Unit plan

Pre-planning 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, and beautiful about this topic? (150 words) As far as the curriculum is concerned, almost every subject is using the concept of slope. For example, in science to find the acceleration from the velocity- time graph, in economics to measure the rate at which changes are taking place; i.e, how demand changes when price changes or how consumption changes when income changes or how quickly sales are growing. Secondly, its application in everyday life makes it important to learn. In particular example say, we are driving or skiing or going on a hill, the steepness matters. The learning expectations from the students are the understanding of four situations when the slope is negative, positive, zero and undefined. Furthermore, the most interesting part of learning about slope is to make their own staircase after finding and then analyzing the slopes of different stairs.

(2) What is the history of the mathematics you will be teaching, and how will you introduce this history as part of your unit? Research the history of your topic through resources like Berlinghof & Gouvea’s (2002) Math through the ages: A gentle history for teachers and others  and Joseph’s (2010) Crest of the peacock: Non-european roots of mathematics, or equivalent websites. (100 words)  At first, I found it is quite difficult to find the history of “slope”. Thereafter, I searched and got that the “Slope” drive from the Latin root slupan for slip. The relation seems to be to the level or ground slipping away as you go forward. The root is also the progenitor of sleeve (the arm slips into it) and, by dropping the s in front we get lubricate and lubricious (a word describing a person who is "slick", or even "slimy") To introduce the history part, I would ask them, did they ever saw or their car slides on the downhill road. If they answered yes, then I would ask them what are the different situations when the car slides.  They would come up with their different answers. From their answer, I will give them the idea of slope from the word slippery.

(3) The pedagogy of the unit: How to offer this unit of work in ways that encourage students’ active participation? How to offer multiple entry points to the topic? How to engage students with different kinds of backgrounds and learning preferences? How to engage students’ sense of logic and imagination? How to make connections with other school subjects and other areas of life? (150 words)  To make it an interesting topic, I would encourage them to find out “why or what are the applications” of learning of about slope. For that I would take a school trip, in which the students will observe the various real-life applications of slope. For instance, stairs, ramps, roofs etc. They will find out that in all these cases, the slope is different. This would be the group activity and they will discuss their findings with their pears. Moreover, to encourage them, I will let them explore the various professions in which knowledge of slope is very important. They will answer carpenters, pilots and flight engineers etc. I can correlate with the lesson that in case if someone out of them is thinking about these professions as a career then they need to know the slope. Thereafter At the end of this activity, they would collect all this data and can easily generalize and visualize the importance of learning slopes.

(4) 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. (100 words) In the project, the students would measure the various slopes of ramps or stairs inside, outside their home. This project will take one day as it includes a home activity too. At least five observations (table form) in which they will write the measurement of rise, run and the slope. After that, they will check on the internet, the standard rise, run and slope. Hence, they will find out which staircase’s measurement is according to the standards. At the end, they will be able to make their own staircase. For that, they will draw their own staircase on the graph with the appropriate measurement of rise, run and slope respectively.

(5) 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) In the formative assessment part, I ask them the objective questions to check their prior knowledge about the slope negative, slope positive and zero. For that, I will use the three flashing light card with green, black and red color.  The main objective is to assess students’ mathematical understanding of slope. The task helps students to link their understandings of steepness to a more precise measure of slope. At the end of the chapter, I will give them the question of 10 mark in which they have to have solve it in steps and will write their corresponding mathematical thinking process. The steps and the process will be of five marks each.

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.

Lessons   1      Slope

Lesson     2     Review

Lesson     3     Practice test

Lesson     4     Slope- intercept form

Lesson     5     General form

Lesson     6    Slope- point form

Lesson     7    Parlllei and perpendicular  lines

Lesson     8    Review

Lesson     9    Practice test

Lesson    10   Project

(b) Write a detailed lesson plan for one of the lessons, which will not be in a traditional lecture/ exercise/ homework format.  Be sure to include your pedagogical goals, topic of the lesson, preparation and materials, approximate timings, an account of what the students and teacher will be doing throughout the lesson, and ways that you will assess students’ background knowledge, student learning and the overall effectiveness of the lesson. Please use a template that you find helpful, and that includes all these elements.

Topic: Slope

Grade: 10

Time: 80 min

Big idea: Encourage the students to identify the different types of slopes and hence finding the slope by using the formula rise over run.

Prescribed learning outcomes:

C5: Determine the characteristics of slope and determine the slope of the graph of a line given two points.

Prerequisite: The student must have an understanding of the basic concepts of a coordinate plane.

Objectives (1 minute): The lesson objectives will be written in the front of the classroom on a dry erase board and discussed with the students.

Material Required: Meter rulers, clinometers, Recording sheets, I pads for the class, Overhead projector, Graph papers, colored pencils.

Hook:  I will start the lesson by  singing or encouraging the students to sing a  poem of  "Jack and Jill" and also showing them the picture of that poem. 

 I will then ask what do they think the reason behind Jack's jack fell down? Is it he slipped or it is because the hill is steep?

Activity 1

Talk with your elbow partner. Was there a time when you experienced a very steep hill? Maybe your experience involved a bicycle, skis, a car, etc. Talk about your experience with your partner. Why does steepness matter? Be prepared to share your story with the class.

Activity 3

 Start with a slide show of simple cases of slope that previously taught--for example, identifying positive, negative, zero or undefined slope visually.

Activity 2

This activity is assign to the group of three students. Teacher will take the students outside and encourage them to find the slope of different staircases, ramps in the school by measuring rise over run.

A) First, they will find out the value of slope of the different staircases in the school

Rise (cm)	Run (cm)	Slope of stair- cases = Rise/Run

B) Thereafter they will find out the slopes of Ramps in a school

Rise (cm)	Run(cm)	Slope of Ramps =Rise/ Run

Activity 3

In their group, they will compare the slopes of ramps and staircases. At the end of discussion they will be able to answer “why” these slopes are different.

Guided Practice:
 The students then will make some stairs that have a specific slope. By folding paper in the form of stair, the students will create, in pairs or small groups, stairs with various slopes. Start with something easy like 4/4 or 2/3, then try 1/10 and 10. Ask students to hold up their stairs each time, which will provide plenty of teachable moments. Ask guiding questions like, "Will stairs with a slope of ___ be more or less steep than the last line we made?" "Would it be easy or hard to climb stairs with a slope of...?" Challenge them to show you zero or undefined slope as well.

Independent Practice: Now I will give them the traditional slope problems to practice. I will encourage them to use their paper to model what they see. Thereafter, they would write the mathematical thinking process by explaining how to find the slope of a line.

Closing: Ask your students to write a short definition for slope in their own words or show an 
 example.




Work Cited: 

Slope of a Straight Line: Types of Slope. (n.d.). Retrieved December 17, 2015, from https://www.pinterest.com/pin/313422455291691644/ 


Derivation of the "m" in the slope equation. (n.d.). Retrieved December 17,2015, from https://www.math.duke.edu/education/webfeats/Slope/Slopederiv.html