Number with Mr Downes

Auston B Cron, Ronan Downes, 16/mar/2020

This page contains links to some of my GeoGebra Books. The books are not like a static textbook because you can interact with the activities and bring the maths to life. Each page of each book contains a specific GeoGebra App. My advice is to jump straight in and explore and only use the instructions if you need them and if they are in a language that you can understand. Many applets are in the form of quizzes that allow you to control the difficulty level and they even keep your score for you! [url]Numbers with Mr Downes[/https://www.geogebra.org/m/knya7xwt] [url]Geometry with Mr Downes[/https://www.geogebra.org/m/n8zan98h] Algebra with Mr Downes https://www.geogebra.org/m/w2gj2a3n[math][list] [*][list=1] [*][*] [/list] [/list][/math] Statistics and probability with Mr Downes Sets with Mr Downes Selected Junior Cycle Skills with Mr Downes Calculus with Mr Downes The Junior Cycle specification lays the groundwork for the transition from arithmetic to algebra. Learners explore representations of numbers and the connections between them, as well as the properties and relationships of binary operations. Learners should learn to use calculators strategically where computation by hand and/or mentally is impractical or less efficient. Leaving certificate learners work on proof and become more proficient at using algebraic notation and the laws of arithmetic and induction to show that something is always true. Miscellaneous Links http://oeis.org/A006881 https://im.kendallhunt.com/MS/teachers/2/2/1/index.html https://www.geogebra.org/m/q3FFs5X3 https://mathvox.com/ ADD ELEMENT

