Identify and Write Fractions: Representational Level

More Teaching Plans on this topic: Concrete

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context

The same variety of authentic contexts used at the concrete level of instruction are continued at the representational level. Explicitly link authentic contexts taught at the concrete level to drawing experiences.

Purpose: to assist students to make meaningful connections between what they know about representing fractional parts with concrete materials to drawing pictures that represent the concrete materials they have used.

Learning Objective 1: Draw representations of fractional parts and write fractions.

Materials:

Teacher -

Concrete materials that represent Area & Measurement Model and which students previously used during concrete level instruction
A visual that depicts the skill students will learn
Candy bar
Chalkboard/dry-erase board/overhead
Chalk/markers/pens for writing
Description:

1.) L ink to student’s prior knowledge & experiences.

Remind students they know how to show wholes and parts of wholes using a variety of materials.
Use concrete materials students have previously used and which represent the Area & Measurement Models to model this.
Have students name the fractional parts as you demonstrate several using each type of concrete material.
2.) I dentify the skill students will learn.

For Example:

During the last few days you have learned to represent parts and wholes using different kinds of materials, and you’ve learned the special names we have for certain parts. Today we are going to learn how to draw pictures to represent parts and wholes as well as the special names for certain parts.

Provide some type of visual that represents the words you are saying (e.g. a short written phrase or two that reflects the learning objective, or a picture that represents the learning objective.)
3.) P rovide rationale/meaning for learning the skill.

For Example:

We’ve already talked about why learning how to break things into equal parts is a really important thing to be able to do. Like we talked about before, you may have something that you want to share with one or more friends. It is helpful to know how to break them into equal parts so each friend gets the same amount. Remember our candy bar example? Maybe you have a candy bar and you want to share it with a friend. Knowing how to break it into equal parts will allow you to share it with your friend.

We also brainstormed some ideas about other objects we might want to break into equal parts. Who remembers some examples?

Prompt students to remember some of the objects they previously listed (e.g. pizza, sets of cards, etc.)
Well, by learning to draw parts and wholes, we will have a way to decide how to break things into parts before we actually do it. Sometimes we may break something into parts and not get the parts equal. Drawing a picture first helps me keep this from happening. I can look at the picture I drew and see where to break the object so that I get equal parts. Let me show you what I mean…

Use a candy bar as an example. Draw a rectangle that represents a candy bar having similar dimensions. Say you want to cut it into two equal pieces. Draw a line that separates the rectangle into two equal pieces, then demonstrate how you can use the picture to help you decide where to break the candy bar into two equal pieces.

Purpose: to provide students a teacher model who clearly demonstrates how to draw fractional parts, how to write fractions using numbers and symbols, and the meaning of the numbers and symbols in a written fraction.

Learning Objective 1: Draw representations of fractional parts and write fractions.

* The Area and Measurement Models are used to teach drawing fractional parts. The Sets Model is not included at the representational/drawing level of instruction because drawing fractional parts with sets of objects can be somewhat cumbersome for children. After students have learned to draw fractional parts using Area and/or Measurement Models you may choose to teach students how to pick out pictures of objects already grouped into sets that represent fractional parts.

Materials:

Teacher –

Appropriate concrete materials that represent the Area and Measurement Models
A visible platform for showing the concrete materials
A visible platform to draw fractional parts, to write the language of fractional parts, and to write fractions
Chalk, overhead pens, dry-erase markers for drawing and writing
Description:

A. Break down the skill drawing fractional parts and writing fractions into learnable parts.

1.) Remodel representing fraction using concrete materials that represent the Area and Measurement Models.

2.) Draw pictures that represent the fraction using the Area and Measurement Models.

3.) Write the fractions (relate to concrete materials, drawings, and language).

Purpose: to provide students a teacher supported transition from seeing and hearing the teacher demonstrate/model drawing fractional parts and writing fractions to performing the skills independently. It also provides the teacher opportunities to check student understanding so she/he can provide more modeling or cueing if needed before students practice independently.

Learning Objective 1: Draw representations of fractional parts and write fractions.

Materials:

Teacher –

Concrete materials that represent Area and Measurement Models
A visible platform for drawing fractional parts and for writing fractions
Chalk, overhead pens, dry-erase marker for drawing and writing fractions
Students –

Paper and pencil for drawing fractional parts and writing fractions
Description:

1.) Scaffold Using a High Level of Teacher Direction/Support

a. Choose one or two places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction. (Choices are shown in red).

