Arithmetic Collected Resources

Dr. Jack L. Jackson II, Apr 6, 2025

This book collects links to some of the best GeoGebra activities related to Arithmetic.

Table of Contents

  1. 1.Natural Number Representation and Operations
    1. Numbers up to the Thousands Place
    2. Writing Numbers in Expanded Form
    3. Guess the Number
    4. Creating the Largest Possible 4-digit Number
    5. Ordering Numbers Less than 10,000
    6. Reading Number Names from 1,000 to 9,999
    7. The Expansion Machine: Standard Form to Expanded Form
    8. The Compression Machine: Expanded Form to Standard Form
    9. Converting Numbers Between Standard and Expanded Form
    10. Reading Number Names from 100 to 999
    11. Writing Number Names from 100 to 999
    12. Numbers in Expanded Form
    13. Rounding Whole Numbers up to the Hundred Thousands Place
    14. The Meaning of Place Value in Decimal Numbers
    15. Identifying Place Values up to the Thousandths Place
    16. Place Value Riddles
    17. Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products
    18. Comparing Products Using Visual Models
    19. Solving Multi-Step Number Problems
    20. Solving Multi-Step Word Problems
    21. Using Order of Operations to Create Numerical Expressions
    22. Using Order of Operations and Grouping Symbols to Create Numerical Expressions
    23. Correcting Errors in an Order of Operations
    24. Translating Word Problems into Numeric Equations
    25. Card Sort: Multiplying and Dividing Integers
    26. Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products
    27. Comparing Products Using Visual Models
    28. Division Models
    29. Multiplication and Division Estimation Game
    30. Estimating Products of 2-digit Numbers
    31. Division Problems with Remainders
    32. Long Division With One-Digit Divisors and Remainders
    33. Division Using an Area Model
    34. Division Word Problems
    35. Multiplication and Division with Multiples of Powers of Ten
  2. 2. Factors, Multiples, and Prime Numbers
    1. Prime Factors and Products Using Visual Models
    2. Is This a Multiple?
    3. Identifying Prime Numbers
    4. Visualizing the Greatest Common Factor Using a Model
    5. Finding the Greatest Common Denominator
    6. Exploring Multiples in a Hundreds Grid
    7. Exploring Multiples in a Hundreds Grid
    8. Finding Multiples Using a Hundreds Grid
    9. Common Multiples in a Hundreds Grid
    10. Finding Common Multiples Using a Hundreds Grid
    11. Expressing Composite Numbers as a Product of Prime Numbers
    12. Factoring with Trees
    13. Making Prime Factorization Trees
    14. Classifying Prime and Composite Numbers
  3. 3. Integer Operations
    1. Adding and Subtracting Integers with Balloons and Sandbags
    2. Adding and Subtracting Integers with Balloons and Sandbags
    3. Adding and Subtracting More Integers with Balloons and Sandbags
    4. Integers Representing Height
    5. Ordering Integers on a Number Line
    6. Comparing Integers
    7. Positive and Negative Numbers in a Bank Account
    8. Solving Absolute Value Problems
    9. Absolute Value of Integers in Money Statements
    10. Visualizing the Commutative Property of Addition
    11. Additive Inverse
    12. Adding Opposites
    13. Multiplying Negative Numbers
  4. 4. Fractions
    1. Comparing Fractions with Unlike Denominators Using Models
    2. Comparing Fractions with Unlike Denominators
    3. Equivalent Fractions with Larger Denominators
    4. Equivalent Fractions with Smaller Denominators
    5. Writing Equivalent Fractions
    6. Visualizing Equivalent Fractions Using Models
    7. Writing Equivalent Fractions Based on a Model
    8. Locating Proper and Improper Fractions on a Number Line
    9. Rounding Mixed Numbers
    10. Comparing Rational Numbers Using a Number Line
    11. Ordering Rational Numbers
  5. 5. Decimals and Percents
    1. Expanding Decimal Numbers
    2. Decimal Tenths on a Number Line
    3. Decimal Hundredths on a Number Line
    4. Identifying Decimals to the Tenths Place on a Number Line
    5. Identifying Decimals to the Hundredths Place on a Number Line
    6. Adding Decimals with Base 10 Blocks
    7. Building Models for Adding Decimals
    8. Decimal Comparisons with Base 10 Blocks
    9. Comparing Decimals up to the Thousandths Place
    10. Matching Place Values of Digits up to Three Decimal Places
    11. Comparing Decimals Using Place Value
    12. Decimal Multiplication Word Problems
    13. Modeling Decimal Multiplication
    14. Writing Numbers Given Digits and Place Values
    15. Writing Expanded Form of Decimals up to the Thousandths Place
    16. Converting Decimals up to the Hundredths Place to Fractions
    17. Rounding Decimals
    18. Rounding Decimals on a Number Line
    19. Estimating the Sum of Decimals up to Two Decimal Places
    20. Percentages and Equivalent Fractions and Decimals
    21. Determining the Percentage in a Model
    22. Representing Percentages as Decimals
    23. Representing Fractions as Percentages
    24. Finding Percentage Increase
    25. Finding the Percentage of a Number Using Tape Diagrams
    26. Setting Up a Percent Proportion
    27. Expressing Percentages as Decimals and Fractions
    28. Identifying Percentage Equivalents
    29. Converting Percentages to Decimals
    30. Converting Percentages to Decimals
  6. 6. Proportional Reasoning
    1. Exploring Scaled Area Calculations
    2. Finding the Area of Similar Figures Using Scale Factor
    3. Finding the Volume of Similar Figures Using Scale Factor
  7. 7. Properties of Exponents
    1. Multiple Multiplications
    2. Writing Equivalent Forms of Expressions with Exponents
    3. Evaluating Fractions Raised to a Power
    4. Multiplying Powers
    5. Power of a Power
    6. Power of a Product
    7. Multiplying Monomials Using Visual Models
    8. Simplifying Algebraic Expressions
    9. Calculating Sums and Differences in Scientific Notation
    10. Expressing Numbers in Scientific Notation
    11. Adding and Subtracting Numbers in Scientific Notation
    12. Multiplying Numbers in Scientific Notation
    13. Dividing Numbers in Scientific Notation
    14. Estimating Rational Numbers on a Number Line
  8. 8. Measurement

