Math Concepts: Fractions, Number Line
What You Can Do: Students can be exposed to fractions in a variety of contexts, and it’s important to emphasize their usefulness by referencing fractions in daily conversation. Expose your children to common phrases that involve fractions, such as “halfway home” and “quarter to seven,” but also introduce them to less common fractions. For instance, measurements in the English system incorporate eighths and sixteenths, and the Rule of Twelfths uses twelfths to estimate the height of the tide in ship navigation.
There are many representations that can be used to explore fractional relationships. Fractions can also be described by a length model, set model, or region model. Distance is a good example of the length model; students can visualize a distance that is three-fourths as long as another. An egg carton is a good example of the set model; filling a carton with five eggs shows a representation of five-twelfths. And the fraction circle described in the lesson Too Big or Too Small (see Related Resources section below) is an example of the region model.
Discuss the various fractions that can be created using the numbers 1-9 for the numerator and denominator. As it turns out, 45 of the 81 possible fractions that can be made have a value less than or equal to 1. Students should investigate this idea on their own. Ask your students questions such as, “Where do most fractions occur?” and “What locations on the number line are most difficult to reach?”
Math in the Game: Students need to understand improper and equivalent fractions to be successful at this game. For instance, it will be helpful to realize that 7/4 is equal to 1.75, which occurs just to the left of 2 on the number line, and students must realize that 9/3 is equal to 3/1 and that both occur at 3 on the number line.
Related Resources: Too Big or Too Small
The second activity of this lesson asks students to create a fraction wheel, which can be used to examine the relative sizes of common fractions with denominators from 2 through 10.
Fun with Fractions (Length Model)
In this five-lesson unit, students use fraction strips and relationship rods to order and compare fractions and to investigate equivalency.
Digging Up Improper Fractions: Converting Improper Fractions to Mixed Numbers for “Dig It” Game
This lesson provides a hands-on approach to converting improper fractions to mixed numbers.