Alignment of Destination Math Courseware with GRADE 4 Benchmarks (B1-B3)

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1 NUMBER SENSE SAM B1 Read write whole numbers in the millions (1.1) 1.1 Read write whole numbers in the millions. I Number Sense Unit: Large Small Whole to One Million Ordering Rounding Whole SAM04102a-B1 Order compare whole numbers (1.2) SAM04102-B2 1.2 Order compare whole to two decimal places. 1 Number Sense Unit: Large Small Ordering Rounding Whole Unit: Introduction Tenths, Hundredths, Thousths Ordering Unit: Essentials of Decimals Investigating Decimal Place alues

2 Order compare whole numbers decimals to two decimal places (1.2) SAM04103-B2 Round whole numbers through the millions to the nearest ten, hundred, thous, ten thous, or hundred thous (1.3) SAM04104a-B1 Identify when a round solutions is called for explain why such a solution may be appropriate (1.4) 1.3 Round whole numbers through the millions to the nearest ten, hundred, thous, ten thous, or hundred thous. 1.4 Decide when a rounded solution is called for explain why such a solution may be appropriate 2 I Number Sense Unit: Large Small Ordering Rounding Whole Number Sense Unit: Large Small Ordering Rounding Whole Unit: Adding Subtracting Decimals Using Place alue Grids Integers & Order of Unit: Adding Subtracting Signed Adding

3 SAM04104-B2 Decide when a rounded solution is called for explain why such a solution may be appropriate (1.4) SAM04105-B3 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, division of whole numbers by whole numbers; explain equivalents of fractions (1.5) SAM04106-B2 1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, division of whole numbers by whole numbers; explain equivalents of fractions (see Stard 4.0) 1.6 Write tenths hundredths in decimal 3 I Fractions Unit: Proper Improper Fractions Proper Fractions Improper Fractions Session 3: Equivalent Fractions Unit: Introduction Session: Tenths, Hundredths, Thousths Unit: Introduction Tenths, Absolute alue Fractions Unit: Essentials of Fractions Recognizing a Fraction Exploring Proper Improper Fractions Session 3: Working Mixed Unit: Essentials of Decimals

4 Write tenths hundredths in decimal fraction notations know the fraction decimal equivalents for halves fourths (e.g., 1/2 = 0.5 or.50; 7/4 = 1 3/4 = 1.75) (1.6) SAM04107-B2 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings relate a fraction to a simple decimal on a number line (1.7) SAM04108a-B2 fraction notations know the fraction decimal equivalents for halves fourths (e.g., _ = 0.5 or.50; 7/4 = 1 _ = Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; relate a fraction to a simple decimal on a number line. 1.8 Use concepts of negative Unit: Division Session: Fractional Parts Geometry Measurement 4 I Hundredths, Thousths Fractions Unit: Proper Improper Fractions Session 3: Equivalent Fractions Unit: Introduction Session 3: Ratios, Decimals, Percents Investigating Decimal Place alues

5 Underst identify the concept of negative numbers in a number line as owing: counting (1.8) numbers (e.g., on a number line, in counting, in temperature, in owing ). Unit: Measurement Session: Temperature I Number Sense Unit: Large Small Session 3: Negative Whole SAM04108-B3 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing") (1.8) SAM04109a-B2 1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, positive decimals. 5 Fractions Unit: Proper Improper Fractions Proper Fractions Improper Fractions

6 Identify on a number line the relative position of positive fractions, positive mixed numbers (1.9) I Unit: Introduction Tenths, Hundredths, Thousths SAM04109-B3 fractions; use concepts of negative numbers: Identify on a number line the relative position of positive fractions, positive mixed numbers, positive decimals to two decimal places (1.9) SAM04110-B1 Extend use understing of whole numbers to the addition subtraction of simple decimals: Estimate compute the sum or difference of whole numbers positive decimals to two places 2.1 Estimate compute the sum or difference of whole numbers positive decimals to two places. 6 Unit: Addition Subtraction of Whole Whole Number Sums Differences Unit: Adding Subtracting Decimals Using Place alue Grids Regrouping Whole

7 7 I (2.1) Between Large SAM04112-B1 Extend use understing of whole numbers to the addition subtraction of simple decimals: Round twoplace decimals to one decimal or the nearest whole number judge the reasonableness of the rounded answer (2.2) SAM04112-B1 Solve problems involving addition, subtraction, multiplication, division of whole numbers, underst the relationships among the operations: Demonstrate understing of, the ability to use, stard algorithms for 2.2 Round two-place decimals to one decimal or the nearest whole number judge the reasonableness of the rounded answer. 3.1 Demonstrate an understing of, the ability to use, stard algorithms for the addition subtraction of multi-digit numbers. Unit: Addition Subtraction Adding Decimals Subtracting Decimal Unit: Introduction Ordering Rounding Unit: Addition Subtraction of Whole Whole Number Sums Differences Between Large Session 3: Regrouping to Hundredths Unit: Essentials of Decimals Session: Rounding Decimals Unit: Adding Subtracting Decimals Using Place alue Grids

