Investigation 2: Investigating Fractions with Manipulatives
Investigating fractions with manipulatives uses physical fraction pieces to explore improper fractions and their mixed number equivalents. In Grade 6 Saxon Math Course 1 (Chapter 2: Problem Solving with Number and Operations), students discover that 7/5 means having 7 one-fifth pieces: arrange 5 of them to form one whole, leaving 2 pieces, yielding 1 and 2/5. The denominator tells the size of each piece and how many pieces make a whole; the numerator tells how many pieces you have. This hands-on method makes the abstract concept of improper fractions concrete before working with algorithms.
Key Concepts
New Concept Improper fractions are fractions that are equal to or greater than $1$. In a fraction equal to $1$, the numerator equals the denominator (as in $\frac{5}{5}$). In a fraction greater than $1$, the numerator is greater than the denominator (as in $\frac{7}{5}$). What’s next This is your introduction to fractions representing more than one whole. Next, you'll use visual models to convert improper fractions into mixed numbers.
Common Questions
How do manipulatives help understand improper fractions?
Physical fraction pieces let you group pieces into wholes. 7 fifths = 5 fifths (one whole) + 2 fifths = 1 and 2/5, making the concept visible without memorizing a rule.
Model 7/5 using fraction manipulatives.
Take 7 one-fifth pieces. Group 5 of them to make 1 whole. 2 pieces remain. Result: 1 and 2/5.
What does the denominator tell you about fraction pieces?
The denominator tells how many equal pieces make one whole. If the denominator is 5, each piece is one-fifth and 5 pieces = 1 whole.
Model 11/4 using manipulatives.
Take 11 quarter-pieces. Group 4 for the first whole, 4 for the second, 3 remain. Result: 2 and 3/4.
Why use manipulatives before learning the algorithm?
Manipulatives make the concept concrete. Students understand what the improper fraction means (more than one whole) before memorizing the division algorithm.