Course Outline

Unit 1: Whole Number Sense

Students learn to read and write numerals and number words through 10,000. They learn about odd and even numbers. They practice arranging objects in space by proximity, demonstrate automatic recall of addition and subtraction facts, and order whole numbers by using the symbols <, =, >. They solve addition and subtraction problems, estimate quantities and numbers of objects, compare whole numbers, and round numbers.

• Numbers Through 10,000
• Odd and Even Numbers
• Read and Write Numerals Through 10,000
• Write Number Words Through 10,000
• Numbers in Expanded Form
• Construct Numbers to 10,000 (parts A, B)
• Compare and Order Numbers Through 10,000
• Compare Numbers Through 500
• Round Numbers Through 10,000

Unit 2: Whole Number Addition and Subtraction

Students learn how addition and subtraction affect whole numbers and how to determine the sum or difference of two whole numbers. They practice story problems in which two quantities are combined, quantities change by addition or subtraction, two quantities are compared by the use of addition or subtraction, and one quantity must be changed to equal another quantity.

• Effects of Addition and Subtraction
• Addition and Subtraction Answers
• Combine and Change Problems
• Compare and Equalize Story Problems

Unit 3: Algebra Thinking

Students learn to use mathematical expressions, equations, and inequalities to represent relationships between quantities. They learn to select the appropriate symbol to show an operation or a relationship that makes a number sentence true, to determine a missing number in an equation or an inequality, and to recognize and describe a linear pattern, such as counting by 5s or multiplying 5 times a number to reach 100, by its rule. They extend linear patterns and solve simple story problems that involve functions.

• Mathematical Expressions
• Expressions and Number Sentences (parts A, B)
• Expression Comparison (parts A, B)
• Missing Symbols
• Missing Values (parts A–C)
• Number Patterns
• Story Problems and Patterns (parts A, B)

Unit 4: Whole Number Multiplication Sense

Students use objects or sketches to solve multiplication problems. They use models to explain multiplication as repeated addition of the same quantity. They learn how to explain and apply the commutative, associative, and zero properties of multiplication. They demonstrate automatic recall of multiplication facts and an understanding of how multiplication affects whole numbers. They learn how to apply the multiplication property of 1.

• Model and Explain Multiplication
• Area Models for Multiplication (parts A, B)
• Understand Multiplication
• Commutative Property of Multiplication
• Multiplication Facts
• Multiplication Facts (parts A–D)
• Associative Property

Unit 5: Whole Number Multiplication

Students use objects or sketches to solve multiplication story problems. They solve multiplication problems involving a multidigit factor and a one-digit factor. They use multiplication to solve story problems that involve equal groups and equal measures and learn how to create story problems that can be represented by a multiplication number sentence.

• Multiplication Story Problems
• Multiply Multidigit by 1-Digit Numbers
• Multiply Equal Groups (parts A, B)
• Multiplication with Equal Measures
• Write Multiplication Stories (parts A, B)

Unit 6: Whole Number Division Sense

Students use objects or sketches to solve division problems. They learn that division is repeated subtraction and the sharing of a quantity into equal groups. They learn the meaning of the ÷ symbol, the division property of 1, division by zero is undefined, and the inverse relationship between multiplication and division.

• Model and Explain Division
• Applying Division Symbols and Rules
• Division as Sharing
• Relating Multiplication and Division
• Use Inverse Relationships
• Effects of Division

Unit 7: Whole Number Division

Students use objects or sketches to solve division story problems. They learn to solve division problems with a multidigit dividend, a one-digit divisor, and no remainder. They practice solving story problems that involves equal groups and equal measures, learn to determine unit cost, and create story problems that can be represented by a division number sentence.

• Dividing with Remainders
• Divide Greater Numbers
• Story Problems with Equal Groups (parts A, B)
• Equal Measures with Remainders
• Divide Money Amounts
• Write Division Story Problems (parts A, B)

Unit 8: Semester Review and Checkpoint

Unit 9: Whole Numbers and Multiple Operations

Students learn how to determine whether addition, subtraction, multiplication, or division is the appropriate operation to use to solve a story problem. They practice solving story problems involving two or more operations and using the order of operations to evaluate an expression.

