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IMF: Visualizing and Montessori Math PART 2

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The document is a presentation on how visualization enhances Montessori mathematics instruction. It discusses strategies for teaching basic multiplication facts using visual tools like the abacus, multiplication board, and charts showing multiples patterns. Strategies include showing how to break down larger multiplication problems into "tens" and "ones" places on the abacus. Charts are used to visualize repeating patterns in multiples of numbers and how they relate to specific multiplication facts.

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How Visualization Enhances Montessori Mathematics PART 2 by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com Montessori Foundation Conference Friday, Nov 2, 2012 Sarasota, Florida 8 16 24 32 40 3 2 5 5 PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 9× 3= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 9× 3= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 9× 3= 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 9× 3= 30 – 3 = 27 © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 4× 8= 20 + 12 = 32 © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 7× 7= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 7× 7= © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 7× 7= 25 © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 7× 7= 25 + 10 + 10 © Joan A. Cotter, Ph.D., 2012
Multiplication Strategies Basic facts 7× 7= 25 + 10 + 10 + 4 = 49 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: 20 + 30 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: 3 + 30 ×2 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + 6 Tens: 20 Ones: 3 + 30 ×2 50 6 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + 6 = 56 Tens: 20 Ones: 3 + 30 ×2 50 6 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: 40 + 20 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 + 20 60 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: + 20 60 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: + 20 60 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: 1 + 20 ×3 60 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + 3 Tens: 40 Ones: 1 + 20 ×3 60 3 © Joan A. Cotter, Ph.D., 2012
Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + 3 = 63 Tens: 40 Ones: 1 + 20 ×3 60 3 © Joan A. Cotter, Ph.D., 2012
The Multiplication Board 1 2 3 4 5 6 7 8 9 10 6×4 6 © Joan A. Cotter, Ph.D., 2012
The Multiplication Board 1 2 3 4 5 6 7 8 9 10 6×4 6 © Joan A. Cotter, Ph.D., 2012
The Multiplication Board 1 2 3 4 5 6 7 8 9 10 7×7 7 © Joan A. Cotter, Ph.D., 2012
The Multiplication Board 1 2 3 4 5 6 7 8 9 10 7×7 7 © Joan A. Cotter, Ph.D., 2012
The Multiplication Board 7×7 © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Twos 2 4 6 8 10 12 14 16 18 20 © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Twos 2 4 6 8 10 12 14 16 18 20 The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Fours 4 8 12 16 20 24 28 32 36 40 The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 6× 4 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 6 × 4 is the fourth number (multiple). © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 8× 7 8 × 7 is the seventh number (multiple). © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Nines 9 18 27 36 45 90 81 72 63 54 The second row is written in reverse order. Also the digits in each number add to 9. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: The tens are the same in each row. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
Multiples Memory © Joan A. Cotter, Ph.D., 2012
Multiples Memory Objective: To help the players learn the multiples patterns. © Joan A. Cotter, Ph.D., 2012
Multiples Memory Objective: To help the players learn the multiples patterns. Object of the game: To be the first player to collect all ten cards of a multiple in order. © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 The 7s envelope contains 10 cards, each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 The 8s envelope contains 10 cards, each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 40 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 56 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 8 7 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 49 56 63 70 24 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory Objective: To help the players master the multiplication facts. © Joan A. Cotter, Ph.D., 2012
Multiplication Memory Objective: To help the players master the multiplication facts. Object of the game: To collect the most cards by matching the multiplier with the product. © Joan A. Cotter, Ph.D., 2012
Multiplication Memory Materials Needed: © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 1 2 3 4 5 6 7 8 9 10 Materials Needed: • Ten basic cards, numbered 1 to 10 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3 1 2 3 4 5 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie note with “3 x” written on it © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it • A manipulative with groups of five © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 21 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 21 3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 taken 7 times equals 21. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 2 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 2 3 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 2 3 12 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 5 3x = 15 3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 3 taken 5 times equals 15. 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Memory 3x = 8 24 3 6 9 12 15 18 1 3 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables © Joan A. Cotter, Ph.D., 2012
