Lesson PlanElementary Mathematics Cycle Level: Cycle three, grade 6

Inquiry: Converting Fractions to

decimals and Percents

Percents of a number

By the end of this lesson, the students will be able to:(Progression of learning, 2009)

Students will be able to represent decimals in a variety of ways Students will be able to read and write numbers written in decimal

notation Students will be able to explain the role of the decimal point Students will be able to express a decimal as a fraction Students will be able to express a decimal as a percentage Students will be able to express a fraction as a percentage Students will be able to express a fraction as a decimal Students will begin to use mathematical vocabulary and symbols

related to percentages (ex: out of 100, %, decimal, tenth, hundredth)

Students will be able to explain a percent as being a proportion in relation to a whole or a portion of a whole expressed as a number between 0 and 100 rather than as a fraction

Group Size & MaterialsThe class consists of approximately 18 students. Thereafter, the students will be divided into three pre-assigned groups of six students, to conduct the learning stations.

Materials: Work with the teacher learning station- Smartboard, copybooks

and percent of a number worksheet Puzzle and Problems learning station- mathematical situational

problem worksheets Manipulatives learning station- Geofix explorations kit, gram unit

interlocking cubes, patterns blocks, mosaic’s challenge, tangram puzzles, geoboard paper and fraction fortress

Fast facts learning station- guess who, pizza boxes, white boards, flash cards and ice cube trays

Strategic games learning station- chess and battleship games Mathematical Vocabulary learning station- a selection of

mathematical dictionaries (example: Lexi-Math by Suzanne Hervieux and Math Appeal: Mind-Stretching Math Riddles by Gregory Tang) and graphic organizer.

Professional Competencies

1) To act as a professional inheritor, critic and interpreter of knowledge or culture when teaching students

I addressed this competency while piloting the teaching/learning situations that were appropriate to the students concerned and the subject content as I demonstrated a thorough understanding of the subject-specific and program specific knowledge and also promoted the creation of meaningful links by the students. I also adopted a critical approach to the subject matter by asking students questions that would help to support their learning towards my instructional goals and objectives.

2) To communicate clearly in the language of instruction, both orally and in writing, using correct grammar, in various contexts related to teaching

I addressed this competency during the execution of my lesson plan by correctly using the mathematical terms specific to the subject at hand and also correcting students mistakes when they would fail to properly pronounce the mathematical terms (example: having the students use the word “denominator “ when referring to the bottom number of a fraction)

3) To evaluate student progress in learning the subject content and mastering the related competencies

When conducting my lesson, I found myself reflecting on my teaching, constantly checking for understanding by having them revoice in their own words what was said. I evaluated their progress by paying attention to how they answered the questions I asked and also analyzing their body language. I would not continue on with the lesson until the students understood each step.

4) To plan, organize and supervise a class in such a way to promote the students learning and social development

I addressed this competency by planning a learning situation and organizing students into groups for the learning stations. Also while teaching a specific group I supervised and kept an eye on the students in the other groups making sure that they were doing what was expected of them.

5) To cooperate with members of the teaching team in carrying out tasks involving the development and evaluation of the competencies targeted in the programs of study, taking into consideration the students concerned

When creating the lesson, I cooperated with the members of the teaching team as they provided me with great suggestions on how to structure my lesson and how to develop my teaching further to ensure the students

understanding. My cooperating teachers helped me to develop a lesson plan that would be conducive and appropriate to the students in her class given how she already knows what their strengths and weaknesses are.

6) To develop teaching/learning situations that are appropriate to the students concerned and the subject content with a view to developing the competencies targeted in the programs of study.

I developed a learning situation with help from my cooperating teaching whilst taking into consideration the needs and characteristics of students with learning disabilities and varied developmental levels. In this way, I participated in the development of a learning situation that is appropriate to the students in the classroom.

7) To pilot teaching/learning situations that are appropriate to the students concerned and the subject content with a view to developing the competencies targeted in the programs of study.

