Math Plus Red (4)

Course Overview

This research-based course focuses on computational fluency, conceptual understanding, and problem solving. This engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. This course continues to emphasize the understanding of numbers and operations. There is a focus on computational fluency in addition, subtraction, multiplication, and division of whole numbers. The course enhances fluency of operations through application in the solving of measurement, geometry, and data analysis problems using mathematical problem-solving techniques. Students make connections between fraction and decimal representation of numbers. Students study equivalences and relationships between fractions and decimals on the number line and with other models. Students develop algebraic thinking as they work with variables and formulas to solve multistep word problems and as they study patterns and rules. They extend their knowledge of geometry through more in-depth classification of shapes and work with lines, angles, and rotations and the connection of geometric concepts to measurement and problem solving. This course includes standards-based tasks, digital literacy skills, and assessment questions.

Course Outline

SEMESTER 1

Unit 1: Whole Number Sense

Students learn to read and write numerals and number words and identify the place value in whole numbers through 1,000,000. They learn to compare, order, and round numbers.

• Place Value Through 1,000,000
• Numbers Through 1,000,000
• Expanded Form Through 1,000,000
• Compare and Order Greater Numbers (parts A, B)
• Use Boundary Numbers for Rounding
• Core Focus

Unit 2: Whole Number Operations

Students learn to estimate sums and differences on a number line and apply standard step-by-step approaches for addition, subtraction, multiplication, and division. They use inverse relationships to simplify computations and check their results. They learn to identify prime numbers and practice plotting whole numbers on a number line. They use models to explain multiplication as repeated addition of the same quantity and division as repeated subtraction. They use concrete objects or sketches of arrays to model multiplication problems. They learn to find all factor pairs of a whole number.

• Estimate Sums and Differences (parts A, B)
• Add Whole Numbers
• Subtract Whole Numbers
• Multiply by 2-Digit Numbers (parts A, B)
• Model and Explain Multiplication
• Area Models for Multiplication (parts A, B)
• Multiply Multidigit by 1-Digit Numbers
• Model and Explain Division
• Division as Sharing
• Different Ways to Divide (parts A, B)
• Dividing with Remainders
• Divide Greater Numbers
• Prime Numbers Less Than 100
• Prime Factorization
• Core Focus

Unit 3: Applications of Operations

Students use parentheses and the order of operations to write and evaluate expressions. They learn about the distributive property and solve story problems involving whole numbers. They apply standard step-by-step approaches for multiplication and addition; use the order of operations to evaluate expressions; and determine whether addition, subtraction, multiplication, or division is the appropriate operation to use to solve a story problem.

• Order of Operations (parts A, B)
• The Distributive Property (parts A, B)
• Story Problems: Solve and Check (parts A, B)
• Core Focus

Unit 4: Lines, Angles, and Rotations

Students identify lines that are parallel, intersecting, or perpendicular. They learn about right, acute, obtuse, and straight angles and relative angle measures. They learn to identify right angles in geometric figures or everyday objects. They learn the attributes of parallelograms, rectangles, and squares. They measure angles to a whole number of degrees and sketch angles.

• Line Pairs
• Types of Angles
• Angles and Rotation
• Angles (parts A, B)
• Core Focus

Unit 5: Fraction Sense

Students learn to represent fractions with a sketch, explain why two given fractions are equivalent, and recognize and determine equivalent fractions. They practice finding fractions between two numbers, writing fractions represented by drawings that show parts of a set or parts of a whole, and identifying a few simple equivalent fractions, such as 1/2 = 2/4. They learn that fractions can be used to represent part of a set, the relationship of a part to a whole, and a rational number on the number line. They learn how fractions and whole numbers can be plotted on a number line.

• Fractions
• Sketch Fractions
• Different Meanings of Fractions (parts A–D)
• Explain Equivalent Fractions (parts A, B)
• Determine Equivalent Fractions (parts A, B)
• Find a Fraction (parts A, B)
• Core Focus

Unit 6: Measurement

Students learn to estimate the length of a line segment to the nearest inch or centimeter and solve measurement-conversion problems using multiplication and division. They solve story problems involving measurement.

