Tuesday, 22 December 2015

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 


 

Saturday, 5 December 2015

John Mason's article reflection



John Mason’s article encourages us as a teachers to invite students to work on the mathematical problems in the same ways as the “scientists and mathematicians” worked. I totally agree with Mason when he said that there are two ways to ask questions from the students. In the first method of asking question, the teacher is looking for the expected answer while in the other method the teacher is listening and observing whatever the student is saying and doing. Hence, the later method encourages the students to reveal their thinking. This makes me to think about the “expectation” of my teacher’s questions when I was in school. Because I taught by the traditional method of teaching, hence no doubt, my teacher’s expectation was also the right answer. For example, when we learnt about the Pythagorean theorem, our teacher proved its proof forwardly and conversely. At that time, we just solved it mathematically on paper and we thought that we were done. But, now when I am thinking about the same theorem, I have so many proofs of this theorem by using hydraulic model of Pythagorean theorem, scrap paper activity and so many other ways in which the students have more opportunity to explore the theorem by having more hands on experience. Hence, I would prefer to ask such questions to my students which would encourage them to discuss and communicate their thinking and methods of approach to the problem

Monday, 30 November 2015

Reflection of today's team teaching on "percentage"

In today's team teaching , I am of the opinion that everyone of us did a great work on their own part . However, we would have done a great lesson if we would  have add some activities,or maths models for percentage.  Also,  the usage of percentage in everyday life should be made clear with more visual aids. According to the evaluation, if their was a little bit loose start then at that time if we support each other then we might handle the starting of the lesson. Overall, in terms of  time-management as well organization ,we did good .
                                 Mistakes indicate that we are learning
                                                       Great work Team!













Teachers: Jessica, Mandeep, Simran

Topic
Intro to Percentages
Grade level
8
PLO
A3 demonstrate an understanding of percents greater than or equal to 0%
Objective
Students will be able to use the given percentage to find the required information.
Students will be able to find percentage of two given whole numbers.
Students will have the understanding of the percentage sign.  
Materials
White board and marker. Lifespan cards.
Prior Knowledge
Students know division and multiplication.
Intro/Hook
4 mins
Percentage sign %, no calculations here.
Discuss how many pennies make up a dollar. (nickels, dimes, quarters). Each group still represents one dollar. On the board, draw out a circle representing a dollar and then fill in 25% to represent 1 quarter.
Development
4 mins
Finding a percent of any number with respect to another number (comparative number)

Here percent represent the fraction with denominator 100,While the number represent the amount.

Example1 -  if i have 40  halloween  candies ,i gave  10 % of candies to my son ,then what is the number of  candies i gave to my son?
Solution-
Here, 40 is comparative number
   10% of 40 candies
= 10/100* 40
=  4 candies to my son

Example 2-   If i have 40 halloween candies ,i gave 10 to my daughter,then what is the percentage of the candies i gave to my daughter?
Solution-  
    10/40*100
=25 % of  the total number of candies to my daughter
Activity
3 mins
-Give each student a “Lifespan” card
- Ask them to fill out the blanks on the card, their age etc
- Explain the question on the card and tell them to do their calculations on the back of the card
- let the students work in pairs of two for 2 minutes
- go around and make sure everyone's clear on the activity
Closure
1 min
go over the idea of percentage and how it can be used in daily life. For ex: at the shopping mall, calculating the time you have left before you have to get ready for school or dividing your food into portions and eat a certain percentage at a time. It becomes very easy to picture what's gone and what's left if you convert things into percentage.



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BC Math 8 and 9 curriculum guide

A3 demonstrate an understanding of percents greater than or equal to 0% [CN, PS, R, V]
  • provide a context where a percent may be more than 100% or between 0% and 1%
  • represent a given fractional percent using grid paper represent a given percent greater than 100 using grid paper
  • determine the percent represented by a given shaded region on a grid, and record it in decimal, fractional, and percent form
  • express a given percent in decimal or fractional form
  • express a given decimal in percent or fractional form
  • express a given fraction in decimal or percent form
  • solve a given problem involving percents solve a given problem involving combined percents (e.g., addition of percents, such as GST + PST)
  • solve a given problem that involves finding the percent of a percent (e.g., A population increased by 10% one year and then 15% the next year. Explain why there was not a 25% increase in population over the two years.)

Saturday, 28 November 2015

Monday, 23 November 2015

Dave Hewitt's video Reflection

Dave Hewitt's video is an excellent example of students centred classroom. The various strategies he used in order to encourage students to participate in class' activities is awesome. The students are encouraged to come to the front to solve the problem . The teachers presence is just to facilitate the students thinking . It was the students who are doing the learning activities rather than teacher. I never thought of that idea of  teaching integers to my class just by tabbing the stick without writing . It was amazing.


Sunday, 22 November 2015

"Arbitrary and Necessary"


  • Dave Hewitt’s article related to “Arbitrary and Necessary” forces me to think that math is not about the memorization of the “arbitrary” terms and names rather than the awareness of the “necessary” mathematical knowledge.  According to Hewitt, “arbitrary” are the conventions, symbols, or the names, which we are using in math. I would say the conventions mean the mathematical language. These conventions are just the choices made at sometime in the past. These did not have any proofs or reasons behind their names or their existence.  For example, why we call tangent as a tangent? We cannot prove the name “tangent” because it is arbitrary. On the other hand, when we talk about the properties of the tangent (it is a line, which touches the given circle at one point), then these properties are the “necessary” for the students. They may have the awareness of this fact or the teacher can introduce tasks, which help students to use their awareness in coming to know what is “tangent”.
  • In my lesson plan, I would try to relate the necessary and arbitrary. For example, I would relate the words tangent and touch (the line which touches the circle). Hence, from the word touch they can easily relate the tangent. Consequently, if they understand about the tangent then they would continue to explore about the properties of the tangent. My role is to encourage and scaffold the students to use their own awareness.