Sommario

  1. Motivation and Review
    1. Year Zoom
    2. Clockface with Roman Numerals
    3. roman numeral conversions
    4. Equivalent Roman Notation Numbers
    5. Place Value Cards - Input
    6. Place Value Cards - Random
    7. Three-digit whole numbers
    8. moodle KOPFRECHNEN Addition/Subtraktion rationale Zahlen(2)
    9. Interesting Math of Phi (Part I)
    10. Multiplying integers (Copy)
    11. Adding and subtracting a negative integer
    12. Numberline
    13. Express in Scientific Notation
    14. Percentages ,prices and sales
    15. Counting Movement of Point to Region
    16. Integers Addition on Number line
    17. A multiplication tables tester
    18. Commutative Law of Multiplication n1b
    19. Copy of Commutative Law of Addition
    20. Suma de natural més fracció inferior a 1
    21. Differenzen zuordnen
    22. Practica la tabla de multiplicar
    23. Number Representation
    24. Adding numbers to 20
    25. Numeri fino all'otto
  2. Properties of Arithmetic
    1. Commutative Law of Multiplication
    2. Commutative Law of Addition
  3. Basics and the Number Line
    1. What's the number?
    2. Quiz on Number Line
    3. Integer number line
    4. What's the number? -- decimal version
    5. Opposite of an integer
    6. Horizontal, vertical and slanted Number Lines.
    7. Place Value: Addition
    8. Inequality: Graph Illustrator
    9. Hundreds Grid
    10. NUMBER LINE
    11. InequalityofIntegers-modified-dhabecker-material-12604
    12. Weird Rounding
    13. Copy of Broken Clock (minutes on fives)
    14. Quiz on Addition and Subtraction of Directed Numbers (1)
    15. Adding Double Digits
    16. Quiz on Mixed Arithmetic Operations of Positive Integers
    17. Addition or Subtraction (100)
    18. Absolute value of an integer
    19. Integers Addition
    20. 小二 | 乘法的認識
    21. Randomized tablesquare - export class set as PDF
    22. Quiz on Multiplication and Division of Directed Numbers
    23. Multiplication Practice
    24. Integer Multiplication
    25. Times tables in circle sectors
    26. Seeing Divisibility
    27. Find Mistakes
    28. multiplication table-1
    29. Multiplication Inventory
    30. Units Digits in Arithmetic
  4. Basic Arithmetic
  5. Integers
    1. Quiz on Addition and Subtraction of Directed Numbers (2)
    2. Integer Addition
    3. Integer Subtraction
    4. Integer Division
    5. Thermometer - Positive and Negative Numbers
    6. Copy of Algebraic sum
    7. Addition and Subtraction of Directed Numbers (2)
    8. Addition and subtraction of integers
    9. Adding Integers
    10. Cliffs and Caves
    11. Non-negative integers shown on the number line
    12. square numbers
    13. Add and Subtract Integers with Counters
    14. Make a Two-Digit Number
    15. Liczby trójkątne i czworokątne
    16. Copy of Triangular Number
    17. The sum of the first N odd numbers
    18. Curious Corridors of Numbers
    19. Polygons and Diagonals
    20. Adding Odd and Even Combinations (Updated)
    21. Sum of First n Cubes 首n個立方數之和
    22. Sum of Squares & Perfect Square 平方和與完全平方
    23. Nombres Hexagonaux centrés (reprise)
    24. Nombres Carrés (reprise)
    25. Nombres Triangulaires (reprise)
    26. Test your Reflexes!
    27. Ten Frames
    28. Effect of changing zero on integer number line
  6. Order
    1. Properties of Algebra
    2. Order of operations - Multiply and divide
    3. Test Yourself: PEDMAS / BIDMAS
    4. Order of operations
    5. Quiz on Multiplication Table
    6. Order of operations - Addition and subtraction
    7. Order of operations - addition, subtraction, division, multiplication and brackets
    8. Multiplying Binomials
  7. Primes-OL Leaving Cert
    1. sieve of eratosthenes
    2. Prime Factors - step by step
    3. Prime Factors 2 to 150
    4. Prime Factorisation of Positive Integers
    5. Smallest k such that m × k is a perfect cube
    6. Fundamental Theorem of Arithmetic
    7. Prime Factorization
    8. Primes with variation of " t "
    9. Sieve of Eratosthenes
    10. Writing a number as a product of its prime factors
    11. Factorization - Visual illustration of divisor pairs
  8. Primes -Higher Level
    1. Copy of Inverse Prime Factoring
    2. Distribution of Primes 2
  9. LCM and GCF
    1. GCF and LCM
    2. Meaning of HCF
    3. Meaning of LCM
    4. Finding H.C.F. by Listing Factors
    5. HCF & LCM of Three Numbers by Short Division
    6. HCF & LCM of Two Numbers by Prime Factorization
    7. Visualize factors of numbers (1 - 90)
    8. Classificazione di numeri
    9. Dzielenie przez 2, 3, 4, 5, 9
    10. Greatest Common Divisor
