The Division Process: Division with Remainders: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

Description:  Meaningful contexts will continue to be used to teach the division process in the form of story situations that have relevance for 9-11 year old students. It is important always to provide story situations that have relevance to your students given their age, cultural backgrounds, and interests

Build Meaningful Student Connections

Purpose: to help students build meaningful connections between what they know about drawing solutions to division problems and finding solutions without the use of drawings.

Materials:

Teacher -

• A visual display of the FASTDRAW Strategy.
• A visual display of the written learning objective: : “Use FASTDRAW to solve division story problems and division equations without drawing pictures.” (*Highlight the phrase “without drawing pictures” to make it stand out.)

Description:

1) L ink to students’ prior knowledge of using FASTDRAW to solve division story problems and to draw solutions to division equations.

For Example:

You have learned to solve division story problems using a strategy. Who remembers the name of the strategy that helps us to solve division story problems? (Elicit the response, “FASTDRAW.”) Yes, FASTDRAW is a strategy that helps us to solve division story problems. (Hold up a display of the FASTDRAW strategy.) What does the “FAST” in FASTDRAW help us to do? (Point to “FAST” and elicit the response, “find the important information in the story problem and set up a division equation.) That’ correct, “FAST” helps us find the important information in the story problem and it also helps us to set up a division equation. What does the “DRAW” in “FASTDRAW” help us to do? (Point to “DRAW” and elicit the response, “it helps us solve the division equation by drawing pictures.”) Excellent! The “DRAW” in the “FASTDRAW” Strategy helps us to solve division equations by drawing pictures

2) I dentify the skill students will learn.

For Example:

For the next few days, we’re going to learn how to use FASTDRAW to solve division story problems and division equations without drawing pictures. (Display and point to the written objective: “Use FASTDRAW to solve division story problems and division equations without drawing pictures.”) What are we going learn to do? (Point to the written objective and elicit the response, “use FASTDRAW to solve division story problems and division equations without drawing pictures.”) Good.

3) P rovide rationale/meaning for the division process; division with remainders.

For Example:

Learning to solve division problems without drawing pictures will come in handy when you have to divide in a hurry. For example, at recess, you and your friends may want to play a game where you have to divide up into teams that have the same number of players on each team. Because you only have a limited amount of time for recess, you want to determine how many players on a team quickly so you can have as much time to play as possible. Being able to divide without drawing pictures will help you start playing faster.

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Provide Explicit Teacher Modeling

Purpose: to provide students a clear teacher model of how to divide (with and without remainders).

Materials:

Teacher -

• A visual display of the FASTDRAW Strategy.
• Appropriate story problems written so that all students can see them. *Color-coding can be faded at this point in instruction, but tell students that number phrases will no longer be color-coded.
• A visual platform to write where all students can see your writing.
• Colored markers/pens/chalk

Students -

• FASTDRAW Strategy Cue sheet.

Description:

A. Break down the skill of solving division story problems/equations without the use of concrete objects or drawings.

*The same steps described in the representational level teaching plan for implementing the FASTDRAW Strategy can be used for implementing the strategy at the abstract level. The only difference is that you will teach students to “answer” the equation (“A” step in DRAW) without drawing pictures.

1) Introduce story problem.

2) Read the story problem aloud and then have students read it with you.

3) Find the important information in the story problem and set up an equation using the steps “FAST” from the “FASTDRAW” Strategy.

a. Find what you are solving for.
b. Ask yourself, what is the important information (circle it).
c. Set up the equation.
d. Tie down the sign.

4) Teach solving a division equation using the steps “DRAW” from the “FASTDRAW” strategy.

a. Determine the sign.
b. Read the problem.
c. Answer (without drawing).

The video clip models the "Answer" step by using repeated addition. See the detailed teaching plan to learn about two additional methods for "answering"/solving the division problem.

d. Write the answer.

5) Model how to solve the story problem by relating the “answer” to the division equation back to the story problem context.

6) Model how to solve division equations by repeating the steps in #4 and #5 at least two or three more times with different division equations.

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Scaffold Instruction

Purpose: to provide students the opportunity to build their initial understanding of how to divide without concrete materials or drawings, and to provide you the opportunity to evaluate your students’ level of understanding after you have initially modeled this skill.

Materials:

• Dependent on the skill you are Scaffolding Instruction for (See the materials listed for the specific skill you want to scaffold under Explicit Teacher Modeling).

Description:

*Scaffolding at the abstract level of instruction should occur using the same process as scaffolding instruction at the concrete and representational/drawing levels of instruction (See the description of Scaffolding Instruction in the Concrete or Representational Level Instructional Plans for this math concept.). The steps listed for each skill during Explicit Teacher Modeling at the Abstract Level should be used as structure for scaffolding your instruction.

A. Scaffold instruction using a high level of teacher direction/support. (Dependent on the needs of your students, you may want to continue to associate drawings to the abstract level division process 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.)

B. Scaffold instruction using a medium level of teacher direction/support. (If you associated drawings with the abstract process for division while scaffolding using a high level of teacher direction/support, then do not include drawings 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.)

C. Scaffold instruction using a low level of teacher direction/support. (Students should actually divide as you prompt them 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.)

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Videos

Learning Objective 1: view  Clip 1

Solves division story problem using FASTDRAW strategy

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