8 addition subtraction of multidigit numbers (3.1) SAM04113-B2 Solve problems involving addition, subtraction, multiplication, division of whole numbers, underst the relationships among the operations: Demonstrate an understing of, the ability to use, stard algorithms for multiplying a multidigit number by a two-digit number for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations to check results (3.2) SAM04114-B2 Solve problems involving addition, subtraction, multiplication, division of whole numbers, underst the relationships among the operations: Solve problems involving 3.2 Demonstrate an understing of, the ability to use, stard algorithms for multiplying a multi-digit number by a twodigit number for dividing a multi-digit number by a onedigit number; use relationships between them to simplify computations to check results. 3.3 Solve problems involving multiplication of multi-digit numbers by two-digit numbers 8 I Unit: Multiplication Division of Whole Twodigit Multipliers Introduction to Long Division Unit: Multiplication Division of Whole Twodigit Multipliers

9 multiplication of multidigit numbers by two-digit numbers (3.3) SAM04115-B2 Solve problems involving addition, subtraction, multiplication, division of whole numbers, underst the relationships among the operations: Solve problems involving division of multidigit numbers by one-digit numbers (3.4) SAM04116-B1 Know how to factor small whole numbers: Underst that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3) (4.1) 3.4 Solve problems involving division of multi-digit numbers by one-digit numbers. 4.1 Underst that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). I Unit: Multiplication Division of Whole Introduction to Long Division Number Sense Unit: as Factors Finding Factors Session: Prime Composite Session: Identifying Common Factors SAM04117-B2 Know how to factor small whole numbers: Know that numbers such as 2, 3, 5, 7, 11 do not have any factors except 1 themselves that 4.2 Know that numbers such as 2, 3, 5, 7, 11 do not have any factors except 1 themselves that such numbers are called prime numbers. 9 Number Sense Unit: as Factors Prime Composite

10 such numbers are called prime numbers (4.2) I Session: Identifying Common Factors ALGEBRA & FUNCTIONS SAM04201a-B2 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Demonstrate understing use of a letter, box or other symbols to represent any number in a simple expression or equation (1.1) SAM04201-B3 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Use letters, boxes, or other symbols to st for any number in simple expressions or equations (e.g., demonstrate understing the use of a concept of a variable) (1.1) 1.1 Use letters, boxes, or other symbols to st for any number in simple expressions or equations (e.g., demonstrate an understing the use of the concept of a variable Number Sense Unit: as Factors Session: Finding Factors Unit: Multiplication Division of Whole Session: Two-Digit Multipliers Unit: Multiplication Division of Whole Session: Introduction to Long Division Fractions Unit: Multiplication Division Session: Finding Products Geometry Unit: Measurement Session: Rectangles Squares 10 Essentials of Algebra Unit: Algebra Fundamentals Introducing ariables

11 Geometry Unit: Coordinate Geometry Algebra Session: The Coordinate Plane I SAM04202-B3 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Interpret evaluate mathematical expressions that use parentheses (1.2) 1.2 Interpret evaluate mathematical expressions that now use parentheses. Algebraic Thinking Unit: Properties Relationships Session: Number Patterns Properties Unit: The Integers Session: Integer Sums Unit: Multiplication Division of Whole Session: Two-Digit Multipliers Integers & Order of Unit: Order of Simplifying Expressions Unit: Multiplication Division Session: Multiplying Decimals Unit: Multiplication Division Session: Dividing Decimals by Whole SAM04203-B2 1.3 Integers 11

12 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms different operations (1.3 SAM04204-B3 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Use interpret formulas (e.g., area = length width or A = lw) to answer questions about quantities their relationships (1.4) Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms different operations 1.4 Use interpret formulas (e.g., area = length x width or A = lw ) to answer questions about quantities their relationships. 12 I Unit: Multiplication Division of Whole Session: Two-Digit Multipliers Unit: Multiplication Division Session: Multiplying Decimals Session: Dividing Decimals by Whole Number Sense Unit: as Factors Session: Finding Factors Unit: Multiplication Division of Whole Session: Two-Digit Multipliers Session: Introduction to Long Division Session: Two-Digit Divisors Geometry & Order of Unit: Order of Introducing the Distributive Property Session 3: Using Grouping Symbols Integers & Order of Unit: Order of Introducing the Distributive Property Essentials of Algebra Unit: Evaluating an Algebraic Expression Combining Like Terms Essentials of Algebra Unit: Evaluating an Algebraic Expression Representing the Dimensions Area of a Rectangle