• Estimating Lengths
• Change Measurement
• Measurements in Stories (parts A, B)
• Core Focus

Unit 7: Semester Review and Checkpoint

SEMESTER 2

Unit 8: Fraction Operations

Students use objects and sketches to solve story problems that involve addition and subtraction of fractions. They practice writing equations, simplify factors in fraction multiplication problems, and multiply and divide with fractions. They demonstrate automatic recall of multiplication facts, represent fractions with sketches, explain why two given fractions are equivalent, and find a fraction between two numbers.

• Add and Subtract Fractions (parts A, B)
• Unlike Denominators (parts A, B)
• Different Ways to Write Products
• Fraction Factors (parts A, B)
• Fraction and Whole Number Products (parts A, B)
• Fraction Division (parts A, B)

Unit 9: Decimals and Equality with Fractions

Students compare and order decimal numbers. They estimate and compute the sum or difference of positive decimal numbers, write tenths and hundredths in decimal and fraction notation and show that the representations are equivalent, and identify fraction and decimal-number equivalents for halves and fourths. They relate decimal numbers to fractions on a number line.

• Compare Decimals
• Add and Subtract Decimal Numbers
• Equivalent Decimals and Fractions
• Halves and Fourths
• Fractions and Decimals (parts A, B)
• Relate Decimal Numbers to Fractions (parts A, B)
• Core Focus

Unit 10: Mathematical Reasoning

Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They use estimation to predict a solution to a story problem and verify the reasonableness of the calculated result. They learn to express solutions clearly and logically, answer to a specified degree of accuracy, and identify different story problems that can be solved by using the same procedures.

• Analyze Story Problems (parts A, B)
• Multistep Problems
• Estimate to Predict and Verify (parts A, B)
• Represent and Explain Story Problems
• State Solutions Clearly (parts A, B)
• Problem-Solving Strategies
• Estimated and Exact Answers
• Core Focus

Unit 10: Mathematical Reasoning

Students practice analyzing story problems by identifying the question, recognizing relevant information, and developing a solution strategy. They use estimation to predict a solution to a story problem and verify the reasonableness of the calculated result. They learn to express solutions clearly and logically, answer to a specified degree of accuracy, and identify different story problems that can be solved by using the same procedures.

• Analyze Story Problems (parts A, B)
• Multistep Problems
• Estimate to Predict and Verify (parts A, B)
• Represent and Explain Story Problems
• State Solutions Clearly (parts A, B)
• Problem-Solving Strategies
• Estimated and Exact Answers
• Core Focus

Unit 12: Algebra Thinking

Students learn to use symbols to stand for variables in simple expressions or equations. They learn that when equal quantities are added to or multiplied by equal quantities, the resulting quantities are equal. They practice solving for one variable in a two-variable equation when the value of the other variable is given. They learn to locate and plot points on a coordinate plane, find the length of horizontal and vertical line segments, and plot linear relationships in the first quadrant of a coordinate plane.

• Expressions and Equations
• Addition Property of Equality (parts A, B)
• Multiply by Equal Quantities (parts A, B)
• Two-Variable Equations (parts A, B)
• The Coordinate Plane
• Line Segments in the Coordinate Plane
• Linear Relationships (parts A, B)
• Core Focus

Unit 13: Perimeter and Area Formulas

Students learn how to find the perimeter of rectangles and squares. They learn to interpret and use formulas to answer questions about quantities and their relationships. They learn how to find the area of rectangles, squares, or figures that can be divided into rectangles or squares. They practice solving story problems that require finding rectangular area.

• Perimeters of Polygons
• Formulas for Perimeters (parts A, B)
• Understand Area
• Areas of Rectangular Shapes
• Formulas for Area (parts A, B)
• Area and Perimeter Story Problems (parts A, B)
• Compare Area and Perimeter
• How Many Squares Does It Take?
• Core Focus

Unit 14: Semester Review and Checkpoint

Number of Lessons and Scheduling

Total Lessons: 180