Identify and Write Fractions: Concrete Level

More Teaching Plans on this topic: Representational

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context

Description:

Contexts include puzzles, sharing parts of a candy bar with friends, as well as story situations that present real-life situations such as cutting a pizza into equal parts for two friends, cutting a long dog leash into to shorter pieces so two friends can both walk their dogs, and dealing a set of cookies into two or more equal sets so two of more children receive the same number of cookies. These authentic contexts are used throughout the teaching process and they are explicitly linked to the skill/concept being taught throughout the teaching plan.

Purpose: to assist students to make meaningful connections between what they know about materials that can be broken into parts and the concept of fractional parts.

Learning Objectives 1 -3

Materials:

Puzzles made from interesting pictures that come in two equal pieces, four equal pieces, and eight equal pieces
Candy bar
Visual for identifying the skill to be learned
Description:

1.) L ink to student’s prior knowledge & experiences about things relevant to their lives that can be broken into parts.

Relate how puzzles are made of pieces and that when they are put together, they make a whole picture. Bring in a several puzzles made from an interesting picture. Have a puzzle that comes in two equal pieces, four equal pieces and eight equal pieces.
2.) I dentify the skill students will learn: How to cut whole objects into equal parts and how the equal parts can be put back together to make the object whole again.

For Example:

Today we are going to learn how to break or cut whole objects into parts, just like the puzzles I just showed. We also are going to learn how the parts can be put together to make the object whole again.

Provide some type of visual that represents the words you are saying (e.g. the puzzle, 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 how to break objects into equal parts.

For Example:

Learning how to break things into equal parts is a really important thing to be able to do. For example, 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. 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. Both of you will feel good. You will feel good because you did something nice for your friend. Your friend will feel good because you gave him some of your candy bar. Your friend will also feel good because he knows you gave him the same amount as you took yourself.

Bring in a candy bar to demonstrate this
Have students brainstorm other objects they might want to break into equal parts and why (e.g. pizza, sets of cards, etc.)

*First teach fractional parts using the Area Model, then teach fractional parts using the Measurement Model, and finally teach fractional parts using the Sets Model. Students should be provided practice opportunities and demonstrate mastery using concrete materials that represent the Area Model (see Instructional Phase 2: Practice Strategies) before providing explicit teacher modeling for the Measurement Model. Students also should be provided practice opportunities and demonstrate mastery using concrete materials that represent the Measurement Model before providing explicit teacher modeling for the Sets Model.

Purpose: to provide students a teacher model who clearly demonstrates the concepts of “parts” and “whole” how to represent fractional parts with concrete materials.

Learning Objective 1: Identify fractions using concrete materials that represent the area model.

Materials:

Teacher -

Appropriate concrete materials that represent the Area Model
A visible platform for demonstrating the concrete materials
A visible platform for each story situation used to model
Description:

A. Break down the skill of identifying fractions using concrete materials that represent the area model into learnable parts.

1.) Introduce a story context that accurately represents the fractional part/provide a visual display.

2.) Read story aloud yourself first/have students read with you second.

3.) Explicitly teach how to pick out the important information.

4.) Recreate the story context using appropriate concrete materials.


5.) Prompt student thinking about the relationship of the parts and the whole represented in the story.

6.) Model parts, whole, and their relationships using the story context.

a. Teach students the language and meaning of ‘two equal parts’ and ‘whole’.
b. Model ‘equal parts’
c. Model ‘whole’
d. Model relationship of ‘parts’ to ‘whole’

7.) Teach students name of fractional part.

8.) Repeat steps 5-6 for same fractional part using at least two different types of materials appropriate for the fraction model being taught.

Learning Objective 2: Identifying fractions using concrete materials that represent the measurement model.

Materials:

Teacher -

Appropriate concrete materials that represent the Measurement Model
A visible platform for demonstrating the concrete materials
A visible platform for each story situation used to model
Description:

A. Break down the skill of identifying fractions using concrete materials that represent the measurement model into learnable parts.

1.) Introduce a story context that accurately represents the fractional part/provide a visual display.

2.) Read story aloud yourself first/have students read with you second.

3.) Explicitly teach how to pick out the important information.