13 I Unit: Measurement Session: Rectangles Squares Session: Triangles Session: Parallelograms Trapezoids Data Analysis Probability Unit: Modeling Displaying Events Session: Displaying Analyzing Data Session: Looking at Chance SAM04205a-B2 Use interpret variables, mathematical symbols, properties to write simplify expressions sentences: Underst that an equation such as y = 3x + 5 can be solved when one variable is given (1.5) SAM04205-B3 Use interpret variables, mathematical symbols, properties o write simplify expressions 1.5 Underst that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given. 13 Essentials of Algebra Unit: Algebra Fundamentals Session 3: Replacing variables in a Formula Essentials of Algebra Unit: Evaluating an Algebraic Expression Session 3: Evaluating Expressions Using

14 sentences: Underst hat an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given (1.5) I Substitution SAM04206-B2 Know how to manipulate equations: Know underst that equals added to equals are equal (2.1) SAM04207-B3 Know how to manipulate equations: Know underst that equals multiplied by equals are equal (2.2) 2.1 Know underst that equals added to equals are equal. 2.2 Know underst that equals multiplied by equals are equal MEASUREMENT & GEOMETRY SAM04401-B2 Underst perimeter area: Measure the area of rectangular shapes, using appropriate units such as square centimeter (cm 2 ), square meter (m 2 ), square kilometer (km 2 ), square inches (in 2 ), square yard (yd 2 ), square mile (mi 2 ) (1.1) 1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter, square meter, square kilometer, square inch, square yard, or square mile SAM04402-B2 1.2 Recognize that rectangles 14 Geometry Unit: Measurement Rectangles Squares Geometry Unit: Measurement

15 Underst perimeter area: Recognize that the rectangles that have the same area can have different perimeters (1.2 SAM04403-B2 Underst perimeter area: Underst that rectangles that have the same perimeter can have different areas (1.3) SAM04404a-B2 Underst perimeter area: Underst use formulas to solve problems involving perimeters areas rectangles squares; use those formulas to find the areas of rectangles squares (1.4) that have the same area can have different perimeters 1.3 Underst that rectangles that have the same perimeter can have different areas. 1.4 Underst use formulas to solve problems involving perimeters areas of rectangles squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes. I Rectangles Squares Geometry Unit: Measurement Rectangles Squares Geometry Unit: Measurement Session 4: Parallelograms Trapezoids SAM04404-B3 Underst perimeter area: Underst use formulas to solve problems involving perimeters areas of rectangles squares; use those formulas to find the areas of more complex figures by dividing the 15

16 figures into basic shapes (1.4) SAM04405-B3 Use two-dimensional coordinate grids to represent points graph lines simple figures: Draw the points corresponding to linear relationships on graph paper (e.g., draw ten points on the graph of the equation y = 3x connect them by using a straight line) (2.1 SAM04406-B3 Use two-dimensional coordinate grids to represent points graph lines simple figures: Underst that the length of a horizontal line segment equals the difference of the x- coordinates (2.2) SAM04407-B3 Use two-dimensional coordinate grids to represent points graph lines simple figures: Underst that the length of a vertical line segment equals the difference of the y- coordinates (2.3) SAM04408-B2 Demonstrate 2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x connect them by using a straight line. 2.2 Underst that the length of a horizontal line segment equals the difference of the x-coordinates 2.3 Underst that the length of a vertical line segment equals the difference of the y- coordinates. 3.1 Identify lines that are 16 I Geometry Unit: Coordinate Geometry Algebra The Coordinate Plane Geometry Unit: Coordinate Geometry Algebra The Coordinate Plane Geometry Unit: Measurement Fundamentals of

17 understing of plane solid geometric objects; use this knowledge to show relationships solve problems: Identify lines that are parallel perpendicular (3.1) SAM04409-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Identify the radius diameter of a circle (3.2) SAM04410-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Identify congruent figures (3.3 I parallel perpendicular. Rectangles Squares Session: Parallelograms Trapezoids 3.2 Identify the radius diameter of a circle. 3.3 Identify congruent figures. Geometry Unit: Coordinate Geometry Algebra Symmetry Transformations Unit: Essentials of Decimals Rounding Decimals Geometry Unit: Geometry Fundamentals Naming Measuring Fundamentals of Geometry Unit: Geometry Fundamentals Session: Recognizing Congruent Angles SAM04411-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Identify figures that have bilateral rotational symmetry (3.4) 3.4 Identify figures that have bilateral rotational symmetry. Geometry Unit: Coordinate Geometry Algebra Symmetry Transformations 17

