Free Christian Curriculum Kindergarten through twelfth grade · free to download

Grade 4 · 16 units · 180 lessons · 1,800 questions

Mathematics

Multi-digit multiplication, long division, fractions and decimals, measurement, geometry, and real-life money math, in 180 lessons.

About this course

Fourth grade is the year the standard algorithms are finished. Numbers stretch to 1,000,000 with reading, writing, comparing, rounding to any place, Roman numerals, and estimation. Addition and subtraction are pushed through multi-digit regrouping and subtracting across zeros. The multiplication facts are drilled all the way to x12 and then extended into two-digit by two-digit multiplication using the area model, partial products, and the standard algorithm. A full unit teaches long division from the ground up, including remainders, zeros in the quotient, estimating quotients, checking with multiplication, and deciding what a remainder means in a real problem. Two units are given to fractions (unit fractions, fractions of a set, number lines, equivalence, simplifying, comparing unlike fractions, improper fractions, fractions as division, adding and subtracting like denominators, mixed numbers, and multiplying a fraction by a whole number), followed by a decimals unit through hundredths with comparing, ordering, converting, adding, subtracting, and rounding.

The course is 180 lessons across 16 units. After the number and operation work, the year covers customary and metric measurement in all three dimensions plus temperature and elapsed time, perimeter, area, and the volume of rectangular prisms; geometry with points, lines, rays, parallel and perpendicular, angle types, classifying triangles, quadrilaterals, circles, symmetry, and slides, flips, and turns; data with tables, bar and line graphs, pictographs, circle graphs, stem-and-leaf plots, and mean, median, mode, and range; and algebra with sequences, input-output tables, variables and expressions, one-step equations, inequalities, and plotting points on a coordinate grid. A problem-solving unit teaches a four-step plan and the standard strategies, a "Math in Real Life" unit applies the year's skills to making change, budgeting, unit prices, cooking with fractions, and building, and a closing unit reviews every strand.

A lesson is planned for about 40 minutes and is written with worked examples set out step by step, often with the long-division or multiplication work drawn out digit by digit, plus lines for you to say and questions for you to ask. Every lesson ends with a ten-question quiz that grades itself, and each carries a KJV verse tied to the day's topic. To be ready, your student should know place value through the thousands, be able to add and subtract with regrouping, have the multiplication facts through x9 at least mostly in memory, and understand what a fraction is. Long division and two-digit multiplication are both taught from scratch here. Pencil, paper, and an eraser are the listed materials, with grid paper useful for the area and coordinate lessons.

What the course covers

What your student will be able to do

Scope and sequence

All 16 units of Mathematics for Grade 4, in the order they are taught.

UnitCoversLessonsQuestions
Unit 1Place Value and Number Sense12120Lessons
Unit 2Addition and Subtraction12120Lessons
Unit 3Multiplication Facts12120Lessons
Unit 4Division Facts12120Lessons
Unit 5Multi-Digit Multiplication12120Lessons
Unit 6Long Division12120Lessons
Unit 7Fractions: Understanding12120Lessons
Unit 8Fractions: Operations12120Lessons
Unit 9Decimals12120Lessons
Unit 10Measurement12120Lessons
Unit 11Geometry10100Lessons
Unit 12Data and Graphing10100Lessons
Unit 13Patterns and Algebra10100Lessons
Unit 14Problem Solving10100Lessons
Unit 15Math in Real Life880Lessons
Unit 16Review and Test Prep12120Lessons

Every lesson, by title

All 180 lesson titles are listed here — nothing is withheld until you download. Open a unit to read its contents.