Multiplication Tables © Joan A. Cotter, Ph.D., 2012
Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 9×3 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 9×3 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 6×6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 6×6 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 7×9 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 7×9 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 7×9 9×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables 7×9 9×7 © Joan A. Cotter, Ph.D., 2012
Multiplication Tables squares © Joan A. Cotter, Ph.D., 2012
Multiplication Tables squares © Joan A. Cotter, Ph.D., 2012
Fraction Chart © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 A hyperbola. © Joan A. Cotter, Ph.D., 2012
Fraction Chart Stairs (Unit fractions) Without numbers. © Joan A. Cotter, Ph.D., 2012
Fraction Naming One divided into 2 equal parts. © Joan A. Cotter, Ph.D., 2012
Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts. © Joan A. Cotter, Ph.D., 2012
Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts. One divided into 4 equal parts. © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 One whole © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 One whole divided into © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 One whole divided into 3 three equal parts © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 One divided by 3 three © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 One divided by 3 three In English, except for half, we use ordinal numbers to name fractions. © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 One divided into 3 equal parts. 1 Read as “one-third.” 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 One divided into 3 equal parts. 1 Read as “one-third.” 3 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War Objective: To help the children realize a unit fraction decreases as the denominator increases. © Joan A. Cotter, Ph.D., 2012
Unit Fraction War Objective: To help the children realize a unit fraction decreases as the denominator increases. Object of the game: To collect all, or most, of the cards with the greater unit fraction. © Joan A. Cotter, Ph.D., 2012
Unit Fraction War © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 4 5 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 4 5 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 8 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 8 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 6 6 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 6 6 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War 1 1 6 6 1 1 3 4 © Joan A. Cotter, Ph.D., 2012
Unit Fraction War © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 Two 1s 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 Two 1s is 2 3 3 © Joan A. Cotter, Ph.D., 2012
Fraction Naming 1 1 1 1 3 3 3 Two 1s is 2 3 3 Read as “two-thirds.” © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many eighths in a whole? © Joan A. Cotter, Ph.D., 2012
Concentrating on One Game Objective: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole. © Joan A. Cotter, Ph.D., 2012
Concentrating on One Game Objective: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole. Object of the game: To find the pairs that make a whole. © Joan A. Cotter, Ph.D., 2012
Concentrating on One © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 5 2 5 © Joan A. Cotter, Ph.D., 2012
Concentrating on One © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 7 8 3 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One © Joan A. Cotter, Ph.D., 2012
Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One 5 8 3 8 © Joan A. Cotter, Ph.D., 2012
Concentrating on One © Joan A. Cotter, Ph.D., 2012
Concentrating on One © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 An interesting pattern. © Joan A. Cotter, Ph.D., 2012
Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Partial Chart © Joan A. Cotter, Ph.D., 2012
Partial Chart 1 2 3 4 5 6 © Joan A. Cotter, Ph.D., 2012
Fraction War Objective: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler. © Joan A. Cotter, Ph.D., 2012
Fraction War Objective: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler. Object of the game: To capture all the cards. © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 3 1 8 4 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? © Joan A. Cotter, Ph.D., 2012
Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? © Joan A. Cotter, Ph.D., 2012
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
IMF: Visualizing and Montessori Math PART 2
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IMF: Visualizing and Montessori Math PART 2

  • 1. How Visualization Enhances Montessori Mathematics PART 2 by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com Montessori Foundation Conference Friday, Nov 2, 2012 Sarasota, Florida 8 16 24 32 40 3 2 5 5 PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012
  • 2. Multiplication Strategies Basic facts © Joan A. Cotter, Ph.D., 2012
  • 3. Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • 4. Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • 5. Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • 6. Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • 7. Multiplication Strategies Basic facts 6× 4= (6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  • 8. Multiplication Strategies Basic facts 9× 3= © Joan A. Cotter, Ph.D., 2012
