# Addition and Subtraction of Positive Fractions and Mixed Numbers

**Strand:** Number

**Outcome:** 5

## Step 5: Follow-up on Assessment

### Guiding Questions

- What conclusions can be made from assessment information?
- How effective have instructional approaches been?
- What are the next steps in instruction?

### A. Addressing Gaps in Learning

- Use manipulatives of various kinds to establish a solid foundation for the meaning of fractions and equivalent fractions.
- Review the relation between mixed numbers and improper fractions, using concrete materials, diagrams and symbols.
- Relate adding and subtracting fractions to adding and subtracting whole numbers. The types of problems involving the addition or subtraction of whole numbers are the same for fraction problems; e.g., part-part-whole, comparison and join or separate problems. Substituting whole numbers for fractions helps students decide which operation to use in solving the problems.
- Encourage students to estimate before calculating to ensure that their answer makes sense and also to develop number sense.
- Use problem contexts that students can relate to and keep the fractions simple initially; i.e., use fractions with like denominators, then use unlike denominators with only one denominator needing to be changed and finally use unlike denominators with both denominators needing to be changed.
- Relate addition to subtraction to help students see the connection.
- Connect the concrete, pictorial and symbolic modes.
- Provide the option for students to use manipulatives as long as needed, even on tests.
- Encourage students to explain their thinking orally if they have difficulty explaining it in writing.

### B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Strategies for Reinforcing and Extending Learning