MAED 314A Unit Plan Template

Name: Vincent Collins

Title of unit and grade/ course: Shape & Space – Math 10

1) Rationale and connections:

a) Why do we consider it important for students to learn this topic? Why is it included in the IRPs? (<>

spatial recognition and navigation is difficult for a lot of students who: can’t visualize shapes in their mind can’t describe a line segment in terms of an equation have difficulty with concepts like slope or rate can’t read maps easily being able to understand geometry and shapes helps with basic organizational and planning skills artists rely on concepts like perspective, size, shade & angle to render an image geometric principles are useful in all branches of mathematics and are necessary to progress in scientific subjects the subject unleashes a world of possible problems to solve and new explorations both in science and art to undertake

b) What are the historical origins and connections for this topic? (<100>

the Egyptians needed to use complex geometry and mathematics to determine the volume of a pyramid and to understand the physics behind building one the Babylonians used the movement and speed of the sun to set units of time and distance the Indians determined the relationship between the sides of right angled triangles, noting many ‘triples’ (e.g. 3,4,5 ; 5,12,13 ; etc.) the Greeks popularized and theorized concepts in geometry to expand the mathematics that described possible solids and volumes relationships between simple objects can be learned at any age and should be encouraged, especially for those who have the mathematical methods modern technology and structure is all derived from ancient principles of geometric relationships

c) How does this topic connect with life outside mathematics? (<100>

art relies heavily on principles of geometry & shapes architecture, construction, landscaping, athletics, exploration & more rely on these principles basic work in home improvement and organization can be more fruitful with a knowledge of geometry dividing a pie into 3 equal pieces can be done by sight, and dividing up any object into fair number of equal pieces is much better done with this knowledge concerns of safety when dealing with ladders, tire irons, shovels, etc. building stadiums so that every participant has a decent view

2) Balanced teaching, assessment and evaluation plan

a) Describe your balanced assessment and evaluation plan. Consider: •teacher, peer and self-assessment; •assessment of student learning, of teaching, and of the unit as a whole •the weighting of marks to take account of summative and formative assessment, instrumental and relational learning

Unit Test: This will be a standard test aimed to familiarize the students with standardized tests (i.e. Provincials) and give a base mark for their progress. Section Test: This will be summative assessment of their progress to make sure they stay on task and to help let the students know where they are. Problem project: This is a task that will allow for more creativity and self-directed learning. The students will take ownership of a concept and present it. Class participation: This is a formative assessment of their progress and growth in my class. The marks are given based on contribution, attention, attendance, behaviour and positive attitude towards learning. Peer presentation: This think-pair-share approach to problem solving allows groups of students half an hour to solve a problem before sharing it with the class. Homework: This is practice of concepts learned and is useful for ensuring retention of information past the classroom door. It will be used sparingly however, because students may already be facing too much homework. In-class worksheets: These are fun activities that allow students to explore concepts at their own speed.

b) Project title and 50-word description CITY DESIGN The students will have to use their knowledge of shapes, space and geometry to design a city that has specific limits of construction. Mainly, there must be at least a certain number of buildings of certain heights that must be a maximum distance away from a water source, and receive a minimum amount of sunlight, given the surrounding buildings. This optimization problem will present many difficulties and be challenging and fun for students.

c) List of 10 lessons with brief topic outline and teaching strategies to be used.

Lesson topic	Teaching strategies/ approaches used
1) Sine & Cosine Laws	-lecture & demonstration of laws -practice problems to work on -group work drawing of perfect circle with calculator and ruler(no protractor/compass)
2) Tangent Law & Pythagoras	-lecture & demonstration of law -proofs of Pythagorean Theorem -worksheet with sample problems
3) Identifying 2-D Objects	-clip from Flatland movie as ‘hook’ -nomenclature of n-sided shapes -problems & homework calculating circumferences and areas of shapes
4) Identifying 3-D Objects	-nomenclature of n-sided solids -problems & homework calculating surface area and volume of solids -section quiz
5) Perpendicular & Parallel Lines (Proofs and problems)	-introduction to basic proofs using deductive, ‘two-column’ problem solving -students working in groups to create their own proofs -proof problems for homework
6) Problems of accuracy and estimation	-measuring heights and distances of macroscopic, real-world objects -problems requiring estimations -problems where accuracy depends on where you’re measuring angles or lengths of a triangle
7) Calculating slope & solving multi-step problems	-lecture & demonstration of calculating the slope of a line -class participation on the board, involving problems with multi-step solutions -section quiz
8) Formalizing lines into equations	-f(x)=m*x+b -calculating intercepts -seat-work and homework calculating lines in 2 (& 3) dimensions
9) Review Day & seat-work time	-review of concepts learned -creation of review sheet to be handed in for marks and returned for the unit test -playing with manipulatives and spending time working on their group project
10) Unit Test	-unit test encompassing everything the students have learned, and challenging them to think outside the box

3) In detail:

a) Lesson plans for three lessons, showing a balanced instructional approach. (Note that you cannot use only lectures, homework, quizzes and tests to pass this assignment – that does not characterize a balanced approach!) Each lesson plan should be one page long.

b) Project plan for the unit project. Include a description, a rationale and a marking scheme (one page total).

LESSON A – Math 10

Unit: Shape & Space

Topic: Identifying 2D Objects

I. PLO:

a. apply the sine and cosine laws to solve problems

II. SWBAT:

a. Calculate angles and lengths of regular 2D objects

b. Estimate solutions to optimization problems involving size

c. Calculate the area of regular and irregular objects

d. Understand the relationship between θ and n for n-sided shapes

III. Teaching Objectives:

a. Challenge the students to re-evaluate their intuition and understanding of ordinary objects with a mathematical perspective

b. Solve optimization problems involving size

IV. Hook: Show a scene from Flatland

a. This is the one where the ‘Sphere’ lifts A. Square off the plane of Flatland and into the realm of the 3D.