  • 9. Multiplication Strategies Basic facts 9× 3= © Joan A. Cotter, Ph.D., 2012
  • 10. Multiplication Strategies Basic facts 9× 3= 30 © Joan A. Cotter, Ph.D., 2012
  • 11. Multiplication Strategies Basic facts 9× 3= 30 – 3 = 27 © Joan A. Cotter, Ph.D., 2012
  • 12. Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
  • 13. Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
  • 14. Multiplication Strategies Basic facts 4× 8= © Joan A. Cotter, Ph.D., 2012
  • 15. Multiplication Strategies Basic facts 4× 8= 20 + 12 = 32 © Joan A. Cotter, Ph.D., 2012
  • 16. Multiplication Strategies Basic facts 7× 7= © Joan A. Cotter, Ph.D., 2012
  • 17. Multiplication Strategies Basic facts 7× 7= © Joan A. Cotter, Ph.D., 2012
  • 18. Multiplication Strategies Basic facts 7× 7= 25 © Joan A. Cotter, Ph.D., 2012
  • 19. Multiplication Strategies Basic facts 7× 7= 25 + 10 + 10 © Joan A. Cotter, Ph.D., 2012
  • 20. Multiplication Strategies Basic facts 7× 7= 25 + 10 + 10 + 4 = 49 © Joan A. Cotter, Ph.D., 2012
  • 21. Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
  • 22. Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
  • 23. Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
  • 24. Multiplication on the AL Abacus Commutative property 5× 6=6× 5 © Joan A. Cotter, Ph.D., 2012
  • 25. Multiplication on the AL Abacus For facts > 5 × 5 7×8= This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 26. Multiplication on the AL Abacus For facts > 5 × 5 7×8= This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 27. Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 28. Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 29. Multiplication on the AL Abacus For facts > 5 × 5 7×8= Tens: 20 + 30 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 30. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 31. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 32. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: + 30 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 33. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + Tens: 20 Ones: 3 + 30 ×2 50 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 34. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + 6 Tens: 20 Ones: 3 + 30 ×2 50 6 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 35. Multiplication on the AL Abacus For facts > 5 × 5 7×8= 50 + 6 = 56 Tens: 20 Ones: 3 + 30 ×2 50 6 This method was used in the Middle Ages, rather than memorize the facts > 5 × 5. © Joan A. Cotter, Ph.D., 2012
  • 36. Multiplication on the AL Abacus For facts > 5 × 5 9×7= © Joan A. Cotter, Ph.D., 2012
  • 37. Multiplication on the AL Abacus For facts > 5 × 5 9×7= © Joan A. Cotter, Ph.D., 2012
  • 38. Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: © Joan A. Cotter, Ph.D., 2012
  • 39. Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: © Joan A. Cotter, Ph.D., 2012
  • 40. Multiplication on the AL Abacus For facts > 5 × 5 9×7= Tens: 40 + 20 © Joan A. Cotter, Ph.D., 2012
  • 41. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 + 20 60 © Joan A. Cotter, Ph.D., 2012
  • 42. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: + 20 60 © Joan A. Cotter, Ph.D., 2012
  • 43. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: + 20 60 © Joan A. Cotter, Ph.D., 2012
  • 44. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + Tens: 40 Ones: 1 + 20 ×3 60 © Joan A. Cotter, Ph.D., 2012
  • 45. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + 3 Tens: 40 Ones: 1 + 20 ×3 60 3 © Joan A. Cotter, Ph.D., 2012
  • 46. Multiplication on the AL Abacus For facts > 5 × 5 9×7= 60 + 3 = 63 Tens: 40 Ones: 1 + 20 ×3 60 3 © Joan A. Cotter, Ph.D., 2012
  • 47. The Multiplication Board 1 2 3 4 5 6 7 8 9 10 6×4 6 © Joan A. Cotter, Ph.D., 2012
  • 48. The Multiplication Board 1 2 3 4 5 6 7 8 9 10 6×4 6 © Joan A. Cotter, Ph.D., 2012
  • 49. The Multiplication Board 1 2 3 4 5 6 7 8 9 10 7×7 7 © Joan A. Cotter, Ph.D., 2012
  • 50. The Multiplication Board 1 2 3 4 5 6 7 8 9 10 7×7 7 © Joan A. Cotter, Ph.D., 2012
  • 51. The Multiplication Board 7×7 © Joan A. Cotter, Ph.D., 2012
  • 52. Multiples Patterns Twos 2 4 6 8 10 12 14 16 18 20 © Joan A. Cotter, Ph.D., 2012
  • 53. Multiples Patterns Twos 2 4 6 8 10 12 14 16 18 20 The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  • 54. Multiples Patterns Fours 4 8 12 16 20 24 28 32 36 40 The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  • 55. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  • 56. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  • 57. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  • 58. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  • 59. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  • 60. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  • 61. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  • 62. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  • 63. Multiples Patterns Sixes and Eights 6 12 18 24 30 6× 4 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 6 × 4 is the fourth number (multiple). © Joan A. Cotter, Ph.D., 2012
  • 64. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 8× 7 8 × 7 is the seventh number (multiple). © Joan A. Cotter, Ph.D., 2012
  • 65. Multiples Patterns Nines 9 18 27 36 45 90 81 72 63 54 The second row is written in reverse order. Also the digits in each number add to 9. © Joan A. Cotter, Ph.D., 2012
