Course Overview
This researchbased 4th Grade math course focuses on computational fluency, conceptual understanding, and problemsolving. The engaging course features new
graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on. This course moves into
applications and properties of operations. Students work with simple fraction and decimal operations, which are applied in the study of measurement,
probability, and data, and mathematical reasoning techniques. Students begin the study of equivalencies between fractions and decimals on the number line
and early work with integers. Algebraic thinking is developed as students work with variables, coordinate graphing, and formulas in problems involving
perimeter, area, and rate. Geometry is extended into greater classification of shapes and work with lines, angles and rotations.
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 100,000,000. They learn to compare, order,
and round numbers.

Place Value Through 100,000,000

Numbers Through 100,000,000

Expanded Form Through 100,000,000

Compare And Order Greater Numbers (parts A, B)

Using Boundary Numbers for Rounding
Unit 2: Whole Number Operations
Students learn to estimate sums and differences on a number line and apply standard stepbystep 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
fractions and 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.

Estimate Sums and Differences (parts A, B)

Add Whole Numbers

Subtract Whole Numbers

Multiply by 2Digit Numbers (parts A, B)

Different Ways to Divide (parts A, B)

Prime Numbers Less Than 100
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 stepbystep 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)

Rate Story Problems (parts A, B)
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.

Line Pairs

Types of Angles

Angles and Rotation
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 AD)

Explain Equivalent Fractions (parts A, B)

Determine Equivalent Fractions (parts A, B)

Find a Fraction (parts A, B)
Unit 6: Measurement
Students learn to estimate the length of a line segment to the nearest inch or centimeter and solve measurementconversion problems using multiplication
and division. They solve story problems involving equal measures. Students learn to identify the appropriate metric and English units and tools to measure
temperature and practice reading thermometers in Fahrenheit and Celsius.

Estimating Lengths

Change Measurement

Measurements in Stories (parts A, B)

Relating Multiplication and Division

Measuring Temperature

Everyday Temperatures
Unit 7: 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 multiplying and dividing 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 8: Decimals and Equality with Fractions
Students compare, order, and round 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 decimalnumber equivalents for
halves and fourths. They relate decimal numbers to fractions on a number line.

Compare Decimals

Order Three Decimal Numbers

Decimal Numbers and Rounding

Add and Subtract Decimal Numbers

Equivalent Decimals and Fractions

Halves and Fourths

Relate Decimal Numbers to Fractions (parts A, B)
Unit 9: Decimals and Equality with Fractions
SEMESTER 2
Unit 10: Probability and Data
Students learn to represent a probability as a fraction, organize all possible outcomes for a simple probability situation, and determine the number of
possible combinations of objects. They learn to design survey questions and collect and represent the data. They learn about the modes for sets of
numerical or categorical data; medians and outliers for numerical data sets; and 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 identify whether specific events are certain, likely, unlikely, or impossible.

Probabilities as Fractions

Organize Outcomes

Find All Possible Combinations

Surveys

Graph Data

Data Representations

Mode, Median, and Outliers
Unit 11: 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 how to apply strategies and results
from simpler problems to similar or more complex problems. 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)

Solve Story Problems That Are Alike

Use Simpler Problems to Solve Harder Ones

Represent and Explain Story Problems

State Solutions Clearly (parts A, B)

ProblemSolving Strategies

Estimated and Exact Answers
Unit 12: Geometry
Students define and sketch different types of triangles and quadrilaterals and identify their attributes. They learn about diameter and radius of circles,
congruent figures, bilateral symmetry, and rotational symmetry. They learn about geometric solids in terms of the shapes of their faces and the number of
faces, edges, and vertices. They learn to sketch a twodimensional representation of a threedimensional object.

Define and Sketch Triangles

Define and Sketch Quadrilaterals (parts A, B)

Identify Diameters and Radii of Circles

Congruent Figures

Bilateral and Rotational Symmetry

Describe Geometric Solids

Geometric Nets
Unit 13: Rational Numbers
Students learn to identify and place negative numbers on a number line, determine missing negative numbers in counting sequences, and use negative numbers
to represent temperature. They use negative numbers in story problems that involve owing money. They identify relative positions of rational numbers on a
number line.

Negative Numbers on the Number Line

Count with Negative Numbers (parts A, B)

Negative Numbers in Everyday Math

Rational Numbers on a Number Line (parts AC)
Unit 14: 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 twovariable 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)

TwoVariable Equations (parts A, B)

The Coordinate Plane

Line Segments in the Coordinate Plane

Linear Relationships (parts A, B)
Unit 15: 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)

Perimeter and Area of Rectangles
.