Unit Plan + 3 Lesson Plans

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name: Tiffany Qi (Yajun Qi)
School, grade & course: Sir Winston Churchill Secondary School, Grade 9, Mathematics

Topic of unit (NOTE: This should be a unit you will actually be teaching on practicum!):

Chapter 8 Probability and Statistics

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words) Taylor mentioned that according to Bruner “If the understanding of number, measure, and probability is judged crucial in the pursuit of science, then instruction in these subjects should begin as intellectually honestly and as early as possible in a manner consistent with the child's forms of thought… If one respects the ways of thought of the growing child, if one is courteous enough to translate material into his logical forms and challenging enough to tempt him to advance, then it is possible to introduce him at an early age to the ideas and styles that in later life make an educated man.” (Taylor, 2011) As can be seen from these sentences, learning probability and statistics topic could help students develop mathematical and logical thinking. It will be beneficial for all the students even in the future. Moreover, according to BC new curriculum, students will have chances to learn about population versus sample, bias, ethics, sampling techniques, misleading stats, analyzing a given set of data (and/or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity and using First Peoples data on water quality, Statistics Canada data on income, health, housing, population. Students could use what they learnt from this topic to analyze real-world problems and get chances to explore further in mathematical way.   Work Cited Taylor, F. M. (2011). Why teach probability in the elementary classroom. Louisiana Association of Teachers Mathematics Journal, 2(1).

(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words) Data Project Description Students could work individually or work in groups of 2or 3.  The final assessment will be a 5-min presentation. There are three options for students to complete this project. Option 1:  Population VS Sample in Statistics Students are expected to understand the basic concepts in Section 8.1-8.2. Make a survey about any topic they feel interested in. Collect some data and introduce the population, sample, sample methods, bias/unbias for the corresponding topic. The final statement will be required to present in their presentation.  For example, favorite TV program survey. Option 2: Measure of Central Tendency and Graph Students are expected to find some data from any topic they feel interested in. Then they should apply what they learned from section 8.3-8.4 and analyze those data. Find mean, median, mode and graph the sample data. The final statement will be required to present in their presentation. For example, employee salaries list. Option 3: Probability Students are expected to find some data from any topic they feel interested in. They need to provide all outcomes of a sample space, number of outcomes of specific events, and the probability of these events. They should choose at least 3 different events in one sample space to analyze collecting data. The final statement will be required to present in their presentation. For instance, the sum of rolling two dice.  Goal Students should be able to apply the mathematical skills they learned in this chapter. Find real world problems they are interested in, analyze the collecting data, and provide their statements for the corresponding topics. Process and Timing Students will have one week for this project. They could collect data by doing research or doing survey or other methods. The final assessment will be a 5-min presentation. Self-assessment and peer-assessment will be required after presentation finish. What the students will be asked to produce Collecting data, results for corresponding options, final statements, a 5-min presentation, self-assessment worksheet, peer-assessment worksheet. How you will assess the project Evaluating the accuracy of students’ results and final statements. Observing presentation. Collecting self-assessment and peer-assessment worksheet.

(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words) To build a fair and comfortable learning environment for students, I am planning to apply formative assessments into every class to help students improve themselves. On the other hand, I will also give students some in-class exercises for them to practice, for example textbook questions or in-class worksheets. After chapter review class, there will be a unit test as well. All the questions in this test can be solved by the methods which mentioned in previous lessons. The following assessments will be used in this unit for teacher to assess and evaluate students. Formative Assessment: Entry/Exit Slips, Discussion, “Kahoot!”, Peer/Self-Assessment, Presentation, Concept Map, Data Project. Summative Assessment: Pop quiz, unit test. (Students could have one and only one chance to redo the quizzes and test if they fail in first time. Both marks will be counted to make sure it is fair.) Informal Assessment: Four Corners, Quick Write, in-class exercises Observational Assessment: Rubrics, direct observation, Peer/Self-Assessment, Checklists. Formal Assessment: Homework, quiz, test.

Elements of your unit plan:

a)  Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.

Lesson	Topic
1	8.1 Population Versus Sample in Statistics
2	8.2 When to use a Population or a Sample in Statistics
3	Analyze Social/Environmental Justice Problems in Statistics
4	8.3 Measure of Central Tendency in Statistics
5	8.4 Misleading Graphs
6	Arts and mathematics
7	8.5 Probability Part I
8	8.6 Probability Part II
9	Thinking Classroom
10	Presentation
11	8.7 Chapter Review
12	Unit Test

b) Write a detailed lesson plan for three of the lessons which will not be in a traditional lecture/ exercise/ homework format.  These three lessons should include at least three of the following six elements related to your mathematical topic. (And of course, you could include more than three!)

