; convert between fractions, decimals, and percents. Goal 5. Find equivalent fractions and fractions in simplest form by applying division rules and concepts from number theory; convert between fractions, mixed numbers, decimals, and percents. Program Goal: Understand Common Numerical Relations Goals 39 Comparing and ordering numbers Goal 6. Compare and order whole numbers up to 20. Goal 7. Compare and order whole numbers up to 1,000. Goal 7. Compare and order whole numbers up to 10,000; use area models to compare fractions. Goal 6. Compare and order whole numbers up to 1,000,000; use manipulatives to order decimals through hundredths; use area models and benchmark fractions to compare and order fractions. Goal 6. Compare and order whole numbers up to 1,000,000,000 and decimals through thousandths; compare and order integers between -100 and 0; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions. Goal 6. Compare and order rational numbers; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions and mixed strategies used to compare fractions and mixed numbers. Goal 6. Choose and apply strategies for comparing and ordering rational numbers; explain those choices and strategies.

4 Content Strand: OPERATIONS AND COMPUTATION Program Goal: Compute Accurately Addition and subtraction facts Goal 1. Use number lines, and mental arithmetic to solve problems involving the addition and subtraction of single-digit whole numbers; demonstrate appropriate fluency with addition and subtraction facts within 5. Goal 1. Demonstrate appropriate fluency with addition and subtraction facts through Goal 1. Demonstrate automaticity with all addition facts through and fluency with the related subtraction facts. Goal 1. Demonstrate automaticity with all addition and subtraction facts through ; use basic facts to compute fact extensions such as Goal 1. Demonstrate automaticity with addition and subtraction fact extensions. Addition and subtraction procedures Goal 2. Use number grids, tally marks, mental arithmetic, and subtraction of 1-digit whole numbers with 2-digit whole numbers; calculate and compare the values of combinations of coins. Goal 2. Use number grids, tally marks, mental arithmetic, paper & pencil, and subtraction of multidigit whole the strategies used; calculate and compare values of coin and bill combinations. Goal 2. Use mental arithmetic, paper-and-pencil subtraction of whole decimals in a money context; describe the strategies used and explain how they work. Goal 2. Use mental arithmetic, paper-and-pencil subtraction of whole decimals through hundredths; describe the strategies used and explain how they work. Goal 1. Use mental arithmetic, paper-and-pencil subtraction of whole numbers, decimals, and signed the strategies used and explain how they work. Goal 1. Use mental arithmetic, paper-and-pencil subtraction of whole numbers, decimals, and signed the strategies used and explain how they work. Copyright Wright Group/McGraw-Hill

5 Copyright Wright Group/McGraw-Hill Content Strand: OPERATIONS AND COMPUTATION cont. Program Goal: Compute Accurately cont. Multiplication and division facts Goal 3. Demonstrate automaticity with multiplication facts through Goal 3. Demonstrate automaticity with multiplication facts through 10 º 10 and proficiency with related division facts; use basic facts to compute fact extensions such as 30 º 60. Goal 2. Demonstrate automaticity with division fact extensions. Goals 41 Multiplication and division procedures arrays, mental arithmetic, paper-and-pencil the multiplication of 2- and 3-digit whole numbers by 1-digit whole numbers; describe the strategies used. mental arithmetic, paper-and-pencil the multiplication of multidigit whole numbers by 2-digit whole the division of multidigit whole numbers by 1-digit whole numbers; describe the strategies used and explain how they work. Goal 3. Use mental arithmetic, paperand-pencil algorithms and the multiplication of whole decimals and the division of multidigit whole decimals by whole numbers; express remainders as whole numbers or fractions as appropriate; describe the strategies used and explain how they work. Goal 2. Use mental arithmetic, paperand-pencil the multiplication and division of whole numbers, decimals, and signed numbers; describe the strategies used and explain how they work.

6 42 Assessment Handbook Content Strand: OPERATIONS AND COMPUTATION cont. Program Goal: Compute Accurately cont. Procedures for addition and subtraction of fractions Procedures for multiplication and division of fractions Goal 5. Use mental arithmetic, and calculators to solve problems involving the addition and subtraction of fractions and mixed the strategies used. mental arithmetic, paperand-pencil algorithms and subtraction of fractions and mixed the strategies used and explain how they work. Goal 5. Use area models, mental arithmetic, paperand-pencil the multiplication of fractions and mixed numbers; use visual models, paper-andpencil methods, and the division of fractions; describe the strategies used. Goal 3. Use mental arithmetic, paperand-pencil algorithms and subtraction of fractions and mixed the strategies used and explain how they work. mental arithmetic, paperand-pencil the multiplication and division of fractions and mixed the strategies used and explain how they work. Copyright Wright Group/McGraw-Hill

