Fractions

Fractions

1. Equivalance

   • Comparing and ordering fractions
     • Number lines
       • Numbers between numbers
         • Fractions between fractions
           • Density property of fractions
     • Improper fractions and mixed numbers
     • Estimation
     • Adaptive reasoning
     • Drawing pictures to represent quantities
   • Benchmarking
   • Converting
     • Decimals
       • Place value
     • Percentages
     • Cross multiplying
     • Ratio
   • Proportionality
     • Use of manipulatives

2. Base-ten number system

   • Four operations
     • Division
       • Partioning
         • Equal shares
           • Part-whole
             • Arrays
             • Partitive division
             • Quotitive division
             • Representations
               • Pictorial
               • Symbols
                 • Fractional notation
               • Physical
               • Concrete
                 • Pattern blocks
                 • Geoboards
                 • Fraction bars
                 • Grid paper
                   • Region model
               • Verbal
               • Authentic
                 • Constructivist learning
         • Residual thinking
     • Subtraction
     • Additon
     • Multiplication
       • Multiplicative thinking
   • Counting
     • E.g. One fourths, two fourths, etc

3. Language

   • Halves
   • Thirds
   • Fourths
   • Fifths
   • Mathematics literature
     • E.g. Hershey's Milk Chocolate Fraction Book

4. Measurement

   • Knowing the relationship between units
   • Fractions as operators
   • Unitising with fractions

5. Place Value