I did this by creating an environment in the classroom where students could engage in meaningful problem solving skills and tasks based on their developmental and academic levels. I also provided students with the materials and worksheets needed to participate in the learning situations. I also guided students towards the understanding of the task at hand providing clear instructions and explanations. I supported the students learning process by asking productive questions and providing feedback or suggestions on what they could do to further improve their learning towards my instructional goals for the lesson.

Specific Subject Competencies: Mathematics (QEP, 2001)

Competency one: Solves a situational problem

This competency is addressed in the Puzzle and Problems learning station where students will be asked to decode mathematical situational problems that involve missing information or that have to be solved in several steps by deriving information from various types of representations (examples: linguistic, numerical, symbolic and graphic)

Students will be asked to explain both orally and in writing their understanding of the situational problem and the development of a solution. This includes the procedure and final answer that is appropriate to the situational problem at hand. The students will use different strategies, which they have already developed in order to work out the solutions.

Students will learn how to analyze a situational problem by filling in the charts found in the back of each situation problem. The chart helps the students mobilize and systematize the mathematical information appropriate to the situational problem in different categories. These include the “what I know category “ “what I want to know” and the essential aspects to think about.

When working collaboratively to solve the situational problems, the students will validate their solution by comparing it with those of their classmates and teachers. Students will be asked to show their work and justify the steps in his or her mathematical procedure using mathematical language.

Competency two: Uses mathematical reasoning

Students will use mathematical reasoning when solving situational problems in the Puzzle and Problems learning station where they will analyze the conditions of a given situations, formulate mathematical judgments and opinions and will also evaluate the suitability of the conjectures appropriate to the situation

In the Work with the teacher learning station, the students will use appropriate concepts and processes and will apply mathematical reasoning when finding the percent of a number. When working with the teacher, students will observe the proper organization of the steps in an appropriate procedure modeled by the teacher and will be given time to practice the proper organization of their own steps when completing the percent of a number worksheet (independent practice). Also, the students will have to correctly justify the steps they have used in the procedure

Students will use mathematical language as a tool and object of reasoning. They will also use the worksheet to help organize their work.

Competency three: Communicates by using mathematical language

In the Mathematical Vocabulary learning station, students will be asked to make use of the selection of different math dictionaries like Lexi-Math and Math Appeal: Mind-Stretching Math Riddles to become familiar with the elements of mathematical language, namely terms, symbols and notations. They will also distinguish between everyday and mathematical meaning of various terms.

They will also be learning how to choose different types of representations (numerical/symbolic) that suit various situations. Students will be asked to explore the math dictionaries and find the definition, characteristics and notations of various mathematical terms. They will then organize their findings in the worksheet provided. As their learning progresses, the definitions will become more and more detailed and complex.

When working with the teacher at the learning station, students will be asked to express his or her ideas using mathematical language by taking into consideration its specific rules and conventions. For example: students will begin to use the word percent or out of 100 and associate the percent symbol or the decimal notation with the mathematical term.

When producing mathematical messages, they will begin to use the different types of representations learnt and refine their choice of math terms and symbols. They will compare information from various sources and in discussion with classmates they will analyze different points of views.

Broad areas of learning

Citizenship and Community LifeThis area of learning is addressed throughout the lesson as the students are given multiple opportunities to interact and cooperate with their classmates in each of the learning stations. This will help to further develop the student’s social competence and to develop an attitude of openness to the world and respect for diversity. In the process, students begin to familiarize themselves with cooperative learning situations, peaceful management and respect for agreements. This area was also targeted as I allowed students to take part in the democratic life of the classroom by having them establish the principle rules and procedures for teamwork specific to the learning stations and had them reflect on what they could do to further improve the smooth functioning of the learning stations. In this way students are involved in the democratic process of the classroom by compromising with others, coming to a consensus with respect for the rights and responsibilities of all students.

