PLEASE NOTE:
This document may contain
a number of charts and graphics that could be problematic for your computer
configuration. It is recommended that
you use the “pdf” version for printing this document and this file for working
with or adapting the Course Profile to meet your instructional needs.
Course Profile
(for a locally developed course)
Essential Mathematics, Grade 9
Unit 1
Course Profiles are professional development materials designed to help teachers implement the new Grade 9 secondary school curriculum. These materials were created by writing partnerships of school boards and subject associations. The development of these resources was funded by the Ontario Ministry of Education and Training. This document reflects the views of the developers and not necessarily those of the Ministry. Permission is given to reproduce these materials for any purpose except profit. Teachers are also encouraged to amend, revise, edit, cut, paste, and otherwise adapt this material for educational purposes.
Any references in this document to particular commercial resources, learning materials, equipment, or technology reflect only the opinions of the writers of this sample Course Profile, and do not reflect any official endorsement by the Ministry of Education and Training or by the Partnership of School Boards that supported the production of the document.
ã Queen’s Printer for Ontario
Public and Catholic School Board Writing Team – Essential Mathematics
John Dallan, Lead Writer, Upper Grand District School Board
Bernie McGarry, Halton District School Board
Tina Noel, Renfrew County Catholic District School Board
Rob Samson, Simcoe Muskoka Catholic District School Board
Shirley Scott, District School Board of Niagara
Emilia Veltri, Lakehead Public District School Board
Jim Vincent, Peel District School Board
Lead Board
Halton District Secondary School Board
Kit Rankin
Susan Orchard
Larry Zavitz
Kelly Terry
With assistance from:
The writing team for the Applied and Academic Grade 9 Public Course Profile
Unit 1: Making Sense of Data
Activity 1 | Activity 2 | Activity
3 | Activity 4 | Activity 5 | Activity 6 | Activity 7 | Activity
8 |
Activity 9 | Activity 10 | Activity 11 | Activity 12 | Activity 13 | Activity 14 | Activity 15
Students develop an understanding of data analysis as a powerful tool for decision making. Students are involved in activities that allow them to collect, organize, and display data from primary and secondary sources. Many contextual problems are studied in which students construct, read, and interpret tables, charts, and graphs and select an appropriate method for displaying data from real-world situations. Emphasis is placed on identifying patterns and relationships, summarizing trends, making predictions, and communicating observations. Students conduct investigations with and without technology to verify or refute their own conjectures using tables, charts, mean line of best fit, and pattern descriptions.
Relationships Strand Specific Expectations: All those in the Relationships Strand
Number Sense Strand Specific Expectations: NS1.02
What follows is a suggested sequence, with timing, for teaching Unit 1. These activities are designed to make sense of mathematics by working through concrete experiences to develop students' understanding of various mathematical concepts. Many skills are developed within the activities themselves. However, the need for remediation and further development of skills will arise from the activities. Time has been allotted within the activities and an additional *260 minutes outside of the activities has been designated for work, as needed, on developing skills.
|
Activity 1 |
What’s My Style? Gather, Organize, and Display Learning Styles Data |
110 minutes |
|
Activity 2 |
Data Collection |
150 minutes |
|
Activity 3 |
Graphing Data |
75 minutes |
|
*Time for activity completion and follow-up work on graphing: 35 minutes |
||
|
Activity 4 |
Collecting and Displaying Data using Tables, Bar and Circle Graphs |
150 minutes |
|
Activity 5 |
Take Your Chances |
75 minutes |
|
*Time for activity completion and follow-up work on per cent: 75 minutes |
||
|
Activity 6 |
Illustrating Data |
150 minutes |
|
Activity 7 |
Walk This Way |
75 minutes |
|
Activity 8 |
Population Explosion |
75 minutes |
|
Activity 9 |
Is There a Pattern? |
75 minutes |
|
Activity 10 |
Misuse of Data |
75 minutes |
|
*Time for activity completion and consolidation of skills: 75 minutes |
||
|
Activity 11 |
Mean Line of Best Fit |
75 minutes |
|
Activity 12 |
Is it Strong Enough? |
75 minutes |
|
Activity 13 |
"Bounce-ability" |
110 minutes |
|
*Time for activity completion and consolidation of unit expectations: 75 minutes |
||
|
Activity 14 |
Summative Activity: Selecting and Constructing Appropriate Graphs |
75 minutes |
|
Activity 15 |
Summative Activity: What's the Connection? |
75 minutes |
Students will arrive in the classroom from varied backgrounds with a wide range of experiences and, for many, limited success in mathematics. This unit takes this issue into account and does not assume students have achieved the expectations of the previous year's course.
· The first activity is intended to help gain some insight into the range of learning styles in the class and to help students better understand themselves as learners. Teachers use this information to balance and adjust the types of learning and assessment activities that they use.
· Students should be encouraged to work in pairs or small groups, but growing independence is a goal. This does not imply that a co-operative learning structure is necessarily in place. At this level, students often find comfort and gain confidence when allowed to sit near a friend and work on the same task. Students need reinforcement or extra direction from the teacher or their peers.