Unit 1: Place Value and Number Sense 12 lessons
  1. 1Ones Tens Hundreds Thousands10 q
  2. 2Ten Thousands and Hundred Thousands10 q
  3. 3Reading and Writing Large Numbers10 q
  4. 4Comparing Whole Numbers10 q
  5. 5Ordering Whole Numbers10 q
  6. 6Rounding to the Nearest Ten and Hundred10 q
  7. 7Rounding to the Nearest Thousand10 q
  8. 8Even and Odd Numbers10 q
  9. 9Number Patterns10 q
  10. 10Roman Numerals10 q
  11. 11Estimation Strategies10 q
  12. 12Place Value Review10 q
Unit 2: Addition and Subtraction 12 lessons
  1. 1Addition Properties10 q
  2. 2Adding Multi-Digit Numbers10 q
  3. 3Adding with Regrouping10 q
  4. 4Subtraction with Regrouping10 q
  5. 5Subtracting Across Zeros10 q
  6. 6Estimating Sums and Differences10 q
  7. 7Addition and Subtraction Word Problems10 q
  8. 8Multi-Step Word Problems10 q
  9. 9Mental Math Strategies10 q
  10. 10Checking Your Work10 q
  11. 11Problem Solving with Addition10 q
  12. 12Addition and Subtraction Review10 q
Unit 3: Multiplication Facts 12 lessons
  1. 1Multiplication as Repeated Addition10 q
  2. 2Multiplying by 0 and 110 q
  3. 3Multiplying by 2 and 310 q
  4. 4Multiplying by 4 and 510 q
  5. 5Multiplying by 6 and 710 q
  6. 6Multiplying by 8 and 910 q
  7. 7Multiplying by 10, 11, and 1210 q
  8. 8Properties of Multiplication10 q
  9. 9Fact Families10 q
  10. 10Missing Factors10 q
  11. 11Multiplication Word Problems10 q
  12. 12Multiplication Facts Review10 q
Unit 4: Division Facts 12 lessons
  1. 1What Is Division10 q
  2. 2Division as Equal Groups10 q
  3. 3Dividing by 2 and 310 q
  4. 4Dividing by 4 and 510 q
  5. 5Dividing by 6 and 710 q
  6. 6Dividing by 8 and 910 q
  7. 7Dividing by 10 11 and 1210 q
  8. 8Division with Remainders10 q
  9. 9Fact Families: Multiplication and Division10 q
  10. 10Missing Dividends and Divisors10 q
  11. 11Division Word Problems10 q
  12. 12Division Facts Review10 q
Unit 5: Multi-Digit Multiplication 12 lessons
  1. 1Multiplying by Multiples of 1010 q
  2. 2Multiplying Two Digits by One Digit10 q
  3. 3Regrouping in Multiplication10 q
  4. 4Multiplying Three Digits by One Digit10 q
  5. 5Estimating Products10 q
  6. 6Multiplying Two Digits by Two Digits10 q
  7. 7The Area Model10 q
  8. 8Partial Products Method10 q
  9. 9Standard Algorithm Practice10 q
  10. 10Multiplying with Zeros10 q
  11. 11Multi-Digit Multiplication Word Problems10 q
  12. 12Multi-Digit Multiplication Review10 q
Unit 6: Long Division 12 lessons
  1. 1Introduction to Long Division10 q
  2. 2Dividing Two Digits by One Digit10 q
  3. 3Long Division with Remainders10 q
  4. 4Dividing Three Digits by One Digit10 q
  5. 5Zeros in the Quotient10 q
  6. 6Estimating Quotients10 q
  7. 7Checking Division with Multiplication10 q
  8. 8Dividing Larger Numbers10 q
  9. 9Interpreting Remainders10 q
  10. 10Long Division Word Problems10 q
  11. 11Long Division Word Problems10 q
  12. 12Long Division Review10 q
Unit 7: Fractions: Understanding 12 lessons
  1. 1What Is a Fraction10 q
  2. 2Parts of a Whole10 q
  3. 3Parts of a Set10 q
  4. 4Fractions on a Number Line10 q
  5. 5Equivalent Fractions10 q
  6. 6Simplifying Fractions10 q
  7. 7Comparing Fractions Same Denominator10 q
  8. 8Comparing Fractions Different Denominators10 q
  9. 9Ordering Fractions10 q
  10. 10Improper Fractions and Mixed Numbers10 q
  11. 11Fractions and Division10 q
  12. 12Fractions Review10 q
Unit 8: Fractions: Operations 12 lessons
