Improper Fractions and Mixed Numbers
Strand: Number
Outcome: 4
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider ways to assess and build on students' knowledge and skills related to fractions. Provide manipulatives such as fraction strips, pattern blocks or fraction circles for students to use, as needed.
Ways to Assess and Build on Prior Knowledge and Skills 
B. Choosing Instructional Strategies
Consider the following instructional strategies for teaching improper fractions and mixed numbers.
- Introduce and reinforce the mixed numbers and improper fractions by using a variety of
real-world contexts that include whole regions and whole sets.
- Connect the mixed numbers and improper fractions to prior knowledge about the meaning of fractions and equivalent fractions.
- Provide students with a variety of problems that apply the concept of mixed numbers and improper fractions. Encourage them to solve the problems in different ways and explain the process. Also, provide time for students to share their solutions with others. Stimulate class discussion to critically evaluate the various procedures. Emphasize understanding, flexibility and efficiency when students select problem-solving strategies.
- Explore problems that develop understanding of fractions as division of numbers (NCTM 2000, p. 33).
- Emphasize the importance of establishing what the whole region or the whole set is before finding fraction names for regions or sets.
- Encourage students to communicate their thinking by connecting manipulatives, diagrams and symbols to represent the concepts.
- First introduce improper fractions as an extension of proper fractions on the number line. Explore the similarities and differences. Then, connect improper fractions to mixed numbers.
- "Create a classroom environment that encourages student exploration, questioning, verification and sense making” (NCTM 1992, p. 5).
- Provide opportunities for students to explore the relationship between mixed numbers and improper fractions.
- To promote flexible thinking, provide a variety of problems in which two out of the following three are given and the third must be found: the whole, the part and the fraction (NCTM 2000, p. 215).
- Encourage students to make and critique generalizations related to mixed numbers and improper fractions.
- When ordering mixed numbers and improper fractions, make connections to prior knowledge of benchmarks and equivalent fractions. Encourage flexibility in choosing strategies to order fractions.
C. Choosing Learning Activities
The following learning activities are examples
that could be used to develop student understanding
of the concepts identified in Step 1.
Sample Activities:
Grade 6