These elements should be thoroughly integrated into the lessons (i.e. not an add-on that the teacher just tells!)

a) history of this mathematics

b) social/environmental justice

c) Indigenous perspectives and cultures

d) Arts and mathematics

e) Open-ended problem solving in groups at vertical erasable surfaces (“thinking classroom”)

f) Telling only what is arbitrary, and having students work on what is logically ‘necessary’

Analyze Social/Environmental Justice Problems in Statistics

Lesson Plan

Subject: ___Mathematics_____ Grade: ___9______	Lesson Number: ___3____of _12______ Time: __70-80_____ minutes Class Profile: 30 students
Big Idea: Students will understand that... Analyzing the validity, reliability, and representation of data enables us to compare and interpret.
Objectives: SWBATs [aim for a maximum of 3 content, and relevant others specific to each category -Students will be able to use some concepts they learned from last two lessons to analyze collecting data - Students will interact in groups to go through real world problems together - Students will be able to present their findings for rest of the class
Content: What students will know. -    Using First Peoples data on water quality, Statistics Canada data on income, health, housing, population -   Analyzing a given set of data (and/or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity - Population versus sample, bias, ethics, sampling techniques, misleading stats		Curricular Competencies: What students be able to do. - Use reasoning and logic to explore, analyze, and apply mathematical ideas - Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving - Use mathematical vocabulary and language to contribute to mathematical discussions - Connect mathematical concepts to each other and to other areas and personal interests
Materials/equipment needed: Laptop, Internet, whiteboard, whiteboard markers, exit slips.
Assessment/Evaluation of Students’ Learning: Assessment: Presentation, Exit Slips. Evaluation: Direct Observation, collecting exit slips, in-class discussion.

	Lesson Stages	What the teacher will be doing	What the students will be doing	Time
1	Warm-up	Show students two videos about social and environmental justice to help them have a brief understanding about this topic. https://www.youtube.com/watch?v=bcWZZeXOegw Social Justice https://www.youtube.com/watch?v=dREtXUij6_c Environmental Justice	Watch these two videos. Think about what is social justice, what is environmental justice.	5-6 mins
2	Practice	Take students to school library. Set up them into groups of 3 and give one reading challenge.	To complete this challenge, students should use the mathematical skills they learned in last two lessons.  Find and analyze some data as evidences to support their corresponding example as one of social/environmental justice problems.	20 -25 mins
3	Discussion	Discussion Time.  Each group will present their examples and evidences for rest of the class.	Each group will have 2-3 mins to present their findings. “Audiences” need to give feedback to presenters and tell them if their examples are social/environmental justice problems or not and why.	35-40 mins
4	Closure	Give students Exit Slips. Ask them the following questions:	Answer these two questions on Exit Slips. Hand in Exit Slips in the end of the class.	4-5 mins

Reflection

1.     Time management might be different for different classes even they are all in the same grade. 2.     Students might have problems about how to do research in school library or how to find effective data for their reading challenges.  Teacher should walk around and give them some help if they need. 3.     Teacher should give back the exit slips in next class with some comments.

Arts and Mathematics

Lesson Plan

Subject: ___Mathematics_____ Grade: ___9______	Lesson Number: ___6____of _12______ Time: __70-80_____ minutes Class Profile: 30 students
Big Idea: Students will understand that... Analyzing the validity, reliability, and representation of data enables us to compare and interpret.
Objectives: SWBATs [aim for a maximum of 3 content, and relevant others specific to each category -Students will be able to use some concepts they learned from last two lessons to build their art project. - Students will interact in groups and work together. - Students will be able to present their characters’ stories for rest of the class
Content: What students will know. -   Analyzing a given set of data (and/or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity - Population versus sample, bias, ethics, sampling techniques, misleading stats		Curricular Competencies: What students be able to do. - Use reasoning and logic to explore, analyze, and apply mathematical ideas - Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving - Use mathematical vocabulary and language to contribute to mathematical discussions - Connect mathematical concepts to each other and to other areas and personal interests
Materials/equipment needed: Color pens/markers, some paper, Graphs, Kahoot, laptop, Internet.
Assessment/Evaluation of Students’ Learning: Assessment: Presentation, Kahoot! Evaluation: Direct Observation, collecting group art project, in-class discussion.