· There are several occasions for teachers to use spreadsheets and data collecting probes in this unit. Provide opportunities to become familiar with technology early in the course to allow greater flexibility in future units.
This unit requires flexibility of timing while at the same time it requires structure so that students are engaged in meaningful tasks. Teachers will be working diagnostically with students to determine what type of support each student requires. Time has been built into the activities to allow for these opportunities.
Students will often be working in pairs or small
groups, but growing independence is also a goal.
Activities that are suggested as teaching tools could be used as assessment tools, and vice versa, since assessment activities should be learning activities.
When students do open-ended, multi-dimensional work that requires them to perform in a situation which calls for mathematics, it is not useful to only score their work on the basis of right or wrong. Teachers need to look at the strengths and weaknesses of the whole piece of work or entire performance as it pertains to the specific expectations conveyed in the purpose of the task. Work can be scored holistically, with consistent standards, using a rubric. Rubrics are required when there is a range of student responses possible and when there is a need for teachers to be much more precise about criteria for assessment. Examples of assessment activities and their scoring rubrics are included in this profile. Rubrics provide an effective means of measuring student performance on the Thinking/Inquiry/Problems Solving and Communication and Applications in unfamiliar settings categories of the Achievement Chart.
Most traditional pencil and paper tests do not offer students opportunities to demonstrate Level 4 performances. This profile includes sample questions for pencil and paper tests that do allow students to demonstrate Level 4 work.
Burrill, G. and P. Hopfensperger., Exploring Linear Relations: Data- Driven Mathematics. Dale Seymour Publications, 1998.
Landwehr, J. and A. Watkins. Exploring Data. Dale Seymour Publications, 1995.
Murphy, E. Tables and Graphs. Dale Seymour Publications, 1995.
Specht, Jim. More Than Graphs: Activities for TI Graphics Calculators. Key Curriculum Press, 1996.
Statistics Canada. Canadian Social Trends (journal). Marketing Division, Publication Sales, Statistics Canada, Ottawa K1A 0T6 (1-800-267-6677).
Swan, M. The Language of Functions and Graphs. Nottingham, England: Shell Centre for Mathematics Education, 1987.
Texas Instruments. Math and Science in Motion: Activities for Middle School. 1997.
Texas Instruments. Explorations: Modelling Motions: High School Math Activities with the CBR. 1997.
MARS ( Mathematics Assessment Service )
http://www.educ.msu.edu/mars
Statistics Canada
http://www.statcan.ca
Time: 110 minutes
In this introductory activity students gather information about their own learning styles and strengths using a Learning Styles Inventory (a website reference is provided). They use the following instruments included in this activity:
· Assessing Your Learning Style (see Resource 1.1 at the end of this activity);
· Determining Intelligences: Howard Gardner’s Multiple Intelligences (see Resource 1.2).
In this activity, the data collected using these instruments is organized into charts at the direction of the teacher and displayed in graphs in a future activity. In addition, information on students’ learning styles gives the teachers useful information about the class and promotes the idea that each student is unique and special. It should be noted that these activities are not meant to rigidly categorize students, but to help them better understand that they all have different strengths that they can use to be successful in learning mathematics.
Strand(s): Relationships
Specific Expectations: RE1.03, 04.
· Copies of the following materials are required for each student:
Assessing Your Learning Style (Resource 1.1);
Gardner’s Multiple Intelligences Cards (Resource 1.2).
· To aid in the collection of class data from the Learning Styles Inventory, a sheet of chart paper or a piece of acetate for the overhead projector is required.
· The student’s scores are compiled and computed by the student as follows:
|
Sample Chart |
|||
|
Students |
Tally of List A Scores |
Tally of List B Scores |
Strengths: Stronger A, Stronger B, or Similar
Strengths |
|
Student 1 |
14 |
9 |
Stronger A |
|
Student 2 |
13 |
12 |
Similar Strengths |
|
Student 3 |
6 |
15 |
Stronger B |
|
Student 4 |
7 |
13 |
Stronger B |
· The teacher should become familiar with the learning styles inventory ahead of time in preparation for any questions which may arise.
· This data should be kept for use in later activities
Student Activity:
· Students complete Resource 1.1 - Assessing Your Learning Style and calculate their dominant learning style. These results are copied for the entire class onto a tally chart of learning styles.
· Students rank the Multiple Intelligence Cards from the one that best describes them to the one that is least like them.
· Students discuss the results with the teacher, looking for trends or patterns after the teacher records the class results.
· Students provide a written answer to the following questions:
1) Is there a relationship between the results of the two activities? (The Learning Styles Inventory and the Multiple Intelligences Cards)
2) Do you agree/disagree with the results you obtained? Why or why not?
Teacher Facilitation:
· Prior to the activity, teachers should review the Resource 1.1 - Assessing Your Learning Style, making sure that the items are understood.
· The teacher should also review the information provided about Gardner’s Multiple Intelligences and the cards that the students use to find their strongest intelligences.
· Introduce the topic with a discussion of the uniqueness of every student - different strengths, talents, and ambitions.
· Introduce the learning styles inventory vocabulary (auditory, visual, tactile/kinesthetic) and Howard Gardner’s Multiple Intelligences (see Resource 1.2, Part B).
