Identify and Represent Equivalent Fractions: Concrete Level

More Teaching Plans on this topic: Representational

Teach Skill with Authentic Conext

Description: A problem context of ordering and sharing pizza is used.

Build Meaningful Student Connections

Purpose: to help students make meaningful connections between what they have experienced with ordering and sharing pizza and identifying and making equivalent fractions.

*The following is a description of how you implement this instructional strategy for Learning Objective 1. A similar process can be used for the other learning objectives in this plan.

Learning Objective 1: Identify and represent equivalent fractions using concrete objects with an area model.

Materials:

Teacher -

• Cardboard pizzas representing a whole, halves, fourths and eighths
• Whiteboard or other visual display or word cards with half, fourth, eighth

Description:

1) L ink to students’ prior knowledge of identifying and representing fractions.

For Example:

How many of you like to eat pizza? What is your favorite kind of pizza? When we share a pizza with others, we are each getting a part of the whole pizza. We can divide the pizza into halves (point to word half on board) or fourths (point to word) or even eighths (point to word). We know that a half, a fourth and an eighth are called fractions. They mean that we have taken a whole, like this whole pizza and divided it equally into parts (show with cardboard pizza slices).

2) I dentify the skill students will learn: Identifying and representing equivalent fractions using concrete objects.

For Example:

Today we are going to learn how to tell if each person is getting the same amount of pizza by looking at the equal parts of pizzas. We are going to look at the different parts and see which ones show the same amount. We are going to study how to identify and make Equivalent (point to word on board) parts. Equivalent parts look different but represent the same amount of a whole.

3) P rovide rationale/meaning for identifying and representing equivalent fractions.

For Example:

Knowing how to do problems like this will help us when we work with fractions. It will help you when you shop to decide how to share things. When you have to share and equally divide things like pizzas, or hershey bars, you can make sure that everyone gets the same amount.

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Provide Explicit Teacher Modeling

Purpose: to provide students with a clear teacher model of how to identify and make equivalent fractions using concrete objects.

Learning Objective 1: Identify and represent equivalent fractions using concrete objects with an area model.

* This skill should first be taught using an area model, then a measurement model, and then a sets model. After completing all phases of the instructional plan with an area model, and measuring student mastery, the concept should then be taught using a measurement model. After completing all phases of the instructional plan with a measurement model, and measuring student mastery, the concept would then be taught using a sets model.

Materials:

Teacher -

• Pizza boxes from different types of pizzas
• Cardboard pizzas that are divided into fourths, eighths, halves, etc.
• Visual display area

Description:

A. Break down the skill of identifying and representing equivalent fractions using concrete objects with an area model.

1) Identify the fractional part shown by each object.

2) Compare fractional parts

Learning Objective 2: Identify and represent equivalent fractions using concrete objects with a measurement model.

* Identifying and representing equivalent fractions should first be taught using an area model, then a measurement model, and then a sets model. After completing all phases of the instructional plan with a measurement model, and measuring student mastery, the concept should then be taught using a sets model.

Materials:

Teacher -

• Fraction strips or bars, or Cuisenaire rods
• Visual display area

Description:

A. Break down the skill of identifying and representing equivalent fractional parts using concrete objects with a measurement model.

1) Identify the fractional part shown by each object.

2) Compare fractional parts.

Learning Objective 3: Identify and represent equivalent fractions using concrete objects with a sets model.

* This skill should first be taught after using an area model, and then a measurement model. After completing all phases of the instructional plan with an area and then a measurement model, and measuring student mastery, the concept should then be taught using a sets model.

Materials:

Teacher -

• Set of mini pizzas (real or construction paper) placed in two horizontal rows of four.
• Four pepperoni slices (real or construction paper)
• String
• Visual display area

Description:

A. Break down the skill of identifying and representing equivalent fractional parts using concrete objects with a sets model.

1) Identify the fractional part represented by each part of the set.

2) Compare fractional parts.

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Scaffold Instruction

Purpose: to provide students an opportunity to build their initial understanding of identifying and representing equivalent fractions using concrete objects and to evaluate your students’ levels of understanding after you have initially modeled the skill.

* The following description is for Learning Objective 1: Identify and represent equivalent fractions using concrete objects with an area model. A similar process could be used for the other learning objectives in this plan.

Materials:

Teacher -

• Cardboard pizzas that are divided into fourths, eighths, etc.
• Word cards with ‘Equivalent’ written on it
• Bags of fraction pieces – one bag has halves, another fourths, etc.
• Visual display area

Students -

• Bags of fraction pieces – one bag has halves, another fourths, etc. Each set of pieces is colored a different color
• Index cards with equivalent written on them

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.

Identify the fractional part shown by each object.

Identify the whole(s).