  1. 1Adding Fractions Same Denominator10 q
  2. 2Subtracting Fractions Same Denominator10 q
  3. 3Adding Mixed Numbers10 q
  4. 4Subtracting Mixed Numbers10 q
  5. 5Fractions and Whole Numbers10 q
  6. 6Multiplying Fractions by Whole Numbers10 q
  7. 7Fraction Word Problems10 q
  8. 8Fractions in Real Life10 q
  9. 9Mixed Number Word Problems10 q
  10. 10Estimating with Fractions10 q
  11. 11Fractions on the Number Line10 q
  12. 12Fraction Operations Review10 q
Unit 9: Decimals 12 lessons
  1. 1Introduction to Decimals10 q
  2. 2Tenths10 q
  3. 3Hundredths10 q
  4. 4Decimals on a Number Line10 q
  5. 5Comparing Decimals10 q
  6. 6Ordering Decimals10 q
  7. 7Relating Fractions and Decimals10 q
  8. 8Adding Decimals10 q
  9. 9Subtracting Decimals10 q
  10. 10Money and Decimals10 q
  11. 11Rounding Decimals10 q
  12. 12Decimals Review10 q
Unit 10: Measurement 12 lessons
  1. 1Customary Units of Length10 q
  2. 2Metric Units of Length10 q
  3. 3Customary Weight: Ounces, Pounds, and Tons10 q
  4. 4Units of Weight and Mass10 q
  5. 5Units of Capacity10 q
  6. 6Elapsed Time10 q
  7. 7Temperature: Fahrenheit and Celsius10 q
  8. 8Perimeter10 q
  9. 9Area of Rectangles10 q
  10. 10Volume of Rectangular Prisms10 q
  11. 11Choosing the Right Unit10 q
  12. 12Measurement Review10 q
Unit 11: Geometry 10 lessons
  1. 1Points Lines and Rays10 q
  2. 2Types of Lines: Parallel and Perpendicular10 q
  3. 3Types of Angles10 q
  4. 4Measuring Angles with a Protractor10 q
  5. 5Classifying Triangles10 q
  6. 6Quadrilaterals10 q
  7. 7Circles10 q
  8. 8Symmetry10 q
  9. 9Transformations: Slides Flips Turns10 q
  10. 10Geometry Review10 q
Unit 12: Data and Graphing 10 lessons
  1. 1Collecting Data10 q
  2. 2Frequency Tables10 q
  3. 3Bar Graphs10 q
  4. 4Line Graphs10 q
  5. 5Pictographs10 q
  6. 6Circle Graphs10 q
  7. 7Mean Median and Mode10 q
  8. 8Interpreting Data10 q
  9. 9Making Predictions from Data10 q
  10. 10Data and Graphing Review10 q
Unit 13: Patterns and Algebra 10 lessons
  1. 1Number Patterns and Rules10 q
  2. 2Input Output Tables10 q
  3. 3Variables and Expressions10 q
  4. 4Writing Equations10 q
  5. 5Solving One-Step Equations10 q
  6. 6Inequalities10 q
  7. 7Coordinate Grids10 q
  8. 8Plotting Points10 q
  9. 9Patterns in Geometry10 q
  10. 10Algebra Review10 q
Unit 14: Problem Solving 10 lessons
  1. 1Understanding the Problem10 q
  2. 2Making a Plan10 q
  3. 3Drawing a Picture10 q
  4. 4Working Backward10 q
  5. 5Guess and Check10 q
  6. 6Making a Table10 q
  7. 7Looking for Patterns10 q
  8. 8Logical Reasoning10 q
  9. 9Multi-Step Problems10 q
  10. 10Problem Solving Review10 q
Unit 15: Math in Real Life 8 lessons
  1. 1Money: Making Change10 q
  2. 2Money: Budgeting Basics10 q
  3. 3Shopping Math — Unit Price and Best Deals10 q
  4. 4Cooking with Fractions10 q
  5. 5Measurement in Building10 q
  6. 6Math in Nature10 q
  7. 7Math in Sports10 q
  8. 8Math in Shopping10 q
Unit 16: Review and Test Prep 12 lessons
  1. 1Place Value and Operations Review10 q
  2. 2Multiplication and Division Review10 q
  3. 3Fractions and Decimals Review10 q
  4. 4Measurement and Geometry Review10 q
  5. 5Data and Algebra Review10 q
  6. 6Word Problem Strategies10 q
  7. 7Test-Taking Strategies10 q
  8. 8Mixed Practice 110 q
  9. 9Mixed Practice 210 q
  10. 10Mixed Practice 310 q
  11. 11End of Year Assessment Prep10 q
  12. 12Math Year in Review10 q