	Lesson Stages	What the teacher will be doing	What the students will be doing	Time
1	Warm-up	Using Kahoot! to go through the review questions for section 8.3-8.4. Make sure in each group, there is at least one electric device. Read aloud each question and may give some sample hints or descriptions to help students follow the whole quiz.	Using the electric device to join the Kahoot! game. By attending this online quiz, students have chances to review some classic questions from section 8.3-8.4.	5-6 mins
2	Practice & Presentation	Group Art Project: Ask students to apply what they learned from section 8.3-8.4 to draw a character. Specific requirements: The length of this character’s name will be the mean value of the length of all group members’ names. The height of this character will be the median value of the height of all group members. (Draw a correct scale for your characters to avoid misleading graph.) The month of birth for this character will be as same as the mode value of all group members. Collect students’ art work in the end of this class.	Students are expected to work in groups of 5. Everyone needs to provide three numbers — length of their names (how many letters in their names), height of them (the unit is cm), month of birth (July represent 7). Create a character for your group. Present your character’s background story for rest of the class. (Every group will have 5 mins.)	25-30 mins 30-35 mins 3-4 mins

Reflection

1.     Time management might be different for different classes even they are all in the same grade.   2.     Make the description of this art project clear enough. As a result, all the students know what they need to do for this project. 3.     If some students feel confused about pervious concepts (mean, median, mode, misleading graph), teacher will give some help.

Thinking Classroom

Lesson Plan

Subject: ___Mathematics_____ Grade: ___9______	Lesson Number: ___9____of _12______ Time: __70-80_____ minutes Class Profile: 30 students
Big Idea: Students will understand that... Analyzing the validity, reliability, and representation of data enables us to compare and interpret.
Objectives: SWBATs [aim for a maximum of 3 content, and relevant others specific to each category - Students will be able to use some concepts they learned from last two lessons to solve corresponding questions - Students will interact in groups to collect experimental data together
Content: What students will know. -   Analyzing a given set of data (and/or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity		Curricular Competencies: What students be able to do. - Use reasoning and logic to explore, analyze, and apply mathematical ideas - Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving - Use mathematical vocabulary and language to contribute to mathematical discussions - Connect mathematical concepts to each other and to other areas and personal interests
Materials/equipment needed: Some dice, whiteboard, whiteboard markers.
Assessment/Evaluation of Students’ Learning: Assessment: Dice Game, Participation of Discussion Evaluation: Direct Observation, in-class exercises (experimental data and theoretical answers), in-class discussion.

	Lesson Stages	What the teacher will be doing	What the students will be doing	Time
1	Warm-up	Ask students to use two strategies to solve the following questions: 1. Two dice are thrown. What is the probability that the sum of two faces is equal to 7? 2. Two dice are thrown. What is the probability that identical faces turn up on the two dice?	Work individually first and try to find the correct answers.   Check your answers with neighbors. Do you use the same methods?  Do you get the same answers?	5-7 mins 3-5 mins
2	Practice	Set up students into groups of 2 or 3. Provide two dice for each group. Let them try to throw dice by themselves and ask them to check their answers with the actual outcomes. Different or same? Round 1: The Maximum throwing number is 10. Round 2: The Maximum throwing number is 20. Round 3: The Maximum throwing number is 30.	Listen carefully and prepare to play 3-round dice game. Try to throw these dice 10 times and take notes for the outcomes. Check outcomes with their answers. See if they are different or not. Try to throw these dice 10 more times and take notes for the outcomes. Check outcomes with their answers. See if they are different or not. Try to throw these dice 10 more times and take notes for the outcomes. Check outcomes with their answers. See if they are different or not.	2-3 mins 8-10 mins 8-10 mins 8-10mins
3	Discussion	Ask each group to provide their experimental data (10 times, 20 times, 30 times) Discussion Time: Why are those data all different/similar? Is there any difference between experimental data and theoretical answers? If yes, Why?	Write down experimental data on whiteboard. Discuss those questions in groups of 3 or 4. Discuss with teacher.	3-5 mins 10-15 mins
4	Closure	Give a brief summary of this class. Ask students if they have any more questions. Collecting in-class exercises (experimental data and theoretical answers)	Take notes if they want. Ask questions if they feel confused about anything. Hand in in-class exercises.	4-5 mins 1-2 mins

Reflection

1.     Time management might be different for different classes even they are all in the same grade. 2.     Make the description of this dice game clear enough. As a result, all the students know what they need to do next. 3.     If some students feel confused about pervious concepts, teacher will give some help.

Google Doc link:

Unit Plan: 

https://drive.google.com/file/d/16mMFV53F9c_3u7jcRceMfwM1mQ_5b0wM/view?usp=sharing

Lesson Plans:
https://docs.google.com/document/d/11y5Rm9dO-m4FxP6s1-qzURlzApp7zyZYYOiVgRtsREM/edit?usp=sharing