- 1. Fractions as Part of a Whole & The Complement to 1
Define the parts of a fraction, understand fractions as the division of two integers, write fractions from visual models, and calculate the complement to 1.
- 2. "Sneaky" Visuals and Unequal Parts
Understand that fractions must represent equal parts. Analyze irregular shapes and partition "sneaky" visuals to find the correct fraction.
- 3. The Number Line (Positive) & Mixed Numbers Visually
Place and identify proper fractions, improper fractions, and mixed numbers on a positive number line.
- 4. The Number Line (Negatives) & Numerical Conversion
Locate negative fractions on a number line using symmetry, and convert between mixed numbers and improper fractions using algorithms.
- 5. Equivalence via Fraction Walls and "The Sneaky 1"
Use visual models (fraction walls) and the multiplicative identity algorithm ("The Sneaky 1") to generate and identify equivalent fractions.
- 6. Simplest Form and Co-Prime Numbers
Simplify fractions by dividing by common factors, use the Greatest Common Divisor (GCD) for one-step simplification, and identify when numbers are co-prime.
- 7. Comparing with Common Denominators
Compare and order fractions by converting them to equivalent fractions with a common denominator.
- 8. Comparing with Common Denominators
Students will be able to compare and order fractions by converting them to a common denominator using the Lowest Common Multiple (LCM).
- 9. Adding & Subtracting Fractions with Like Denominators
Students will be able to add and subtract fractions that share the same denominator, simplify the results, and express answers greater than 1 as mixed numbers.
- 10. Fractions – Adding & Subtracting with Unlike Denominators
Add and subtract fractions with unlike denominators by finding the Lowest Common Multiple (LCM) to create equivalent fractions.
- 11. Fractions – Finding a Fraction of an Amount
Calculate a fraction of a quantity by dividing by the denominator and multiplying by the numerator, and understand that the word "of" means multiply.
- 12. One Number as a Fraction of Another
Express one quantity as a fraction of another quantity and simplify the result to its lowest terms.
- 13. Finding the Whole (Referent Whole - Unit Fractions)
Find the total original amount (the referent whole) when given a unit fraction of that amount, using inverse operations and bar models.
- 14. Fractions – Finding the Whole from Non-Unit Fractions
Calculate the referent whole when given a non-unit fraction of an amount by dividing by the numerator and multiplying by the denominator.
- 15. Fractions – Multiplying Fractions
Multiply fractions using an area model to understand the algorithm, and apply cross-simplification to multiply efficiently.
- 16. Dividing Fractions & The Reciprocal
Define the reciprocal of a fraction, and divide fractions by converting the division into multiplication using the reciprocal.
- 17. Order of Operations with Fractions
Apply the order of operations (BIDMAS/BODMAS) to calculate expressions involving fractions, including brackets and squaring fractions.
- 18. Contextual Multi-Step Problems & Unit Mastery Review
Apply fraction operations to solve complex, multi-step word problems involving geometry and scaling, analyze mathematical reasoning for errors, and demonstrate mastery of all unit concepts.