  • 66. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 67. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 68. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 69. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 70. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 71. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 72. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 73. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 74. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 75. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 76. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  • 77. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: The tens are the same in each row. © Joan A. Cotter, Ph.D., 2012
  • 78. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  • 79. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  • 80. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  • 81. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  • 82. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  • 83. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  • 84. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  • 85. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  • 86. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  • 87. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  • 88. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  • 89. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • 90. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • 91. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  • 92. Multiples Memory © Joan A. Cotter, Ph.D., 2012
  • 93. Multiples Memory Objective: To help the players learn the multiples patterns. © Joan A. Cotter, Ph.D., 2012
  • 94. Multiples Memory Objective: To help the players learn the multiples patterns. Object of the game: To be the first player to collect all ten cards of a multiple in order. © Joan A. Cotter, Ph.D., 2012
  • 95. Multiples Memory 7 14 21 28 35 42 49 56 63 70 The 7s envelope contains 10 cards, each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
  • 96. Multiples Memory 8 16 24 32 40 48 56 64 72 80 The 8s envelope contains 10 cards, each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
  • 97. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 98. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 99. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 100. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 © Joan A. Cotter, Ph.D., 2012
  • 101. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 102. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 103. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 40 © Joan A. Cotter, Ph.D., 2012
  • 104. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 105. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 106. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 107. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 108. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 109. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 110. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 111. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 56 70 8 © Joan A. Cotter, Ph.D., 2012
  • 112. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 113. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 114. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 © Joan A. Cotter, Ph.D., 2012
  • 115. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 © Joan A. Cotter, Ph.D., 2012
  • 116. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 8 7 © Joan A. Cotter, Ph.D., 2012
  • 117. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
  • 118. Multiples Memory 7 14 21 28 35 42 49 56 63 70 24 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
  • 119. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 8 7 14 © Joan A. Cotter, Ph.D., 2012
  • 120. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 © Joan A. Cotter, Ph.D., 2012
  • 121. Multiplication Memory Objective: To help the players master the multiplication facts. © Joan A. Cotter, Ph.D., 2012
  • 122. Multiplication Memory Objective: To help the players master the multiplication facts. Object of the game: To collect the most cards by matching the multiplier with the product. © Joan A. Cotter, Ph.D., 2012
  • 123. Multiplication Memory Materials Needed: © Joan A. Cotter, Ph.D., 2012
  • 124. Multiplication Memory 1 2 3 4 5 6 7 8 9 10 Materials Needed: • Ten basic cards, numbered 1 to 10 © Joan A. Cotter, Ph.D., 2012
  • 125. Multiplication Memory 3 1 2 3 4 5 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) © Joan A. Cotter, Ph.D., 2012
  • 126. Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie note with “3 x” written on it © Joan A. Cotter, Ph.D., 2012
  • 127. Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it © Joan A. Cotter, Ph.D., 2012
  • 128. Multiplication Memory 3 1 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it • A manipulative with groups of five © Joan A. Cotter, Ph.D., 2012