4.) Recreate the story context using appropriate concrete materials.

5.) Prompt student thinking about the relationship of the parts and the whole represented in the story.

6.) Model parts, whole, and their relationships using the story context.

a. Teach students the language and meaning of ‘two equal parts’ and ‘whole’.
b. Model ‘equal parts’
c. Model ‘whole’
d. Model relationship of ‘parts’ to ‘whole’

7.) Teach students name of fractional part.

8.) Repeat steps 5-6 for same fractional part using at least two different types of materials appropriate for the fraction model being taught.

Learning Objective 3: Identifying fractions using concrete materials representing the sets model.

Materials:

Teacher -

Appropriate concrete materials that represent the Sets Model
A visible platform for demonstrating the concrete materials
A visible platform for each story situation used to model
Description:

A. Break down the skill of identifying fractions using concrete materials that represent the sets model into learnable parts.

1.) Introduce a story context that accurately represents the fractional part/provide a visual display.

2.) Read story aloud yourself first/have students read with you second.

3.) Explicitly teach how to pick out the important information.

4.) Prompt student thinking about the relationship of the parts and the whole represented in the story.

5.) Model parts, whole, and their relationships using the story context.

a. Teach students the language and meaning of ‘two equal parts’ and ‘whole’.
b. Model ‘equal parts’
c. Model ‘whole’
d. Model relationship of ‘parts’ to ‘whole’

7.) Teach students name of fractional part

8.) Prompt students’ thinking about the relationship between the parts and the whole (repeat step #4).

9.) Repeat steps 5-6 for same fractional part using at least two different types of materials appropriate for the fraction model being taught.

Purpose: to provide students a teacher supported transition from seeing and hearing the teacher demonstrate/model representing fractional parts with concrete materials to performing the skill 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: Identifying fractions using concrete materials that represent the area model.

Materials:

Teacher –

Area concrete materials
A visible platform for showing concrete materials
The appropriate story situation made visible to students
Students –

Appropriate Area Model concrete materials
Description:

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

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)

For Example:

Restate the story situation used from Explicit Teacher Modeling – “Ok, everybody. I’ve showed you several examples of cutting a shape into equal parts and you’ve helped me see the relationships of the parts to the whole. Now we’re going to do several more together, except this time I want you to help me out even more. The first time, I want you to help me with two questions. Then, you’ll help me with more and more until you are asking the questions and I will answer them with you. Let’s reread the story about Velma’s mom and the pizza.” (Read the story aloud with your students.)

Re-introduce the area manipulative (should be one used during Explicit Teacher Modeling – e.g. fraction circle/pieces) – ”Now, like we did before, I’ll use this fraction circle and pieces to represent the pizza and its parts.” (Show students the fraction circle and two “one-half” pieces.)

Relate/prompt students to think that the circle represents the “whole” piece of pizza – “What does this circle represent? (Elicit the response, “the whole pizza.”) That’s right, this circle piece represents Velma’s mother’s whole pizza.”

Demonstrate/prompt students to think how “cutting” the circle into two equal parts is like cutting the pizza into two equal parts – “Now, what do I need to do in order to “cut” the circle in two equal parts like Velma’s mom did with the pizza? (Elicit the response, “find two pieces that are equal in size and that when put together are the same size as the circle.”) Excellent thinking. I’ll do that now.”

Teacher asks questions/Teacher answers questions about the relationships of the parts to each other and to the whole.
How many parts are there now? – “(Find the two “one-half” pieces and place them on top of the circle or “whole.” Relate that I know these are the correct pieces because the sides do not overlap, pointing to this feature.) Ok, now I need to ask myself, how many parts are there in all? Hmm, I can count them. (Count the parts aloud, pointing to them and picking them up to show they are separate parts.) I have two parts.”
How many parts were there before I “cut” the circle? – “Now, let me think. How many parts were there before I cut the circle into two parts? I know there was only one part. It was the whole circle. (Remove the two “one-half” pieces to reveal the circle underneath. Pick the circle up and demonstrate that it is one whole.).”
Are the parts the same size? – “Now, I can look again at the parts. It’s important to know if they are equal, because Velma’s mom wanted each child to get the same amount of pizza. How can I figure this out. Oh, I know, I can put one part on top of the other part. (Put one of the “one-half” pieces on top of the other. Show how they are the same size by pointing to the edges and relating that there is no overlap.) Now I know the parts are two equal parts.”

