Math Professional Learning - Making Sense of Fractions

During club day on December 9th, all math teachers participated in professional learning on Making Fractions Make Sense for Kids.  Our learning target was: I can internalize instructional practices and resources that will help students understand fractions at a deeper level.  We read and discussed the article "10 Practical Tips for Making Fractions Come Alive and Make Sense" by Doug M. Clarke, Anne Roche, and Annie Mitchell, and participated in an activity (Fraction Fish) that can be used to build conceptual knowledge of adding and subtracting fractions.

 

10 Tips for Making Fractions Come Alive and Make Sense

(Source: 10 Practical Tips for Making Fractions Come Alive and Make Sense" 

by Doug M. Clarke, Anne Roche, and Annie Mitchell. The ten tips are listed below:

1. Give a greater emphasis to the meaning of fractions than on procedures for manipulating them.
2. Develop a generalizable rule for explaining the numerator and denominator of a fractions.

3. Emphasize that fractions are numbers, making extensive use of number lines in representing them.

4. Take opportunities early to focus on improper fractions and equivalences.

5. Provide a variety of models to represent fractions.

6. Link fractions to key benchmarks and encourage estimation. 

7. Give emphasis to fractions as division.

8. Link fractions, decimals, and percents whenever possible.

9. Take the opportunity to interview students one on one with rich tasks to gain awareness of thinking and strategies.

10. Look for examples and activities that can engage students in thinking about fractions in particular and rational number ideas in general.

Big Takeaways

• Fractions are difficult to teach and learn because of the different interpretations (constructs), representations (models), and coding conventions (5/4, 1 1/4, 1.25, etc.)
• Fractions can represent 1) Part-whole, 2) Measurement, 3) Division (3 divided by 5 is 3/5), 4) An operator (3/4 of 12), and 5) A ratio.
• Teachers have typically defined a fraction by telling students "the denominator tells you how many parts the whole has been broken into, and the numerator tells you how many of these parts to take, count, or shade in".  This works well if the fraction is between 0 and 1. The authors suggested this explanation: "In the fraction a/b, b is the name or size of the part and a is the number of parts".
• Benchmarking (comparing to 0, 1/2, or 1) should be used to estimate and compare fractions.