Ready Set Math Module 9: Fractions Concepts: From Part-Whole to Measurement
Ready Set Math Module 10: Fractions Concepts: Coordinating Fractional Units
Blog post written by: Melissa Wilke and Kurt Kinsey
Fraction action, we’ve got fractions!
Why can fraction instruction and learning be so difficult for both teachers and students?
Typical fraction instruction has students starting out by shading and counting pre-partitioned shapes and quickly moves to memorizing rules, often with little to no understanding.
Many students get stuck in the part-whole domain of fractions which can make understanding addition, subtraction, multiplication, and division of fractions quite difficult. It is important to recognize how we can build understanding and support students in making sense of fractions through a conceptual approach rather than rote procedures.
Fractions concepts can build on students’ part-whole understanding of fractions and extend to learning opportunities for knowing fractions as measures. This allows students to coordinate and reason with unit fractions, proper fractions, and the whole.
The trajectory for this learning involves distinct stages of teaching and learning:
- Part-whole relationships and partitioning a continuous whole into equal shares
- Identifying a unit fraction when removed from the whole
- Iterating a unit fraction to create the related whole
- Reason with the size of a proper fraction to create the related whole
- Reason with a unit fraction to create an improper fraction
- Coordinating and reasoning with a variety of fractional units
The two Ready Set Math modules, Fractions Concepts: From Part-Whole to Measurement and Fractions Concepts: Coordinating Fractional Units, incorporate the learning progression and trajectory to create a strong foundation for developing reasoning to coordinate different fractional units to compare, add, subtract, and multiply fractions.
In the first module, Fractions Concepts: From Part-Whole to Measurement,
students are engaged in a variety of learning experiences.
To support part-whole thinking, students partition a rectangle into equal shares up to 5. The use of rectangles of different sizes is used to create and name unit fractions within a whole. Learning progresses to using fractional language (one-fourth instead of one out of four equal shares) and using formal notation (i.e., ¼). Instruction extends into the measurement world which includes removing a unit fraction from the whole, naming the fraction and then iterating or repeating the unit fraction to create or re-create a whole. Rectangles and colored fraction strips (i.e., Cuisenaire Rods) are key instructional settings used to support the development of measurement thinking.
The learning extends further into the measurement world of fractions in the second module,
Fractions Concepts: Coordinating Fractional Units.
The learning progression begins with coordinating and reasoning with a unit fraction, proper fraction, and the whole. Next, students engage in reasoning with unit fractions, the whole, and improper fractions to build understanding of fractions beyond a whole.
Once students can coordinate and reason with different fractions, they explore co-measures as a means to compare any two fractions, find a fraction of a fraction (multiplication), and combine and find the difference of two fractions. Rectangles and colored fraction strips (i.e., Cuisenaire Rods) are again key instructional settings used to support the development of thinking and strategies for these fraction concepts.
Throughout the modules, teachers are supported in- the- moment with professional learning and teaching tips for implementation and facilitation. These moments are aligned with Math Recovery research and best practices through our Guiding Principles bringing awareness to the intricacies of supporting students in developing fraction knowledge.
Learn more about Ready Set Math from US Math Recovery®