• The Order of Operations
• Choose the Correct Operation (parts A, B)
• Use More Than One Operation (parts A, B)

Unit 10: Geometry

Students learn how to identify right angles and the measure of angles greater than or less than a right angle. They learn to classify polygons according to the number of sides; the attributes of isosceles, equilateral, and right triangles; and the attributes of parallelograms, rectangles, and squares. They learn to identify and describe common solid geometric figures.

• Right Angles and Other Angles
• Identify and Classify Polygons
• Triangles
• Parallelograms
• Identify and Classify Solids
• Combine Solids to Create New Shapes

Unit 11: Decimals and Money

Students learn to identify decimal place values through thousandths. They practice solving story problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation.

• Decimal Place Values
• Money in Decimal Notation
• Money Story Problems (parts A–C)

Unit 12: Fractions and Probability

Students learn about fractions as part of a set, the relationship of a part to a whole, and a rational number on the number line. They learn to write the fraction represented by a drawing that shows parts of a set or parts of a whole. They compare and order unit fractions and use objects or sketches to solve simple story problem involving addition or subtraction of fractions. They solve and simplify addition and subtraction problems involving fractions with like denominators and learn that a simple fraction and a decimal amount can represent the same quantity. They learn to identify whether specific events are certain, likely, unlikely, or impossible; record the possible outcomes for a simple event; summarize and display the results of a probability experiment; and use the results of a probability experiment to predict future events.

• Represent and Name Fractions (parts A, B)
• Compare and Order Fractions (parts A, B)
• Model Fraction Story Problems
• Add and Subtract Like Fractions
• Fractions and Decimals (parts A, B)
• Probability
• Identify, Record, and Display Outcomes
• Use Data to Make Predictions

Unit 13: Measurement: Length and Time

Students learn the appropriate tools and metric and English units for measuring the length of objects. They practice estimating and measuring the length of an object to the nearest centimeter, 1/2 inch, and 1/4 inch. They learn to tell time to the nearest minute, determine elapsed time to the nearest minute, and use a calendar to determine elapsed time.

• Tools and Units for Measuring Length
• Estimate and Measure Centimeters
• Estimate and Measure Inches (parts A, B)
• Telling Time in Minutes
• Determine Elapsed Time in Minutes
• Elapsed Time on a Calendar

Unit 14: Measurement: Capacity and Weight

Students learn the appropriate tools and metric and English units for measuring liquid volume and weight. They practice estimating and measuring liquid volume to the nearest liter and cup, and weight of an object to the nearest gram and ounce. They write simple unit conversions as expressions and equations and use simple unit conversions, such as centimeters to meters, to solve problems.

• Capacity
• Measure to the Nearest Liter
• English Units of Capacity
• Measure in English and Metric Units
• Measure in Grams
• Measure Weight in Ounces and Pounds
• Unit Conversions
• Unit Conversions (parts A, B)

Unit 15: Mathematical Reasoning

Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They learn how to break a multistep story problem into simpler steps, predict solutions to story problems, and apply strategies and results from simpler problems to similar or more complex problems. They practice mathematical reasoning in story problems by using words, numbers, symbols, charts, graphs, tables, diagrams, and models; learn how to express solutions with appropriate mathematical notation, terms, and accurate language; and check the accuracy of a calculation in a story problem.

• Analyze Story Problems (parts A–C)
• Understand Multistep Problems
• Estimate to Predict Solutions
• Strategies to Solve Complex Problems
• Story Problem Reasoning (parts A–C)
• Explain Solutions to Problems
• Exact and Approximate Solutions
• Check Accuracy of a Calculation

Unit 16: Perimeter, Area, and Volume

Students learn to determine the perimeter of a polygon with whole-number side lengths. They practice using multiplication and division to solve story problems involving rectangular area. They learn to estimate or determine the number of squares or cubes required to cover the area of a solid figure.

• Find the Perimeter of Objects
• Rectangular Area
• Surface Area
• Find the Volume of a Solid
• Perimeter, Area, and Volume

Unit 17: Semester Review and Checkpoint