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Lesson Plan 2: With technology integration

integration of technology have been highlighted in orange

 

Pathwise Instruction Plan

Teacher: Ms. Hylton

Grade: 3rd

Subject: Mathematics

Topic: Investigating Fractions with Pattern Blocks

(Lesson plan adapted from NCTM Illuminations Investigating Fractions with Pattern Blocks lesson planà http://illuminations.nctm.org/Lesson.aspx?id=1308)

 

1. Learning Objectives

What Standards (National or State) is this lesson targeting?

 

CCSS.MATH.CONTENT.3.NF.A.1- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

 

CCSS.MATH.CONTENT.3.G.A.2- Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

 

What are your objectives for student learning in this lesson?

 

At the end of this lesson, students will be able to:

  • Explain their understanding of a fraction being a part of a region

  • Identify fraction relationships among pattern blocks

 

Why have you chosen these objectives?

These objectives have been chosen in essence that our classroom is an atmosphere that allows students to explore mathematics through problem solving. This is an introductory lesson on fractions, thus students will be able to gain practice in problem solving and reasoning with fractions as they explore the relationships that lie between various parts and wholes. Communication is an essential part of the classroom, thus it is desired that students use their communication skills as they work in pairs and whole group discussions to explain their reasoning of fraction relationships and positively influence one another’s mathematical learning.

 

2. Content Knowledge

 

a. What is the underlying content knowledge that you must help the students to understand?

This lesson will help students understand that the “region” represents the “whole,” and parts of that whole (fractions) are all congruent. Through exposure to a variety of shapes, students will also come to understand that regions are not limited to the circle and rectangle and thus will be able to understand the relationship that lies between the parts and wholes, despite of region type.

 

 b. What are the tricky pieces in the content?

The tricky piece of this lesson will be orally communicating the relationship found between various parts and wholes. The answer is not enough. Students are expected to explain their reasoning to their solution. In essence that this can be tricky, scaffold student understanding by asking what they already know about fractions or the relationship between the whole and part. From there create various questions to help further student understanding.

 

c. When you deconstruct the content you are teaching, what are the pieces that are essential for children to understand?

It is essential for children to understand the relationship that lies between parts and wholes. Fractions can be very complex, thus through the use of pattern blocks students can concretely see these relationships.

 

3. Student Grouping

How will you group students for instruction? Why have you chosen this grouping?

Students will be grouped into pairs by mixed math ability. This grouping has been chosen because this is an introductory lesson on fractions, thus the teacher will be able to get an idea of each student’s understanding in regards to fractions and provide further differentiation as needed.

 

4. Methods

 

a. What teaching method(s) will you use for this lesson?

  • Whole group discussion

  • Partner work (Think-Pair-Share)

  • Independent work

 

b. Why have you chosen this method or these methods?

The above teaching methods will help the students to share their thinking will keeping them engaged in their learning. By having students work in pairs they are able to scaffold one another in their understanding of the relationship between parts ad wholes. Further more through whole group discussion, students are able to share their strategies, which makes their thinking public and has the potential to cause a shift in the class’ thinking as a whole.

 

What students need differentiation in this lesson in order to be successful? How will you differentiate for these student needs?

Students (low math ability, students with disabilities, etc.) whom may have a hard time communicating their understanding will need to be supported throughout this lesson in order for their learning to be successful. Thus the teacher will need to partner students with another student who will support their understanding, as well as facilitate the classroom and guide students understanding through questioning such as:

  • What do you know about this part in relationship to its whole?

  • What do you think?

  • How do you know?

  • Are you sure? Why?

 

5. Activities

 

Opening (20 minutes):

At the beginning of the lesson, have students get into their math partner groups. As students are heading into their groups, instruct one student per group to one iPad from the charging cabinet. Each partner group will receive 1 activity sheet. The activity sheet should be passed out faced down. Instruct students not to turn them over until they have been instructed to begin working in their partner groups. Once partner groups are situated with their materials, tell students that today we will be engaging in an exploration activity using Hands- On Pattern Blocks App (students have previously used this app are our familiar with its use). The activity sheet has all the information students will need. Review partner group and technology rules and ask students if they have any questions before they begin. Once questions have been answered, allow partner groups to flip over the activity sheet and begin working (remind students to place both names on the sheet).

 

As students are working in their partner groups, facilitate the classroom and listen to students’ solutions, ask questions about how they solved their problems (How do you know? Are you sure?), and make decisions about which students will share in order to generate a productive math discussion. In making the decision of which students will share, choose based upon their reasoning when you spoke to them in their groups. Even if there “answer” is not correct, the answer is not enough and thus their reasoning could lead to meaningful class discussion in which the students’ reasoning as a whole can be impacted.

 

Note: If a group is having trouble completing one of the questions, be sure to intervene and present students with guiding questions that will help use their problem-solving skills.

 

Main activity or activities (30 minutes):

After about 15-20 minutes or when all students groups have completed the activity (whichever comes first), have groups to put away their iPads (can leave on their desk as long as they are put away) and get ready to discuss their solutions.