One whole lesson, exactly as it comes

This is a real lesson taken from the middle of the course — the teaching text, the practice, the homework, and the first three quiz questions with their answers. It is not a marketing excerpt.

Unit 8: Fractions: Operations · Lesson 7

Fraction Word Problems

40 minutesPencilPaperEraser

What this lesson is for

  • Students will understand and practice Fraction Word Problems
  • Students will solve problems related to this topic

Train up a child in the way he should go: and when he is old, he will not depart from it.

Proverbs 22:6

Fraction Word Problems: Multiplication and Division

"Whatsoever thy hand findeth to do, do it with thy might." — Ecclesiastes 9:10

Work done with might requires skill and understanding. Multiplication and division word problems extend our ability to solve real-life tasks that matter — distributing resources, measuring land, planning a feast.

Say to your child: "Multiplication often appears when we take a fraction OF something — OF is the clue word. Division appears when we ask how many equal groups fit into a total."

Clue words for multiplication: of, times, product, each group gets Clue words for division: how many groups, split evenly, each piece, fits into

Problem 1 — fraction of a set: Mrs. Johnson baked 24 cookies. She gave 3/4 of them to the church potluck. How many? ` 3/4 × 24 = (24 ÷ 4) × 3 = 6 × 3 = 18 cookies `

Problem 2 — fraction × fraction: A field is 5/6 mile wide and 2/3 mile long. What is its area? ` 5/6 × 2/3 = 10/18 = 5/9 square miles `

Problem 3 — whole ÷ fraction: You have 6 yards of ribbon. Each bow needs 1/3 yard. How many bows? ` 6 ÷ 1/3 = 6 × 3 = 18 bows `

Problem 4 — whole ÷ fraction: A shepherd has 9 gallons of water. Each sheep drinks 3/4 gallon. How many sheep can drink? ` 9 ÷ 3/4 = 9 × 4/3 = 36/3 = 12 sheep `

Problem 5 — multiplication with simplification: A jar holds 5/6 cup of honey. You fill 3 jars. Total honey? ` 3 × 5/6 = 15/6 = 5/2 = 2½ cups `

Check your answer: Always ask — does this answer make sense for the story? If 12 sheep each drink 3/4 gallon, total water used = 12 × 3/4 = 9 gallons ✓.

Ask your child: "When you see 'how many groups of ¼ fit into 5,' do you multiply or divide? What is the answer?" (Divide; 5 ÷ 1/4 = 20.)

Guided practice

  1. Sarah baked 24 cookies. She gave 1/3 to her friend. How many did she give?

    Show the steps and the answer

    Find 1/3 of 24: divide 24 by 3 = 8. Multiply by 1 = 8 cookies.

    Answer: 8

  2. A plank is 7 1/2 feet long. You cut off 2 1/4 feet. How much remains?

    Show the steps and the answer

    7 1/2 - 2 1/4. Convert: 7 2/4 - 2 1/4 = 5 1/4 feet.

    Answer: 5 1/4

  3. A shepherd has 30 sheep. 2/3 are adults. How many are adults?

    Show the steps and the answer

    Find 2/3 of 30: divide 30 by 3 = 10. Multiply by 2 = 20 sheep.

    Answer: 20

Homework

Complete the practice problems for Fraction Word Problems.

Note for the parent

Today's lesson covers Fraction Word Problems. Estimated time: 40 minutes. Encourage independent work but be available for questions.

The first three of this lesson's 10 questions

Mary baked 24 muffins and gave 1/3 to her neighbor. How many did she give?

  1. 3
  2. 6
  3. 8
  4. 12
Show the answer

Answer: 8

A plank is 7 and 3/4 feet. You cut off 2 and 1/4 feet. How much is left?

  1. 5 feet
  2. 5 and 1/2 feet
  3. 6 feet
  4. 5 and 1/4 feet
Show the answer

Answer: 5 and 1/2 feet

The word 'of' in a word problem usually means:

  1. Subtract
  2. Add
  3. Divide
  4. Multiply
Show the answer

Answer: Multiply

Another 7 questions follow in the lesson itself, each one graded the moment it is answered.