V. Lecture: Provide students formal definitions of 2D objects

a. Nomenclature of n-sided objects from n=1-10

b. Relationship between θ and n

c. Formalism for calculating the areas

VI. Participation: Provide the students with cookie cutters and pieces of paper

a. Challenge different groups to maximize the number of cookie cutter shapes they can fit on a pre-determined size piece of paper

b. Have the students determine which shape can be replicated in the least amount of space

c. Probe the students understanding of symmetry to determine if they know of shapes that replicate themselves with no space left behind (tessellations)

VII. Homework: Time given at the end of class to begin homework

a. Assign students homework that has them calculate (or at least estimate) the areas of difficult shapes (both regular and irregular)

VIII. Conclusion: Reiterate the power of sine & cosine in solving problems

a. Show the students how an understanding of mathematical formalism can help with solving simple problems like how many gingerbread men can I fit on one cooking sheet.

IX. Assessment: Homework, Observation, In-class worksheet, Unit Test

LESSON B – Math 10

Unit: Shape & Space

Topic: Problems of accuracy and estimation

I. PLO:

a. Solve problems involving distances between points in the coordinate plane

b. Solve problems involving midpoints of line segments

II. SWBAT:

a. Take measurements of objects with high degrees of accuracy

b. Make calculations and estimations of unfamiliar objects

c. Understand the importance of accuracy and measurement

d. Understand the difference in accuracy between measuring angles and measure lengths of a triangle

III. Teaching Objectives:

a. Gain an ability to estimate and calculate distances and sizes with a high degree of accuracy

b. Use geometry to make measurements of systems of lines and angles

IV. Hook: How many windows are in the Empire State building?

a. Show how one could estimate the number of windows based on the number of windows present in a given floor

b. Estimate the amount of light that the Empire State building emits as a function of the total area of the windows

V. Practical Activity: A practical calculation of the real-world

a. In groups of 3-4, the students are permitted to tour the school grounds estimating the total volume of the school

b. The students are permitted pencils, paper and calculators (no tape measures, protractors or rulers).

c. One group (bright students looking for an extra challenge), will be tasked with calculating the volume, but they are not allowed to exit the school to do it.

VI. Reporting: Students return to the classroom

a. Groups present and justify their answer for the class

b. The group that had to find their answer from within the school will present and justify their answer

c. Class will compare answers and discuss methods of accuracy

VII. Homework: Time given at end of class if possible:

a. Write up a list of possible improvements to the task of calculating the volume of the school

b. Write on the importance of accuracy in measurement, inference, estimation and calculation

VIII. Conclusion: Estimation is an important skill to develop and practice

IX. Assessment: Assessment will be based on problem solving ability, creativity, thoughtfulness, planning and results

LESSON C – Math 10

Unit: Shape & Space

Topic: Formalizing lines into equations

I. PLO:

a. Solve problems involving rise, run and slope of line segments

b. Determine the equation of a line, given information that uniquely determines the line

II. SWBAT:

a. Why the form f(x)=m*x+b is important and where it comes from

b. How to calculate or estimate slope

c. How to plot functions and determine intercepts

d. Model 3D examples of objects on a 2D page

III. Teaching Objectives:

a. Have students understand meaning of m & b in the equation

b. Have students understand how to navigate a graph based on information given

IV. Lecture: Do some examples of equation writing for unknown/unique line segments

a. Plot f(x) = -3x+6

b. Plot f(t) = 1.4t – 1.4

c. If f(3)=6 and f(6)=12, what is f(x)?

d. If f(1000)= 2 and f(2000)=4, what is f(x)?

V. Participation: A wayward traveler

a. A traveler has traversed a large city in a rather unorthodox pattern. If t represents the time in minutes that it took the traveler to walk about, graph x(t) and y(t) for the position in the x-direction and y-direction.

b. Have the students write their answer as step functions to describe the turning of a corner as going from the description of one line to the next

c. i.e. x(t) = 5t - 0<3 for round trip.

7t-6 - 3<6

-x+42 - 6<42

VI. Homework: Give seatwork time if possible

a. Complete the ‘wayward traveler’ problem

b. Complete problems from text book.

VII. Conclusion: This equation writing is very useful and has applications in science as well.

VIII. Assessment: Successful completion of homework and participation in class.

PROJECT – Math 10

Unit: Shape & Space

Topic: Planning & Optimization of Space

Premise: You have been asked by a developer to use you keen math skills to develop an ideal tourist destination off the coast of a local ocean front. The problem is that the developer won’t make money (hence he won’t want to hire you), unless you can get the conditions and demands of the hotels just right. The bigger (and therefore, more hotel space) you can make the properties, the more money you will make.

Conditions:

1. You are only allowed to build towers that are 100ft by 100ft and the developer can only afford to build on 150,000 sq. ft of land.
2. Each tower can have a maximum height of 500ft, but since each tower requires a minimum amount of sunshine, some towers can’t be built as high to avoid casting long shadows. At noon, at least 50% of each south-most tower face (side that is facing the sun) must have direct sunlight given that the sun shines down at 30° from the south horizon of the district.
3. Each tower must be beside a water source, whether it is the ocean or a channel that has been dug in the precious land to allow the water to access remote towers. For daily operation, each tower requires 5 cubic ft. of water for every cubic ft. of tower occupied.

Your task: Design your ideal vacation district, including a drawing of hotel locations, waterfront and the water channel.

Record the height, location, % of sunshine, and water consumption of each hotel tower.

What is the total volume (in cubic ft.) of the towers in your district?

Sample district: