Lessons Integrating Information and Communication Technology within a Curriculum Area
Author 
Sarah Petrie (SSRSB) 
Title 
Math Relationships 
Grade Level 
9 
Subject Area 
Mathematics 
Overview of unit/lessons/activities (assumptions of prior knowledge/learning) 
Students will understand the input/output relation between numbers in linear, quadratic, and exponential relations. Students will be able to recognize and create graphs that are produced by each type of relation. 
Correlations to ICT and curriculum outcomes 
Mathematics Outcomes:
ICT Outcomes:

Projected timeline for preparation and for carrying out activities 
6 lessons (1 hour duration each) 
Equipment Requirements: (computers, software, etc) 
These activities provide support for concepts from Chapter 2 in Mathematics 9: Focus on Understanding
Software:

Teaching materials provided (Blacklines, worksheets, templates, teacher materials) 
Different Orders : This worksheet allows students to explore the relationship between cost of a pizza and the number of toppings. Students will create tables, graphs and use words to describe this relation. (Word format) (pdf format) Different Graphs for Different Relations: This worksheet is a companion for lesson 3 – creating different shaped graphs for different relations. (Word format) (pdf format) Graphing Linear Functions with Excel – This document provides step by step directions for creating an Excel spreadsheet and making a linear chart from it. (Word format) (pdf format) Graphing Exponential Functions with Excel – This document provides step by step directions for creating an Excel spreadsheet and making an exponential chart from it. (Word format) (pdf format) Patterns : This is a file of the questions for students to consider as they use the Statistics Canada website for gathering data. (Word format) (pdf format) Websites: Venn Diagram : This website will allow you to type your own instructions for a triVenn diagram, and then print a copy of the assignment for your students. Function machine – Students test various inputs and their outputs to find the patterns for an unknown function. Students can write equations after predicting the outputs. This applet requires Java. Grapher – Students can type in assigned equations. They can graph up to 3 different functions at once. They can then examine the graphs. This applet requires Java. Create a Graph and Graph Tutorial – These resources are provided for students who would like to create one of several types of graph. The graphs can be designed and saved after they are created. Exploring Linear Functions : This site includes information about mathematical relationships, with an interactive applet that allows students to change the slope and the yintercept to see their effects on the line. The page includes questions and ideas for teachers. (Tutorial) Pizza Lab – This site supports the paper and pencil activity, Different Formats (Word format) (pdf format) Exponential growth – mini lesson on exponential growth, students can read problem, view data collected then link to graph that represents the relationship. 
Resources available for teacher/student use (websites, references, etc) 
Websites: Function machine – Students test various inputs and their outputs to find the patterns for an unknown function. Students can write equations after predicting the outputs. This applet requires Java. Grapher – Students can type in assigned equations. They can graph up to 3 different functions at once. They can then examine the graphs. This applet requires Java. Create a Graph and Graph Tutorial – These resources are provided for students who would like to create one of several types of graph. The graphs can be designed and saved after they are created. Exploring Linear Functions : This site includes information about mathematical relationships, with an interactive applet that allows students to change the slope and the yintercept to see their effects on the line. The page includes questions and ideas for teachers. (Tutorial) Pizza Lab – This site supports the paper and pencil activity. Different Orders. (Word format) (pdf format) Exponential growth – mini lesson on exponential growth, students can read problem, view data collected then link to graph that represents the relationship.
Worksheets and files: Different Orders : This worksheet allows students to explore the relationship between cost of a pizza and the number of toppings. Students will create tables, graphs and use words to describe this relation. (Word format) (pdf format) Concept Map of Math Relations (sample) – sample file (Inspiration 6 format) (Inspiration 7 format) Concept Map of Math Relations (empty) – empty file for student assignment (Inspiration 6 format) (Inspiration 7 format) Concept Map of Math Relations (student) – partial file for students requiring some assistance with assignment (Inspiration 6 format) (Inspiration 7 format) Different Graphs for Different Relations: This worksheet is a companion for lesson 3 – creating different shaped graphs for different relations. (Word format) (pdf format) Graphing Linear Functions with Excel – This document provides step by step directions for creating an Excel spreadsheet and making a linear chart from it. (Word format) (pdf format) Graphing Exponential Functions with Excel – This document provides step by step directions for creating an Excel spreadsheet and making an exponential chart from it. (Word format) (pdf format) Patterns : This is a file of the questions for students to consider as they use the Statistics Canada website for gathering data. (Word format) (pdf format) Venn Diagram – Inspiration – You could use the file as the master copy of a threecircle Venn diagram. It can be completed electronically using the LCD projector so students can follow along and contribute ideas. It could then be posted to the teacher website, if available. (Inspiration 6 format) (Inspiration 7 format) 
Detailed instructions for each activity or lesson (teacher notes, activity information, learning strategies, teacher role, student roles) 
Lesson 1: (12 class periods) This lesson is designed to start students thinking about relationships between variables (outcome C1). They will be introduced to various types of relationships, such as linear, quadratic and exponential. Warm Up: First introduce the students to a simple function machine on the web. An LCD projector would be useful to show the website to the entire class. The web address is:
Main lesson: From the discussion of function machines; ask if any students had machine codes they couldn’t crack. This could lead to a discussion of ‘not simple equations’. The sample Inspiration concept map on Math Relations (Inspiration 6 version) (Inspiration 7 version) can help you develop students’ understanding of different relations and how each is defined. Students will be creating their own Math Relations concept map, using Inspiration. Their completed assignments should be similar to the sample file Math Relations (Inspiration 6 format) (Inspiration 7 format) (web version).
With a list of different predicable relationships, have your students research choose a topic that interests them and research it through ESTAT on the Statistics Canada website: http://estat.statcan.ca The students should be looking for answers to questions such as: Is there a pattern with the numbers? If yes, what is the pattern? If not why might this be? Refer to the questions provided in the document Patterns (Word format) (pdf format) If possible, review the Statistics Canada website with your students, showing them how to research different topics and keywords.
Students can write their answers in their Math journal. You will need to have a discussion with the class regarding the types of data they found. This assignment could be done in small groups (23 people) at a computer. As students rotate to the computer to do research, others can be brainstorming predictable patterns and creating a master list to display for the class. The Statistics Canada site has many helpful resources for educators and students, including:
Lesson 2: This lesson will focus on Mathematics outcomes C1 and C3. This lesson will have students working with paper and pencil, and using the Internet to check their answers. Materials needed:
Begin the class by speaking about predictable prices. Some questions you could ask include: Why is it important to know how much something is going to cost? Is it OK to estimate? Stimulate students' thinking, guiding them to consider how one variable affects another, e.g., amount vs. cost. Pass out the Different Orders worksheets and have the students complete them in small groups, creating graphs, tables (and finding equations – for Level 3 questions; including slope and y intercept). Visit the Internet Pizza site to design topics, find prices, and discuss monetary differences. Students should be able to comment on the different ways of representing data used in the lesson.
Lesson 3: This lesson will introduce students to the different shapes made with the different relations. Students will use Grapher (a graphing applet on the Internet) or graphing calculator. This lesson would be optimal if all students had access to Grapher or to a graphing calculator, as it allows some ‘play’ time to try various changes and see how they affect the graph. Materials: This activity supports concepts from pages 8084 of the Mathematics 9 textbook.
*Challenge: Have students write their best guess of equations from looking only at the graphs.
Lesson 4: Start the lesson with a discussion of Venn diagrams and how they organize similarities and differences. An electronic Venn diagram made with Inspiration is available for use (Inspiration 6 format) (Inspiration 7 format). This file can be printed for students to work on at their desks. Students can add to their Venn diagram as the teacher works on the electronic master copy via an LCD projector, overhead projector, or on the board. A threecircle Venn diagram assignment can also be created online to print and give your students. This activity supports concepts from pages 8183 of the Mathematics 9 textbook – comparison of relations. The Geometer’s Sketchpad activity in the textbook (Explore Relations Using The Geometer’s Sketchpad, pp 9093) further explores relations through technology. If students have not had a chance to become familiar with the software, additional time may be needed to complete these activities.
Lesson 5 and Lesson 6: The following two lessons deal with using spreadsheets and creating graphs. There are some excellent lesson plans accessible through the Internet (see links below). This lesson could take place over several days if you want to include outcomes on collecting data that students could then put into their spreadsheet. *This can also be a good preparation for science fair project work. The Mathematics 9 textbook offers a worksheet and activity (from the CD) – Speed = distance/time This information could also be used in the spreadsheet activity. Other ideas for collecting data:

Student products expected 
Lesson 1: Students complete their Concept Map of Math Relations either in hard copy or saved to the hard drive. There are three versions of this document.
Rubric for assessing concept maps (Word format) (pdf format) Lesson 3 : Venn Diagram comparing Math Relations – After lesson 3, assess whether students can recognize similarities and differences among the three relations. This can be expanded on as the unit progresses. It can be done using Inspiration or on hard copy. (Inspiration 6 format) (Inspiration 7 format) Lesson 5 : Finished product print out spreadsheet and graph. 
Samples (include teacher notes, assessment information, student work if available) 
Sample Concept Map of Math Relations (Inspiration 6 version) (Inspiration 7 version) 
Logistics (organization, grouping, management issues, access to technology) 
You will need to ensure that all necessary software is installed and you are familiar with it prior to beginning these lessons. An LCD projector will help you guide students through various activities as an entire class, such as the concept mapping and the Statistics Canada website. Many of the activities provided here can allow for flexibility in grouping. Students can work in small groups or individually for various activities. Where possible, activity stations can be used to allow students to access the 34 computers in the classroom. While some students work on spreadsheets and mini tutorials, other students can be using graphing calculators in small groups, and completing assigned tasks from the textbook. 
Assessment information (e.g., rubrics for products and/or process) 
Students turn in their Math Relations Concept Map (Inspiration 6 format) (Inspiration 7 format) and Venn diagrams (Inspiration 6 format) (Inspiration 7 format) for evaluation. A rubric for assessing concept maps is provided. (Word format) (pdf format) Assess students’ work completed from the worksheets: Different Orders (Word format) (pdf format) Different Graphs for Different Relations (Word format) (pdf format) 
Possible extensions 
The Geometer’s Sketchpad supports creating and changing relations and viewing graphs. This would allow students to print their graphs instead of sketching them. They can also produce a table of values to go with their equations and graphs using the software. 
Adaptations for students requiring additional support 
Students could concentrate more time on how to define linear, quadratic and exponential through vocabulary strategies. Various activities may be adapted for students requiring additional support, such as the Concept Map of Math Relations which is also provided partially completed to make it easier to fill in. (Inspiration 6 format) (Inspiration 7 format)

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