 

Note: At this time take out anchor chart and record the relationships students find for each problem, this will serve as a concrete reference as students move toward more abstract work in lessons to come.

 

Choose one student (this group was chosen as you were facilitating the class) to come to the SMARTboard and use the Mathtoybox Pattern blocks to demonstrate their group’s strategy for solving the first question of the activity, which states, “How many green triangles are in one blue rhombus?” Group should have found that two green triangles cover one blue rhombus. Once the student has shared their group’s strategy, allow the rest of the class to state whether they agree with their strategy (Problem #1 is a simple problem thus students should have used a similar trial and error strategy to solve the problem).

 

Choose another student and ask: From looking at their strategy, what can we say about the relationship between two green triangles and one blue rhombus? Allow the student to come to the SMARTboard and use the online pattern blocks to demonstrate the relationship. Student should respond along the lines that the relationship between the two green triangles and one blue rhombus is equal because when you place the two green triangles on the blue rhombus none of the rhombus is left showing, thus it takes two green triangles to make one rhombus. Allow other students to comment on the groups sharing and explain their understanding of the relationship. Okay, so if it takes two green triangles to make one blue rhombus, what is one green triangle in relation to the blue rhombus? Make sure it is clear that the relationship that lies between the pattern blocks is that two green triangles is equal to one blue rhombus. So if the rhombus is the whole, the triangles are each halves of the whole. Therefore, one green triangle is one-half of the blue rhombus.

 

Facilitate discussion into problem #2, which states, “How many green triangles are in one red trapezoid?” Have a student come the SMARTboard and use the online pattern blocks to share their group’s strategy for problem #2. Student’s group should have found that three green triangles are in one red trapezoid. Allow other groups to share their opinion of the group’s strategy.

 

Choose another student and ask: From looking at their strategy, what can we say about the relationship between three green triangles and one red trapezoid? Allow the student to come to the SMARTboard and use the online pattern blocks to demonstrate the relationship. Student should respond along the lines that three triangles are equal to one red trapezoid. Allow other students to comment on the groups sharing and explain their understanding of the relationship. Okay, so if it takes three green triangles to make one red trapezoid, what is one green triangle in relation to the red trapezoid? Make sure it is clear that the relationship that lies between the pattern blocks is that three green triangles is equal to one red trapezoid. So, if the red trapezoid is the whole, the green triangles are each thirds that can of the whole. Therefore, one green triangle is one-third of the red trapezoid.

 

Facilitate discussion into problem #3, which states, “How many green triangles are in one yellow hexagon?” Have a student come the SMARTboard and use the online pattern blocks to share their group’s strategy for problem #3. The student’s should have found that six green triangles are in one yellow hexagon. Allow other groups to share their opinion of the group’s strategy.

 

Choose another student and ask: From looking at their strategy, what can we say about the relationship between six green triangles and one yellow hexagon? Allow the student to come to the SMARTboard and use the online pattern blocks to demonstrate the relationship.  Student should respond along the lines that six green triangles are equal to one yellow hexagon. Allow other students to comment on the groups sharing and explain their understanding of the relationship. Okay, so if it takes six green triangles to make one yellow hexagon, what is one green triangle in relation to the yellow hexagon? Make sure it is clear that the relationship that lies between the pattern blocks is that six green triangles is equal to one yellow hexagon. So if the yellow hexagon is the whole, the green triangles are each sixths of the whole. Therefore, one green triangle is one-sixth of the yellow hexagon.

 

Facilitate discussion into problem #4, which states, “How many blue rhombuses are in one yellow hexagon?” Have a student come the SMARTboard and use the online pattern blocks to share their group’s strategy for problem #4. The student’s group should have found that three blue rhombuses are in one yellow hexagon. Allow other groups to share their opinion of the group’s strategy.

 

Choose another student and ask: From looking at their strategy, what can we say about the relationship between the three blue rhombuses and one yellow hexagon? Allow the student to come to the SMARTboard and use the online pattern blocks to demonstrate the relationship. Student should respond along the lines that the three blue rhombuses are equal to one yellow hexagon. Allow other students to comment on the groups sharing and explain their understanding of the relationship. Okay, so if it takes three blue rhombuses to make one yellow hexagon, what is one blue rhombus in relation to the yellow hexagon? Make sure it is clear that the relationship that lies between the pattern blocks is that two green triangles is equal to one blue rhombus. So if the yellow hexagon is the whole, the blue rhombuses are each thirds of the whole. Therefore, one blue rhombus is one-third of the yellow hexagon. Is this fraction relationship similar to another pair of shapes we have looked at? Students should realize that this fraction is similar to three green triangles and one red trapezoid. If they don’t realize this, bring it to their attention. Although they have the same fraction relationship, what is the difference between them? The difference is between the parts and wholes, but the fraction is still the same.

 

Facilitate discussion into problem #5, which states, “How many red trapezoids are in one yellow hexagon?” Have a student come the SMARTboard and use the online pattern blocks to share their strategy for problem #5. The student’s group should have found that two red trapezoids are in one yellow hexagon. Allow other groups to share their opinion of the group’s strategy and explain their understanding of the relationship. For this problem, other groups might have positioned the red trapezoids differently, thus allow students’ of these groups to share so that students can see that position of the blocks doesn’t interfere with relationship.