  10. Indices
    1. Integer Base/Exponents
    2. Quiz on Concept of Power
    3. Meaning of Negative Indices 負指數的意義
    4. Quiz on Negative Indices 負指數：測驗
    5. Quiz on Laws of Indices
    6. Scientific Notation 科學記數法
    7. Quiz on Scientific Notation 科學記數法：測驗
    8. Exponential (index) notation
    9. Graphs of Exponential Functions 指數函數的圖像
    10. The meaning of indices (no negative)
    11. Comparing Large Numbers w a Number Line
    12. Scientific Notation-Section 4.1
    13. Scientific Notation
    14. multiplying powers of 2
    15. Law of exponents
    16. Forest Decay
    17. Fractional Exponents-Section 4.3
    18. Practice with steps: Solving Indices Equation types Ex4
  11. Rationals
    1. Ordering Fractions
    2. Fractions of Shapes
    3. Fraction Models
    4. TR KAY - Equivalent Fractions
    5. Improper to Mixed Fractions
    6. Mixed to Improper Fractions
    7. Quiz on Arithmetic Operations of Fractions
    8. Exploring Multiplying Fractions by Partitioning
    9. Compare proper and improper fractions
    10. Rational and Irrational Numbers in Decimal Form
    11. Arranging fractions, decimals, and percents
    12. Patterns in decimals (rational / recurring/ irrational)
    13. Fractions on Number Line
    14. Dividing Fractions
    15. Operations with fractions
    16. Ordenar fracciones
    17. RationalSort
    18. Identifying Rational vs Irrationals
    19. Converting Decimals to Fraction
    20. Moving Place Value
    21. The Power of Ten
    22. Copy of NS1-03-P1 Compare Numbers with Number Line
    23. Fracción de un número. Fraction of a number.
    24. Adding Unit Fractions
    25. Adding and subtracting of mixed numbers
  12. Real
    1. Circumference and Pi
    2. Representació aproximada de nombres reals. Fita de l'error
    3. Construcció d'un rectangle auri
    4. Number Theory Sets
    5. Venn Diagram Real Numbers
    6. locating reals on a number line
    7. Sets of Real Numbers 8th
    8. The Real Number System
    9. The Real Number System
    10. Quiz on Estimation of Values of Surds 估算根式的值：測驗
    11. Simplify Surds Recognise the integer
    12. Surds question generator
    13. Simplifying Surds
    14. adding-surds
    15. Surd Rules
    16. Surds
    17. REAL NUMBERS
    18. Classifying Real Numbers
    19. Simplifying Radicals Assessment
    20. Surd Spiral (Spiral of Theodorus)
    21. Spiral of Pythagoras
    22. Pythagoras Theorem and its Converse -free
    23. SurdText example
  13. Complex
    1. Operations on Complex Numbers 複數的運算
    2. Complex
    3. The nth roots of unity
    4. Suma de números complejos
  14. Enrichment
    1. Quiz on Divisibility by 2, 3, 4, 5, 6, 8, 9 and 10
    2. Diagonal Problem
    3. Diagonal Problem Explained in Chinese!
    4. From Binary/ Hexadecimal To Denary 二／十六進制轉十進制
    5. From Denary to Binary/ Hexadecimal 十進制轉二／十六進制
    6. Divisibility Tests
    7. Can we divide by 3
    8. Dividing in a Ratio 按比分物
    9. Double Bracket Expansion
    10. Pascal's Triangle
    11. Fibonacci numbers
    12. Kolorowy płot / Colorful fence
    13. Pierwiastek sześcienny / Cube roof
    14. Teacher Links
    15. Teacher Links
    16. Sistema de numeració decimal i binari
    17. Simplify Expressions with Exponents-Section 4.2
    18. 2_get_2geh_rekenen2
  15. PDFs
    1. LC Number Syllabus
    2. ActiveMaths_1_Contents
    3. ActiveMaths_2_Contents
    4. ActiveMaths_3_Contents
    5. ActiveMaths_4_1__Contents
    6. LC-Syllabus Introduction
    7. Number-Strand-Priamry5th6thclass-reduced
    8. material-emeygq5j
    9. JC_Mathematics_Specification__Number
    10. Primary School Number Review
  16. Logs
    1. Quiz on Indices and Logarithms 指數和對數：測驗
    2. Properties of Logarithms 對數的性質
    3. Graphs of Logarithmic Functions 對數函數的圖像
  17. Special Numbers
    1. Number of prime factors
    2. Eratosthenes sil (finne primtall)
    3. Euler's Prime Generating Polynomial
  18. Relegated
    1. Our brilliant place-value notation
    2. Place Value with Number Dots
    3. Broken Clock (minutes on fives)
    4. What's My Number? (Multiple formats)
    5. Lined Paper 單行紙 (Landscape 橫向)
    6. Grid Paper 方格紙 (Portrait 縱向)
    7. Grid Paper 方格紙 (Landscape 橫向)
    8. Distance et unité de longueur
    9. Converting cm and mm
    10. Part-Part-Whole Model using Bar and Circles
    11. Find the L.C.M
    12. HCF and LCM Formative Assessment
    13. Prime
    14. Prime Factors
    15. Prime Factorization Activity with Help
    16. Find the GCF of up to 5 numbers.
    17. GEOMETRIA AMB EL MCD I EL MCM
    18. Multiplicative Commutativity
    19. Distribution of Primes
  19. Number systems

1.

Motivation and Review

  • 1. Year Zoom
  • 2. Clockface with Roman Numerals
  • 3. roman numeral conversions
  • 4. Equivalent Roman Notation Numbers
  • 5. Place Value Cards - Input
  • 6. Place Value Cards - Random
  • 7. Three-digit whole numbers
  • 8. moodle KOPFRECHNEN Addition/Subtraktion rationale Zahlen(2)
  • 9. Interesting Math of Phi (Part I)
  • 10. Multiplying integers (Copy)
  • 11. Adding and subtracting a negative integer
  • 12. Numberline
  • 13. Express in Scientific Notation
  • 14. Percentages ,prices and sales
  • 15. Counting Movement of Point to Region
  • 16. Integers Addition on Number line
  • 17. A multiplication tables tester
  • 18. Commutative Law of Multiplication n1b
  • 19. Copy of Commutative Law of Addition
  • 20. Suma de natural més fracció inferior a 1
  • 21. Differenzen zuordnen
  • 22. Practica la tabla de multiplicar
  • 23. Number Representation
  • 24. Adding numbers to 20
  • 25. Numeri fino all'otto

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2.

Properties of Arithmetic

  • 1. Commutative Law of Multiplication
  • 2. Commutative Law of Addition

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3.

Basics and the Number Line

Here we focus on counting and the natural numbers. Usually we use a horizontal number line increasing to the right. If we turn it so that it is vertical we make up the positive ( increasing ) direction. Spend time exploring the applets.

  • 1. What's the number?
  • 2. Quiz on Number Line
  • 3. Integer number line
  • 4. What's the number? -- decimal version
  • 5. Opposite of an integer
  • 6. Horizontal, vertical and slanted Number Lines.
  • 7. Place Value: Addition
  • 8. Inequality: Graph Illustrator
  • 9. Hundreds Grid
  • 10. NUMBER LINE
  • 11. InequalityofIntegers-modified-dhabecker-material-12604
  • 12. Weird Rounding
  • 13. Copy of Broken Clock (minutes on fives)
  • 14. Quiz on Addition and Subtraction of Directed Numbers (1)
  • 15. Adding Double Digits
  • 16. Quiz on Mixed Arithmetic Operations of Positive Integers
  • 17. Addition or Subtraction (100)
  • 18. Absolute value of an integer
  • 19. Integers Addition
  • 20. 小二 | 乘法的認識
  • 21. Randomized tablesquare - export class set as PDF
  • 22. Quiz on Multiplication and Division of Directed Numbers
  • 23. Multiplication Practice
  • 24. Integer Multiplication
  • 25. Times tables in circle sectors
  • 26. Seeing Divisibility
  • 27. Find Mistakes
  • 28. multiplication table-1
  • 29. Multiplication Inventory
  • 30. Units Digits in Arithmetic

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4.

Basic Arithmetic


    Questo capitolo non contiene ancora delle risorse.

5.

Integers

http://oeis.org/wiki/Welcome

  • 1. Quiz on Addition and Subtraction of Directed Numbers (2)
  • 2. Integer Addition
  • 3. Integer Subtraction
  • 4. Integer Division
  • 5. Thermometer - Positive and Negative Numbers
  • 6. Copy of Algebraic sum
  • 7. Addition and Subtraction of Directed Numbers (2)
  • 8. Addition and subtraction of integers
  • 9. Adding Integers
  • 10. Cliffs and Caves
  • 11. Non-negative integers shown on the number line
  • 12. square numbers
  • 13. Add and Subtract Integers with Counters
  • 14. Make a Two-Digit Number
  • 15. Liczby trójkątne i czworokątne
  • 16. Copy of Triangular Number
  • 17. The sum of the first N odd numbers
  • 18. Curious Corridors of Numbers
  • 19. Polygons and Diagonals
  • 20. Adding Odd and Even Combinations (Updated)
  • 21. Sum of First n Cubes 首n個立方數之和
  • 22. Sum of Squares & Perfect Square 平方和與完全平方
  • 23. Nombres Hexagonaux centrés (reprise)
  • 24. Nombres Carrés (reprise)
  • 25. Nombres Triangulaires (reprise)
  • 26. Test your Reflexes!
  • 27. Ten Frames
  • 28. Effect of changing zero on integer number line

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6.

