Relations And Functions Unit Plan Copy

Math C&I for Majors Unit Plan Template

Title of Unit

Relations and Functions

Subject

Math

Grade Level Time Frame

10C Honours 7 days

Reilly Matthews

Developed By

Stage 1 - Identify Desired Results Learning Outcomes What relevant goals will this unit address? (include all relevant GLO(s) & SLO(s))

General Outcome  Develop algebraic and graphical reasoning through the study of relations. Specific Outcomes  Interpret and explain the relationships among date, graphs and situations  Demonstrate an understanding of relations and functions Big Mathematical Ideas Which big mathematical ideas (e.g. place value, algebraic reasoning, etc.) does this unit address? Consult Charles (2005) and Hurst and Hurrell (2014)   

A relation associates the elements of one set with the elements of another set A function is a special type of relation for which each element of the first set is associated with a unique element of the second set A linear function has a constant rate of change and its graph is a non-vertical straight line.

Cross curricular Competencies How will this unit promote the CCC?

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Managing information: organizing sets of data and finding the correct properties of the data. Communication: being able to graph the data in the proper way and understand the given graphs. Also learning vocabulary is important in this unit (ie. Domain and range).

Essential Questions What provocative questions will foster inquiry into the content? (open-ended questions that stimulate thought and inquiry linked to the content of the enduring understanding) 1. What are different ways that we can communicate sets of data? 2. Where can we find relations and functions in our daily lives? Knowledge: What knowledge will student acquire as a result of this unit? This content knowledge may come from the indicators, or might also address pre-requisite knowledge that students will need for this unit.

Skills What skills will students acquire as a result of this unit? List the skills and/or behaviours that students will be able to exhibit as a result of their work in this unit. These will come from the indicators.

Students will know...

Students will be able to…

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Why data points should or should not be connected on the graph for a situation Why some relations are not functions, but all functions are relations Rules for determining whether graphs and sets of ordered pairs represent functions

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Graph, with or without technology, a set of data, and determine the restrictions on the domain Describe a possible situation for a given graph Sketch a possible graph for a given situation Determine, and express in a variety of ways, the domain, and range of a graph, a set of ordered pairs or a table of values Determine if a set of ordered pairs represents a function Sort a set of graphs as functions or non-function

Stage 3 – Learning Plan Monday SLO: Demonstrate an understanding of relations and functions

Tuesday SLO: Interpret and explain the relationships among data, graphs, and situations

Description: (5.1 5.2). We will be going over two topics. First, representing relations. We will talk about “sets”, “elements” and “relations”. We will describe different relations in graphs and tables and represent them using arrow diagrams, ordered pairs and tables. Second, we will talk about properties of functions. We will discuss what makes a function, and what does not. We will also look at domain, range and variables. We will also look at how to solve functions.

Description: (5.3 5.4 5.5) First, we will look at interpreting and sketching graphs. We will look at what lines of the graph means, as well as what the different segments represent. We will also look at how to draw a graph and label the axis. Second, we will talk about graphing data. I will give data that the students will graph properly. Third, we will look at graphs of relations and functions. This topic, we will look at functions and how to draw them on a graph. We will also learn how to tell if a relation is a function by looking at the graph. All topics will be looked at through slides and examples.

Both topics will be looked at through SMART board slides, as well as class examples. Assessment: Formative. I will observe the students while they do examples. They will also complete an assignment. Pg. 262 #3a, 4, 5, 6, 9, 12. And pg. 270 #4, 5, 6ac, 7bd, 9a, 14, 15a, 19 Essential question: What are different ways that we can communicate sets of data?

Assessment: Formative. I will observe the students while the do examples. They will also complete an assignment. Pg. 281 #3, 5, 8, 10, 13, 17. Pg. 286 #1. And Pg. 294 #4, 5, 7, 9, 11. Essential question: What are different ways that we can communicate sets of data?

CCC: Managing information CCC: Communication

Wednesday SLO’s: Demonstrate an understanding of relations and functions, and Interpret and explain the relationships among data, graphs, and situations

Thursday SLO’s: Demonstrate an understanding of relations and functions, and Interpret and explain the relationships among data, graphs, and situations

Description: (Review). Today will be a work day for the students. They can work on assignment 1 or 2, or they can work on the “checkpoint” on page 274-275 and page 298-299.

Description: (Quiz). Students will have the whole class time to write a quiz. This quiz will cover topics 5.1-5.5

Assessment: Formative. I will observe the students while they work, and also gauge what kind of questions they ask me. If there are multiple questions about the same concept, I will go over an example with the class. Essential question: Where can we find relations and functions in our daily lives? (There will be questions in the textbook that make this clear). CCC: Managing information and communication.

Assessment: Summative. This quiz will be taken for marks. I will mark it that night and return it the next day for formative assessment as well. If there are concepts that many struggled with, I will take time to go over it again.

Friday SLO: Interpret and explain the relationships among data, graphs, and situations Description: (5.6 5.7). First we will talk about properties of linear relations. We will look at patterns in graphs, and decide what makes a function linear. Next, we will look at interpreting graphs of linear functions. We will talk about what different points on the graph means and look at horizontal and vertical intercept points. We will also look at solving these functions. Assessment: Formative. I will observe the students while they work on examples in the notes. They will also complete an assignment. Page 308 #3, 4, 5, 6(i, iii, v), 8, 10, 14 18 and page 319 #4, 7, 10, 12, 18, 20 Essential question: What are different ways that we can communicate sets of data? CCC: Communication

SLO’s: Demonstrate an understanding of relations and functions, and Interpret and explain the relationships among data, graphs, and situations

SLO’s: Demonstrate an understanding of relations and functions, and Interpret and explain the relationships among data, graphs, and situations

Description: (Review). Today will be a work day for the students. They can work on assignment 3, or they can work on the “review” on page 326.

Description: (Unit final). Students will have the whole class to work on the unit test. This will cover 5.1-5.7.

Assessment: Formative. I will observe the students while they work, and also gauge what kind of questions they ask me. If there are multiple questions about the same concept, I will go over an example with the class.

Assessment: Summative. This test will be marked. Students can look over their tests when they are marked, however they can’t keep them.

Essential question: Where can we find relations and functions in our daily lives? (There will be questions in the textbook that make this clear). CCC: Managing information

Assess and Reflect (Stage 4) This unit went very well. The students had a hard time grasping the concept of domain and range. In the future I would add an extra day and work more on domain and range as a class. I had lots of questions about it after and before class. The unit as a whole felt a little bit crammed. There wasn’t much work time and to go over the quiz, which I think would have been beneficial. Working in groups for this unit and collaborating also might have been better for the students. This unit the students had a new seating plan and the stronger students really started helping the students who have been struggling. I made my own test this unit, and it went very well. I looked at each lecture and made sure to include parts from each. This unit is a great introduction into linear functions. I need to make sure they fully understand these concepts before we go into this unit.