Cross Curricular Competencies: Mathematics (QEP, 2001)

Competency one: To use information

Students will exercise this competency in the Mathematical Vocabulary learning station where they are asked to gather information from mathematical sources placed at their disposal to find definitions to new mathematical concepts and terms. Moreover, comparing and contrasting information from different sources and to distinguish essential and secondary knowledge

In the Puzzles and Problems learning station, students will be asked to make use of the information in the problem and place it in different categories according to what pieces of information they know, what pieces of information they are missing and the essential aspects they must think about according to the specific problem at hand. They are then asked to put this new information to use in new contexts.

Competency two: Solves problems

Students will be addressing this competency in the Puzzle and Problems learning station where they will have to analyze and identify the components of a simple mathematical situational problem and provide an explanation about how these certain components define a problem. They will list possible solutions and evaluate them whilst taking into account the mathematical resources at their disposal.

Once they have completed the problem, they will justify their choice of solutions and procedures and make connections between them. In the process, they begin to recognize the similarities to situational problems previously solved.

Competency three: To exercise critical judgment

When solving situational problems, the students will exercise their critical judgment when comparing and

contrasting information from different problems and determining which pieces of information are suitable to the problem and which are not. They will also critically judge the different informational sources by distinguishing essential and secondary knowledge.

Competency five: Adopts effective work methods

When participating in the learning centers, students will adopt effective working methods by following the learning station schedule. The students will also adapt his or her work method to the task and the content at hand as well as readjust his/her actions as required.

After having completed each round of the learning stations, students will be asked to provide comments on how they think the round went. In this way, they are asked to examine the success of the learning stations and recognize what was effective and what did not work well.

Competency eight: Cooperates with others

Students will cooperate with their classmates in each of the structured learning stations. They will begin to adopt appropriate attitudes and behaviors whilst recognizing the needs of others. They will actively participate in the work of the team and contribute to improving the way the team works together.

In the process, they begin to recognize which tasks can be more easily carried out by means of teamwork and they learn to solve problems collectively, which involves comparing points and testing possible solutions. When solving situational problems collectively, students will justify their viewpoints and respect those of others.

In this way they are contributing to team efforts, managing conflict, recognizing the benefits of teamwork, coming up with desirable improvements and adapting his/her behavior to team members and teacher.

Competency nine: Communicates appropriately

In the Mathematical Vocabulary learning station, students become familiar with the rules, codes and conventions that are associated with mathematical modes of communication and know when to use it. In the process, they begin to evaluate and monitor their communication efforts as well as become much more sensitive to the effects of the use of different mathematical modes of communication.

When solving the situational problems, the students analyze the communication situation and can identify and explain one or more mathematical mode of communication suited to the given context.

Time Lesson

8-10 minutes

Introduction:

I will begin the lesson by advising the students that they will be participating in the learning stations as a

review for their end of the year ministerial exam. Each learning station will be used to revise the content they have learnt throughout the year and each learning center will have activities that will help to strengthen their math skills. The teacher will make clear the consequences, instructions and expectations for participation in their learning stations. The teacher will have all the names of the students in each of the three groups projected on the smart board. The teacher will set the timer and advice the students that they will have twenty minutes to work at their learning stations. When the timer rings after twenty minutes, this will be a cue for the students that it is time for them to rotate to another learning station (clearly state the expectations for the specific activity). The teacher will also provide the students with the learning station schedule so that the students will be aware of which learning station they will have to go to next.

Development :

Differentiation of mathematics instruction: Developing mathematical instruction that acknowledges individual differences Learning in ways that are suitable for and meaningful to them. Provide choice for students to decide which learning station they want to explore that are

reflective of various learning styles. If the student is not understanding a specific station, the student will be asked to remain at that

specific station for an additional round to clarify and solidify any misunderstandings. Make accommodations- adjust worksheets to encourage thinking at various levels (example:

Separating problems on the worksheet, large print, less problems on one page so that is it less overwhelming and highlight important parts in color)- altering learning expectations

Vary methods of of instruction and ways to demonstrate their learning. Think about the degree of complexity of the task and problems on the worksheets/ modify it

accordingly At the work with the teacher learning station- vary the delivery style so that it is suitable and

appeals to the styles of learners sitting in front of you. (Example- talk at a slower rate and change tone and pitch, break down tasks into manageable chunks, step by step instruction of finding the percent of a number, minimize distractions and represent the mathematical concepts in multiple ways)

Pre-made groups for the learning station- group students according to ability or interest. Provide extended time to complete tasks and allow for additional tools, steps and explanations to

facilitate their task (example- have students use a calculator or have them keep a multiplication chart close by to facilitate task or use more visuals to reinforce their learning)

****Depending on the learning centers schedule. Only three out of the seven learning stations will be assigned for each class.