Order

  • 1. Properties of Algebra
  • 2. Order of operations - Multiply and divide
  • 3. Test Yourself: PEDMAS / BIDMAS
  • 4. Order of operations
  • 5. Quiz on Multiplication Table
  • 6. Order of operations - Addition and subtraction
  • 7. Order of operations - addition, subtraction, division, multiplication and brackets
  • 8. Multiplying Binomials

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Primes-OL Leaving Cert

  • 1. sieve of eratosthenes
  • 2. Prime Factors - step by step
  • 3. Prime Factors 2 to 150
  • 4. Prime Factorisation of Positive Integers
  • 5. Smallest k such that m × k is a perfect cube
  • 6. Fundamental Theorem of Arithmetic
  • 7. Prime Factorization
  • 8. Primes with variation of " t "
  • 9. Sieve of Eratosthenes
  • 10. Writing a number as a product of its prime factors
  • 11. Factorization - Visual illustration of divisor pairs

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Primes -Higher Level

  • 1. Copy of Inverse Prime Factoring
  • 2. Distribution of Primes 2

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LCM and GCF

  • 1. GCF and LCM
  • 2. Meaning of HCF
  • 3. Meaning of LCM
  • 4. Finding H.C.F. by Listing Factors
  • 5. HCF & LCM of Three Numbers by Short Division
  • 6. HCF & LCM of Two Numbers by Prime Factorization
  • 7. Visualize factors of numbers (1 - 90)
  • 8. Classificazione di numeri
  • 9. Dzielenie przez 2, 3, 4, 5, 9
  • 10. Greatest Common Divisor

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Indices

  • 1. Integer Base/Exponents
  • 2. Quiz on Concept of Power
  • 3. Meaning of Negative Indices 負指數的意義
  • 4. Quiz on Negative Indices 負指數：測驗
  • 5. Quiz on Laws of Indices
  • 6. Scientific Notation 科學記數法
  • 7. Quiz on Scientific Notation 科學記數法：測驗
  • 8. Exponential (index) notation
  • 9. Graphs of Exponential Functions 指數函數的圖像
  • 10. The meaning of indices (no negative)
  • 11. Comparing Large Numbers w a Number Line
  • 12. Scientific Notation-Section 4.1
  • 13. Scientific Notation
  • 14. multiplying powers of 2
  • 15. Law of exponents
  • 16. Forest Decay
  • 17. Fractional Exponents-Section 4.3
  • 18. Practice with steps: Solving Indices Equation types Ex4

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Rationals

Topic:Numbers, Rational Numbers Explore rational numbers and irrational numbers here. Rational numbers can be expressed in the form p/q where p, q are integers and q 0, and they may be terminating decimals or non terminating but repeating. Irrational numbers are decimals which are non terminating and non repeating For rational number 3/23 see that the digits 1304347826086956521739 is repeated, if we set the the slider "number of digits in column to show" to 22 digits. What happens if you change the slider value? Try the rational number 2/17 Adjust the slider "number of digits in column to show" such that you can see the repetition of digits. What are the digits repeated? Explore the other rational numbers and irrational numbers! For example, why some rational numbers have non terminating decimals (but with recurring or repeated digits) like 3/23 above while some have terminating decimals like 3/25 or 3/75, or 7/140 ? Hint: Consider the denominator of the fraction in the lowest terms. What are the prime factors of the denominator?

  • 1. Ordering Fractions
  • 2. Fractions of Shapes
  • 3. Fraction Models
  • 4. TR KAY - Equivalent Fractions
  • 5. Improper to Mixed Fractions
  • 6. Mixed to Improper Fractions
  • 7. Quiz on Arithmetic Operations of Fractions
  • 8. Exploring Multiplying Fractions by Partitioning
  • 9. Compare proper and improper fractions
  • 10. Rational and Irrational Numbers in Decimal Form
  • 11. Arranging fractions, decimals, and percents
  • 12. Patterns in decimals (rational / recurring/ irrational)
  • 13. Fractions on Number Line
  • 14. Dividing Fractions
  • 15. Operations with fractions
  • 16. Ordenar fracciones
  • 17. RationalSort
  • 18. Identifying Rational vs Irrationals
  • 19. Converting Decimals to Fraction
  • 20. Moving Place Value
  • 21. The Power of Ten
  • 22. Copy of NS1-03-P1 Compare Numbers with Number Line
  • 23. Fracción de un número. Fraction of a number.
  • 24. Adding Unit Fractions
  • 25. Adding and subtracting of mixed numbers