*Follow this process for at least two ways of drawing fractional parts (e.g. circles and rectangles/bars). As students begin drawing fractional parts independently, they can choose which way is easiest or most efficient for them. Also, include each of the fractional parts you modeled during this phase of scaffolding (e.g. ‘one-half,’ ‘one-fourth,’ & ‘one-eighth.’)

For Example:

Remind students of the pizza or dog leash story situation used from Explicit Teacher Modeling at the concrete level.

Decide which “type” of drawing you will use (e.g. circles, rectangles/bars, etc.) and relate your choice to actual concrete material. Also relate why you chose this type of drawing.

Think of what the concrete material looks like – “Hmm, ‘one-half’ can be represented by a circle with a ‘one-half’ piece on top.

Think of what the concrete material looks like – “Hmm, what does ‘one-half’ look like with circle pieces? (Elicit the response, ‘one-half’ can be represented by a circle with a ‘one-half’ piece on top.) Great. ‘One-half can be represented by a circle with a ‘one-half’ piece on top. Thanks for helping me out.”

Think of how to draw the “part” – “How can I draw the ‘part’ or ‘one-half’? Oh yea, I can draw a line first that separates the whole circle into two equal parts.”
Draw the line(s) that represent the fractional part. – “Now I have two equal parts, but what I need to represent is one of the two equal parts, or ‘one-half’. How can I do that? Let’s see, I know with my circle pieces, the ‘one-half’ piece is a darker color than the circle piece. Ok, I can shade in one of the parts.”
Shade in the appropriate “part” that represents the fractional part.

Teacher asks questions/Teacher answers questions about the drawing and it relationship to the concrete material and the fractional part.
“Do I have my whole represented? (Elicit the response, “Yes, you drew a circle that represents the whole circle when we use circle pieces.”) That’s right, the circle I drew represents a ‘whole’ circle piece.”
Do I have the part represented? – “Yes, I drew a line to separate the whole circle into two equal parts and then I shaded in one part.”
Does my drawing represent ‘one-half’? – “Yes, I have a whole circle cut into two equal parts and one part is shaded. The part that is shaded represents ‘one-half’ of the whole circle.”
a. Maintain high level of teacher direction/support for another example if students demonstrate misunderstanding/non-understanding; move to a medium level of teacher direction/support if students respond appropriately to the selected questions/prompts.

2.) Scaffold Using a Medium Level of Teacher Direction/Support

a. Choose several more places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction.

For Example:

Remind students of the pizza or dog leash story situation used from Explicit Teacher Modeling at the concrete level.

Decide which “type” of drawing you will use (e.g. circles, rectangles/bars, etc.) and relate your choice to actual concrete material. Also relate why you chose this type of drawing.
Think of what the concrete material looks like – “Hmm, what does ‘one-half’ look like with circle pieces? (Elicit the response, ‘one-half’ can be represented by a circle with a ‘one-half’ piece on top.) Great. ‘One-half can be represented by a circle with a ‘one-half’ piece on top. Thanks for helping me out.”
Think of how to draw the “whole” piece and draw it – “Now, how can I draw the ‘whole’? (Elicit the response, “you can draw it by drawing a circle.”) Excellent thinking. I can represent the whole by drawing a circle. I’ll do that now.”
Think of how to draw the “part” – “How can I draw the ‘part’ or ‘one-half’? Oh yea, I can draw a line first that separates the whole circle into two equal parts.”
Draw the line(s) that represent the fractional part. – “Now I have two equal parts, but what I need to represent is one of the two equal parts, or ‘one-half’. How can I do that? (Elicit the response, “you can shade in one of the parts.”) That’s correct. Why does shading in one of the two equal parts represent ‘one-half’? (Elicit the response, “because the ‘one-half’ piece is a darker color and it is one of two equal parts of a whole circle.”)”
Shade in the appropriate “part” that represents the fractional part.
Teacher asks questions/Teacher answers questions about the drawing and it relationship to the concrete material and the fractional part.
“Do I have my whole represented? (Elicit the response, “Yes, you drew a circle that represents the whole circle when we use circle pieces.”) That’s right, the circle I drew represents a ‘whole’ circle piece.”
“Do I have the part represented? (Elicit the response, “Yes, you drew a line to separate the whole circle into two equal parts and then you shaded in one part.”) Great! I drew a line first that cut the whole circle into two equal parts and then I shaded one of the parts.”
Does my drawing represent ‘one-half’? – “Yes, I have a whole circle cut into two equal parts and one part is shaded. The part that is shaded represents ‘one-half’ of the whole circle.”
b. Maintain medium level of teacher direction/support for another example if students demonstrate misunderstanding/non-understanding; move to a low level of teacher direction/support if students respond appropriately to the selected questions/prompts.