The seven learning stations:

1) The Manipulative learning station- In this station, students will be using different types of manipulatives to help strengthen a specific math skill learnt throughout the year. For example: students can chose to use the base-ten blocks to review place value or the fraction fortress to visualize fractions, compare equivalent fractions and building fractions to make a whole. Students can also choose to solve

tangram puzzles, which will help to further develop their geometrical knowledge and reasoning.

2) The Puzzle and Problems learning station- In this station, students will be given a selection of different situational problems they can choose from. The situational problems touch upon the various mathematical skills that were developed throughout the year. Some of these include fractions, divisions, area and perimeter etc. Behind each of the problems is a chart that students will be asked to fill out. The chart serves as a guide for the students helping them to systematize the information from the problem into different categories. The three categories include What I know, what I am looking for and it is essential to think about. There will also be a space for the students to show their work in a clear and organized manner to justify their answer when solving the problem. This way the teacher will have better access to their thinking and be able to assess the students understanding accordingly.

3) The Ketchup and Pickles learning station: In this station, students will be given the opportunity to complete or catch up on any unfinished math homework or situational problems from previous classes.

4) In the Mathematical Vocabulary learning station, students will be required to choose a mathematical term from the list provided, to research further using the mathematical resources placed at their disposal. They will be given time to explore the different mathematical dictionaries like Lexi-Math and Math appeal and gather information which they will use to fill out their graphic organizer. Students will be asked to write the mathematical term of their choice in the circle in the middle of the page and find its definition, its characteristics and provide both an example and a non-example.

5) The fast facts learning station: In this station, students will be asked to use a variety of different materials to practice their fast math skills. This includes small white boards to practice long divisions, ice cube trays with two dice balls where the students will throw the dices in the ice tray and whichever two numbers the dice falls on, they will have to multiply in a fast paced manner. Students could also play the teacher-made math guess-who game where students will ask each other questions to help guess what number the other student has. For example, one student can ask their classmate if their number is prime or composite or they can ask whether their number is divisible by two.

6) The Strategy learning station- in this station, the students will strengthen their problem solving and critical thinking skills by playing various strategic games like chess and battleship. These games not only help to further develop the students reason, memory and logic, but most importantly they help to sharpen their probability skills. For example, the battleship game will help to familiarize students on how grids work, how to represent a sequence of events on a graph and better understand the relationship between columns and rows.

7) The work with the teacher learning station- In this learning station, a small group of students will gather around the smart board, where the teacher will introduce a new mathematical concept they have not yet covered. For this lesson, the teacher will introduce students to the percent of a number. The teacher will begin by eliciting students’ prior knowledge from the previous class. The teacher begins by revisiting the mathematical concepts of converting fractions into decimals and percentages. I will say something like “Can anyone tell me what a percentage mean?” “Last class we spoke about different places where we have seen the percentage symbol. “ Does anyone want to share where they have seen a percent sign” The students will provide their answers. The teacher will then say something

like “so we know that the word percent means out of 100” The teacher will then have different math examples of percent of a number already written on the smart board. For example, 20 % of 75. “How can we represent 20 % on a fraction” “The way I remember is that there are two zero’s in the percent symbol and there are two zero’s in 100. “20 out of 100 can also be written as 20 hundreds or 2 tenths. Once we have written the number as a fraction the teacher will have the students explain how to change the percentage into a decimal.

