Unit Plan

EDCP 342A Unit planning

Yeni Yoo
St. John’s School, Math 8

Ratios, Rates, and Percentages

Preplanning questions:

(1) Why do we teach this unit to secondary school students? This unit explores the concepts of ratios, rates, and percentages. The unit focuses on some of the most essential mathematical skills that students could apply in their everyday lives. Students will learn to compare ratios, find equivalent ratios, do scale drawings, convert between percents, fractions, and decimals, etc. Such mathematical skills will be strongly needed in students’ future lives and will enable students to evaluate important factors more precisely and make more reasoned decisions. Students will find such mathematical skills interesting and useful as they explore more and more real-world applications where they could connect the mathematical concepts and demonstrate their knowledge through problem solving.

(2) A mathematics project connected to this unit: Students will design their dream classroom using their knowledge of ratios. Students will use scale drawing skills to draw their dream classroom on a graphic paper. They will demonstrate how they found dimensions of the classroom and converted those to a new scale. They will be provided some online shopping malls where they could look up for furniture and equipment for interior design. They will need to use those resources to design their classroom, specify original dimensions of every item they use on a separate sheet of paper, and show work how they found new dimensions for scale drawing. The aim of the project is for students to apply the mathematical skills they have learned to a real-world problem and develop their understanding. Students will be given some of the in-class time to start on the project and ask questions if needed. They will be required to finish the work as homework and be given about two weeks to complete. Students will be assessed based on their understanding of the content and communication skills. They will need to demonstrate a clear knowledge and application of math skills they learned in class to complete the problem accurately. The overall work should also be presented clearly: detailed, well-organized, and easy to follow.

(3) Assessment and evaluation: Throughout the unit, there will be various forms of assessments, including weekly take-home assignments, bi-weekly quizzes, a math project, described above, a unit test, and frequent in-class discussions. Weekly take-home assignments, bi-weekly quizzes, and in-class discussions will be formative assessments that will be used to check students’ levels of understanding and progress on the content. Weekly assignments will be mainly straightforward problems requiring basic knowledge of the content and be checked randomly during class. Quizzes will be short, for about 10-15 minutes, mainly focusing on the essential math skill students have recently learned in class. In-class discussions will take place when there is a debatable question, through which students will demonstrate their critical thinking and communication skills. A math project and a unit test will be summative assessments that will be used to check students’ overall understanding of the content of the unit. The math project will assess students applying their mathematical skills, including creative thinking and communication skills, to the real world. The unit test will take the whole class time for students to write and test them on the overall understanding of the entire unit. It will consist of various parts, such as T/F questions, matching questions, and short answer questions.

Elements of your unit plan:

Lesson	Topic
1	Introduction to Ratio
2	Ratio Visualization
3	Ratio Application
4	Proportional Relationships
5	Introduction to Rates
6	Introduction to Percents
7	Percents, Fractions, and Decimals
8	Percents of Numbers
9	Percentage Change
10	Unit Test

Lesson Plan of Lesson 1: Introduction to Ratio

Topic: Ratio	Grade: Math 8	Date: Dec 15, 2017	Duration: 60 minutes
Lesson Overview	(History of Mathematics) This lesson focuses on the meaning of ratio and when we use this idea. In this lesson, we will discuss some basic examples of the usage of ratio. Students will also be introduced to its history.
Prior Knowledge	No required knowledge.
Learning Objective/Goals	Develop mathematical understanding through problem solving       Through history research activities, engage in connecting to other cultures       Explain and justify mathematical ideas and decisions

Materials and Equipment Needed for this Lesson

Electronic devices (laptop, tablets, or phones)         Papers

  

	Lesson Stage	Class & Teacher Activities	Time
1	“Hook”	What is ratio? (TPS) Students will be asked if they know what ratio means, when we use this idea, what we need to measure it, etc. Students will first be given a minute to think about then discuss the questions in pairs and, finally, share their final ideas to the class. Summarize all the information about ratio and correct if needed: when it is used, how it is represented, and some examples of part-to-part and part-to-whole ratios. Ask students if they are aware of any ratios in the surroundings, such as ratios of the sides of their phones and tablets. Introduce students to the idea of the golden ratio and some examples of it. Students will need to find more detailed history and usage of it through the research activity.	10 min
2	Presentation	Introduction to History Research Activity Students will be introduced to an activity, where they will work in groups of 3-4 people. Each group will be given a paper where they will draw their K-W-L-Q charts.	5 min
3	Practice & Production	History Research Activity (KWLQ) Groups will first write down what they know about ratios under K (know) and come up with questions, or anything that they are unsure about our today’s topic, and write those under W (want to know). The ideas can be based on our class discussion on 'what is ratio' and the brief explanation about the golden ratio. The ideas can be about the history of ratio but not necessarily. If there are any unanswered or arising questions, they can write those under W column. Then students are encouraged to research about the history of the concept. For about 15 minutes, with their electronic devices, students will research the topic and try to answer all their inquiries. Anything they have found will go under L (learned), and whatever they could not answer and they wish to find will go under Q (further questions). Students will be given 5 minutes to prepare for their mini-presentations. When all the groups are ready, each group will present their KWLQ chart to the class (roughly 3 minutes each).	40 min
4	Closure	Announcements Students are expected to find answers to their remaining questions under Q section for take-home assignment.	5 min

Assessment/ Evaluation of Students’ Learning

The posters each group has made and their presentations will be formal assessments. Teacher will assess students’ research and communication skills. Students are also expected to work collaboratively during the activity. Teacher will check on their take-home assignments next class, which will be a part of formative assessment.

