Grade Four Mathematics   (#5012060)

Version for Academic Year:

Course Standards

General Course Information and Notes

Version Description

The benchmarks in this course are mastery goals that students are expected to attain by the end of the year. To build mastery, students will continue to review and apply earlier grade-level benchmarks and expectations.

General Notes

In grade 4, instructional time will emphasize four areas: (1) extending understanding of multi-digit multiplication and division; (2) developing the relationship between fractions and decimals and beginning operations with both; (3) classifying and measuring angles and (4) developing an understanding for interpreting data to include mode, median and range.

Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

English Language Development ELD Standards Special Notes Section:
Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:
http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

General Information

Course Number: 5012060
Course Path:
Abbreviated Title: GRADE FOUR MATH
Course Length: Year (Y)
Course Type: Core Academic Course
Course Level: 2
Course Status: State Board Approved

Educator Certifications

One of these educator certification options is required to teach this course.

Student Resources

Vetted resources students can use to learn the concepts and skills in this course.

Original Student Tutorials

Additive Angles: Wondrous Windows:

Decompose and compose various angles while exploring clocks and windows in this interactive tutorial.

Type: Original Student Tutorial

Archetypes – Part Two: Examining Archetypes in The Princess and the Goblin:

Read more from the fantasy novel The Princess and the Goblin by George MacDonald in Part Two of this three-part series. By the end of this tutorial, you should be able to compare and contrast the archetypes of two characters in the novel.

Make sure to complete all three parts of this series!

Click HERE to view "Archetypes -- Part One: Examining an Archetype in The Princess and the Goblin."

Click HERE to view "Archetypes -- Part Three: Comparing and Contrasting Archetypes in Two Fantasy Stories" [coming soon].

Type: Original Student Tutorial

Archetypes – Part One: Examining an Archetype in The Princess and the Goblin:

Learn to determine the key traits of a main character named Princess Irene in excerpts from the fantasy novel The Princess and the Goblin by George MacDonald. In this interactive tutorial, you’ll also identify her archetype and explain how textual details about her character support her archetype.  

Make sure to complete all three parts of this series! 

Click HERE to view "Archetypes -- Part Two: Examining Archetypes in The Princess and the Goblin."

Click HERE to view "Archetypes -- Part Three: Comparing and Contrasting Archetypes in Two Fantasy Stories" [coming soon]. 

Type: Original Student Tutorial

The Power to Cure or Impair: The Importance of Setting in "The Yellow Wallpaper" -- Part One:

Learn to identify aspects of setting and character as you analyze several excerpts from “The Yellow Wallpaper," a chilling short story by Charlotte Perkins Gilman that explores the impact on its narrator of being confined to mostly one room. You'll also determine how the narrator’s descriptions of the story’s setting better reveal her emotional and mental state.

This interactive tutorial is Part One in a two-part series. By the end of Part Two, you should be able to explain how the narrator changes through her interaction with the setting. Click below to launch Part Two.

The Power to Cure or Impair: The Importance of Setting in 'The Yellow Wallpaper' -- Part Two 

Type: Original Student Tutorial

The Power to Cure or Impair: The Importance of Setting in "The Yellow Wallpaper" -- Part Two:

Continue to examine several excerpts from the chilling short story “The Yellow Wallpaper” by Charlotte Perkins Gilman, which explores the impact on its narrator of being confined to mostly one room. In Part Two of this tutorial series, you'll determine how the narrator’s descriptions of the story’s setting reveal its impact on her emotional and mental state. By the end of this tutorial, you should be able to explain how the narrator changes through her interaction with the setting.

Make sure to complete Part One before beginning Part Two. Click HERE to launch "The Power to Cure or Impair: The Importance of Setting in 'The Yellow Wallpaper' -- Part One." 

Type: Original Student Tutorial

The Mystery of the Past: How the Form of a Villanelle Contributes to Meaning in "The House on the Hill":

Explore the mysterious poem “The House on the Hill” by Edwin Arlington Robinson in this interactive tutorial. As you explore the poem's message about the past, you’ll identify the features of a villanelle in the poem. By the end of this tutorial, you should be able to explain how the form of a villanelle contributes to the poem's meaning.

Type: Original Student Tutorial

A Giant of Size and Power – Part Two: How the Form of a Sonnet Contributes to Meaning in "The New Colossus":

Continue to explore the significance of the famous poem “The New Colossus” by Emma Lazarus, lines from which are engraved on the pedestal of the Statue of Liberty. 

In Part Two of this two-part series, you’ll identify the features of a sonnet in the poem "The New Colossus." By the end of this tutorial, you should be able to explain how the form of a sonnet contributes to the poem's meaning. 

Make sure to complete Part One before beginning Part Two.

Click HERE to launch "A Giant of Size and Power -- Part One: Exploring the Significance of 'The New Colossus.'"

Type: Original Student Tutorial

Analyzing the Beginning of The Red Umbrella – Part Two: How Setting Influences Characters:

Continue to explore excerpts from the beginning of the historical fiction novel The Red Umbrella by Christina Diaz Gonzalez in Part Two of this two-part series. In Part Two, you'll examine how setting influences characters.

Make sure to complete Part One first. Click HERE to launch "Analyzing the Beginning of The Red Umbrella -- Part One: How Setting Influences Events." 

Type: Original Student Tutorial

A Giant of Size and Power -- Part One: Exploring the Significance of "The New Colossus":

In Part One, explore the significance of the famous poem “The New Colossus” by Emma Lazarus, lines from which are engraved on the pedestal of the Statue of Liberty. 

This famous poem also happens to be in the form of a sonnet. In Part Two of this two-part series, you’ll identify the features of a sonnet in the poem. By the end of this tutorial series, you should be able to explain how the form of a sonnet contributes to the poem's meaning. Make sure to complete both parts!

Click HERE to launch "A Giant of Size and Power -- Part Two: How the Form of a Sonnet Contributes to Meaning in 'The New Colossus.'"

Type: Original Student Tutorial

Analyzing the Beginning of The Red Umbrella – Part One: How Setting Influences Events:

Explore excerpts from the beginning of the historical fiction novel The Red Umbrella by Christina Diaz Gonzalez in this two-part series. In Part One, you'll examine how setting influences events. In Part Two, you'll examine how setting influences characters.

Make sure to complete both parts! Click HERE to launch Part Two.

Type: Original Student Tutorial

CPALMS Aquarium: Part 3 Division with Larger Numbers:

Learn more about division with larger numbers in this aquarium-themed, interactive tutorial. 

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

Type: Original Student Tutorial

CER: Writing a Great Paragraph:

Learn how to write a great "CER" paragraph that includes a claim, evidence, and reasoning with this interactive tutorial.

Type: Original Student Tutorial

Wubble Double Trouble:

Join Pete as he explores patterns within patterns with feisty Wubbles and Dipples in this interactive tutorial.

Type: Original Student Tutorial

Comparing Fractions with Square Foot Gardens Part 2:

Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials

This is Part 2 in a two-part series. Click HERE to open Part 1,  “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Type: Original Student Tutorial

Return to Deciland: Locating Decimals on a Number Line:

Learn about decimals on a number line and comparing decimals to save the Decis from a wizard's spell in this interactive tutorial.

Type: Original Student Tutorial

Mama's Pizza, Butterflies, and Comparing Fractions Part 1:

Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.

Type: Original Student Tutorial

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

Personification in "The Railway Train":

Explore the poem “The Railway Train” by Emily Dickinson in this interactive tutorial. Learn about personification and vivid descriptions and determine how they contribute to the meaning of a poem. 

Type: Original Student Tutorial

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.  

This is part 1 of a two-part series. Click HERE to open Part 2.

Type: Original Student Tutorial

Reading into Words with Multiple Meanings:

Explore Robert Frost's poem "Mending Wall" and examine words, phrases, and lines with multiple meanings. In this interactive tutorial, you'll analyze how these multiple meanings can affect a reader’s interpretation of the poem.

Type: Original Student Tutorial

Logging Lengths with Line Plots:

Learn how to create a line plot and analyze data in the line plot in this interactive tutorial.  You will also see how to add and subtract using the line plot to solve problems based on the line plots.

Type: Original Student Tutorial

Deci Land Escape:

Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.

Type: Original Student Tutorial

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student tutorial.

Type: Original Student Tutorial

Don't Plagiarize: Cite Your Sources!:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources, creating a Works Cited page, and avoiding academic dishonesty!

Type: Original Student Tutorial

Map the ROC: Angle Measure:

Learn how to measure angles with a protractor to help get a robot through an obstacle course in this interactive tutorial.