1.

1.Natural Number Representation and Operations

These are activities about representing natural numbers and whole numbers, and performing operations with them. These include base 10 block activities for representing numbers in standard Hindu-Arabic form. These also include representations in other bases, and in other ancient numeration systems. It also includes visualizations of addition, subtraction, multiplication, and division and their properties.

  • 1. Numbers up to the Thousands Place
  • 2. Writing Numbers in Expanded Form
  • 3. Guess the Number
  • 4. Creating the Largest Possible 4-digit Number
  • 5. Ordering Numbers Less than 10,000
  • 6. Reading Number Names from 1,000 to 9,999
  • 7. The Expansion Machine: Standard Form to Expanded Form
  • 8. The Compression Machine: Expanded Form to Standard Form
  • 9. Converting Numbers Between Standard and Expanded Form
  • 10. Reading Number Names from 100 to 999
  • 11. Writing Number Names from 100 to 999
  • 12. Numbers in Expanded Form
  • 13. Rounding Whole Numbers up to the Hundred Thousands Place
  • 14. The Meaning of Place Value in Decimal Numbers
  • 15. Identifying Place Values up to the Thousandths Place
  • 16. Place Value Riddles
  • 17. Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products
  • 18. Comparing Products Using Visual Models
  • 19. Solving Multi-Step Number Problems
  • 20. Solving Multi-Step Word Problems
  • 21. Using Order of Operations to Create Numerical Expressions
  • 22. Using Order of Operations and Grouping Symbols to Create Numerical Expressions
  • 23. Correcting Errors in an Order of Operations
  • 24. Translating Word Problems into Numeric Equations
  • 25. Card Sort: Multiplying and Dividing Integers
  • 26. Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products
  • 27. Comparing Products Using Visual Models
  • 28. Division Models
  • 29. Multiplication and Division Estimation Game
  • 30. Estimating Products of 2-digit Numbers
  • 31. Division Problems with Remainders
  • 32. Long Division With One-Digit Divisors and Remainders
  • 33. Division Using an Area Model
  • 34. Division Word Problems
  • 35. Multiplication and Division with Multiples of Powers of Ten

1.1.