 

Choose another student and ask: From looking at their strategy, what can we say about the relationship between the two red trapezoids and one yellow hexagon? Allow the student to come to the SMARTboard and use the online pattern blocks to demonstrate the relationship. Student should respond along the lines that the two red trapezoids are equal to one yellow hexagon. Allow other students to comment on the groups sharing and explain their understanding of the relationship. Okay, so if it takes two red trapezoids to make one yellow hexagon, what is one red trapezoid in relation to the yellow hexagon? Make sure it is clear that the relationship that lies between the pattern blocks is that two red trapezoids is equal to one yellow hexagon. So if the yellow hexagon is the whole, the red trapezoids are halves of the whole. Therefore, one red trapezoid is one-half of the yellow hexagon. Is this fraction relationship similar to another pair of shapes we have looked at? Students should realize that this fraction relationship is similar to the two green triangles and the blue rhombus. If don’t realize this, bring it to their attention. Although they have the same fraction relationship, what is the difference between them? The difference is between the parts and wholes, but the fraction is still the same.

 

To extend student thinking present them with the following question (use the online pattern blocks on the SMARTboard to represent student understanding thus far and to represent present question): If we know that two green triangles make up one blue rhombus and three green triangles make up one red trapezoid, is there a way to represent the red trapezoid using the blue and green pattern blocks? Implement Think-Pair-Share and allow students to think individually for about 3 minutes using their iPad and then work in their partner groups using the Hands-On Pattern Blocks app to concretely demonstrate their thinking. As students are working, facilitate the classroom and listen to students’ solutions, ask questions about how they solved the question (What is the fractional between the parts and whole? How do you know? Are you sure?)

 

After about 5 minutes, choose two students to share their group’s strategy using the online pattern blocks. The students should state that because two green triangles is equal to one blue rhombus (or one green triangle is one-half of one blue rhombus) and three green triangles is equal to one red trapezoid (or that one green triangle is one-third of the red trapezoid), they could construct the trapezoid using one blue rhombus and one green triangle. Once they have shared their strategy, allow the rest of the class to state whether they agree with their strategy and share their understanding/ strategies if necessary. If one green triangle is one-third of the red trapezoid, what is the relationship between the blue rhombus and the red trapezoid? Facilitate a classroom discussion that will lead students to realize and understand that if one green triangle is one-third of the red trapezoid and one-half of the blue rhombus then one blue rhombus is two-thirds of the red trapezoid.

 

Closing (10 minutes):

In order to continue extending student thinking and gage understanding of parts and wholes, allow students to continue discovering other relationships using two or more pattern blocks. Present students with the following question: Are there other ways to represent the yellow hexagon using more than one color block? If so, what is their fractional relationship to the yellow hexagon? Again implement the strategy of Think-Pair-Share, but this time instead of sharing in whole group, have students to individually record (pictorially) the relationship found between the pattern blocks. Students will use the Hands-On Pattern Block App to explore this question and take a screenshot of their work. Once students are finished they will then upload their screenshot to their personal blog (Kidblog) and along with at least 3 sentences explaining the fractional relationships they found.

 

Note: If students are having trouble, intervene and provide guiding questions to help students think meaningfully of the relationship that lies between the yellow hexagon and other shapes.

                       

6. Materials

What instructional materials will you use, if any?

 

Why have you chosen these specific materials?

The above materials have been chosen because they are of extreme value to our hands-on and explorative classroom environment. Through these materials, students are equipped to engage in problem solving and reasoning skills with fractions as they investigate the relationships between various parts and wholes. Specifically, the SMARTboard, online pattern blocks, and Kidblog allow students to employ their communication skills in an effort that new discoveries can be made as a class and teachers can have a clear understanding of student knowledge. More so, the anchor chart will be posted in the classroom and thus serve as a reference for students as we move on to more abstract work.

 

7. Evaluation

 

Before the Lesson:

  • Informally evaluate whether students were listening to the instructions given, by asking students to repeat the directions.

 

During the Lesson:

  • Students’ responses as they are working in partner groups will be informally monitored (the teacher will intervene if students are struggling).

  • Students will also be informally evaluated during whole group discussion on their understanding of the relationship that lies in a part (fraction) being apart of a whole (Objective #1) through the use of teacher observation notes.

 

After the Lesson:

  • Student recordings in their blogs will be evaluated to see if students were able to communicate (pictorially and written) the various relationships found between the yellow hexagon and other pattern blocks (Objective #2). Recordings will also serve as an aid in making instructional decisions about student understanding of fraction relationships, and thus the teacher can seek to differentiate future lessons according to student needs.

 

 

Adapted for University of Florida from Pathwise Instruction and Reflection Form by Vicki Wilson for Salt Fork (Region 10) RPDC and Muskingum Valley Educational Service Center/Muskingum College Goals 2000 grant.

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