Unit Plan

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

Your name: Ashley WU
School, grade & course: R.A McMath Secondary, Grade 8 Math

Topic of unit:  Percent, Ratio and Rate

Preplaning 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? The big idea of this topic, according to the curriculum, is to know about how numbers present, compare and describe the quantity of ratios, rates, and percents. In my point of view, this topic is included in the curriculum in order for students to know about what percentage and ratios stands for in their daily life and in some research results. With this point of knowledge, they are able to carry on doing math and statistics in higher grades, know some basic knowledge of doing survey and research, and do shopping more efficiently. This topic is also related to distributing limited resources, which is a part in the following chapters in their textbook. It could be a chance to do preview of the next chapter and learn some basic idea of time-management skill. Distributing resource is relevant to division so that students can do some revision on that.  Teachers could also do a small math history workshop about how ancient Egyptian distribute things (do divisions).

(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) The name of the project is “Giant Recipe”, and is related comparing rates and ratio. The topic is about students imagine them lying on a huge dish and their height equals to the diameter of the dish. They need to search on recipe of a type of food and place their food on the dish, or they will “be eaten by the giant (in story)”. Students need to figure out the amount of ingredient needed for them to cook the food and how long will they need to make these ingredients into cooked-food. This is the setting of the story project, and students will be working in pairs or trios to finish this project. In the last class, they will be presenting in front of the class about their finished story within 5 minutes. They are expected to write their stories down and give steps how how they figured out number results, and their story paper will be collected. They are also encouraged to produce other works like posters and drawing, however, the art product will not be assessed. Their clearance of presenting and the accuracy of number results will be regarded as their performance in the chapter. Students will also do a peer-assessment after finishing the presentation. Here is a rubric of the presentation. Essential Elements Quality Indicator Students show clear interpretation and the step is easy to follow 3 – Steps are easy to follow, and the result is accurate. 2 – Steps could be followed, and the result is correct. 1 – Difficult to follow steps, and big mistake in result. N – No questions answered. Student is cooperative in the project and uses math knowledge in the story. 3 – Be cooperative and connected with math. 2 – Be cooperative most times and tried to connect with math. 1 – Showed some teamwork, but did not do math. N – Did not participate. Teacher will usually give same grade to every member in the group unless the one of the students is not showing any work or being marked badly in peer-assessment.

(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) Students will be assessed as follows - The performance in classroom and workshops (Participants in activities and etc) - The completeness of homework and assignment - The final assessment (project and chapter exam) In this chapter, there will be chapter test, and it could not be replaced by the project. Students will be assessed with both test and project, and both of them are short. Homework will not be marked, but checked on completeness instead. If student could not show their work, they will not get full credit on this. If there is any plagiarism observed, student will be marked as not completing homework, and the issue will be reported to advisors, parents and principal(if possible).

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	Relating Fractions, Decimals, and Percents
2	Fractions and Distributing Resources
3	Calculating Percents
4	Solving Percent Problems
5	Sales and Discount + “Comparison Market”
6	Exploring Ratios
7	Equivalent Ratio
8	Revision and Workshop “Fact of Water”
9	Exploring Rates
10	Comparing Rates
(11)	Small revision and chapter test.
(12)	Presentation of project

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’

Subject: Mathematics	Grade: Grade 8	Date: Feb 5th, 2018	Duration: 80 min
Lesson Overview	This lesson is about introducing basic idea of distributing resource and some math history of how Ancient Egyptian divide things.
Class Profile	20 Students, they are either native English speakers or at least level 4 ELL students.

Content

Students will know about how do divide things in term of fractions and how it is related to percentage. They will also know about math history related to division and fractions.

Materials and Equipment Needed for this Lesson

Pen or pencil. Notebook. Fraction Circles.

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	Share a joke at the beginning. Fraction circles will be handed out for students to figure out why the joke is funny. The joke is “You better cut the pizza in four pieces because I am not hungry enough to eat six”.	10 minutes
2.	Presentation	Do a small revision about how to convert fraction into percentage. Ask students how would they share several pizzas with several people, and show their method by using the fraction circles. The number of people could not be 2 or square or cube value of 2. Students will do the activity with their neighbors. After doing in groups, one of each group will go on white board and show their math steps and the divide circle on board.	25 minutes
3.	Math History	Introduce how Ancient Egyptian divide things by showing one example question. Ask students if they could find ancient Egyptian way to do the question. And they need to present in front of the class again.	40 to 45 min
4.	Reward	This will be 5 more minutes break for them if they finished everything.	0 to 5 min

Assessment/Evaluation of Students’ Learning

Students will be working most of time in this class, they could do discussions and use fraction circle to solve problems. Teachers will observe students and see if they are working on math. This part is not in their curriculum and distributing resource is what they will learn in the next chapter. They will not be assessed on their quality of presentation as long as they tried.

