Saturday, July 2, 2011
Friday, December 10, 2010
The Unit Plan
Title of unit: “Representing data, Ratios, Rates, and proportional Reasoning”
Grade 8, math basic
1) Rationale and connections:
a) Why do we consider it important for students to learn this topic? Why is it included in the IRPs? |
The 21st century is an information era; we are constantly bombarded by tremendous amount of data on a daily basis. These data are usually represented by graph, ratios, and rates. For example, “2/3 of Canadians watched the 2010 Winter Olympic men’s hockey Canada-USA gold medal game,” “Nearly 1 in 3 kids want an iPad for the holidays.” How do we interpret these information and data? Are they accurate? Thus, it is crucial for children to understand how a graph is used to represent the data from a given situation. More importantly, with the skills of ratios, rates, and proportional reasoning, students can solve problems in a variety of different contexts. |
b) What are the historical origins and connections for this topic? |
| In prehistory, early humans created the first information graphics: cave paintings and later maps. Map-making began several millennia before writing, and the map at Çatalhöyük dates from around 7500 BCE. Later icons were used to keep records of cattle and stock. The Indians of Mesoamerica used imagery to depict the journeys of past generations. Illegible on their own, they served as a supportive element to memory and storytelling. |
c) How does this topic connect with life outside mathematics? |
The use of graphics, ratios, rates, and proportional reasoning can be seen almost everywhere in our lives. In science, arts, linguistic, and business areas, we will use graphical representation, ratios, rates, and proportional reasoning to convey ideas. Hence, this unit will help students solve problems in various subjects. |
Balanced teaching assessment and evaluation plan.
Both formative and summative assessments will be used for the course. The formative assessment will be mainly focus on the teacher-students, students-students assessment during the classroom discussion, group activities. Whereas the summative assessment will base on the chapter-end test and the unit project.
Assessment for learning:
1. Use the Math Link introduction on the chapter to activate student’s prior knowledge about the skills and processes that will be covered in this chapter.
2. Have students develop a journal to explain what they personally know about the topics, including how they are similar, and how they differ
3. Use BLM includes all the warm-ups, one to be used at the beginning of each section. Each warm-up provides cumulative review questions for the entire student resource to that point, as well as mental math practice.
Assessment as Learning:
Ask students to keep track of any problems they are having in “What I Need to Work” on the sections of their chapter Foldable.
Evaluation:
Evaluation is based on both summative and formative tasks. The summative tasks – tests will have a larger effect on your final mark than formative tasks like assignments and quizzes. Each unit will have both formative and summative evaluations.
Formative tasks will be marked according to the following scale:
It is students’ responsibilities to hand in the homework on time. Each late day will lost 10% of the homework mark.
Homework 10%
Quizzes 10%
Project 15%
Test 50%
Class participation 15%
c) Lesson sequence, topic outline and teaching strategies to be used.
Lesson topic | Teaching strategies/ approaches used |
1).Chapter 1 Opener | In advance, collect or have students bring in some sports cards. Explain the focus of the chapter on representing data using different types of graphs. |
2) 1.1.Advantages and Disadvantages of Different Graphs | Will have students collect data about students’ height, crate a frequency table, and display the data on a graph of their choice |
3). 1.2. Different Graphs | Will use “Explore the Math” lead students to discover that the size of the intervals on a graph can be misleading. Ask students share their ideas about how they know if a graph is distorted |
4) 1.3 Critiquing Data Presentation | Will have class read and discuss the section title, opening paragraph, article, and large question in the Explore the Math. Direct students to the Did You Know> to clarify the meaning of “run”. Then, have students use Master 16 KWL Chart to identify what they know and want to know about critiquing data presentations |
5Chapter 1 Wrap it Up | Introduce the problem and clarify the assessment criteria. Encourage students to use any data related the music industry that they may have researched for the Check Your Understanding questions and the Math Link of section 1.2. Emphasize the importance of producing complete and accurate graphs. |
6)Chapter 2 Opener | Tell students that they will learn about ratios and rates and different strategies for solving problems involving ratios and rates. Ask them to recall what they know about ratio notation and have them identify examples of ratios in their daily life. |
7) 2.1.Two-Term and Three-term Ratios | Have students discuss t he photo and its enlargement, explain that when enlarging an image, the image produced id mathematically similar to the original image. This means that all of the dimensions of the original are multiplied by the same amount, and produces an image that has the same proportions and the original. |
8) 2.2.Rates | Have students examine the photo and discuss similarities and differences between taking a horse’s heart rate and taking their own heart rate. Ask them to explain how heart rate is different from a ratio. |
9) )2.3.Proportional Reasoning | Have students read and discuss the examples of how people use proportion. Have students share how they use proportional reasoning in daily life |
10) Project Presentation & Peer Assessment | Students will present their projects to the rest of the class. Students will also assess other groups’ projects |
Lesson 1. Advantages and disadvantages of different graphs (75 minutes)
Math 8 Basic
Zhi Song Lian
Materials: meter stick, chalk or masking tape, ruler, grid paper, coloured pencils.
