Adding and Subtracting Fractions with Mixed Numbers: Representational Level

More Teaching Plans on this topic: Concrete, Abstract

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context

Description: Continue to link adding fractions with mixed numbers by drawing to meaningful contexts such as the Pizza Party example described in the Concrete Level Instructional Plan. This is especially important as you teach students to solve story problems by drawing using the FASTDRAW Strategy. Additionally, make explicit links to concrete experiences when teaching the drawing process.

Build Meaningful Student Connections

Purpose: to assist students to build meaningful connections between what they know about adding fractions with mixed numbers using concrete materials to adding fractions with mixed numbers by drawing.

Learning Objective 1: Add fractions with mixed numbers by drawing pictures that represent concrete materials

Materials:

Teacher –

• Appropriate concrete materials to solve a pre-determined equation involving addition of fractions with mixed numbers.
• A platform for visually displaying the equation and concrete materials so all students can see.
• The written objective: “add fractions with mixed numbers by drawing” (*Highlight “by drawing” to cue students.).
• Chalkboard/dry-erase board/overhead to show examples of drawing solutions to other types of problems based on student suggestions.

Description:

1) L ink to students’ prior knowledge of adding fractions with mixed numbers using concrete materials.

For Example:

We’ve learned to add fractions that have mixed numbers using concrete materials. Let’s review this process. (Display an appropriate equation and prompt students to direct you as you solve the equation together using concrete materials.)

2) I dentify the skill students will learn: Adding fractions with mixed numbers by drawing pictures that represent concrete materials.

For Example:

Today, we’re going to learn how to solve equations where we need to add fractions with mixed numbers by drawing pictures rather than using concrete materials. (Display the written objective, “add fractions with mixed numbers by drawing.”) What are we going to learn today? (Point to the written objective and elicit the response, “add fractions with mixed numbers by drawing.”) Excellent! We are going to learn how to add fractions with mixed numbers by drawing pictures instead of using concrete materials.

3) P rovide rationale/meaning for adding fractions with mixed numbers by drawing pictures that represent concrete materials.

For Example:

You may already know of ways to draw pictures to solve other kinds of problems. (Elicit student knowledge about drawing pictures to solve other kinds of problems – e.g. addition, subtraction, multiplication, and division of whole numbers; drawing circles/rectangles with partitions to represent fractions; etc.) Being able to draw pictures to solve a problem can be very helpful when you don’t have concrete materials available to you. Drawing is kind of like using concrete materials except that you draw pictures that represent the concrete objects instead of using the concrete objects themselves. It provides you a faster way to solve these kinds of problems. Since you already know how to use concrete materials to solve problems that involve addition of fractions with mixed numbers, drawing solutions to these problems is a natural next step for you.

Provide Explicit Teacher Modeling

Purpose: to provide students a clear teacher model of drawing pictures to solve story problems and equations involving addition of fractions with mixed numbers.

Learning Objective 1: Add fractions with mixed numbers by drawing pictures that represent concrete materials.

Materials:

Teacher –

• A visual medium for writing and drawing (e.g. chalkboard, dry-erase board, chart paper.)
• Markers/pens for writing and drawing.
• Prepared equations that represent addition of fractions with mixed numbers. Color code whole numbers and fractions consistent with color-coding used to identify these concepts in story problems/equations used at the concrete level of understanding
  (e.g. 3 1/3 + 1 2/3 = __.)

Description:

A. Break down the skill of adding fractions with mixed numbers by drawing pictures that represent concrete materials.

1) Discover the sign/operation

2) Read the problem and identify the wholes and fractional parts represented by the problem.

3) Draw the wholes and fractional parts.

4) Combine the “wholes” by counting them.

5) Combine the fractional parts into “wholes” by circling them. - View Video

6) Add the pictures that represent the “wholes.”

7) Add the pictures of the fractional part that remains and say what they represent.

8) Say what the total/sum means and write the answer.

Learning Objective 2: Use the FASTDRAW Strategy to solve story problems and equations that involve addition of fractions with mixed numbers by drawing solutions.

Materials:

Teacher –

• A visual display of the FASTDRAW and DRAW Strategy.

F ind what you are solving for.
A sk yourself, “What is the important information?”
S et up the equation.
T ie down the sign.
D iscover the sign.
R ead the problem.
A nswer the problem, or draw and check.
W rite the answer.

• A visual medium for writing and drawing (e.g. chalkboard, dry-erase board, chart paper.)
• Markers/pens for writing and drawing.
• Prepared story problems and/or equations that represent addition of fractions with mixed numbers. Color code whole numbers and fractions consistent with color-coding used to identify these concepts in story problems/equations used at the concrete level of understanding (e.g. 3 1/3 + 1 2/3 = __.)

A. Break down the skill of using the FASTDRAW Strategy to solve story problems and equations that involve addition of fractions with mixed numbers by drawing solutions.

1) Introduce story problem.

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

3) Teach finding the important information in the story problem and setting 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 drawing solutions using the steps “DRAW” from the “FASTDRAW” strategy.

a. Determine the sign.

b. Read the problem.

c. Answer, or draw and check.

d. Write the answer.

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

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

Scaffold Instruction

Purpose: to provide students the opportunity to build their initial understanding of how to add fractions with mixed numbers by drawing, 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 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, “combining sets of concrete materials that represent fractions with mixed numbers,” in the Concrete Level Instructional Plan.). The steps used during Explicit Teacher Modeling should be used as structure for scaffolding your instruction.

*To see a description of scaffolding instruction for the FASTDRAW Strategy, see the Representational/Drawing Level instructional plan for the math concept, “Division Process and Division with Remainders/SOL 5.5.

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 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.

B. 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 demonstrate the ability to respond accurately to your prompts.

C. 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.

Videos

Learning Objective 1: view  Clip 1
Add fractions with mixed numbers by drawing pictures that represent concrete materials.