Reflection

It is actually a better chance for students to know this when learning fraction, but it is not too late. This is a chance for them to “play with toys” and know some interesting facts of math. This less more like a workshop rather than a traditional classroom. It is actually students going to work and present, what teachers need to do is to manage classroom and make sure if students are working on the right way.

Subject: Math	Grade: 8	Date: Feb 14th, 2018	Duration: 80 min
Lesson Overview	This lesson is about percentage and how it is related to discount in shopping situation. Students will do a discussion and debate around an open question.

Content

Students will know what discount means in terms of money. They will also learn how to compare prices between two stores.

Materials and Equipment Needed for this Lesson

Examples of coupon and promotion brochure. Projector

	Lesson Stages	Learning Activities	Time Allotted
1.	Reading	Use projector and read the promotion brochure and some coupon with students. Ask students what do discount on the coupon or brochure means (e.g. how much money do they need to pay and how much they save).	30 min
2.	Debate	Give students an open-ended question and let students with same choice stay together and do a discussion. After that, students will speak about why they made the choice and try to persuade other students to agree with them. The question is “Store A is 20% off everything. Store B reduce $10 from the label price and have a 10% discount. If you want to buy a pair of shoes, which store would you go?”.	35 min
3.	Closure	Change the question by providing the price of the product, and ask students if they stick with their choice. Then change the price and ask the same question again. Do a summary of this topic – that is, we could make better decision if more information is provided.	15 min

Assessment/Evaluation of Students’ Learning

Students performance will be assessed. If they are active in the discussion and could explain their reason clearly, they deserve a mark.

Reflection

If we give out open-ended question, students are expected to give more explanation on their answers. The question assigned is also the question with more than one answers, so that we should not evaluate students on their answers. However, thinking about questions with more than one solution (or no solution) is a good chance to improve their critical thinking skill. Doing discussion and debate can improve their speaking skill, and giving them such chance also means we encourage them to speak up their opinions. This class can also be done outside classroom, they can either do discussion in a meeting room or rotunda. I thought about going to show them around grocery stores but give up my idea since it is too difficult to manage the class.

Subject: Math	Grade: 8	Date: Feb 22nd, 2018	Duration:  80 min
Lesson Overview	This lesson will be divided into two parts. The first part will be done in computer lab, and students will do a research on some data of usable water resource. In the second part, students will go to chemistry or physics lab. In the lab, there will be a big water tank. Students will be asked to imagine the water tank as all water on earth and take out only the usable water resource out of the tank.

Content

Students will do revision of equivalent ratio by doing this activity. They will also learn more about water resources and why people need to save water.

Materials and Equipment Needed for this Lesson

Huge water tank that can carry 10 liters of water. Small beaker. Pen or Pencil Scratch paper. Note.

	Lesson Stages	Learning Activities	Time Allotted
1.	Internet research	Give out students few questions for them to figure out. -          What is the percentage of water on Earth? -          What is the percentage of fresh water on earth? -          How much percent of fresh water is usable? -          How much percentage of water is usable? -          How much water does one person consume per year? -          What do you think about this research result? Students will do research on Internet on the questions above and take notes.	35 min
2.	Lab Operation	Take students to chemistry/physics lab, where there is a huge water tank containing 10 liters of water. Students will be asked to use knowledge of equivalent ratio to figure out how much water is usable if the water tank is considered as all water on Earth. They need to take usable water out by using the beaker.	30 min
3.	Small talk and Reflection	Students will talk about what they feel about this activity and what do they think of doing in the future. They need to write an exit slip for this class.	15 min

Assessment/Evaluation of Students’ Learning

This is a workshop related to environment justice. Their exit slip will be collected in the next class and will be read (for teachers to see if they are aware of water resource issue). They will be observed by teachers during the class. They will all have chance to talk about their opinion in the last part of the lesson.

Reflection

Social justice and environmental justice issue is the topic that is considered to be difficult to teach in math class. However, it is the topic that every teacher need to talk about. In this unit, students learn about ratios and percentage, which are easy to relate to problems in reality. Instead of staying in classroom, they will do the activities in two different classrooms. The changing of place may raise their curiosity. Since students are in grade 8 and may have never used beaker. It is also a chance for them to try using beakers for measurement (and would help with their chemistry learning in higher grade).