`Measuring Mixed NumbersKaren Trout                    Sumner Math and Science Academy                               4320 W. 5th Avenue                               Chicago IL 60624                               (312) 534-6730Objectives:   Grade 5     -Students will discover the need and every day use of mixed numbers.     -Students will measure different lengths to the nearest fraction of an       inch.     -Students will review the equivalent values of fractions (for example:        2/4=1/2).     -Students will review how to come up with the common denominator and why.     -Students will add mixed numbers phenominologically and then       algorithmically.Materials Needed:     -1 pair of scissors per student     -1 ruler per student     -5 pieces of tape per student     -1 worksheet per student     -1 piece of scratch paper per student     -Construction paper of different colors     -Large clear container with graduated cups     -Measuring cup set     -Bucket full of milky water (mix in a little corn starch)Strategy:     1.  Before class, use your construction paper to make a couple sets of fraction bar charts (be sure to include whole, halves, fourths, eighths, and sixteenths).  Use different colors for each different fraction length, and make your pieces board size.     2.  If you have a large container that does not have graduated cups, just place a strip of tape down one side of the container, then pour a cup of water in at a time and mark the level for each cup on the piece of tape.     3.  Create a worksheet that has about 4 different problems similar to the example below.  Draw different length bars that the students will have to measure individually, cut out, connect, and then remeasure as a whole unit. They will only be measuring the length of these rectangles or bars which shouldbe at various lengths between 1/2 an inch and 5 inches.  This is a sketchy example of what one problem would look like:     Measure these lengths as accurately as you can, then cut them out, tapethem together and remeasure the length of these two together:              `ffffffffffffffffffffffffp              `fffffffffffffffp    w                        w              w               w    w                        w      +       w               w   =    w                        w              w               w    affffffffffffffffffffffffq              afffffffffffffffq     4.  Begin the class with this question:  "Pretend you are a zookeeper and your responsibility is to feed the baby animals their formula each day.  The baby porcupine eats 2 1/2 cups of formula, the baby seal eats 5 1/4 cups, and the baby ape eats 7 3/4 cups.  How much baby formula do you need to make to feed all three of the baby animals?"     5.  Allow the class time to reflect on the problem and then explain that they are going to need to understand how to add mixed numbers in order to solve this problem.  Demonstrate for them briefly on the board how they are going to use the worksheet.  They are to measure the length of each bar and write that length inside the figure.  Then they are to cut out each bar and connect them with tape onto the piece of scratch paper they have been given.  They should now have a longer bar which they are to measure and write down the total length of the two bars combined.      6.  When they have completed this worksheet go back and compare some of their answers.  Then using the fraction pieces which you will have taped up on the board, show them the different lengths.  If they measured 3 1/2 inches forone bar, show them 3 1/2 in fraction pieces.  If their second bar was 1 1/4 inches long, then show them 1 1/4 in fractions.  Demonstrate for them how to add those two fractions of different denominators (1/4 and 1/2) by replacing the 1/2fraction piece with two 1/4 pieces and finding their length to remain the same.  Using the fraction pieces, continue to visualize for them how we come up with a common denominator when adding fractions of unlike denominators.     7.  When you feel they have grasped this concept, you then go back to your original question about feeding the baby animals.  This time have them find the common denominator between 1/2 and 1/4 and then add their mixed numbers together to get the total amount of baby formula needed.     8.  Finally, to prove whether or not the answer they got on the baby formula was correct, have someone come up and measure out the amount of cups fed each baby animal.  Have them take the milky water (water and a little corn starch) out of the bucket and carefully pour it into your graduated, clear container.  The amount of formula that is now in the container should be the same as the amount of cups the class came up with on paper.Conclusion:The students visualize adding mixed numbers physically by adding different lengths together to the nearest fraction of an inch and by adding cups together.  Then they discover the simplified algorithmic process which reduces the amount of work they need to do.  However now they also understand why they need to add mixed numbers and what mixed numbers are.  In conclusion, their performance should improve greatly as they comprehend the usefulness of these skills and what it is that they are actually doing when they come up with a common denominator and add their mixed numbers together.`