Numbers up to the Thousands Place

Create numbers with models expressed in expanded form. Engage with whole numbers up to the thousands place.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
How many hundreds make one thousand?
– GeoGebra Content Team

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2.

2. Factors, Multiples, and Prime Numbers

  • 1. Prime Factors and Products Using Visual Models
  • 2. Is This a Multiple?
  • 3. Identifying Prime Numbers
  • 4. Visualizing the Greatest Common Factor Using a Model
  • 5. Finding the Greatest Common Denominator
  • 6. Exploring Multiples in a Hundreds Grid
  • 7. Exploring Multiples in a Hundreds Grid
  • 8. Finding Multiples Using a Hundreds Grid
  • 9. Common Multiples in a Hundreds Grid
  • 10. Finding Common Multiples Using a Hundreds Grid
  • 11. Expressing Composite Numbers as a Product of Prime Numbers
  • 12. Factoring with Trees
  • 13. Making Prime Factorization Trees
  • 14. Classifying Prime and Composite Numbers

2.1.

Prime Factors and Products Using Visual Models

Find factors of whole numbers. Detect patterns in arrangements of dots to products.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
What did you notice about the clusters of dots?[br]
How did you use the dots to help find the factors?[br]
What would 100 dots look like if you arranged them as clusters of primes in a circle? 200?
– GeoGebra Content Team

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3.

3. Integer Operations

These activities explore integer operations: addition, subtraction, multiplication, division, powers, and roots, and the properties of these operations.

  • 1. Adding and Subtracting Integers with Balloons and Sandbags
  • 2. Adding and Subtracting Integers with Balloons and Sandbags
  • 3. Adding and Subtracting More Integers with Balloons and Sandbags
  • 4. Integers Representing Height
  • 5. Ordering Integers on a Number Line
  • 6. Comparing Integers
  • 7. Positive and Negative Numbers in a Bank Account
  • 8. Solving Absolute Value Problems
  • 9. Absolute Value of Integers in Money Statements
  • 10. Visualizing the Commutative Property of Addition
  • 11. Additive Inverse
  • 12. Adding Opposites
  • 13. Multiplying Negative Numbers

3.1.

Adding and Subtracting Integers with Balloons and Sandbags

Add and subtract integers by building expressions using balloons and sandbags in this interactive activity.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
What direction did the basket move when you added balloons? Sandbags?
What direction did the basket move when you subtracted balloons? Sandbags?
Suppose the basket had a starting position of 35 and you removed 5 sandbags. Where would the basket end up? 
– GeoGebra Content Team

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4.

4. Fractions

These activities explore ways of interpreting fractions, representing rational numbers as fractions, and understanding and performing operations on rational numbers in fractional form and in mixed number form.

  • 1. Comparing Fractions with Unlike Denominators Using Models
  • 2. Comparing Fractions with Unlike Denominators
  • 3. Equivalent Fractions with Larger Denominators
  • 4. Equivalent Fractions with Smaller Denominators
  • 5. Writing Equivalent Fractions
  • 6. Visualizing Equivalent Fractions Using Models
  • 7. Writing Equivalent Fractions Based on a Model
  • 8. Locating Proper and Improper Fractions on a Number Line
  • 9. Rounding Mixed Numbers
  • 10. Comparing Rational Numbers Using a Number Line
  • 11. Ordering Rational Numbers

4.1.

Comparing Fractions with Unlike Denominators Using Models

Compare fractions with unlike denominators using visual models in this interactive activity.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
Comparing fractions with the same denominator is easy. For example, comparing [math]\frac{3}{4}[/math] with [math]\frac{1}{4}[/math], we know that 3 parts out of 4  are greater than 1 part out of 4. Using a similar concept and without finding a common denominator, how would you compare fractions with the same numerators?
– GeoGebra Content Team

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5.