9 Copyright Wright Group/McGraw-Hill Content Strand: DATA AND CHANCE cont. Goals 45 Program Goal: Understand and Apply Basic Concepts of Probability cont. Quantitative probability Goal 4. Predict the outcomes of simple experiments and test the predictions using manipulatives; express the probability of an event by using out of language. Goal 4. Predict the outcomes of experiments and test the predictions using manipulatives; summarize the results and use them to predict future events; express the probability of an event as a fraction. Goal 4. Predict the outcomes of experiments, test the predictions using and summarize the results; compare predictions based on theoretical probability with experimental results; use summaries and comparisons to predict future events; express the probability of an event as a fraction, decimal, or percent. Goal 3. Use the Multiplication Counting Principle, tree diagrams, and other counting strategies to identify all possible outcomes for a situation; predict results of experiments, test the predictions using and summarize the findings; compare predictions based on theoretical probability with experimental results; calculate probabilities and express them as fractions, decimals, and percents; explain how sample size affects results; use the results to predict future events.

10 46 Assessment Handbook Content Strand: MEASUREMENT AND REFERENCE FRAMES Program Goal: Understand the Systems and Processes of Measurement; Use Appropriate Techniques, Tools, Units, and Formulas in Making Measurements Length, weight, and angles Goal 1. Use nonstandard tools and techniques to estimate and compare weight and length; identify standard measuring tools. Goal 1. Use nonstandard tools and techniques to estimate and compare weight and length; measure length with standard measuring tools. Goal 1. Estimate length with and without tools; measure length to the nearest inch and centimeter; use standard and nonstandard tools to measure and estimate weight. Goal 1. Estimate length with and without tools; measure length to the nearest 1_ 2 inch and 1_ 2 centimeter; draw and describe angles as records of rotations. Goal 1. Estimate length with and without tools; measure length to the nearest 1_ 4 inch and 1_ 2 centimeter; use tools to measure and draw angles; estimate the size of angles without tools. Goal 1. Estimate length with and without tools; measure length with tools to the nearest 1_ 8 inch and millimeter; estimate the measure of angles with and without tools; use tools to draw angles with given measures. Goal 1. Estimate length with and without tools; measure length with tools to the nearest 1 16 inch and millimeter; estimate the measure of angles with and without tools; use tools to draw angles with given measures. Area, perimeter, volume, and capacity Goal 2. Partition rectangles into unit squares and count unit squares to find areas. Goal 2. Describe and use strategies to measure the perimeter of polygons; find the areas of rectangles. Goal 2. Describe and use strategies to measure the perimeter and area of polygons, to estimate the area of irregular shapes, and to find the volume of rectangular prisms. Goal 2. Describe and use strategies to find the perimeter of polygons and the area of circles; choose and use appropriate methods, including formulas, to find the areas of rectangles, parallelograms, and triangles, and the volume of a prism; define pi as the ratio of a circle s circumference to its diameter. Goal 2. Choose and use appropriate formulas to calculate the circumference of circles and to solve area, perimeter, and volume problems. Units and systems of measurement relationships between days in a week and hours in a day. relationships among inches, feet, and yards; describe relationships between minutes in an hour, hours in a day, days in a week. relationships among U.S. customary units of measure and among metric units of measure. relationships among U.S. customary units of measure and among metric units of measure. Copyright Wright Group/McGraw-Hill

11 Copyright Wright Group/McGraw-Hill Content Strand: MEASUREMENT AND REFERENCE FRAMES cont. Program Goal: Understand the Systems and Processes of Measurement; Use Appropriate Techniques, Tools, Units, and Formulas in Making Measurements cont. Money Goal 2. Identify pennies, nickels, dimes, quarters, and dollar bills. Goal 2. Know and compare the value of pennies, nickels, dimes, quarters, and dollar bills; make exchanges between coins. Goal 4. Make exchanges between coins and bills. Program Goal: Use and Understand Reference Frames Temperature temperature using appropriate vocabulary, such as hot, warm, and cold; identify a thermometer as a tool for measuring temperature. Goal 3. Identify a thermometer as a tool for measuring temperature; read temperatures on Fahrenheit and Celsius thermometers to the nearest 10. Goal 5. Read temperature on both the Fahrenheit and Celsius scales. Goals 47 Time Coordinate systems Goal 4. Describe and use measures of time periods relative to a day and week; identify tools that measure time. a calendar to identify days, weeks, months, and dates; tell and show time to the nearest half and quarter hour on an analog clock. Goal 6. Tell and show time to the nearest five minutes on an analog clock; tell and write time in digital notation. Goal 4. Tell and show time to the nearest minute on an analog clock; tell and write time in digital notation. ordered pairs of numbers to name, locate, and plot points in the first quadrant of a coordinate grid. ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid. Goal 3. Use ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid.