What comes with the download

180 full lessons

Across 16 units, each with objectives, a teaching passage written to be read aloud, guided practice, and homework.

1,800 quiz questions

Graded the instant they are answered, each with the explanation of why that answer is right.

A gradebook that works

Every score kept, a running average maintained, and a breakdown unit by unit — all in the file itself, nothing sent anywhere.

Progress and attendance

Tick lessons off as they are finished, watch the completion bar fill, and mark days present, absent, or excused.

Report card and certificate

Both printable, with your student's name, the grades, and the dates already filled in.

Backup you control

Export every record to a file you keep, and read it back later. A lost browser cache cannot take the year with it.

An answer key

Hidden from the student by default, there for the parent marking the work.

Nothing that phones home

No ads, no affiliate links, no analytics, no fonts fetched from elsewhere. Unplug the network cable and every one of these files still works.

What you will need

Drawn from the materials named across all 180 lessons of this course. Most families already own most of it.

Download Mathematics — Grade 4

Free, and free of everything else. 19 files, 18.6 MB in total. No account, no email address, no payment. What you download carries no advertising, no affiliate links and no tracking of any kind.

Use it on a screen

Open any of these straight from a folder or a USB stick. They run in the browser with the network cable unplugged, and nothing is ever sent anywhere.

HTMLInteractive ClassroomThe whole course as a working school: quizzes that grade themselves, a gradebook with a running average, a progress bar, attendance, a printable report card, and a certificate of completion.grade-4-math-classroom.html 2.9 MBHTMLFlashcard AppEvery quiz question turned into a self-testing card, with shuffle and review-the-missed-ones.grade-4-math-flashcards-app.html 654 KBHTMLRead-Aloud EditionLarge type, one lesson per screen, laid out for a parent reading aloud to a younger student.grade-4-math-readaloud.html 1003 KBHTMLLesson PlannerThe course spread across teaching days, with a box to tick as each lesson is finished.grade-4-math-planner.html 75 KB

Print it

Page-numbered and laid out for paper. Print the whole year at once, or one unit the night before you teach it.

PDFPrintable LessonsEvery lesson, in teaching order, formatted for reading and printing.grade-4-math-print.pdf 3.0 MBPDFFillable WorkbookType answers on screen and save, or print blank pages to write on by hand.grade-4-math-workbook.pdf 1.5 MBPDFAnswer KeyEvery question answered, for the parent or teacher marking the work.grade-4-math-answer-key.pdf 296 KBPDFCopywork PagesHandwriting practice drawn from this course's own Scripture and sentences.grade-4-math-copywork.pdf 70 KBPDFPrintable FlashcardsCut-apart cards with fronts and backs aligned for double-sided printing.grade-4-math-flashcards-print.pdf 3.3 MBPDFPrintable PlannerThe day-by-day plan on paper, for a binder or the refrigerator door.grade-4-math-planner.pdf 164 KB

Edit it, or read it your own way

The same course in open, ordinary file formats. Rewrite a lesson, drop a unit you do not need, or load it on an e-reader.

DOCXMicrosoft WordFully editable. Change wording, add your own notes, delete what does not fit your family.grade-4-math.docx 373 KBRTFWord ProcessorOpens in Word, LibreOffice, Pages, or Google Docs.grade-4-math.rtf 2.3 MBEPUBE-Reader EditionFor a Kindle, Kobo, tablet, or phone reading app.grade-4-math.epub 323 KBMDMarkdownPlain-text source with the headings intact, for note-taking apps and static site tools.grade-4-math.md 1000 KBTXTPlain TextThe whole course as unformatted text — the most portable copy there is.grade-4-math.txt 982 KBCSVFlashcards (CSV)Import into Anki, Quizlet, or a spreadsheet.grade-4-math-flashcards.csv 140 KBTSVFlashcards (TSV)Tab-separated, for importers that prefer it that way.grade-4-math-flashcards.tsv 132 KBHTMLCopywork (HTML)The copywork sheets as a browser page you can print from.grade-4-math-copywork.html 6 KBHTMLFlashcards (HTML)The cut-apart cards as a browser page you can print from.grade-4-math-flashcards-print.html 476 KB

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