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Real

  • 1. Circumference and Pi
  • 2. Representació aproximada de nombres reals. Fita de l'error
  • 3. Construcció d'un rectangle auri
  • 4. Number Theory Sets
  • 5. Venn Diagram Real Numbers
  • 6. locating reals on a number line
  • 7. Sets of Real Numbers 8th
  • 8. The Real Number System
  • 9. The Real Number System
  • 10. Quiz on Estimation of Values of Surds 估算根式的值：測驗
  • 11. Simplify Surds Recognise the integer
  • 12. Surds question generator
  • 13. Simplifying Surds
  • 14. adding-surds
  • 15. Surd Rules
  • 16. Surds
  • 17. REAL NUMBERS
  • 18. Classifying Real Numbers
  • 19. Simplifying Radicals Assessment
  • 20. Surd Spiral (Spiral of Theodorus)
  • 21. Spiral of Pythagoras
  • 22. Pythagoras Theorem and its Converse -free
  • 23. SurdText example

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Complex

  • 1. Operations on Complex Numbers 複數的運算
  • 2. Complex
  • 3. The nth roots of unity
  • 4. Suma de números complejos

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14.

Enrichment

Lingage, Integration,Connection, Extended Sense Making

  • 1. Quiz on Divisibility by 2, 3, 4, 5, 6, 8, 9 and 10
  • 2. Diagonal Problem
  • 3. Diagonal Problem Explained in Chinese!
  • 4. From Binary/ Hexadecimal To Denary 二／十六進制轉十進制
  • 5. From Denary to Binary/ Hexadecimal 十進制轉二／十六進制
  • 6. Divisibility Tests
  • 7. Can we divide by 3
  • 8. Dividing in a Ratio 按比分物
  • 9. Double Bracket Expansion
  • 10. Pascal's Triangle
  • 11. Fibonacci numbers
  • 12. Kolorowy płot / Colorful fence
  • 13. Pierwiastek sześcienny / Cube roof
  • 14. Teacher Links
  • 15. Teacher Links
  • 16. Sistema de numeració decimal i binari
  • 17. Simplify Expressions with Exponents-Section 4.2
  • 18. 2_get_2geh_rekenen2

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15.

PDFs

Some aspects of number sense are: counting, skip counting, place value, one-to-one correspondence, ordering numbers, comparing numbers, patterns, counting money, telling time, and mental math. From a broader perspective, number sense can be thought of as a flexible understanding of numbers

  • 1. LC Number Syllabus
  • 2. ActiveMaths_1_Contents
  • 3. ActiveMaths_2_Contents
  • 4. ActiveMaths_3_Contents
  • 5. ActiveMaths_4_1__Contents
  • 6. LC-Syllabus Introduction
  • 7. Number-Strand-Priamry5th6thclass-reduced
  • 8. material-emeygq5j
  • 9. JC_Mathematics_Specification__Number
  • 10. Primary School Number Review

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16.

Logs

  • 1. Quiz on Indices and Logarithms 指數和對數：測驗
  • 2. Properties of Logarithms 對數的性質
  • 3. Graphs of Logarithmic Functions 對數函數的圖像

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17.

Special Numbers

https://artofproblemsolving.com/ebooks/intro-number-theory-ebook/c6s1

  • 1. Number of prime factors
  • 2. Eratosthenes sil (finne primtall)
  • 3. Euler's Prime Generating Polynomial

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18.

Relegated

  • 1. Our brilliant place-value notation
  • 2. Place Value with Number Dots
  • 3. Broken Clock (minutes on fives)
  • 4. What's My Number? (Multiple formats)
  • 5. Lined Paper 單行紙 (Landscape 橫向)
  • 6. Grid Paper 方格紙 (Portrait 縱向)
  • 7. Grid Paper 方格紙 (Landscape 橫向)
  • 8. Distance et unité de longueur
  • 9. Converting cm and mm
  • 10. Part-Part-Whole Model using Bar and Circles
  • 11. Find the L.C.M
  • 12. HCF and LCM Formative Assessment
  • 13. Prime
  • 14. Prime Factors
  • 15. Prime Factorization Activity with Help
  • 16. Find the GCF of up to 5 numbers.
  • 17. GEOMETRIA AMB EL MCD I EL MCM
  • 18. Multiplicative Commutativity
  • 19. Distribution of Primes

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19.

Number systems


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