12 48 Assessment Handbook Content Strand: GEOMETRY Program Goal: Investigate Characteristics and Properties of Two- and Three-Dimensional Geometric Shapes Lines and angles Goal 1. Draw line segments and identify parallel line segments. Goal 1. Identify and draw points, intersecting and parallel line segments and lines, rays, and right angles. Goal 1. Identify, draw, and describe points, intersecting and parallel line segments and lines, rays, and right, acute, and obtuse angles. Goal 1. Identify, describe, compare, name, and draw right, acute, obtuse, straight, and reflex angles; determine angle measures in vertical and supplementary angles and by applying properties of sums of angle measures in triangles and quadrangles. Goal 1. Identify, describe, classify, name, and draw angles; determine angle measures by applying properties of orientations of angles and of sums of angle measures in triangles and quadrangles. Plane and solid figures Goal 1. Identify and describe plane and solid figures including circles, triangles, squares, rectangles, spheres, and cubes. Goal 1. Identify and describe plane and solid figures including circles, triangles, squares, rectangles, spheres, cylinders, rectangular prisms, pyramids, cones, and cubes. Goal 2. Identify, describe, and model plane and solid figures including circles, triangles, squares, rectangles, hexagons, trapezoids, rhombuses, spheres, cylinders, rectangular prisms, pyramids, cones, and cubes. Goal 2. Identify, describe, model, and compare plane and solid figures including circles, polygons, spheres, cylinders, rectangular prisms, pyramids, cones, and cubes using appropriate geometric terms including the terms face, edge, vertex, and base. Goal 2. Describe, compare, and classify plane and solid figures, including polygons, circles, spheres, cylinders, rectangular prisms, cones, cubes, and pyramids, using appropriate geometric terms including vertex, base, face, edge, and congruent. Goal 2. Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Program Goal: Apply Transformations and Symmetry in Geometric Situations Goal 2. Identify and describe similar and congruent figures and describe their properties; construct a figure that is congruent to another figure using a compass and straightedge. Transformations and symmetry Goal 2. Identify shapes having line symmetry. Goal 2. Identify shapes having line symmetry; complete line-symmetric shapes or designs. Goal 3. Create and complete twodimensional symmetric shapes or designs. Goal 3. Create and complete twodimensional symmetric shapes or designs; locate multiple lines of symmetry in a twodimensional shape. Goal 3. Identify, describe, and sketch examples of reflections; identify and describe examples of translations and rotations. Goal 3. Identify, describe, and sketch examples of reflections, translations, and rotations. Goal 3. Identify, describe, and sketch (including plotting on the coordinate plane) instances of reflections, translations, and rotations. Copyright Wright Group/McGraw-Hill

13 Copyright Wright Group/McGraw-Hill Content Strand: PATTERNS, FUNCTIONS, AND ALGEBRA Program Goal: Understand Patterns and Functions Patterns and functions Goal 1. Extend, describe, and create visual, rhythmic, and movement patterns; use rules, which will lead to functions, to sort, make patterns, and play What s My Rule? and other games. Goal 1. Extend, describe, and create numeric, visual, and concrete patterns; solve function machines, What s My Rule? tables, and Framesand-Arrows diagrams. Goal 1. Extend, describe, and create numeric, visual, and concrete patterns; describe rules for patterns and use them to solve problems; use words and symbols to describe and write rules for functions involving addition and subtraction and use those rules to solve problems. Goal 1. Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; use words and symbols to describe and write rules for functions involving addition, subtraction, and use those rules to solve problems. Goal 1. Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; use words and symbols to describe and write rules for functions that involve the four basic arithmetic operations and use those rules to solve problems. Goal 1. Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; write rules for functions involving the four basic arithmetic operations; represent functions using words, symbols, tables, and graphs and use those representations to solve problems. Program Goal: Use Algebraic Notation to Represent and Analyze Situations and Structures Goal 1. Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; represent patterns and rules using algebraic notation; represent functions using words, algebraic notation, tables, and graphs; translate from one representation to another and use representations to solve problems involving functions. Goals 49 Algebraic notation and solving number sentences Goal 2. Read and write expressions and number sentences using the symbols +, -, and =. Goal 2. Read, write, and explain expressions and number sentences using the symbols +, -, and = and the symbols > and < with cues; solve equations involving addition and subtraction. Goal 2. Read, write, and explain expressions and number sentences using the symbols +, -, =, >, and <; solve number sentences involving addition and subtraction; write expressions and number sentences to model number stories. Goal 2. Read, write, and explain number sentences using the symbols +, -,,, =, >, and <; solve number sentences; write expressions and number sentences to model number stories. Goal 2. Use conventional notation to write expressions and number sentences using the four basic arithmetic operations; determine whether number sentences are true or false; solve open sentences and explain the solutions; write expressions and number sentences to model number stories. Goal 2. Determine whether number sentences are true or false; solve open number sentences and explain the solutions; use a letter variable to write an open sentence to model a number story; use a pan-balance model to solve linear equations in one unknown. Goal 2. Determine whether equalities and inequalities are true or false; solve open number sentences and explain the solutions; use a pan-balance model to solve linear equations in one or two unknowns; use trial-and-error and equivalent equations strategies to solve linear equations in one unknown.

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