Fractions are divisions. They describe the sections, parts or “units” that are created when you divide one whole something into equal parts.
That one whole something could be a length of adding machine tape, a shape, a unit of measure (cm, kg, km, hour, minute) or a set or group designated as one as in a herd, a unit of “place value” (ten, one, hundred etc.) pan of cookies, bag of candies.
A key BASIC to success with fractions: Learners are able to refer back to the whole.
If you identify by shading, removing or simply talking about one third, the learner is able to identify one third of what? That is why I encourage teachers to begin their work with fractions by paper folding. Paper folding allows students to keep the “whole” in sight. Fractions are embedded in “wholes”.
I call this deck Fraction Wholes. It is images that have been equally divided. Students trace and label the one. Then divided their drawn “one” into the fractional parts as shown on the card. Next they label each part as a unit fraction. Then they label the whole diagram as a fractional whole equal to 1 what? I then challenge them to :
- find a partner whose card represents the same fractional whole
- fold paper to demonstrate and label the same fractional parts and whole, then compare the model they drew to the model they folded. How are they the same, how are they different. The Fraction Book contains different types of worksheets to give ideas for other ways to use the deck.
- trace the same whole again but look for a different way to divide it into the same fraction. Be careful to keep the “parts” equal size. Is it possible for your shape?
This deck contains shapes that have Shaded Parts. Students can trace label and identify as a fractional whole. Then identify the fraction that describes how much is shaded and how much is not. These cards continue to support number sense for fractions. We hope to see fairly automatic response to how many not shaded, once the shaded section is identified. This exercise supports the development of “inverse” thinking as well as equal and equivalence.
This card demonstrates 1/3 is white. Two thirds are brown. It can be used to create equations like
1/3 + 2/3 = 3/3 or 1 1 – 1/3 = 2/3.
This card can be interpreted several ways. I see 3 fourths are orange, one fourth is white. But I could also call the orange 9 twelfths and the white 3 twelfths. I could record the following:
6/12 + 3/12 + 3/12 = 12/12 or 1. 9/12 + 3/12 = 12/12. 1/4 + 3/4 = 1
Focusing on more than just naming the shaded part deepens students’ understandings of how fractional parts are related and prepares them for making sense of equivalence and addition with like or unlike denominators.
There are 2 decks that focus on making sense of Fractions as Parts of a Set. Now the whole is assigned a value and the representation is simply that, a way to represent an idea. These puzzle cards prompt diagramming, reasoning and connect multiplication, division and fractions together.
There are 2 decks. One is more challenging than the other.
Equivalent Fraction Sets
Students are encouraged to “see” fractional parts inside other fractional parts. As they note which fractions are related, they develop lists of related fractions. The patterns that emerge can help them to construct conceptual understandings of how equivalent fractions are related. This set of cards has 2 related fractions on each card.
I call this set COOL FRACTIONS. These cards challenge students to see fractions inside fractions without all the parts showing.
I use them to practice Partitioning Strategies.