How many polar bears? How many fish? What about Plankton?

Counting up the pieces – even if they are different sizes. There are two young kids trying to determine how many pieces of licorice they have. The problem was that the pieces were different sizes of licorice, so if they added them up…

Counting up the pieces – even if they are different sizes. The licorice comes in 2 different sizes, so the best they could do was count how many of each size and that doesn’t really satisfy them so they decide to line the licorice up end to end and measure…

Counting up the pieces – even if they are different sizes. Ok, this might work, but they’ve changed from finding the number of pieces of licorice to total length in inches of licorice. Is there another way? What if they cut them all into the same size piece and then counted those pieces? So, where is the cleaver?

Counting up the pieces – even if they are different sizes. WAIT! They can’t just start hacking up the licorice, they need to cut them all to the same size without any left over. Look for a pattern. Notice that 1 large piece is equal to 1 and a ½ medium pieces. So if we cut the medium pieces in half and the large pieces in thirds, all the pieces would be the same size.

Counting up the pieces – even if they are different sizes. Ok, cut the big pieces into 3 equal parts and the medium pieces into 2 equal parts. That should make all the pieces the same size.

Counting up the pieces – even if they are different sizes. Now they are all the same size and the kids can quickly count them up and say that they have 21 small pieces of licorice. Now they can divide them up to share equally.

Adding fractions are the same idea or pattern Take the two fractions below. The bottom numbers or denominators actually tell you the size of the pieces. The larger the number the smaller the size. There are 5 large pieces and 2 medium pieces. Why is it that the larger bottom number means smaller size pieces?

Adding fractions are the same idea or pattern the Least Common Multiple To determine what size to cut the pieces into, you find the Least Common Multiple of the sizes. Actually, with fractions we call it finding the Common Denominator 6 is the LCM or the Common Denominator

Adding fractions are the same idea or pattern 6 is the third multiple of 2 so we “cut” the five large pieces into 3’s or 5x3 6 is the second multiple of 3 so we “cut” the 2 medium pieces into 2’s or 2x2

Adding fractions are the same idea or pattern Instead of 5 large pieces we have 15 small pieces, and instead of 2 medium pieces we have 4 small pieces and we can combine all the pieces together. now altogether we have 19 small pieces!

Adding fractions are the same idea or pattern Simple, I know, but the pattern is the same for easy fractions as complicated ones we call them rational polynomials. We went from 3 different sizes Large, medium, small To a common size of tiny. 2: 2, 4, 6, 8, 10, 12, 14, 16 3: 3, 6, 9, 12, 15, 18 4: 4, 8, 12, 16, Do you see why we only add or subtract the top numbers and leave the bottom alone? What patterns do you see in finding a common denominator and changing all the fractions to the same size? Explain what we did in a complete sentence?

Writing in complete sentences. What we did. We multiplied the bottom number (denominator) and the top number (numerator) by the same number. That number is the number of jumps to get to the common size. Divide the common denominator (size) by the bottom number and the number you get is what you multiply by the top number (numerator). The bottom number times what will give you the common denominator? What ever it is, multiply the top number by it.

Student Practice Add the fractions together. 3x8 = 24 so multiply the 1 by 8 to get 8 6x4 = 24 so multiply the 5 by 4 to get 20 8x3 = 24 so multiply the 5 by 3 to get 15