18 I SAM04412-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Know the definitions of a right angle, an acute angle, an obtuse angle; underst that 90, 180, 270, 360 are associated, respectively 1/4, 1/2, 3/4, full turns (3.5) SAM04413-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: isualize, describe, make models of geometric solids (e.g., prisms, pyramids.) in terms of the number shape of faces, edges, vertices; interpret twodimensional representations of threedimensional objects; draw patterns (of faces) for a solid that, when cut folded will make a 3.5 Know the definitions of a right angle, an acute angle, an obtuse angle. Underst that 90,180,270, 360 are associated, respectively, _, _, _, full turns. 3.6 isualize, describe, made models of geometric solids (e.g., prisms, pyramids) in terms of the number shape of faces, edges, vertices; interpret twodimensional representations of three-dimensional objects; draw patterns (of faces) for a solid that, when cut folded, will Geometry Unit: Measurement Lines, Angles Circles Fundamentals of Geometry Unit: Geometry Fundamentals Naming Measuring Angles Defining Complementary Supplementary Angles 18

19 model of the solid (3.6) SAM04414-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) identify their attributes (3.7) 3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) identify their attributes I Geometry Unit: Measurement Session 3: Triangles Fundamentals of Geometry Unit: Triangles Classifying Triangles by Sides SAM04415-B2 Demonstrate an understing of plane solid geometric objects use this knowledge to show relationships solve problems: Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid) (3.8) 3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid). STATISTICS, DATA ANALYSIS, AND PROBABILITY SAM04301a-B2 1.1 Formulate survey questions; systematically collect represent data on a number line; coordinate graphs, tables, charts. Organize, represent, interpret numerical categorical data, clearly communicate their findings: Systematically collect represent data on a number line; 19 Geometry Unit: Measurement Rectangles Squares Session 4: Parallelograms Trapezoids Data Analysis Probability Unit: Modeling Displaying Events Displaying Analyzing Data Fundamentals of Statistics Unit: Interpreting Constructing Graphs Session: Exploring Line Graphs

20 coordinate graphs, tables (1.1) SAM04301-B3 Organize, represent, interpret numerical categorical data, clearly communicate their findings: Formulate survey questions; systematically collect represent data on a number line; coordinate graphs, tables, charts (1.1) SAM04302-B3 Organize, represent, interpret numerical categorical data, clearly communicate their findings: Identify the mode(s) for sets of categorical data, the mode(s), median, any apparent outliers for numerical data sets (1.3) SAM04303-B3 Organize, represent, interpret numerical categorical data, clearly communicate their findings: Interpret one- 1.3 Interpret one- twovariable data graphs to answer questions about a situation. 20 I Data Analysis Probability Unit: Modeling Displaying Events Displaying Analyzing Data Fundamentals of Statistics Unit: Interpreting Constructing Graphs Session: Exploring Bar Graphs Fundamentals of Statistics Unit: Interpreting Constructing Graphs Session: Interpreting Pie Charts Fundamentals of Statistics Unit: Interpreting Constructing Graphs Exploring Line Graphs Exploring Bar Graphs Session 3: Interpreting Pie Charts

21 two-variable data graphs to answer questions about a situation (1.3) SAM04304-B3 Make predictions for simple probability situations: Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams) (2.1) 2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams). 21 I Data Analysis Probability Unit: Modeling Displaying Events Looking at Chance Fundamentals of Probability Unit: Simple Probability Defining Expressing Probability Calculating Probabilities on a Color Wheel Fundamentals of Probability Unit: Probability of Combined Events Calculating the Probability of Independent Events Determining the Sample Space of an Experiment Session 3: Calculating the Probability of Mutually Exclusive Events

22 SAM04305-B3 Make predictions for simple probability situations: Express outcomes of experimental probability situations verbally numerically (e.g., 3 out of 4; 3/4) (2 2.2 Express outcomes of experimental probability situations verbally numerically (e.g., 3 out of 4; _) I Data Analysis Probability Unit: Modeling Displaying Events Looking at Chance Fundamentals of Probability Unit: Simple Probability Calculating Probabilities on a Color Wheel Session 3: Determining Probability of Complementary Events Fundamentals of Probability Unit: Probability of Combined Events Calculating the Probability of Independent Events Determining the Sample Space of an Experiment Session 3: Calculating the Probability of Mutually Exclusive Events 22

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