Compass, protractor, Varity of magazines and newspapers with graphs
related to music of sports
Compass, protractor, Varity of magazines and newspapers with graphs
related to music of sports
Teaching Objectives: To introduce the concept of using a graph as a visual way of displaying data. Have students consider that the following questions when they create a graph.
1. What type of graph will you use?
1. What type of graph will you use?
2. What portion of the data will you display?
3. How will the display communicate your message?
Learning Objective: By the end of this lesson, students will have a clear overview of what they will learn in this chapter.
What You Will Learn
1.To compare how different graphs represent the same data.
1.To compare how different graphs represent the same data.
2. To identify the advantages and disadvantages of different graphs.
3. To explore how data can be misrepresented.
4. To justify using a specific graph to represent data.
Bridge (10 minutes): Show students various types of graph from newspaper, magazines and sports cards. Explain the focus of the chapter on representing data using different types of graphs.
Pretesting (15 minutes): Have students discuss where they have seen graphs used. Ask students brainstorm who uses graphs and for what purposes. Read the introduction and draw students’ attention to the data on the sports cards they have collected. Encourage them to think of ways to display the data on the card .Make sure to elicit ideas from all class members.
Main activities (30 minutes): Reactivate students’ skills in creating graphs. Work with students to make a checklist for construction each type of graph. Have students work in groups of 4 to create a classroom display of checklists for each type of graph.
For examples:
For a bar graph:
o Decide on a scale
Title and label the x-axis
Title and label the x-axis
o Title and label the y-axis.
o Plot the categories along the x-axis.
o Plot the values along the y-axis.
o Add a title.
Similar for circle, line, and pictographs
Post Test (10 minutes): Ask students to write an exit slip about “What I have learned”
Summary (10 minutes): summarize the types of graphs that we will focus and 4 key learning objectives.
Lesson 4. Critiquing Data Presentation
Math 8 Basic
Zhi Song Lian
Materials:
BLM 1–4 Chapter 1 Warm-Up Master, 12 Percent Circles grid paper, Master 8 Centimetre Grid Paper, ruler, coloured pencils, compass, protractor, Foldable, the article of “Salmon Run of British Columbia, Canada”
Teaching Objectives:
To explain how a graph is used to represent the data from a given situation.
Learning Objective:
By the end of this lesson, students will Critique ways in which data is presented and be able to justify the choice of a graphical representation for a given situation and its corresponding data set.
Bridge (10 minutes):
Introduce the article of “Salmon Run of British Columbia, Canada”
http://www.kanada-british-columbia.de/en/salmon_run/index.html
Ask students who have watched the salmon run before?
Pretesting (15 minutes):
Read the section title, opening paragraph, and article as well as the big question in the Explore the Math (p. 28). Read the Did You Know? to clarify the meaning of run. Ask students what is different about the bars in the graph (stacked bars). Point out the Literacy Link that explains the meaning of stacked bar graph.
Main activities (35 minutes):
In the Explore the Math, have students analyse a graph.
Students complete the warm-up questions for section 1.3 on BLM 1–4 Chapter 1 Warm-Up
Have students complete the Explore the Math independently and then compare answers with a partner before discussing the results as a class.
Work through the example (pp. 29–30) to illustrate how to critique a graph.
Post Test (10 minutes):
Reflect on Your Findings #4 (p. 29) (Assessment as Learning)
Show You Know questions (p. 30) (Assessment for Learning)
Have students discuss sample graphs and use the Key Ideas outline to critique them. Listen as they do their critique
Summary (5 minutes):
Summarize the key factors when critiquing a graph.
It is important to consider several factors:
Graph type: Is the graph the best choice for displaying the data?
Graph format: Is the graph designed in a way that represents the data accurately?
Graph usefulness: Is the graph informative? Does the graph support a claim or an argument?