We have looking at finding equivalent fractional parts. Now, I am going to give you another problem and have you help me with it. I have two pizzas here. I have cut up one pizza into six pieces and one pizza into eight pieces. First I need to decide if these two pizzas are the same size. How do you think we could do that? Right, _____ please come up and show us whether these two pizzas are the same size. Boys and girls, _____ put all the pieces for the pizza I cut up into sixths and laid them on top of the pizza that I cut into eighths. Are they the same size? Yes, they are.

Identify the number of parts that are in each fractional part

I said I cut this pizza into eighth equal pieces, and I cut this pizza into six equal pieces. I am going to give four of the eight pieces of this pizza to Jason. If I give four of the eight pieces to Jason, I wonder what fractional part of the pizza he will have? Well, four of eight pieces will be four eighths. And I am going to give three of the six pieces to Marisa. If I give three of the six pieces to Marisa. What fractional part of the pizza does she have? Right, three sixths. So, what fractional part of this pizza does Jason have? Right, four eighths. And what fractional part of this pizza does Marisa have? Correct again, three sixths. Well, they have different fractional parts, but I wonder if they have the same amount of pizza?

Compare fractional parts.

Manipulate the pieces to see if they take up the same amount of space.

Each person has a different number of pieces. Jason, let’s put your pieces down first. 1,2,3,4 of eight pieces. Jason has four eighths of the pizza. How can we see if Marisa has the same amount? Right, we can put her pieces on top of Jason’s. If they cover Jason’s and take up the same amount of space, then we know that they have the same amount of pizza. Well, let’s try it.
Label fractional parts as equivalent/nonequivalent

Look, Marisa’s pieces cover all of Jason’s pieces. They take up the same amount of space. That tells us that Jason and Marisa have the same amount of pizza. They have equivalent fractional parts (put word card next to display of pizza pieces). How did we know that Jason’s four eighths were equivalent to Marisa’s three sixths? Right, we put them on top of each other to see if they took up the same area, the same amount of space.

b. Maintain a 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.

Identify the fractional part shown by each object.

Identify the whole(s).

For the next problem, I want you to help me even more. This time I am going to use fraction circles. Look at these bags. In this bag I have twelve pieces that make a circle. In this bag I have six pieces that make a circle. One of these circles is divided into twelve pieces and one of them is divided into six pieces. What’s the first thing I need to do? Right, first I need to decide if these two circles are the same size. How do you think we could do that? Right, _____ please come up and show us how to do that. Are they the same size? Yes, they are.

Identify the number of parts that are in each fractional part

Let’s see if four pieces from this circle (point to circle divided into twelfths) is the same as two pieces from this circle (point to circle divided into sixths). What fractional part is shown by these four pieces? Well, the circle is divided into twelve equal parts, and I have four of them, so that is four twelfths. What fractional part is shown by these two pieces (point to sixths). Right, two sixths, because the circle is divided into six pieces and I have two of them.

Compare fractional parts.

Manipulate the pieces to see if they take up the same amount of space.
Now what do I need to do? Right, I need to put them on top of each other. Do they take up the same amount of space? Yes, they do.

Label fractional parts as equivalent/nonequivalent.

These fractional parts take up the same amount of space, so we can say that they are equivalent (label with word card). What is the fraction here? Right, four twelfths is equivalent to___ two sixths.

b. Maintain a 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 responses. Direct students to replicate the process at their desks as you work together.

Identify the fractional part shown by each object.

Identify the whole(s).

For the next problem, I am going to have you do it at your desks. Each of you has two bags that have fraction circle pieces in them. One of the bags has red fraction pieces and one of the bags has blue fraction pieces. What’s the first thing you need to do? Right, you need to decide if the two circles are the same size. Show me how you are going to do that? Right, you put all the red pieces down to make a circle and then put all the blue pieces down to make another circle on top of them. Each person’s circles are the same size. How many red fraction pieces are there ? Right, four. How many blue fraction pieces? Right, eight.

Identify the number of parts that are in each fractional part

Now I want you to pick 3 of the red fraction pieces and 6 of the blue pieces. What fractional part is shown by these three red pieces? Right, three fourths. What fractional part is shown by the six blue pieces? Right, six eighths.

Compare fractional parts.

Manipulate the pieces to see if they take up the same amount of space.
Now what do you need to do? Right, you need to put them on top of each other. Do they take up the same amount of space? Yes, they do.
Label fractional parts as equivalent/nonequivalent

If fractional parts take up the same amount of space, we say that they are ______? Right, equivalent. Label your equivalent fraction pieces with an index card that says equivalent. Tell me what are the two equivalent fractions you have shown? Right, three fourths is equivalent to six eighths.

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

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Videos

Learning Objective 1: view  Clip 1, Clip 2
Identify and represent equivalent fractions using concrete objects with an area model.

Learning Objective 3: view  Clip 1, Clip 2
Identify and represent equivalent fractions using concrete objects with a measurement model.

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