and Subtracting Fractions with Mixed Numbers: Representational
Teaching Plans on this topic: Concrete, Abstract
2: Practice Strategies
Purpose: to provide students multiple opportunities to practice choosing drawings that represent solutions to equations involving addition of fractions with mixed numbers.
Learning Objective 1: Add fractions with mixed numbers by drawing pictures that represent concrete materials.
Instructional Game/ Board Game
- Develop a master set of prompts for cards: Each prompt consists of an equation involving addition of fractions with mixed numbers and three drawings depicting possible solutions. Each example is designed to fit one side of a 4 x 5 note-card. A master set of “drawing solutions” is also developed that includes the correct solution for each example. Each “correct” drawing should also fit one side of a 4 x 5 note-card.
- Each prompt should be numbered so you can determine which prompts individual students respond to and evaluate their performance/understanding (*students write number of card they respond to on a sheet of paper as they play the game). This “master” serves as an “Key” for evaluating student responses.
- Multiple decks of cards with prompts on one side and answers on the other side. 4x5 note-cards can be used and prompts and corresponding answers can be glued/pasted on opposite sides of a card. Cards can be laminated for protection.
- Make copies of the masters described above to make as many decks as needed for your class.
- Appropriate number of generic game boards (e.g. manila folders or tag-board with multiple spaces that have “start” and “finish” spaces.
- Provide enough spaces so all students playing the game have multiple response opportunities).
- Appropriate number of dice or spinners and game pieces for students.
- Each group playing game needs a game board, dice or spinner, appropriate number of game pieces, and one deck of response cards.
- Each student needs a sheet of notebook paper to record the card number they responded to and whether they got it correct or not.
Students play in small groups. Each player has a game piece to move along the path of the game board. Students roll a die or spin a spinner. To move, students must pull a card from the deck and choose the appropriate drawing that solves the given equation. The card is turned over to reveal the answer. The student who gets to the finish space wins. To include some “suspense” to the game, several cards in the deck could be “bonus” cards where students move additional spaces if they respond correctly. Several spaces on the game board could also direct students to “move forward” or “move back” a certain number of spaces if landed on. Each card in the deck is numbered and students record the number card they respond to as well as whether they answered it correctly or not on a sheet of notebook paper. The teacher monitors students’ social and academic behavior as they work, providing positive reinforcement, specific corrective feedback, and answering questions as appropriate. Students turn in their individual response sheets at the end of the game. The teacher reviews individual response sheets using the master key to evaluate individual student understanding.
Instructional Game Steps:
1.) Introduce game.
2.) Distribute materials.
3.) Provide directions for game, what you will do, what students will do, and reinforce any behavioral expectations for the game.
4.) Provide time for students to ask questions.
5.) Model how to respond to the card prompts (model the skill within the context of the game).
6.) Provide time for students to ask questions about how to respond.
7.) Model how students can keep track of their responses.
8.) Play one practice round so students can apply what you have modeled. Provide specific feedback/answer any additional questions as needed.
9.) Monitor students as they practice by circulating the room, providing ample amounts of positive reinforcement as students play, providing specific corrective feedback/ re-modeling skill as needed.
10.) Play game.
11.) Encourage students to review their individual response sheets, write the total number of “correct” responses under the “C” (Correct) column and do the same for the “H” (Help) column.
12.) Review individual student response sheets to determine level of understanding/proficiency and to determine whether additional modeling from you is needed.
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Learning Objective 2: Use the FASTDRAW Strategy to solve story problems and equations that involve addition of fractions with mixed numbers by drawing solutions.
Structured Peer Tutoring
Purpose: to provide students multiple opportunities to practice solving story problems involving addition of fractions with mixed numbers.
- Develop a master “Learning Sheet”: Each “learning sheet” has multiple story problems with the prompts “FAST” and “DRAW” beneath each story problem. Appropriate space is provided under “FAST” for student to write the equation and appropriate space is provided under “DRAW” for students to draw their solutions and write the answer. (Students highlight important information and set up the equation for “FAST” while they draw the solution and write the answer for “DRAW.”) Advanced students can assist making up story problems that reflect addition of fractions with mixed numbers.
- A master “Answer Key” for the learning sheet.
- Make appropriate number of copies for the learning sheet and answer key. These can be laminated and students can use dry-erase pens to save copying time/expense if you use this activity multiple times.
- FASTDRAW Strategy poster or master cue sheet (Lists the steps of the FASTDRAW Strategy. An example of how to apply the strategy to story problems involving addition of fractions with mixed numbers can be included as a cue for students – show story problem with important information highlighted appropriately, the equation written, drawings, and the answer written.)
- Each student receives one learning sheet.
- Each student pair receives one answer key.
- Each student has one sheet of notebook paper for recording points.
- Pencils for writing and drawing.
- FASTDRAW Strategy Cue sheets for each student
Students work in pairs by responding to learning sheets. The learning sheet has multiple story problems that involve adding fractions with mixed numbers. For each problem, students have to do two things. First, they must use FAST to find the important information in the story problem and set up the equation. Second, they must use DRAW to solve the equation and answer the story problem. The period is divided into two equal time frames. One student in each pair is the “coach” for the first period while the other student is the “player.” Students switch roles for the second time period. The “coach” reads the story problem and prompts the “player” to use FAST to find/highlight the important information and set up an equation. Then, the coach prompts the player to use DRAW to solve the equation and answer the story problem. The coach checks the player’s responses using the answer key after the player completes each example, providing positive reinforcement and specific corrective feedback. The coach can also award points based on student responding - “2 pts.” for getting each part of the example correct (FAST & DRAW); “1 pt.” for re-working the example based on feedback and solving it correctly. Tallies can be made on a sheet of notebook paper that serves as a scoring sheet. The teacher signals when students switch roles and monitors student social and academic behavior as they work, providing positive reinforcement, specific corrective feedback, and answering questions as appropriate. Students turn in their individual learning sheets and point sheets at the end of the activity. The teacher reviews individual student learning sheets and point sheets to evaluate their 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. highlighting
important information; setting up equation, drawing solution,
4) Divide the practice period into two equal
segments of time. One student in each pair will be the player
respond to the questions/prompts given by the coach. The other
student will be the coach and will say each question or prompt
on the learning sheet. The coach will check the answer key,
and provide feedback regarding the player’s response (e.g.
positive verbal reinforcement for accurate responses and corrective
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.
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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