The teacher will then remind students of the steps we have to take when converting a percent into a decimal (modeled/guided practice). In order to change the percent into a decimal we must move the decimal point two spots to the left” For example: 20 percent you would move the invisible decimal point at the end of the number two spots to the left. “Then you simply multiply by 50. Remember the word “of” means to multiply in math. “So 20 percent of 50 is 20 percent multiplied by 50. Now that we have converted the fraction into a decimal, all we have left to do is multiply 0.20 x 50. The teacher will develop with the students the steps required to calculate the percent of a number.

20 % of 50 0.20 x 50 0.20 x 50 + 00 1000 10. 00

The teacher will say something like “when trying to decide where the decimal point will be placed in the answer, remember that because there are two spots after the decimal point in the problem there must be two spots after the decimal point in the answer. The decimal placement will be right between 10 and 00 (10.00). After having modeled for the students the steps taken to find the percent of a number, the teacher will then ask students to come up to the smartboard and complete one math example on their own and explain out loud each step while they are doing it so that the others students can have access to the student’s thinking (constructing their own knowledge of the subject matter at hand).

The teacher will repeat the process with a few more examples. Once the examples are completed on the smartboard, the teacher will provide the students with a percent worksheet where they will have to practice what they had just learnt on the smartboard (independent practice). If they have not completed the worksheet by the end of the class, they will have to finish it for homework.

After every 20 minutes right before the students move on to the next learning station, the teacher will ask the students to reflect on how they think the learning stations went. How was the noise level? Did

you learn something new in your learning station? Did you encounter a problem or challenge? How did you overcome it? What can we do as a class in the next round to help ensure the success of the learning stations? This way the teacher is interacting with the students about the rules and procedures for the learning stations and involving them in the decision making process of managing the learning stations to ensure that it functions smoothly.

Formative assessment/evaluation:

The teacher will assess the students by having them complete the worksheets for homework as this will help to determine whether or not the students understood what the teacher explained on the smartboard. The teacher will also assess the situation problems that were completed in the puzzles and problems learning station as well as the graphic organizers that were completed in the Mathematical vocabulary learning station. The teacher will use the results of the worksheets to determine where the students are at and to check for understanding. The teacher will then tailor or adapt the subsequent lessons to focus on the main aspects of the students’ answers that they did not understand or could not solve. This will help to solidify any uneasiness and misunderstandings.

Self reflection:

After having conducted this specific lesson in my present field experience, I took the time to reflect on my teaching performance whilst taking into consideration the comments and suggestions offered by both my cooperating math teacher and supervisor. During the lesson, I used my teaching voice effectively, which helped to engage the students and maintain their focus. I asked students to explain steps using the smartboard as they solved problems and asked students to comment and express any difficulties they had encountered in a center before switching to the next. I organized the students into groups and encouraged them to participate. I also kept an eye on students in other stations while working with a specific group. I was able to develop a wonderful relationship with the students and constantly reinforced positive behavior and good work using high fives and thumbs up. I exhibited a very positive and enthusiastic approach to the subject matter and accept constructive criticism well. The lesson was very clear and met objectives. However, I should be careful not to make written examples on the smartboard too cluttered and think about how to organize my board in a clearer manner so that the students do not get confused and could successfully follow the steps. Instead of talking over the students, I should use some different signals that would help with the management of the learning centers. This could include finger to the lips, waiting patiently or visual cues. I should have also asked more questions to each member of the group as I was demonstrating the method. This way I could consistently check for understanding before moving on to the next step. I should also work on my time management skills and pace my teaching, using smooth transitions between the stations and also making sure that everything is covered for that class. During the lesson, I found myself rushing through the subject matter at times because of my lack of time management skills. I also should have formulated tentative questions before the lesson so that I would have been more prepared and I would have used these questions to have students discover concepts on their own rather than revealing the answers within the questions I ask. Another thing I would definitely improve in subsequent lessons is to pay keen attention to my delivery style when teaching making sure that it is tailored towards the students sitting in front of me. Also I should adjust my voice quality by lowering the tone of voice when teaching because sometimes it could impede on the learning of the students in the other learning stations.