  • 129. Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 130. Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 131. Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 132. Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 133. Multiplication Memory 5 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 134. Multiplication Memory 5 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 135. Multiplication Memory 5 21 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 136. Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 137. Multiplication Memory 3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 138. Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 139. Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 140. Multiplication Memory 3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 141. Multiplication Memory 3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 142. Multiplication Memory 21 3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 143. Multiplication Memory 3x = 3 taken 7 times equals 21. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 144. Multiplication Memory 3x = 2 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 145. Multiplication Memory 3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 146. Multiplication Memory 3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 147. Multiplication Memory 3x = 2 3 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 148. Multiplication Memory 3x = 2 3 12 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 149. Multiplication Memory 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 150. Multiplication Memory 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 151. Multiplication Memory 5 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 152. Multiplication Memory 5 3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 153. Multiplication Memory 5 3x = 3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 154. Multiplication Memory 5 3x = 15 3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 155. Multiplication Memory 3x = 3 taken 5 times equals 15. 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 156. Multiplication Memory 3x = 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 157. Multiplication Memory 3x = 8 24 3 6 9 12 15 18 1 3 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  • 158. Multiplication Tables © Joan A. Cotter, Ph.D., 2012
  • 159. Multiplication Tables © Joan A. Cotter, Ph.D., 2012
  • 160. Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
  • 161. Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
  • 162. Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
  • 163. Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
  • 164. Multiplication Tables A rectangle 3 × 6 © Joan A. Cotter, Ph.D., 2012
  • 165. Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
  • 166. Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
  • 167. Multiplication Tables © Joan A. Cotter, Ph.D., 2012
  • 168. Multiplication Tables 9×3 © Joan A. Cotter, Ph.D., 2012
  • 169. Multiplication Tables 9×3 © Joan A. Cotter, Ph.D., 2012
  • 170. Multiplication Tables 6×6 © Joan A. Cotter, Ph.D., 2012
  • 171. Multiplication Tables 6×6 © Joan A. Cotter, Ph.D., 2012
  • 172. Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
  • 173. Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
  • 174. Multiplication Tables 4×7 © Joan A. Cotter, Ph.D., 2012
  • 175. Multiplication Tables 7×9 © Joan A. Cotter, Ph.D., 2012
  • 176. Multiplication Tables 7×9 © Joan A. Cotter, Ph.D., 2012
  • 177. Multiplication Tables 7×9 9×7 © Joan A. Cotter, Ph.D., 2012
  • 178. Multiplication Tables 7×9 9×7 © Joan A. Cotter, Ph.D., 2012
  • 179. Multiplication Tables squares © Joan A. Cotter, Ph.D., 2012
  • 180. Multiplication Tables squares © Joan A. Cotter, Ph.D., 2012
  • 181. Fraction Chart © Joan A. Cotter, Ph.D., 2012
  • 182. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 © Joan A. Cotter, Ph.D., 2012
  • 183. Fraction Chart Stairs (Unit fractions) 1 © Joan A. Cotter, Ph.D., 2012
  • 184. Fraction Chart Stairs (Unit fractions) 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 185. Fraction Chart Stairs (Unit fractions) 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 186. Fraction Chart Stairs (Unit fractions) 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 187. Fraction Chart Stairs (Unit fractions) 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 188. Fraction Chart Stairs (Unit fractions) 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 189. Fraction Chart Stairs (Unit fractions) 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 190. Fraction Chart Stairs (Unit fractions) 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 191. Fraction Chart Stairs (Unit fractions) 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 192. Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 193. Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 © Joan A. Cotter, Ph.D., 2012
  • 194. Fraction Chart 1 Stairs (Unit fractions) 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 A hyperbola. © Joan A. Cotter, Ph.D., 2012
  • 195. Fraction Chart Stairs (Unit fractions) Without numbers. © Joan A. Cotter, Ph.D., 2012
  • 196. Fraction Naming One divided into 2 equal parts. © Joan A. Cotter, Ph.D., 2012
  • 197. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts. © Joan A. Cotter, Ph.D., 2012
  • 198. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts. One divided into 4 equal parts. © Joan A. Cotter, Ph.D., 2012
  • 199. Fraction Naming 1 One divided into 3 equal parts. 1 One whole © Joan A. Cotter, Ph.D., 2012
  • 200. Fraction Naming 1 One divided into 3 equal parts. 1 One whole divided into © Joan A. Cotter, Ph.D., 2012
  • 201. Fraction Naming 1 One divided into 3 equal parts. 1 One whole divided into 3 three equal parts © Joan A. Cotter, Ph.D., 2012
  • 202. Fraction Naming 1 One divided into 3 equal parts. 1 One divided by 3 three © Joan A. Cotter, Ph.D., 2012
  • 203. Fraction Naming 1 One divided into 3 equal parts. 1 One divided by 3 three In English, except for half, we use ordinal numbers to name fractions. © Joan A. Cotter, Ph.D., 2012
  • 204. Fraction Naming 1 One divided into 3 equal parts. 1 Read as “one-third.” 3 © Joan A. Cotter, Ph.D., 2012
  • 205. Fraction Naming 1 1 1 1 3 3 3 One divided into 3 equal parts. 1 Read as “one-third.” 3 © Joan A. Cotter, Ph.D., 2012