Lesson Plan of Lesson 3: Ratio Application

Topic: Ratios	Grade: Math 8	Date: Dec 15, 2017	Duration: 60 minutes
Lesson Overview	(Arts and Mathematics) This lesson focuses on real-life applications of ratio and proportion. In this lesson, we will discuss possible situations where we would need mathematical knowledge of ratios and proportions in our daily lives, such as when preparing meals and estimating the size of a country by looking at a map. Students will be introduced to a math project, in which they are expected to creatively redesign their classroom using their mathematical skills.
Prior Knowledge	Students have learned to find equivalent ratios and present ratios using visuals, such as number lines, tables, and diagrams.
Learning Objective/Goals	Apply mathematical ideas to real-life problems using reasoning and logic       Estimate reasonably       Visualize to explore mathematical concepts       Use scale drawings to represent real-life objects on paper

Materials and Equipment Needed for this Lesson

Whiteboard, basic markers       Graph paper for all students

  

	Lesson Stage	Class & Teacher Activities	Time
1	“Hook”	Why do we need to know ratios? Students will be asked to come up with real-life situations where they would need to apply their mathematical knowledge of ratios and proportions in their everyday lives. Main points or examples will be written down on the board, by the teacher or a student. It is important to engage all students in the discussion and make sure they know why they are learning ratios. The last application to discuss will be scale drawing. Students will discuss about why and when we do scale drawings and how scale drawings are done.	10 min
2	Presentation	A Math Project: My Dream Classroom Students will be introduced to basic methods of doing scale drawings using their knowledge of ratios. Then the math project described above will be introduced and explained. Students will be given specifics of the project, such as which mathematical skills they are expected to apply to solving problems, the criteria that the final work should meet, and the deadline.	15 min
3	Practice & Production	Working on the project The first thing students are expected to do is measure the dimensions of the classroom. They will use whatever unit they would want to use, cm, m, feet, or steps. They will use their mathematical skills to scale down the dimensions they have, and they will show work. Students are expected to use the class time wisely to either ask teacher questions about the project or research for classroom interior designs they would want to refer to. As the next lesson is on Proportional Relationships, students will then be introduced to more examples of scale drawings, which will provide them with more practice opportunities. This lesson is more focused on planning their project.	30 min
4	Closure	Announcements Wrap up 5 minutes before the end of class. Make sure they know all the criteria they are expected to meet and the deadline for the project.	5 min

Assessment/ Evaluation of Students’ Learning

There will be informal assessments during class. Students are expected to ask questions regarding scale drawing and the project. Teacher will consistently walk around to see if students are on task and know what to do. Students are expected to at least measure dimensions of the classroom and start designing their dream classroom by the end of class.

Lesson Plan of Lesson 8: Percents of Numbers

Topic: Percentages	Grade: Math 8	Date: Dec 15, 2017	Duration: 60 minutes
Lesson Overview	(Social/environmental justice) This lesson focuses on the concept of percent and the percent of a number. In this lesson, we will try to represent children with an immigrant background in Canada in percents and discuss the diversity of the population.
Prior Knowledge	Students have learned about ratios and rates and how percents can be converted to decimals and fractions.
Learning Objective/Goals	Find what percent one number is of another       Estimate percents of numbers reasonably       Compare percents of numbers       Visualize to explore mathematical concepts       Represent mathematical ideas in symbolic forms

Materials and Equipment Needed for this Lesson

Whiteboard, basic markers        3 red, 3 yellow, 1 green, 8 blue, 5 white, 3 black flash cards

  

	Lesson Stage	Class & Teacher Activities	Time
1	“Hook”	Population in Canada Students will be asked if they know how many percent the total population in Canada makes out of the world population. Let them guess without searching, then tell them what they need to know to find the percentage (the total population in Canada and the world population).	2 min
2	Presentation	Percent of a Number When students find the numbers (the total population in Canada and the world population), let students guess first how to find the percentage of the total population in Canada out of the world population. Some students might already know but wait until everyone is engaged in guessing, then show them how to find the percent of a number. Show students other simple examples just for them to practice. (Teacher can make a student come up to the board and solve the problems instead.) Solving the problems, teacher will show students various ways to represent the percent: a pie chart, area chart, and/or bar chart.	13 min
3	Practice & Production	Percent of a Number Activity Assume the number of students represents the population of Canada and distribute the flash cards, red, yellow, green, and blue, to everyone (not everyone has to have a card but make sure a student does not have multiple cards). The green card represents people 65 years of age and older (3.6%), the blue cards represent children 14 years of age and younger (40%) in 1871. The red cards represent people 65 years of age and older (16.9%), and yellow cards represent children 14 years of age and younger (16.6%) in 2016. Make each colour stand up at a time and explain what the colours represent. Make students come to the board and calculate the percent of a number and then give them the exact percentage. At this point, ask students what they think of this generational shift, what consequences this might have caused, and what they predict the future percentages will be. If time permits, distribute students the remaining cards, white and black. The white cards represent people 65 years of age and older (23%), and the black cards represent children 14 years of age and younger (16%) in 2031 (these are estimates from population projections). Let students calculate the percents and then give them exact numbers. Encourage those students who have not gone to the board yet. Explain students the reason and consequences of the generational shift, such as the first baby boomers turning 65 and older and leaving the labour market. Explain them the significance of it: pension, health care and services for those people and proportionately fewer people in the labour market. Note: The class is 20 students. Resource: www.statcan.gc.ca/	40 min
4	Closure	Announcements Wrap up 5 minutes before the end of class. Remind students that there will be a mini quiz next class on the percentage section and that they are expected to know how to convert amongst three representations of percent, percents, fractions, and decimals, and how to find the percent of a number.	5 min

Assessment/ Evaluation of Students’ Learning

There will be an informal assessment. Teacher will assess students' communication skills and their understanding of today's topic. Teacher will again check on their understanding of today's topic next class with formative assessment.