How many parts of the total number of parts is this one? – “I wonder how many parts each part represents out of the total number of parts. Well, I can answer this by counting the total number of parts. There are ‘one, two’ parts (Point to each part as you count it.) Now, if I take one part, it represents one of two parts. (Pick up one part and say “one.” Put the part back down). Now, I can count the total number of parts. (Count the parts aloud.) I have two total parts. That means this part (point to one of the “one-half” pieces) is one of two total parts. (Repeat this for the other part as well.) Another name for this part is “one-half.”

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. (Choices are shown in red)

For Example:

Prompt students to think how to relate the circle as being the “whole” piece of pizza – “Ok, everybody. You’ve helped me find the parts and the whole for one/several example(s). Now we’re going to do several more together. Because you all are doing such a great job, I’m going to have you help me even more with this one. What can we use to represent the pizza and its parts? (Elicit the response, “a fraction circle and fraction pieces.” Show students the fraction circle and two “one-half” pieces.) What does this circle represent? (Hold up the fraction circle and elicit the response, “the whole pizza.”) That’s right, this circle piece represents Velma’s mother’s whole pizza.”

Prompt students to think how to simulate cutting the pizza into two equal parts. – “Now, what do I need to do in order to “cut” the circle in two equal parts like Velma’s mom did with the pizza? (Elicit the response, “find two pieces that are equal in size and that when put together are the same size as the circle.”) Excellent thinking. I’ll do that now.” (Find the two “one-half” pieces and place them on top of the circle or “whole.”) How can I check to see if these are the correct pieces?” (Elicit the response, “put one piece on top of the other and see if they are the same size/see if the sides are smooth.”) (Demonstrate that the sides do not overlap.)

Teacher asks questions/teacher or students answer questions about the relationships of the parts to each other and to the whole.

How many parts are there now? – “Ok, now I need to ask myself, how many parts are there in all? Hmm, how can I do that? (Elicit the response, “we can count them.”) Yes, we can count them. Let’s count them. I’ll point to them and you count out loud. (Point to them as students count aloud.) How many parts are there? (Elicit the response, “there are two parts.”) Yes, there are two parts.”

How many parts were there before I “cut” the circle? – “Now, let me think. How many parts were there before I cut the circle into two parts? I know there was only one part. It was the whole circle. (Remove the two “one-half” pieces to reveal the circle underneath. Pick the circle up and demonstrate that it is one whole.)”

Are the parts the same size? – “Now, I can look again at the parts. It’s important to know if they are equal, because Velma’s mom wanted each child to get the same amount of pizza. How can I figure this out? (Elicit the response, “put one part on top of the other part.”) Great thinking! (Put one of the “one-half” pieces on top of the other.) How can I tell that they are equal? (Elicit the response, “because the edges are smooth/don’t overlap.”) That’s right, the edges match up exactly (Point to the edges.) So, are the parts equal parts? (Elicit the response, “yes.”) Now I know the parts are two equal parts.”

How many parts of the total number of parts is this one? – “I wonder how many parts each part represents out of the total number of parts. Well, I can answer this by counting the total number of parts. There are ‘one, two’ parts (Point to each part as you count it.) Now, if I take one part, it represents one of two parts. (Pick up one part and say “one.” Put the part back down). Now, I can count the total number of parts. (Count the parts aloud.) I have two total parts. That means this part (point to one of the “one-half” pieces) is one of two total parts. Another name for this part is “one-half.” (Repeat this for the other part as well.)”
B. Maintain medium 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.

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

When students demonstrate increased competence, do not model the process. Ask students questions and encourage them to provide all the responses. Distribute concrete materials so students can replicate the process at their desks.

For Example:

Prompt students to think how to relate the circle as being the “whole” piece of pizza – “Ok, everybody. You’ve helped me find the parts and the whole for several more examples. Now, you are going to use the circles and circle pieces I just gave you to answer my questions. Now, like we did before, we’ll use these fraction circles and pieces to represent the pizza and its parts. Everybody, show me the fraction circle that represents a ‘whole.’ (Encourage students to raise the appropriate piece – check student understanding and provide corrective feedback as needed.) Great job.”

