My students are now half way through the chapter on fractions. They seem confident in performing the different operations, but a few are still unsure of how to reduce fractions.
Although I have stressed learning the Divisibility Rules for 2, 5, 10, and the digital root for 3, 6, 9, (September 21st posting) some still have difficulty since they do not know their multiplication tables. This week we made Pattern Sticks, a visual and kinesthetic aid, similar to a multiplication chart like the one on the left. Notice that an extra column (blue) has been added to the chart. (In this space, a hole is punched so that a 1" ring can be inserted to store all of the sticks in one place.) .
On the right are the directions for making the Pattern Sticks using a multiplication chart.
(Side note: My students cut out individual Pattern Sticks which I prefer over cutting a multiplication chart apart. If you are intetested in these, see the link under the scary fingers.)
I then gave the students fractions such as 9/36 to reduce. Using the Pattern Sticks, they looked for a column where a 9 and a 36 were lined up in the same one. They easily found it on the 1 strip and the 4 strip. They then took the two strips and lined up the two so that the 9 was over the 36. (see illustration above) By going to the left, they discovered that 9/36 is the same as 1/4. This is 9/36 in its lowest terms. Also notice that all the fractions in the illustration above are equivalent fractions: fractions that have the same value. We also used the Pattern Sticks to determine what number to divide by and to change improper fractions to mixed numbers.
On a more elementary level, the Pattern Stricks can be used to practice skip counting. I purchase those scary, wearable fingers at Halloween time. (You can purchase them in bulk from the Oriental Trading Company.) My students wear one for such activities as this.I call them the Awesome Fingers of Math!For some reason, when wearing the fingers, students tend to actually point and follow along when skip counting.(If you like this idea, be sure that each student uses the same finger every time to avoid germs, etc. Keeping it in a zip lock bag with the child’s name on the bag worked best for me. Believe it or not, when I taught middle school, the students would paint and decorate the fingernails!)
If you are interested in learning more about Pattern Sticks and how to use them in your classroom, check out the resource entitled Pattern Sticks: A Math Tool for Skip Counting & Reducing Fractions at Teachers Pay Teachers. Just click on the link under the scary fingers.