Fraction Visuals

Explicit Instruction/Teacher modeling

• Lead students in an exploration of the variety of types of fractions and different places we see or use them. First, gather their background knowledge on fractions by facilitating a brain dump of all things related to the concept.
• Display and pose these questions to students: Where or when in your life have you experienced fractions? How did you know it was a fraction?
• Place students into effective partnerships and have them answer the questions with the support of these sentence stems: "I have seen fractions in ____. I know it is a fraction because ____."
• Invite a few students to share their answers.
• Tell students that today they will be exploring the structure of a fraction and various ways to draw or visually represent a fraction. Inform them they will become experts on explaining and describing fractions because they will practice talking and writing about them multiple times using key mathematical terms. Tell students that in this lesson they will be supported by sentence starters and peer interaction.
• Read aloud this word problem: "Elisa slices a loaf of bread into 10 slices and then she eats 1 slice. How could you show the fraction of the loaf of bread that Elisa ate?" Model to students how to draw a bar model, split it into 10 equal parts and color in one part to represent the 1/10 of the loaf that she ate. Write 1/10 next to the bar model. Explain that you could also represent this fraction in a different way, such as by drawing 10 rectangles to represent the 10 slices of bread and shade one rectangle. Lastly, show how you could draw a number line from 0 to 1, with sections of 1/10, 2/10, 3/10, etc., and circle the 1/10.
• Explain that all of these visual representations or drawings of this fraction are valid. Essentially, they mean the same thing. Tell students that they will explore these ways of drawing and explaining fractions.

Guided Practice

• Hand out the Fraction Terms worksheet to students and display a teacher copy on the document camera. Tell them that they will go over the structure of a fraction and key terms in the fraction.
• Read aloud the teaching box on the top and emphasize the parts of a fraction which include two whole numbers and a line in the middle. State that the number on top of the line is called the numerator and it represents the parts being counted. Explain that the number below the line is called the denominator and it signifies the total parts that make up the whole.
• Explain that in this worksheet, they will see a shape that has been divided into equal parts, with some of the parts shaded or colored in. To the right of the shape, students are to write the numerator and the denominator to create a fraction that is represented by the drawing.
• Call for a student volunteer to be your partner as you model how to orally describe these fractions. Complete the first two fractions with your partner and use the following sentence stems to describe one of the fractions:
  • "In this fraction, the numerator is ____ because ____. The denominator is ____ because ____. The fraction can be read as ____." (e.g., "In this fraction, the numerator is 6 because 6 parts are shaded in. The denominator is 10 because there are ten total equal parts in the drawing. The fraction can be read is six-tenths.")
• Have students work with their partner to determine the fraction represented by each image and describe it to their partner.
• Review the worksheet as a whole group and call on students to explain their reasoning behind the answers using the sentence frame above. Confirm or correct students' explanations.

Group work time

• Tell students that they will now practice drawing fractions and talking about each representation 3 times with different partners.
• Place students into groups of 4 and ensure they are sitting near each other. Assign each member of the group a letter (A, B, C, or D).
• Hand out a blank piece of paper to each student and instruct them to fold it into three sections (like a pamphlet). On the document camera, model to students how you draw the fraction 2/3 in three different ways (options include bar model, shape model, circle, triangle, square, number line, part of a group). Note: draw each visual representation in each of the three sections of the divided paper.
• Model how you write a description of the drawings using the sentence frames below on the back of the paper on which you drew the 3 drawings.
  • "This visual representation shows the fraction ____. I drew ____ and ____ to show ____." (e.g., "This visual representation shows the fraction 2/3. I drew a number line from 0–1 with 3 equal parts called 1/3, 2/3, and 3/3 and circled the the 2/3 to show that this fraction is between 0 and 1." OR "This visual representation shows the fraction two-thirds. I drew three balls and colored two of them blue to show that 2/3 of the balls are blue.")
  • "I drew ____. ____ parts out of ____ total parts of ____ can be expressed as ____ (fraction). This number can be read as ____ (word form)." (e.g., "I drew a circle divided into 3 equal parts and colored in 2 of the parts. 2 parts out of 3 total parts of the pie can be expressed as 2/3. This number can be read as two-thirds.")
• Assign a fraction for each letter of the group. For example, the A's get 1/4, the B's get 3/5, the C's get 5/6, and the D's get 3/8. Instruct students to draw the same fraction in different ways and write descriptions of their drawings on the other side of the paper. Remind them to use the sentence frames as support and to always write in complete sentences.
• Have students share all of their drawings and explanations with the three members of their group. For the first sharing, they are allowed to refer to their written description for support but for the second and third explanation, they are to only look at the visual representations of the fraction.
• Circulate and offer assistance as needed. Listen in to student conversations and observe if they become stronger and clearer in their explanations by the third time.