Prompt students to think how to simulate cutting the pizza into two equal parts. – “Now, everybody show me the pieces that represent two equal parts of the whole pizza/circle. (Encourage students to raise the appropriate piece – check student understanding and provide corrective feedback as needed.) Good thinking guys. Ok, what does the circle represent? (Elicit the response, “the whole pizza.”) That’s right, this circle piece represents Velma’s mother’s whole pizza. Now, you’ve already showed me the two pieces that represent the parts of the pizza that Velma’s mother cut. How can you show that those two pieces when put together equal the whole pizza? (Elicit the response, we can put them on top of the ‘whole’ circle piece.) That’s right. Everybody do that now. (Monitor student responses, providing specific corrective feedback as needed.) Now, how do we know these parts equal the whole? (Elicit the response, “because the edges are smooth/don’t overlap.) Wonderful! We know because the edges are smooth.” (Point this out with your pieces.)

Teacher asks questions/students answer questions and about the relationships of the parts to each other and to the whole and demonstrate their understanding with their manipulatives.
How many parts are there now? – “How do I find out how many parts there are? (Elicit the response, “we can count them.”) Yes, we can count them. How many parts do we have? (Elicit the response, “there are two parts.”) Yes, there are two parts.”
How many parts were there before I “cut” the circle? – “Now, let me think. How many parts were there before I cut the circle into two parts? (Elicit the appropriate response.) Yes, there was only one part. It was the whole circle. (Remove the two “one-half” pieces to reveal the circle underneath. Pick the circle up and demonstrate that it is one whole.)”
Are the parts the same size? – “How many parts were there before I cut the circle into two parts? (Elicit the response, “there was only one part, the whole circle.”) Yes, the circle was the whole pizza before we cut it into parts. How can you show this? (Elicit the response, “by taking off the two pieces on top.”) Good job! Let’s all do that now. (Remove the two “one-half” pieces to reveal the circle underneath.) Ok, everyone, pick up the circle and show each other that it is one whole. Now, just to check again, let’s be sure that the two parts are equal since Velma’s mom wanted each child to get the same amount of pizza. How can I figure this out? (Elicit the response, “put one part on top of the other part.”) Great thinking! Everybody do that now. (Monitor students’ work, provide specific corrective feedback as needed.) How can I tell that they are equal? (Elicit the response, “because the edges are smooth/don’t overlap.”) That’s right, the edges match up exactly (Point to the edges.) So, are the parts equal parts? (Elicit the response, “yes.”) Now I know the parts are two equal parts.
“How many parts of the total number of parts is this one? (Elicit the appropriate response) Yes, we need to decide how many parts each part is out of the total number of parts. How can we answer that question? (Elicit the response, “by counting the total number of parts.”) Good. Let’s count the total number of parts. Point to your parts and count aloud. Ready, count. How many parts are there? (Elicit the response, “two.”) Great, there are two parts. Now, if I take one part, it represents how many of the two parts? (Elicit the response, “one of two parts.”) Great, it represents one of two parts. Everybody hold up one part. (Check student responding, provide specific corrective feedback as needed) How many parts? (Elicit the response, “one part.”) Yes. Now pick up the two parts. (Check student responding, provide specific corrective feedback as needed) Out of how many parts? (Elicit the response, “out of two parts.”) (Pick up one part and say “one.” Put the part back down). Good the first part you held up represents one of two parts. Everybody say that. (Elicit the response, “one of two parts.”) What’s another name for this part? (Elicit the response, “one-half.”) (Repeat same process for the other part as well.)

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 each of the fractional parts taught during Phase 1- “Initial Acquisition of Skill.” A separate practice lesson should also be provided for each Fraction Model taught. 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. The practice activities described in this teaching plan can be used for all three Fraction Models (Area, Measurement, & Sets).

Videos

Learning Objective 1: view  Clip 1, Clip 2, Clip 3, Clip 4, Clip 5

Identify fractions using concrete materials that represent the area model.