1. Starting with just a multiplication board, some acetate strips (cut from different colored report covers), or colored counters you can bring the “magic” alive to help students with problem solving.

2. X123456789101112 1123456789101112 224681012141618202224 3369121518212427303336 44812162024283236404448 551015202530354045505560 661218243036424854606672 771421283542495663707784 881624324048566472808896 9918273645546372819099108 10 20304050607080 100110120 11 22334455667788 110121132 12 24364860728496108120132144 Finding Equivalent Fractions Numbers on the board form equivalent fractions whether the numerator is directly on top of the denominator or the numerator and denominator are separate. Take ½ for example (marked by red circles). As you read across the board horizontally, note that each fraction from L to R is equal to ½. ½ = { 2 / 4, 3 / 6,... 12 / 24 }. Take 4 / 7 for example (marked by purple circles). As you read across the board horizontally, note that each fraction from L to R is equal to 4 / 7. 4 / 7 = { 8 / 14, 12 / 21,... 48 / 84 }.

3. X123456789101112 1123456789101112 224681012141618202224 3369121518212427303336 44812162024283236404448 551015202530354045505560 661218243036424854606672 771421283542495663707784 881624324048566472808896 9918273645546372819099108 10 20304050607080 100110120 11 22334455667788 110121132 12 24364860728496108120132144 Adding and Subtracting Unlike Fractions Here is a different approach for students who are having problems adding and subtracting fractions with unlike denominators. Before you begin, ensure students know the difference between “like” and “unlike” fractions and understand “common multiples” and “least common denominator” (LCD). Step 1 - Finding the LCD For example: When adding 1 / 7 + 2 / 5. Place one of the acetate strips over the 5s row and the other over the 7s row. Beginning with the greater number “7”, cross-reference the multiples in each row until you find the lowest matching multiple. This will be the least common multiple or LCD; in this case, “35”.

4. X123456789101112 1123456789101112 224681012141618202224 3369121518212427303336 44812162024283236404448 551015202530354045505560 661218243036424854606672 771421283542495663707784 881624324048566472808896 9918273645546372819099108 10 20304050607080 100110120 11 22334455667788 110121132 12 24364860728496108120132144 Adding and Subtracting Unlike Fractions Now we must convert 1 / 7 and 2 / 5 to equivalent fractions each with a denominator of 35. Step 2 – Convert the first fraction 1 / 7 Starting with 1 / 7, Place on colored acetate strip over the 1s row and the other over the 7s row. Equivalent fractions for 1 / 7 are now highlighted on the table. Move along the denominator (7s) row until you come to the LCD, “35”. Now move up this column until you reach the highlighted number in the 1s row which is “5”. By doing this you show that 1 / 7 = 5 / 35.

5. X123456789101112 1123456789101112 224681012141618202224 3369121518212427303336 44812162024283236404448 551015202530354045505560 661218243036424854606672 771421283542495663707784 881624324048566472808896 9918273645546372819099108 10 20304050607080 100110120 11 22334455667788 110121132 12 24364860728496108120132144 Adding and Subtracting Unlike Fractions Now we must convert 1 / 7 and 2 / 5 to equivalent fractions each with a denominator of 35. Step 3 – Convert the second fraction 2 / 5 Now follow the same steps for 2 / 5. Place on colored acetate strip over the 2s row and the other over the 5s row. Equivalent fractions for 2 / 5 are now highlighted on the table. Move along the denominator row (5s) until you come to the LCD, “35”. Now move up this column until you reach the highlighted number in the 2s row which is “14”. By doing this you show that 2 / 5 = 14 / 35.

6. Adding and Subtracting Unlike Fractions Step 4 – Add (or subtract) the like fractions 1 / 7 + 2 / 5 = 5 / 35 + 14 / 35 = 19 / 35 Resources Forsten, C. (2005). Math Strategies You Can Count On: Tools & Activities to build Math Appreciation, Understanding & Skills. Peterborough, NH: Crystal Springs Books. Kohfeldt, Joyce. Innovative Educational Support Systems. 2008. 2 November 2008.