· Discuss how information about learning styles can help students and teachers.
· Read the learning styles inventory aloud and have students complete it with you.
· Record the students’ results on the prepared class chart and discuss the results with the class.
· Collect the students’ lists for future reference.
· Lead the students through the Multiple Intelligences cards activity and then record the class results on the grid chart paper. The three strongest intelligences could be tallied for each student in the following manner.
|
|
|
X |
|
|
|
|
|
X |
|
|
|
|
|
X |
|
|
|
X |
|
X |
|
|
|
X |
X |
X |
|
|
|
X |
X |
X |
|
|
|
linguistic |
logical/mathematical |
visual/spatial |
------- |
------ |
The teacher can assign a short, journal writing activity to summarize what students have learned about themselves (this provides the teacher an opportunity to assess students’ abilities to communicate in writing).
Terence, Parry and Gregory Gayle. Designing Brain Compatible Learning. Skylight Publishing, 1998.
Chapman, Carolyn. If the Shoe Fits. Skylight Publishing, 1993.
Instructions:
If you agree with the statement mark that item with a 4, if not leave it blank.
o People say you have terrible handwriting.
o You don’t like silent films, pantomimes, or charades.
o You would rather perform (or listen to) music than do (or view) art, and you would rather listen to a tape than look at a filmstrip.
o You sometimes leave out words when writing, or sometimes you get words or letters backwards.
o You can spell out loud better than when you have to write it down.
o You remember things that you talked about in class much better than things you had read.
o You dislike copying materials from the blackboard or bulletin board.
o You like jokes or riddles better than cartoons or crossword puzzles.
o You like games with lots of action or noises better than checkers or most other board games.
o You understand better when you read aloud.
o Sometimes you make math mistakes because you don’t notice the sign or because you read the numbers or directions wrong.
o It seems like you are the last one to notice something new—e.g., that the classroom was painted or that there is a new bulletin board display.
o Map activities are just not your thing.
o You must struggle to keep neat notes and records.
o You must use your finger as a pointer when you read.
o You hum frequently or whistle to yourself when you are working.
o Sometimes your eyes just bother you, but your eye test was normal, or, you have glasses that your eye doctor says are right for you.
o You hate to read from the computer, especially when the backgrounds are busy.
o Matching test questions are a problem to sort out (over and above not knowing some of the answers).
o Sometimes when you read you mix up words that look similar (pill-pull, bale-hale).
o It seems like you always have to ask somebody to repeat what s/he said.
o Sometimes you may find yourself day dreaming, maybe staring out the window when you were really trying to pay attention to something.
o Often you know what you want to say, but you just can’t think of the words.
o Sometimes you may be accused of talking with your hands or calling something a thing- a-ma-jig or a what-cha-ma-call-it.
o You have been in speech therapy some time previously (or currently).
o You may have trouble understanding a person who is talking to you when you are unable to watch the person’s face while s/he is speaking.
o You would rather receive directions in a demonstration format than in spoken form.
o When you watch TV or listen to the radio, someone is always asking you to turn it down.
o People who know you say that you say “Huh?” too much.
o You would rather demonstrate how to do something than make a speech.
o Spoken words that sound similar (bell-bill, pin-pen, Mary-marry) give you trouble. Sometimes you can’t tell them apart.
o You have trouble remembering things unless you write them down.
o You like board games such as checkers better than listening games.
o Sometimes you make mistakes when speaking (like saying “He got expended from school.”).
o You like art work better than music.
o You have to go over most of the alphabet in order to remember which letter comes first (e.g., whether M comes before R).
o You like it better when someone shows you what to do rather than just telling you.
o You usually answer questions with yes or no rather than with complete sentences.
o You can do a lot of things that are hard to explain with words (like fixing machines or doing macrame).
o Often you forget to give verbally received messages (such as telephone messages) to people unless you write them down.
o You are always drawing little pictures on the edges of your papers, or doodling on scratch paper.
TOTAL 4’s FROM:
List A _________________ List B _________________
My Personality Type: _____________________________
This Learning Style Assessment tool is found at <http://snow.utoronto.ca/Learn2/lstyle.htm
Cut the information below into their separate boxes.
Instructions · Place a 4 beside all the words that describe what you like, what you are good at, and how you best learn. · You will need to add up all the 4’s that were placed in each box and put this number on the bottom line where it says total. |
A· I LIKE: Building Drawing things Designing Making pictures · I’M GOOD AT: Imagining Charting/Mapping Creating models · I LEARN BEST THROUGH: Using My Mind’s Eye Using Colours/Pictures Memorizing Layout TOTAL 4’s: ___________ |
B· I LIKE: Interacting Talking Working with People · I’M GOOD AT: Understanding Others Leading/Organizing Communicating Negotiating · I LEARN BEST THROUGH: Sharing Collaborating Observing Others TOTAL 4’s: ___________ |
C· I LIKE: Sounds Rhythm Playing Instruments Singing · I’M GOOD AT: Recognizing Sounds Musical Memory Manipulating Sound Creating Music · I LEARN BEST THROUGH: |