Beginning in third grade, students learn that fractions represent portions of a whole. The Common Core Standards ask that third-grade students understand the concept of equivalent fractions and be able to compare two fractions. Fourth- and fifth-grade students begin to order fractions and perform simple operations such as adding and subtracting. Simple projects can help students to develop both an understanding of fractions and basic skills in manipulating and using fractions in real-life situations.

## Fraction Basics

A basic project involving paper gives students an introduction to the concept of fractions. Give students six strips of paper of equal length to begin. Have students choose one strip of paper to represent the whole amount -- or one. Students then cut the second strip in half to see that 1/2 represents one of two pieces of a whole. With the remaining strips of paper, students can create representations of different fraction values, always keeping in mind that fractions are portions of a whole.

## Budding Architects

Basic principles of architecture introduce students to fractions and measurements. Begin by having students measure objects of different lengths with a ruler. Provide students with pictures to measure, or have them measure objects around the classroom such as pencils, crayons or the sides of books. Next, have students draw lines to measure specific lengths. For example, ask students to draw lines 2 inches long, 2 1/2 inches long and 2 3/4 inches long. Finally, ask students to design a home given specifications for measures of certain elements of the home, such as the height and width of a door and dimensions of windows. You can also provide students with specifications for background items or the distance from neighboring homes.

## Dining and Discounts

Role-playing and games involving money give students the opportunity to practice understanding and using fractions. You can provide students with paper money and coins in various denominations to explain that receiving change at a store means you are receiving a fraction of a dollar. For example, after explaining that there are four quarters in a dollar, students can figure out that one quarter is 1/4 of a dollar. Or students can learn that a penny is 1/10 of a dime (or 1/100 of a dollar). After giving students an introduction to concept of fractions in money, present scenarios for purchasing items and receiving change. Students can figure out what fraction of their money they will receive as change. For example, if they purchase candy for 50 cents, they will be paying half a dollar and receiving half a dollar as change.

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## Math Masterpieces

A fraction lesson can be integrated into a simple art project. Begin by creating a 10-by-10 grid to give students 100 squares where they will create a mosaic. Next, ask students to devise a color scheme or pattern for their artwork. Students should think about ways they can create patterns or images within the grid. For example, students might alternate colors in each row or column. Or, they might create a diamond pattern in the center of the grid. Ask students to calculate the fraction amount each color makes up in the grid. For example, if 10 squares are blue, they would figure out that blue squares make up 10/100 of the grid. Encourage more advanced students to reduce the fraction to find that 1/10 of the grid is blue.

#### References

- The Actuarial Foundation; Math Academy Dining Out!
- DigitalLesson.com: Amateur Architect
- Mathematics Teaching in the Middle School; Masterpieces to Mathematics; Christopher Scaptura, Jennifer Suh, and Greg Mahaffey
- National Council of Teachers of Mathematics: Illuminations: Making and Investigating Fraction Strips
- Common Core State Standards Initiative: Number & Operations _ Fractions

#### Photo Credits

- Ingram Publishing/Ingram Publishing/Getty Images