Type: Original Student Tutorial

Avoiding Plagiarism and Citing Sources:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources and avoiding academic dishonesty!

Type: Original Student Tutorial

Equivalent Fractions Part 1: Sharing at the Shelter:

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial. This is part 1 of a 2 part series.

Type: Original Student Tutorial

Dash or Bash: Discovering Angles:

Discover what an angle is by helping to program a robot through an obstacle course in this interactive tutorial.

Type: Original Student Tutorial

Happy Halloween! Textual Evidence and Inferences:

Cite text evidence and make inferences about the "real" history of Halloween in this spooky interactive tutorial. 

Type: Original Student Tutorial

Plagiarism: What Is It? How Can I Avoid It?:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources and avoiding academic dishonesty!

Type: Original Student Tutorial

"Beary" Good Details:

Join Baby Bear to answer questions about key details in his favorite stories with this interactive tutorial. Learn about characters, setting, and events as you answer who, where, and what questions.

Type: Original Student Tutorial

Equivalent Fractions, Part 2: Patterns in the Multiplication Table:

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial. 

This is part 2 of a 2 part series. Click HERE to open Part 1. 

Type: Original Student Tutorial

Educational Games

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Type: Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Decimal and Fraction:

This interactive Flash applet has students match fractions with their equivalent one- or two-place decimals. Students have a chance to correct errors until all matches are made.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Problem-Solving Tasks

Listing fractions in increasing size:

The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.

Type: Problem-Solving Task

How Many Tenths and Hundredths?:

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Explaining Fraction Equivalence with Pictures:

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

Dimes and Pennies:

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Type: Problem-Solving Task

Using Place Value:

Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

Type: Problem-Solving Task

Using Benchmarks to Compare Fractions:

This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.

Type: Problem-Solving Task

Money in the piggy bank:

This task is designed to help students focus on the whole that a fraction refers to. It provides a context where there are two natural ways to view the coins: As equal parts of the set of coins in the piggy bank, and As money so each coin is assigned its monetary value. The important thing to realize here is that two different fractions can describe the same situation depending on what you choose to be the whole.

Type: Problem-Solving Task

Double Plus One:

The purpose of this task is to help students gain a better understanding of patterns. This task is meant to be used in an instructional setting.

Type: Problem-Solving Task

Running Laps:

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

Tutorials

Number Pattern Example: Growing Sequence:

In this Khan Academy tutorial video a table is used to track a growing sequence of design.

Type: Tutorial

Angles and arcs:

in this tutorial, students will learn about central angles and arcs of a circle.

Type: Tutorial

Angle Measurements and Circle Arcs:

This Khan Academy tutorial video demonstrates the relationship between the measurement of an angle and the arc of a circle.

Type: Tutorial

Angle Basics:

This Khan Academy tutorial video presents how an angle is formed and labeled.

Type: Tutorial

Comparing Two Decimals with a Visual Model:

In this Khan Academy tutorial video two decimals are compared using grid diagrams.

Type: Tutorial

Decimals as Words:

In this Khan Academy video decimals are written and spoken in words.

Type: Tutorial

Decimals and Fractions from Grid and Number-Line Representations:

The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.

Type: Tutorial

Grid Representations of Decimals:

The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.

Type: Tutorial

Equivalent Fractions: Visual Models:

This Khan Academy video illustrates that fraction a/b is equivalent to fraction (a x n)/(b x n).

Type: Tutorial

Division: The importance of place value:

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. Being able to perform the standard algorithm is the end goal, but it helps to understand how and why this process works.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.

Type: Tutorial

Angle Basics:

This video discusses the definition of an angle and how to name an angle.

Type: Tutorial

Introduction to Decimals:

This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.

Type: Tutorial

Virtual Manipulatives

Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

  • Match fractions using numbers and pictures
  • make the same fractions using different numbers
  • Match fractions in different picture patterns
  • Compare fractions using numbers and patterns

Type: Virtual Manipulative

Fraction Finder- Number Line:

In this activity, you will graphically determine the value of two given fractions represented as points on a number line. You will then graphically find a fraction whose value is between the two given fractions and determine its value.

Type: Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

Follow the Pattern. Which shapes go next?:

Students select the shape that goes next in the pattern and place it in the row, then identify the overall pattern.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this course.