Adding and Subtracting Fractions with Mixed Numbers: Concrete Level

More Teaching Plans on this topic: Representational, Abstract

PHASE 2: Practice Strategies

Receptive/Recognition Level

Purpose: to provide students multiple opportunities to practice selecting equations involving addition of fractions with mixed numbers that match concrete representations.

Learning Objective 3: Solving equations involving addition of fractions with mixed numbers using concrete materials.

Structured Peer Tutoring

Materials:

Teacher –

• Appropriate number of concrete materials (area model) for each example.
• A set of three cards for each concrete example. Each card in the set has written on it a different equation involving addition of fractions with mixed numbers (one of which is the correct solution for the concrete example.) The equation that matches the concrete example has a star or some other cue on the back to designate it as the correct solution.
• Master copy of answer key for examples.
• Timer of clock for keeping time.

Students –

• Each student in each pair has a sheet of notebook paper to write their responses and
  a sheet of notebook paper to record their partner’s points
• Pencils for writing
  
  

Description:

Activity:

Students work in pairs. One student is the “coach” for half of the period and one student is the “player.” Students switch roles for the second half of the period. Each student has a response sheet where they write their responses. Each student pair moves to each numbered example of concrete objects. The player examines the concrete objects and selects the card with the appropriate equation written on it, writing the equation they choose on their response sheet next to the appropriate number. The coach checks the player’s response by checking the back of the card to see which one has a star written. The coach awards two points for correct responses. If the player responds incorrectly, the coach provides appropriate feedback. Tallies can be written on a separate sheet of notebook paper or in the margin beside each prompt. The teacher signals student pairs when it is time for students to switch roles. As students practice, the teacher circulates the room monitoring student behavior, providing specific corrective feedback, providing positive reinforcement, and prompting student thinking. Students total their points and turn in both their individual learning sheets and point sheets. The teacher reviews individual student learning sheets and point sheets to evaluate student understanding.

Structured Peer Tutoring Steps:

1) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible).

2) Review directions for completing structured peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).

3) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both what the coach does (e.g. checks answers by turning cards over; provide corrective feedback; record points) and how the player responds (e.g. examining the concrete example; choosing the card with the matching equation; writing the equation on their response sheet).

4) Divide the practice period into two equal segments of time. One student in each pair will be the player and will respond to the examples with concrete materials. The other student will be the coach. For accurate responses, the coach awards 2 pts. For inaccurate responses, the coach provides appropriate corrective feedback

5) Provide time for student questions.

6.) Signal students to begin.

7) Signal students when it is time to switch roles.

8) Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.

9) Students turn in response sheets and point totals.

10) Teacher reviews response sheets/point totals to evaluate student understanding.

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Expressive Level

Purpose: to provide students multiple opportunities to practice combining sets of concrete materials that represent fractions with mixed numbers (Structured Peer Tutoring) or to solve equations involving addition of fractions with mixed numbers using concrete materials (Structured Cooperative Learning Groups).

Learning Objective 1: Combine two sets of concrete materials that represent fractions with mixed numbers.

Structured Peer Tutoring

Materials:

Teacher –

• Appropriate number of concrete materials (area model) for each student pair.
• Master copy of a learning sheet with multiple prompts: Each prompt 1.) identifies what sets of concrete materials should be combined (e.g. “two circles and three ‘one-fourth’ pieces plus one circle and one ‘one fourth’ piece.”) and, 2.) includes the statement “Say the total.”
• Master copy of answer key for learning sheet: For each prompt the answer key identifies what the concrete materials should look like when combined –e.g. “four whole circles and no ‘one-fourth’ pieces.” (*Pictures could also be drawn to cue students who have reading problems.
• Timer or clock for keeping time.

Students –

• Each student in each pair has a learning sheet.
• Each student pair has an appropriate set of concrete materials.
• Each student pair has copy of answer key for coach to check player’s responses.
• Pencils for writing
  

Description:

Activity:

Students work in pairs. One student is the “coach” for half of the period and one student is the “player.” Students switch roles for the second half of the period. Each student has a learning sheet with appropriate prompts (See description of learning sheet under “Materials.”) The coach gives the prompts from the learning sheet and the student uses concrete objects to respond. The coach checks the player’s responses by examining the concrete objects and by consulting the answer key provided to each student pair. The coach awards two points for correct responses. If the player responds incorrectly, the coach provides appropriate feedback and then the player attempts the same set of prompts again. The coach awards the player one point if their second response is accurate. Tallies can be written on a separate sheet of notebook paper or in the margin beside each prompt. The teacher signals student pairs when it is time for students to switch roles. As students practice, the teacher circulates the room monitoring student behavior, providing specific corrective feedback, providing positive reinforcement, and prompting student thinking. Students total their points and turn in both their individual learning sheets and point sheets. The teacher reviews individual student learning sheets and point sheets to evaluate student understanding.

Structured Peer Tutoring Steps:

1) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible)

2) Review directions for completing structured peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).

3) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both what the coach does (e.g. reads the questions/prompts on the learning sheet; checks answers using answer key; provide corrective feedback; record points) and how the player responds (e.g. combining concrete materials; saying what the total represents).

4.) Divide the practice period into two equal segments of time. One student in each pair will be the player and will respond to the questions/prompts given by the coach, using concrete materials. The other student will be the coach and will say each question or prompt on the learning sheet. The coach will then write the response in the appropriate space on the player’s learning sheet, check the answer key, and provide feedback regarding the player’s response (e.g. positive verbal reinforcement for accurate responses and corrective feedback for inaccurate responses.) For inaccurate responses, the coach provides feedback and the player attempts the question a second time. The first response is crossed out and the second response is recorded. The coach records two points for correct responses on the first attempt and one point for correct responses on a second attempt.

5) Provide time for student questions.

6) Signal students to begin.

7) Signal students when it is time to switch roles.

8) Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.

9) Students turn in learning sheets and point totals.

10) Teacher reviews learning sheets/point totals to evaluate student understanding.

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