Identify and Represent Equivalent Fractions

Description: In this lesson, a paper folding game that children play is emphasized.

Purpose: to help students make meaningful connections between what they have experienced with working with concrete objects and using paper folding and drawings to identify and make equivalent fractions.

* The following is a description of how you implement this instructional strategy for Learning Objective 1.

Learning Objective 1: Use drawings and other representations to identify equivalent fractions.

Materials:

Teacher –

Paper cube, folded and unfolded,
Description:

1.) L ink to students’ prior knowledge of identifying and representing fractions.

For Example:

How many of you love to make those folded paper blocks that ask questions like “What’s your favorite number? What is your favorite color? Who do you love?” Well, today we are going to fold paper and work on equivalent fractions.

2.) I dentify the skill students will learn.

For Example:

We have been using objects like fractions bars and circles to work on equivalent fractions. Today we are going to find out how we can use paper and pencil to show equivalent (point to word on board) fractions. Remember that equivalent fractions look different but show the same amount of a whole.

3.) P rovide rationale/meaning for identifying and representing equivalent fractions.

For Example:

If we can learn to draw our answers, it will help us when we start adding and subtracting fractions.

Purpose: to provide students with a clear model of how to identify and make equivalent fractions using drawings and other representations.

Learning Objective 1: Use paper folding and drawing to identify equivalent fractions.

* This skill should first be taught using an area model, than a measurement model, and then a sets model. After completing all phases of the instructional plan with an area model, and measuring student mastery, the concept should then be taught using a measurement model. After completing all phases of the instructional plan with a measurement model, and measuring student mastery, the concept would then be taught using a sets model.

Materials:

Teacher –

Paper
Markers, colored pencils, crayons
White or chalkboard
Description:

A. Break down the skill of identifying equivalent fractions using paper folding/drawing.

1. Identify the first fraction.

2. Compare the second fraction to the first.

Learning Objective 2: Use drawings to represent equivalent fractions.

Materials:

Teacher –

Chocolate bar
Markers, colored pencils, crayons
White or chalkboard
Description:

A. Break down the skill of representing equivalent fractions using drawings.

1.) Identify the first fraction.

2.) Draw an equivalent fraction.

3.) Compare the second fraction to the first.

Purpose: to provide students an opportunity to build their initial understanding of how to identify and represent equivalent fractions using drawings.

Materials:

* Dependent on the skill (See materials listed for the specific skill under Explicit Teacher Modeling).

Description:

Scaffolding at the representational/drawing level of instruction should occur using the same process as scaffolding instruction at the concrete level of instruction (See the description of Scaffolding Instruction for “identifying and representing equivalent fractions using concrete objects with an area model. A similar process could be used for the other learning objectives in this plan.). The steps used during Explicit Teacher Modeling should be used as structure for scaffolding your instruction.

1. Scaffold instruction using a high level of teacher direction/support (*Dependent on the needs of your students, you may want to continue to associate concrete materials with drawings at this level as described under Explicit Teacher Modeling.) *Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.

2. Scaffold instruction using a medium level of teacher direction/support (*If you associated concrete materials with drawings while scaffolding using a high level of teacher direction/support, then do not include concrete materials during this phase of scaffolding). *Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.

3. Scaffold instruction using a low level of teacher direction/support (*Students should actually draw as you prompt during this phase of Scaffolding Instruction.). *Move students to independent practice of the skill only after they demonstrate the ability to perform the skill with limited prompting from you.

Purpose: To provide students with multiple practice opportunities identify and represent equivalent fractions using drawings. A similar process could be used for the other learning objectives in this plan.

Learning Objective 1: Identify equivalent fractions using paper folding and/or drawing.

Structured Cooperative Learning/Instructional Games

Materials:

Teacher –

Overhead with transparencies of problem sheets
Bell
Students -

Set of problem sheets. Each shows a labeled drawing of a fraction and three drawings of possible equivalent fractions.
Description:

Activity:

Children will work in groups of 4 or 5 students. Each group will have a set of problem sheets numbered 1-10. The teacher will choose a problem 1-10. Each team is to look at the correspondingly numbered problem sheet and decide which of the three choices shows an equivalent fraction. After the teacher rings the bell, one member of a team will report their answer. Teams can earn points for each correct decision.

Cooperative Learning Groups Steps:

1.) Provide explicit directions for the cooperative group activity including what you will do, what students will do, and reinforce any behavioral expectations for the game.

2.) Arrange students in cooperative groups. Groups should include students of varying skill levels.

3.) Assign roles to individual group members and explain them:

a. Materials manager (gets the materials)

b. Time keeper (makes sure that group stays on task)

c. Reporter (reports group’s answer)

d. Encourager(s) (encourages each person)

4.) Distribute materials.

5.) Model one example of skill(s).

a. Look at problem.

b. Look at answer choices

c. Decide which is correct answer,

d. Make sure that the team agrees with the decision before time is called.

6.) Review/model appropriate cooperative group behaviors and expectations.

a. Agree or disagree with a teammate’s decision.

b. Listen while teams are sharing decisions.

c. Attend to classmates showing examples on board.