Lesson 7 Two –Term and Three-Term Ratios
Math 8 Basic
Zhi Song Lian
Materials:
BLM 1–4 Chapter 1 Warm-Up Master, 12 Percent Circles grid paper, Master 8 Centimetre Grid Paper, ruler, coloured pencils, compass, protractor, Foldable, the article of “Salmon Run of British Columbia, Canada”
Teaching Objectives:
To develop students’ number sense.
To develop students’ understanding of ratio.
Learning Objective:
Express a two-term ratio from a given context in the forms 1:2 or 1 to 2.
Express a three-term ratio from a given context in the forms 1:2:3 or 1 to 2
to 3.
to 3.
Express a part to part ratio as a part to whole fraction, e.g., frozen juice
water; 1 can concentrate to 4 cans of water can be represented as
water; 1 can concentrate to 4 cans of water can be represented as
Bridge (5 minutes)
Ask students what is the width and breadth (in inches) of the different photo sizes?
Solutions: 3R (3.5 x 5 inch); 4R (4 x 6 inch); 5R (5 x 7 inch); 8R (8 x 10 inch)
Tell students that picture of these sizes of mathematically similar to one and another.
Pretesting (10 minutes):
Discuss the photos (p. 46), have students estimate how many times larger the bigger picture is compared to the original(the left-bottom one)
Main activities (40 minutes):
Divide students into groups of 4 and have them use rulers to carry out “Explore the Math”. Once complete, have students discuss their findings in the class.
Work through Examples 1 and 2 (pp. 47–50) as a class. Have students complete each Show You Know before going on.
As a class, discuss the Key Ideas (pp. 50–51).
Post Test (10 minutes):
Assign practise questions and have students work on these questions in groups of 3, then go over the solutions as a class.
Summary (10 minutes):
Summarize the key ideas of the lesson:
1) A part-to –part ratio compares different parts of a group.
2) A part-to –whole ratio compares one part of a group to the whole group.
3) A part-to-whole ratio can be written as a fraction, a decimal, and a percent.
Unit Project
Meal Plan.
Students will plan an international meal that will serve 10 people. Include at least one dish from each of the following categories:
a soup, salad, or appetizer
a main course
a dessert
a soup, salad, or appetizer
a main course
a dessert
Create your meal plan
Finalize your invitation to the meal. Ensure that your logo design has an area of 36 cm2
Finalize your invitation to the meal. Ensure that your logo design has an area of 36 cm2
a) And uses colours or measurements to show each of the following ratios:
4:3 , 2:3:4
4:3 , 2:3:4
b) Record your three recipes. Beside each recipe, write the amount of each ingredient you need to serve 10 people.
c) Justify your calculations for one recipe in part (b)
d) Calculate the total cost of serving one of your dishes to your guests. Show your work.
e) The evaluation rubric will be provided.
The evaluation of the project
The project will be evaluated by the following rubric.
4-Level Project Rubric
Score/Level | Holistic Descriptor | Specific Question Notes |
4 (Exceeds Expectations) | Applies/develops thorough strategies and mathematical processes making significant comparisons/connections that demonstrate a comprehensive understanding of how to develop a complete solution Procedures are efficient and effective and may contain a minor mathematical error that does not affect understanding Uses significant mathematical language to explain their understanding and provides in-depth support for their conclusion | • provides a complete and correct solution with possibly a minor calculation error that does not affect understanding of the problem |
3 (Fully Meets Expectations) | Applies/develops thorough strategies and mathematical processes for making reasonable comparisons/connections that demonstrate a clear understanding Procedures are reasonable and may contain a minor mathematical error that may hinder the understanding in one part of a complete solution Uses appropriate mathematical language to explain their understanding and provides clear support for their conclusion | • provides a complete response with weak communication or missing justification or • provides a complete response with one recipe missing or • provides a complete response with an error in calculation or area or one incorrect ratio for part a) |
2 (Meets Minimum Expectations) | Applies/develops relevant mathematical process making minimal comparisons/connections that lead to a partial or incomplete solution Procedures are basic and may contain a major error or omission Uses simple language to explain their understanding and provides minimal support for their conclusion | • correctly completes parts a) and b) with justification of one of the recipes and at most two minor calculation errors or • correctly completes parts b) and c) or • correctly completes parts a), b), and c) for one recipe or • provides a correct response to parts a) and c) based on an incorrect part b) |
1 (Not Yet Within Expectations) | Applies/develops an initial start that may be partially correct or could have led to a correct solution Communication is weak or absent | • makes an initial correct start to part a) or part b) |
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