“Speak in Fractionese, if you please!”
I loved learning this fraction phrase from a favorite mathematics methods professor and it carried over into my own math classroom. Reminding my students to refer to the part and whole of every fraction developed stronger number sense and understanding of fractions in general.
A simple yet effective method for developing stronger fraction sense can be borrowed from the younger grades: skip counting. When we teach students in the lower grades to skip count, we prepare them for repeated addition and ultimately multiplication. Why not use the same strategy with fractions?
- Patterns – students will see and begin to internalize patterns as they skip count. Students need to see that fractions have a lot of similarities to whole numbers because most students are pretty comfortable with whole numbers.
- Fraction Addition – how many students still add the denominators when trying to add fractions in your class? As mentioned with patterns, seeing the similarities to whole numbers will help students understand the function of the denominator. Understanding the reason for “when we add we have to keep the same denominator” gives meaning to this fraction rule.
- Fraction Multiplication – Just as skip counting whole numbers in lower grades promotes repeated addition that ideally leads to multiplication, so does skip counting with fractions. If students are comfortable skip counting by 1/6’s, then they will understand why 1/6 x 12 is 12/6 or 2. The patterns that emerge from skip counting will have students multiplying unit fractions by whole numbers in no time!
- Whole Group – When introducing fractions or as a warm up, students can skip count by any given fraction as a chorus. Start with unit fractions (1/2, 1/3, 1/8, etc) and soon challenge students to count by non-unit fractions (3/8, 2/5, 9/4, etc). Even students who struggle with number sense will hear the patterns and participate more as time goes on.
- Small Group – Using dry erase boards, notebook paper, or worksheets with blank number lines, have students begin demonstrating their skip counting on the number line. Students will begin to see that the “jumps” need to have equal spacing and will begin to see why improper fractions have a mixed number name as well. As students begin multiplying unit fractions and whole numbers, counting whole number jumps on the number line will give struggling students a tool to use as they start to see multiplication patterns with fractions.
- Centers – Students can draw a fraction card from a stack and draw out as many jumps as you wish for them to complete. Reusing blank number lines is easy – simply place a page with blank number lines printed into a plastic sheet protector and provide students with dry erase markers and pieces of felt to erase. Eventually students can choose to use this tool with word problems or practice problems. An example with a printed sheet is shown below:
- Morning Work – Students can skip count by a given fractional amount as part of their morning work
- During Math Class – See the whole group, small group, and centers ideas
- Before or after Recess, Lunch, Pack Up Time – Use the whole group chorus method to have students practice fluency during downtime in the classroom. I know I always had 5 random minutes to fill every day and loved using activities like this to promote fluency.
- In Games – Students can play a math version of Sparkle (normally a spelling game). Give students a starting fraction and ending fraction that is a multiple of the starting fraction. Once a student reaches the ending fraction, the next student says “Sparkle” and the next student sits down. Continue play until one student remains. There are lots of directions for Sparkle online – check out this explanation!
As you can see, it’s not very difficult to fit in this beneficial strategy during the school day. Consistent practice with fractions will give students confidence and stronger number sense.
How do you see fitting in skip counting with fractions?