Unit: Fractions and Measurement

Lesson 3: Equivalent Fractions

Manipulatives

Grade: 3

MST State Standards:

• Standard 3: Mathematics

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

• Use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances.
• Use concrete materials to model numbers and number relationships for whole numbers and common fractions, including decimal fractions.

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

o Construct tables, charts, and graphs to display and analyze real-world data.

o Use multiple representations (simulations, manipulative materials, pictures, and diagrams) as tools to explain the operation of everyday procedures.

Objectives: SWBA to…

• Find equivalent fractions.
• Make use of fraction strips.

Aim:

• How can we find equivalent fractions?

Materials:

• Piece of paper to be folded
• Marker
• Practice worksheet
• Smartboard/chalkboard
• Set of fraction strips for each student
• Large fraction strips for the teacher
• Student set of rulers
• Set of stacking blocks representing fractions

Assessment:

• Students will be assessed during the lesson as the teacher asks students to compare fractions on their own and find equivalent pairs. The teacher will view the students’ understanding while walking around to ensure students are correctly lining up the fraction strips.
• Students will be assessed on their work in class when they compile a class list, and on the completion on their practice worksheet.

Procedure:

1. To begin, the teacher will begin with an introductory demonstration to equivalent fractions. The teacher will take a piece of paper, fold it in half, and then color one half with a marker. He or she will ask students, “What fraction tells how much is colored?” The correct answer is ½.

2. The teacher will then fold the piece of paper in half again. “How many equal parts are now? What fraction tells how many are colored?” The correct fraction is ²/₄. ½ and ²/₄ are called equivalent fractions because they name the same amount of colored area of the paper.

3. Following the demonstration, the teacher gave each student an envelope of fraction strips. As the students are able to use their own fraction strips, the teacher will demonstrate with the enlarged fraction strips on the front board. Students will be asked to look at two fraction strips (ie. ½ and ¹/₆) and to use their ruler to find a common line.

½

½

^1/6

^1/6

^1/6

^1/6

^1/6

^1/6

4. Using the above fraction strips students should see that ½ is equivalent to ³/₆. This will continue until all fraction strips (up to twelfths) have been compared to a fraction at least once. During this time the teacher will ask students, “Can you find any equivalent fractions to share with the class?”

The following is my modified procedure while teaching:

5. Students did not clearly understand the fraction strips. Therefore, a new manipulative was used, which was the fractional stacking blocks.

6. The teacher will explain the concept of the stacks, that each stack is broken into a different number of pieces. The teacher will start with the most basic stacks such as ½ and ¹/₄. The teacher will then move onto comparing different fractions. While doing so, the students will count out loud as the teacher stacks one block at a time for determining an equivalent.

7. Once students have an understanding, the teacher will ask students to name examples of equivalent fractions and will then write them to make a list on the board.

8. After the lesson, students will have an opportunity to work independently on a worksheet for practice.

Key Questions:

• What is the fraction for the colored part?
• How are [these] fractions alike?
• What is equivalent fraction?

Adaptations for Special Need & enrichment differentiation:

• Many different manipulatives were used during instruction to accommodate many learning styles among the students.
• Each student being able to use fractions strips for themselves at their desk is very helpful for them. They are learning on their own by exploring.
• Having each student count out loud with the stacking blocks helps students to better grasp the concept rather than just watching and listening to the teacher.

Follow-up Assignments

• Students will have a worksheet for practicing equivalent fractions.

Reflection and Revision:

• While teaching this lesson I found that I needed to better accommodate my students. When we had first used just the fraction strips they did not understand which fractions were equivalent to one another. I then realized that I needed to change my method of instruction during the lesson. I then tried explaining equivalent fractions using the stacking blocks. This method seemed to work best for the students and they were able to understand.