  • 206. Unit Fraction War Objective: To help the children realize a unit fraction decreases as the denominator increases. © Joan A. Cotter, Ph.D., 2012
  • 207. Unit Fraction War Objective: To help the children realize a unit fraction decreases as the denominator increases. Object of the game: To collect all, or most, of the cards with the greater unit fraction. © Joan A. Cotter, Ph.D., 2012
  • 208. Unit Fraction War © Joan A. Cotter, Ph.D., 2012
  • 209. Unit Fraction War 1 1 4 5 © Joan A. Cotter, Ph.D., 2012
  • 210. Unit Fraction War 1 1 4 5 © Joan A. Cotter, Ph.D., 2012
  • 211. Unit Fraction War © Joan A. Cotter, Ph.D., 2012
  • 212. Unit Fraction War 1 1 8 © Joan A. Cotter, Ph.D., 2012
  • 213. Unit Fraction War 1 1 8 © Joan A. Cotter, Ph.D., 2012
  • 214. Unit Fraction War © Joan A. Cotter, Ph.D., 2012
  • 215. Unit Fraction War 1 1 6 6 © Joan A. Cotter, Ph.D., 2012
  • 216. Unit Fraction War 1 1 6 6 © Joan A. Cotter, Ph.D., 2012
  • 217. Unit Fraction War 1 1 6 6 1 1 3 4 © Joan A. Cotter, Ph.D., 2012
  • 218. Unit Fraction War © Joan A. Cotter, Ph.D., 2012
  • 219. Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
  • 220. Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
  • 221. Fraction Naming 1 1 1 1 3 3 3 © Joan A. Cotter, Ph.D., 2012
  • 222. Fraction Naming 1 1 1 1 3 3 3 Two 1s 3 © Joan A. Cotter, Ph.D., 2012
  • 223. Fraction Naming 1 1 1 1 3 3 3 Two 1s is 2 3 3 © Joan A. Cotter, Ph.D., 2012
  • 224. Fraction Naming 1 1 1 1 3 3 3 Two 1s is 2 3 3 Read as “two-thirds.” © Joan A. Cotter, Ph.D., 2012
  • 225. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 226. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 227. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 228. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 229. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 230. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many eighths in a whole? © Joan A. Cotter, Ph.D., 2012
  • 231. Concentrating on One Game Objective: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole. © Joan A. Cotter, Ph.D., 2012
  • 232. Concentrating on One Game Objective: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole. Object of the game: To find the pairs that make a whole. © Joan A. Cotter, Ph.D., 2012
  • 233. Concentrating on One © Joan A. Cotter, Ph.D., 2012
  • 234. Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
  • 235. Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
  • 236. Concentrating on One 3 5 © Joan A. Cotter, Ph.D., 2012
  • 237. Concentrating on One 3 5 2 5 © Joan A. Cotter, Ph.D., 2012
  • 238. Concentrating on One © Joan A. Cotter, Ph.D., 2012
  • 239. Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
  • 240. Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
  • 241. Concentrating on One 3 8 © Joan A. Cotter, Ph.D., 2012
  • 242. Concentrating on One 7 8 3 8 © Joan A. Cotter, Ph.D., 2012
  • 243. Concentrating on One © Joan A. Cotter, Ph.D., 2012
  • 244. Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
  • 245. Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
  • 246. Concentrating on One 5 8 © Joan A. Cotter, Ph.D., 2012
  • 247. Concentrating on One 5 8 3 8 © Joan A. Cotter, Ph.D., 2012
  • 248. Concentrating on One © Joan A. Cotter, Ph.D., 2012
  • 249. Concentrating on One © Joan A. Cotter, Ph.D., 2012
  • 250. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5? © Joan A. Cotter, Ph.D., 2012
  • 251. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5? © Joan A. Cotter, Ph.D., 2012
  • 252. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9? © Joan A. Cotter, Ph.D., 2012
  • 253. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9? © Joan A. Cotter, Ph.D., 2012
  • 254. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 An interesting pattern. © Joan A. Cotter, Ph.D., 2012
  • 255. Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 256. Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 257. Partial Chart © Joan A. Cotter, Ph.D., 2012
  • 258. Partial Chart 1 2 3 4 5 6 © Joan A. Cotter, Ph.D., 2012
  • 259. Fraction War Objective: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler. © Joan A. Cotter, Ph.D., 2012
  • 260. Fraction War Objective: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler. Object of the game: To capture all the cards. © Joan A. Cotter, Ph.D., 2012
  • 261. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 262. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
  • 263. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
  • 264. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4 © Joan A. Cotter, Ph.D., 2012
  • 265. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 266. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
  • 267. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
  • 268. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4 © Joan A. Cotter, Ph.D., 2012
  • 269. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 270. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 © Joan A. Cotter, Ph.D., 2012
  • 271. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 © Joan A. Cotter, Ph.D., 2012
  • 272. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 3 1 8 4 © Joan A. Cotter, Ph.D., 2012
  • 273. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 274. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 © Joan A. Cotter, Ph.D., 2012
  • 275. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? © Joan A. Cotter, Ph.D., 2012
  • 276. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? © Joan A. Cotter, Ph.D., 2012