3.) Scaffold Using a Low Level of Teacher Direction/Support

a. When students demonstrate increased competence, do not model the process. Ask students questions and encourage them to provide all the responses. Direct students to replicate the process at their desks as you work together.

For Example:

Remind students of the pizza or dog leash story situation used from Explicit Teacher Modeling at the concrete level. (e.g. What is the story we are acting out?)
Model deciding which “type” of drawing you will use (e.g. circles, rectangles/bars, etc.) and relate your choice to actual concrete materials. Also relate why you chose this type of drawing. - “Alright, you’ve helped me draw fractional parts several times. You are going to draw one with me this time. What kind of drawing should we use for this fractional part? (Elicit responses and choose one to do.) Why might this be a good one to use? (Elicit several student ideas). Great reasons. Let’s get started.”
Think of what the concrete material looks like – “Hmm, what does ‘one-half’ look like with circle pieces? (Elicit the response, ‘one-half’ can be represented by a circle with a ‘one-half’ piece on top.) Great. ‘One-half can be represented by a circle with a ‘one-half’ piece on top. Thanks for helping me out.”
Think of how to draw the “whole” piece and draw it – “Now, how can we draw the ‘whole’? (Elicit the response, “we can draw it by drawing a circle.”) Excellent thinking. We can represent the whole by drawing a circle. Let’s all do that now.”
Think of how to draw the “part” – “How can we draw the ‘part’ or ‘one-half’? (Elicit the response, “we can draw a line first that separates the whole circle into two equal parts.”) That’s right. Let’s all do that now.”
Draw the line(s) that represent the fractional part. – “Now we have two equal parts, but what is it that we need to represent? (Elicit the response, “one of the two equal parts, or ‘one-half’.”) Yes. How can we do that? (Elicit the response, “we can shade in one of the parts.”) That’s correct. Why does shading in one of the two equal parts represent ‘one-half’? (Elicit the response, “because the ‘one-half’ piece is a darker color and it is one of two equal parts of a whole circle.”) Wonderful thinking. Let’s all shade in one of the parts.”
Shade in the appropriate “part” that represents the fractional part.
Teacher asks questions/Teacher answers questions about the drawing and it relationship to the concrete material and the fractional part.
“Do we have my whole represented? (Elicit the response, “Yes, we drew a circle that represents the whole circle when we use circle pieces.”) That’s right, the circle we drew represents a ‘whole’ circle piece.”
“Do we have the part represented? (Elicit the response, “Yes, we drew a line to separate the whole circle into two equal parts and then we shaded in one part.”) Great! We drew a line first that cut the whole circle into two equal parts and then we shaded one of the parts.”
“Does our drawing represent ‘one-half’? (Elicit the response, “Yes, I have a whole circle cut into two equal parts and one part is shaded. The part that is shaded represents ‘one-half’ of the whole circle.”) I think you’ve got it. Excellent job guys!”

b. When you are confident students understand, ask individual students to direct the problem solving process or have the class direct you: Students ask the questions and you and the students respond/perform the skill.

*Practice should be provided for drawing each of the fractional parts taught during Phase 1- “Initial Acquisition of Skill” and for writing the fraction using numbers and symbols. This teaching plan provides a detailed description of two practice activities, one at the receptive or recognition level of understanding and one at the expressive level of understanding. The receptive/recognition level of understanding requires students to “recognize” the correct response from a given set of possible responses. This is an easier task than expressing what you know from memory recall. The expressive level of understanding requires students to actually perform the skill when given an appropriate prompt. This level of understanding is more difficult and demonstrates a more advanced level of understanding. For students with learning problems, it is important to remember that their learning occurs most efficiently in increments of understanding. Developing success and understanding at the receptive/recognition level provides them a sound foundation for success at the expressive level.

Videos

Learning Objective 1: view  Clip 1, Clip 2

Draw representations of fractional parts and write fractions.