5. Decimals and Percents

These activities investigate decimal representation of numbers and operations with numbers in decimal and percentage form.

  • 1. Expanding Decimal Numbers
  • 2. Decimal Tenths on a Number Line
  • 3. Decimal Hundredths on a Number Line
  • 4. Identifying Decimals to the Tenths Place on a Number Line
  • 5. Identifying Decimals to the Hundredths Place on a Number Line
  • 6. Adding Decimals with Base 10 Blocks
  • 7. Building Models for Adding Decimals
  • 8. Decimal Comparisons with Base 10 Blocks
  • 9. Comparing Decimals up to the Thousandths Place
  • 10. Matching Place Values of Digits up to Three Decimal Places
  • 11. Comparing Decimals Using Place Value
  • 12. Decimal Multiplication Word Problems
  • 13. Modeling Decimal Multiplication
  • 14. Writing Numbers Given Digits and Place Values
  • 15. Writing Expanded Form of Decimals up to the Thousandths Place
  • 16. Converting Decimals up to the Hundredths Place to Fractions
  • 17. Rounding Decimals
  • 18. Rounding Decimals on a Number Line
  • 19. Estimating the Sum of Decimals up to Two Decimal Places
  • 20. Percentages and Equivalent Fractions and Decimals
  • 21. Determining the Percentage in a Model
  • 22. Representing Percentages as Decimals
  • 23. Representing Fractions as Percentages
  • 24. Finding Percentage Increase
  • 25. Finding the Percentage of a Number Using Tape Diagrams
  • 26. Setting Up a Percent Proportion
  • 27. Expressing Percentages as Decimals and Fractions
  • 28. Identifying Percentage Equivalents
  • 29. Converting Percentages to Decimals
  • 30. Converting Percentages to Decimals

5.1.

Expanding Decimal Numbers

Explore how numbers up to the thousandths place can be written in expanded form and how decimal place values can be represented.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
What number could be written as [math]\left(3\times1\right)+\left(4\times\frac{1}{100}\right)+\left(6\times10\right)[/math]?
– GeoGebra Content Team

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6.

6. Proportional Reasoning

These activities are focused on proportional reasoning.

  • 1. Exploring Scaled Area Calculations
  • 2. Finding the Area of Similar Figures Using Scale Factor
  • 3. Finding the Volume of Similar Figures Using Scale Factor

6.1.

Exploring Scaled Area Calculations

Explore the effect of scale factors on areas of similar geometric figures.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
Why is the scale factor for areas the scale factor of lengths squared?
The area of a circle is [math]50\textit{ }in^2[/math]. Describe how to find the area of a circle that has a radius twice as long.
– GeoGebra Content Team

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7.

7. Properties of Exponents

  • 1. Multiple Multiplications
  • 2. Writing Equivalent Forms of Expressions with Exponents
  • 3. Evaluating Fractions Raised to a Power
  • 4. Multiplying Powers
  • 5. Power of a Power
  • 6. Power of a Product
  • 7. Multiplying Monomials Using Visual Models
  • 8. Simplifying Algebraic Expressions
  • 9. Calculating Sums and Differences in Scientific Notation
  • 10. Expressing Numbers in Scientific Notation
  • 11. Adding and Subtracting Numbers in Scientific Notation
  • 12. Multiplying Numbers in Scientific Notation
  • 13. Dividing Numbers in Scientific Notation
  • 14. Estimating Rational Numbers on a Number Line

7.1.

Multiple Multiplications

Explore exponential notation as repeated multiplication by creating fractals.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
In your own words, describe what a [i]base [/i]is.
In your own words, describe what an [i]exponent [/i]is.
What is the base of [math]4^3[/math]? What is the exponent?[br]
Is [math]2^3=3^2[/math]? Can you find another example where swapping the base and the exponent results in the same value?
– GeoGebra Content Team

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8.

8. Measurement


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