Math Plus Yellow (5)

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 builds on student understanding of numbers and operations by making connections between place value, decimals, and fractions; introducing multiplication and division of decimal numbers; and extending understanding of fraction operations. The course focuses on computational fluency in multiplication and division of whole numbers through the use of standard algorithms. The course enhances fluency of operations with whole numbers, fractions, and decimals through application in the solving of measurement, geometry, and data-analysis problems using mathematical problem-solving techniques. Students continue to develop algebraic thinking as they work with variables and formulas to solve multistep word problems; they further study patterns and rules; and they are introduced to representing problems graphically using the coordinate plane. They extend their knowledge of geometry through the use of the classification of shapes into hierarchies based on their attributes, the introduction of three-dimensional figures and volume, 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 Numbers and Powers

Students learn to estimate or calculate sums, differences, products, and quotients in whole-number problems. They apply standard step-by-step approaches for addition, subtraction, multiplication, and division; use estimation to predict solutions to story problems; learn patterns of place values; and are introduced to bases and powers.

• Round Whole Numbers in Story Problems
• Estimate and Find Sums and Differences
• Estimate Sums and Differences (parts A, B)
• Multiply Multidigit Whole Numbers
• Divide Multidigit Whole Numbers
• Multiply and Divide Whole Numbers
• Place-Value Patterns
• Bases and Exponents (parts A, B)
• Core Focus

Unit 2: Geometry

Students learn to identify, measure, and draw angles, perpendicular and parallel lines, rectangles, and triangles with appropriate math tools. They predict, describe, and perform transformations on two-dimensional shapes. They learn about right, acute, obtuse, and straight angles; lines that are parallel, intersecting, and perpendicular; and different types of triangles and quadrilaterals. They learn the attributes of isosceles, equilateral, and right triangles, parallelograms, rectangles, and squares.

• Angles (parts A, B)
• Perpendicular and Parallel Lines
• Define and Sketch Triangles
• Define and Sketch Quadrilaterals (parts A, B)
• Special Quadrilaterals
• Construct Triangles and Quadrilaterals
• Angles and Triangles (parts A, B)
• Angles in a Quadrilateral (parts A, B)
• Core Focus

Unit 3: Fractions: Multiplication & Division

Students learn to multiply and divide fractions and explain a step-by-step approach. They simplify factors in fraction multiplication problems in which numerators and denominators have common factors. They multiply and divide fractions by whole numbers to solve story problems.

• Use Models to Multiply Fractions
• Multiply Fractions (parts A–C)
• Multiplication as Scaling
• Different Meanings of Fractions
• Understand Division of Fractions
• Fraction Division (parts A, B)
• Core Focus

Unit 4: Problems Involving Fractions

Students learn to solve story problems involving addition, subtraction, multiplication, and division of fractions. They use objects or sketches to solve story problems that involve addition or subtraction of fractions. They solve and simplify problems that involve addition or subtraction of fractions with unlike denominators.

• Solve Fraction Story Problems (parts A, B)
• Add and Subtract Fractions (parts A–D)
• Core Focus

Unit 5: Decimals: Addition and Subtraction

Students learn to compare, order, and expand decimals. They learn to round decimal numbers to any place through hundredths, estimate the sum or difference in problems involving decimal numbers, and solve addition or subtraction problems involving decimal numbers. They learn how to verify that the calculated result of a problem involving addition or subtraction of decimal numbers is reasonable. They solve story problems involving addition or subtraction of decimal numbers.

• Compare Decimals
• Compare and Expand Decimals
• Order Three Decimal Numbers
• Round Decimals Through Hundredths
• Estimate Decimal Sums/Differences (parts A, B)
• Reasonable Answers and Decimal Problems
• Solve Story Problems with Decimals (parts A, B)
• Core Focus

Unit 6: Decimals: Multiplication and Division

Students practice solving multiplication and division problems that involve decimal numbers and verify that the calculated results are reasonable.

• Estimate Decimal Products, Quotients (parts A–C)
• Multiply and Divide Decimals (parts A–C)
• Compute Decimal Story Problems (parts A–C)
• Core Focus

Unit 7: Semester Review and Checkpoint

SEMESTER 2

Unit 8: Algebra

Students learn to use letters to represent unknown values in expressions and equations. They learn to apply the distributive property in equations or expressions with variables. They evaluate simple algebraic expressions and use expressions or equations to answer questions about a problem.

• Understand Variables in Algebra (parts A, B)
• Use the Distributive Property (parts A, B)
• One Variable in Algebraic Expressions
• Expression and Equation Problems (parts A–C)
• Core Focus

Unit 9: Coordinate Graphs

Students learn to identify and graph ordered pairs in all quadrants of a coordinate plane. They learn to use the situation presented in a problem to describe the meaning of each coordinate of an ordered pair displayed on a graph. They practice graphing and writing equations to solve problems that involve a linear function.

• Quadrants in the Coordinate Plane
• Ordered Pairs
• Graph or Write an Equation (parts A–D)
• Core Focus

Unit 10: Perimeter, Area, and Volume

Students learn to find the perimeter of plane figures. They connect area to surface area using nets. They learn to use squares to approximate the area of an irregular shape. They learn to determine the volume of a solid figure. They practice constructing cubes and rectangular boxes from two-dimensional patterns and determining the surface area. They learn to differentiate among appropriate units to measure perimeter, area, and volume.

• Perimeter of a Plane Figure
• Nets, Solids, and Surface Area
• Area of Irregular Shapes
• How Many Cubes Does It Take?
• Volume of Solid Figures (parts A, B)
• Units of Perimeter, Area, and Volume
• Core Focus

Unit 11: Math Reasoning: Methods and Strategies

Students learn to prioritize and sequence the information in a story problem that involves multiplication or division of decimal numbers. They use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning in nonroutine or complex problems. Students learn to apply strategies and results from simple story problems involving fractions to more complex problems and how to break a multistep whole-number story problem or money problem into simpler parts. They learn how to identify and represent decimal numbers, fractions, mixed numbers, and positive and negative integers on a number line.

• Steps to Solve Story Problems (parts A, B)
• Break Down Multistep Problems
• Mathematical Reasoning Methods (parts A, B)
• Choose and Use Strategies (parts A–C)
• Solve Simple to Complex Problems (parts A, B)
• Core Focus

Unit 12: Math Reasoning: Solutions

Students learn to express clear and logical solutions to equal-measures problems and rate problems. They learn to use estimation in addition and subtraction of fractions to verify whether calculated results are reasonable. They learn the advantages of exact solutions and approximate solutions to problems involving addition or subtraction of decimal numbers, and give answers to a specified degree of accuracy, such as hundredths. They convert among units within a given measurement system. They learn to make precise calculations and use the situation presented in a problem involving decimal-number operations to check the validity of the result.

• Solve Problems Logically
• Estimation and Reasonable Answers
• Change Measurement
• Measurements in Story Problems
• Decimal Solutions
• Reasonable Solutions
• Core Focus

Unit 13: Data Analysis and Representation

Students practice organizing and displaying single-variable data in histograms, line plots, and circle graphs and learn how to interpret information displayed in a graph or table. They learn how to use fractions to compare different data sets. They learn which types of graphs are appropriate for various data sets.

• Organize Data to Draw Histograms (parts A, B)
• Create Circle Graphs
• Line Plots (parts A, B)
• Interpret Graphs and Tables
• Fractions, and Graphs
• Choose an Appropriate Graph
• Core Focus

Unit 14: Semester Review and Checkpoint

Number of Lessons and Scheduling

Total Lessons: 180