7.) Provide opportunity for students to ask questions.

8.) Teacher monitors and provides specific corrective feedback & positive reinforcement.

a. Circulate around the tables and check on children’s responses.

b. Make sure that each child receives feedback on his/her decision.

c. Ask each child in the class to share his/her decisions at least once either with the entire class or individually with the teacher.

Purpose: to provide students multiple opportunities to represent equivalent fractions using drawings.

Learning Objective 2: Represent equivalent fractions using drawings.

Planned Discovery Activity

Materials:

Teacher –

Sample drawing and response
Students -

A set of problem sheets. Each sheet will show a fraction and a drawing for that fraction. Some drawings will show an area model, some will show a fraction strip – measurement model, and some drawings will show a sets model. Each drawing will be numbered.
A set of numbered learning sheets
Pencil for drawing/writing
Description:

Activity:

Students will work in pairs. Each pair will have a set of problem sheets. Students will choose a numbered drawing and draw and label as many equivalent fractions as they can on the corresponding numbered learning sheet.

Planned Discovery Activity Steps:

1.) Develop Planned Discovery Activity Learning Sheet as described under Materials.

2.) Distribute the Planned Discovery Activity Learning Sheet and provide clear directions for completing the activity, including appropriate behavioral rules.

3.) Model how to complete one example for each of the three types of fractional models included on the Planned Discovery Learning Sheet (and model appropriate behaviors as needed).

4.) Provide students with appropriate materials.

5.) Monitor students as they practice, providing appropriate corrective feedback, prompting student thinking, providing positive reinforcement, and modeling or cueing as needed.

6.) At the conclusion of the activity, provide students with solutions to the Planned Discovery Activity Learning Sheet. Elicit student examples, providing students with appropriate feedback and model several examples provided by students. Emphasize why the examples represent the fractions.

7.) Review student response sheets and note special difficulties individual students may be having and/or progress they are making.

Purpose: to provide the teacher with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a way to visualize their learning/progress.

Materials:

Teacher-

Appropriate prompts if they will be oral prompts
Appropriate visual cues when prompting orally
Students:

Appropriate response sheet/curriculum slice/probe
Graph/chart
Description:

Steps for Conducting Continuous Monitoring and Charting of Student Performance:

1.) Choose whether students should be evaluated at the receptive/recognition level, the expressive level, or both.

2.) Choose appropriate criteria to indicate mastery.

3.) Provide appropriate prompts in an appropriate format (receptive/recognition or expressive) so students can respond:

* Based on the skill, your students’ learning characteristics, and your preferences, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with prompts), or oral in nature with visual cues (e.g. teacher shows several drawings/choices on overhead then prompts students to say which drawing shows the correct solution for the problem), or a combination of both (e.g. teacher shows problem and then prompts students to circle which of several drawings shows the correction solution).

4.) Provide students with the materials to complete each task.

5.) Provide directions on how to complete each task.

6.) Conduct evaluation.

7.) Count corrects and incorrects (you and/or students can do this dependent on type of curriculum slice/probe used).

8.) You and/or the students will plot their responses on a suitable chart. A goal line that represents proficiency should be visible on each student’s chart. For representational level of understanding this should be 100%. for 8 –10 trials.

9.) Talk with children about their progress as it relates to.the goal line and their previous performance. Prompt them to self evaluate.

10.) Evaluate whether student(s) is ready to move to the next level of understanding or has mastered the skill by demonstrating 100% accuracy for 8-10 trials over 2-3 days.

11.) Determine whether you need to alter or modify your instruction based on student performance.

Flexible Math Interview

Purpose: to provide the teacher with additional diagnostic information in order to check student understanding, and plan and/or modify instruction accordingly.

Materials:

Teacher –

5 pictures for student to color in equivalent fractions
Students -

Paper, pencils
Description:

With individual students or in small groups, the teacher will have students draw solutions to given problems. The teacher will ask students to explain how their drawings show the solution to the problem. The teacher should note errors or misconceptions while the student is “teaching”, but the teacher should not stop the student for correction purposes. By having the student complete the entire explanation, the teacher will gain a better understanding of the student’s thinking. The teacher confers with students regarding specific errors or misconceptions afterwards.

Purpose: to provide periodic student practice activities and teacher directed review of this skill after students have mastered it.

1. Partner Drills

Materials:

Flash Cards showing two drawings of fractions, answers (equivalent/non-equivalent on back of card)
Description:

Students can do this individually or in pairs. The student will look at a flashcard and identify the two pictures as showing equivalent or non-equivalent fractions. Students can check themselves by turning the card over.

2. Math Center

Materials:

Sets of numbered, laminated cards showing drawings of fractions using various models (set, area, measurement). Each card is vertically divided and has the drawing on one side and a space for student drawing on the other
Marker for drawing
Answers drawn on answer sheet in envelope
Description:

Students will choose a card and draw one or more equivalent fractions. Answers can be checked using an answer sheet.