Unit Planning for Data Management for Grade 5 (with extensions for Gr 4 & 6)Overall Expectations: Created by: Laura Sergento, Shalini Khanna, Debbie Stockton, Margaret Gorham

Grade 5 -collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs;-read, describe, and interpret primary data and secondary data presented in charts and graphs,including broken-line graphs

Specific Expectations:

Grade 5 -collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs;-read, describe, and interpret primary data and secondary data presented in charts and graphs,including broken-line graphs- collect data by conducting a survey or an experiment - calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs- collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs (including broken-line graphs) that have appropriate titles, and labels

Success Criteria and Misconceptions

Success Criteria for unit:- I can create various graphs (broken-line, bar graph, circle graph)- I can interpret data that I find in a table or in a graph-I can conduct a survey and make a graph with the results-I can calculate the mean of a set of data Strategies: Make a table, predict and verify, solve a similar question

Tools: cubes for building bar graphs, cubes for calculating mean, graph paper, sticky notes for building bar graph, United Nations data, Excel, computers

Why might students struggle with data management? (See each 3 part lesson) (Based on Marian Small’s research in Leaps and Bounds)

Lesson BeforeActivating Prior

Knowledge

Hands On!Task

AfterCongress

Questions

Diagnostic

N/A

EQAO Questions relating to a bar

N/A What was the question asked to

diagram build this bar graph?

Sub Task #1LG: Students will be able to differentiate between a bar graph and a circle graph, and graph data collected in a class activity.

Look at a bar graph and answer questions regarding the purpose and type of graph.

Students use their bodies to create a visual circle graph, after which they use Excel to graph the data and respond to questions.

Three groups will share their graphs. Answer question: what are the similarities and differences between the graphs.

What challenges did you face during this activity? How did looking at the bar graph help you with this activity?

Sub Task #2LG: Students will be able to create and conduct a survey and graph the results.

Look at a bar graph and answer questions highlighting the elements of a graph and drawing conclusions from data.

Students will develop a survey question, survey their classmates, graph their results and draw a conclusion.

Bansho - looking for conclusions that reflect the purpose of the survey.

What was the most important part of the activity? How do you know?What challenges did you face? What would you do differently next time?Why is it important to label graphs correctly?

Sub Task # 3LG: Students will look at a broken-line graph and be able to read, interpret and draw conclusions from data

Look at a broken-line graph.Answer question: What does this graph tell you?

Students will work in groups to analyze 2 broken-line graphs which have no titles or axis titles. They will come up with scenarios that these graphs could represent. The students must come up with the necessary titles.

Bansho - Students explain the various scenarios they invented. As a group we will reflect on when it is best to use broken-line graphs.

Why did your group choose to have time along the x axis? Does a broken-line graph work best to show change over time? Why?

Sub Task #4LG: Students will read and interpret data then create a broken-line graph with this data

Look at a table of data from the U.N. website (Statistics on Literacy rates)Answer question: do you “see” any trends by looking at this data in a table? How would you want to display this information to help the reader understand it

Students build their own broken-line graphs (Using Excel) by choosing one of the countries from the U.N. website (www.data.un.org) and comparing boys to girls literacy rates over time.

Gallery Walk- Students print off and post up their broken-line graphs. Then as a class we discuss the trends and we noticed and how the broken-line graph helped us to see the trends.

How did the broken-line graph help you see the trends? What does it mean if the line is going up? What does it mean if the line is going down? What does it mean if the line stays flat? Do you think it’s easier to interpret the data in a table or in a graph?

best?

Sub Task #5LG: Students will be able to collect information about urban populations and display it effectively using a graph.

Create a human bar graph by arranging ourselves on the carpet and then a 2-dimensional bar graph using sticky notes on a white board.

Gather and organize data on the percent of people living in urban settings for selected countries.

A gallery walk displaying the different ways students organized the data and the different countries that were chosen

Why did you choose to use this graph?How did you decide on a scale for your graph?Which type of graph displays the data most effectively? Why?What might you add to let someone not from our class make meaning of this graph?How does the data compare for each continent?How do the various continents compare with Canada?

Sub Task #6LG: Students will be able to collect information about schooling for boys and girls, create a graph using Excel and compare the similarities and differences.

Re-arrange the 2 colours of stickies on the bar graph from previous class to show the difference in data for boys and girls. Find another way to do it.

Collect and organize information using Excel showing the educational expectancy in selected countries for boys and girls and compare the differences and similarities.

Congress:Chose three or four graphs to display for discussion. Post them alongside the students’ work from the previous class.

Why might children in other countries not get the same education as childrenWhat were some of the challenges in using Excel to create your bar graph?How did Excel make your job easier? in Canada?What do you notice about the number of years of education a boy gets and the years a girl goes to school?Why might there be a difference?

Sub Task #7LG: Students will learn how to calculate the mean and the mode for a

Provide students with a set of data (6, 10, 10, 5, 9) and interlocking cubes that they can use to make

Provide the table and the double bar graph to the students that shows ‘life expectancy rates’ among men

Math Congress: Highlight three chosen pieces of work where students explain their findings from

Is the mean the most effective measure of ‘average’ in this case?

small set of data.

towers to represent each of the values.Ask: “Can you rearrange the cubes so that all the towers have the same number of cubes”

and women in 6 countries including Canada. (http://unstats.un.org/unsd/demographic/products/socind/)Students will work with their Math partner to analyze the data and answer the questions:What trends you see in the data? How can we use this data? Calculate mean and mode.

the data.Congress questions: What is the general trend you see in Life expectancy rate in women and men?What is interesting about the data?

Can you explain how the extreme values in the set affect the mean but not the mode?

Sub Task #8LG: Students will be able to create a stem and leaf plot to

illustrate the life expectancy

rate in men.

Students will be able to compare thesimilarities and differences inthe two sets of related data bydetermining the

median andthe mode.

Students will look at the table and stem and leaf plot (displayed on the white board (using Elmo) drawn from the table values on the life expectancy rate in women in the previous lesson.Ask: What does this graph tell you? What is this graph called?How is it different from broken line graph, bar graph or circle graph?.

Work with your Math partner to create a stem and leaf plot for the life expectancy rate (at 60 years) in men from the above provided table and answer the following questions:Compare the two related sets of data (life expectancy rates in women and men)What have you noticed?Find the median and mode.

Math Congress:Choose three or four plots to display for discussion. Students will display their findings using Elmo.Congress Questions: How do you know your median is correct? What does it tell you?How do you know your mode is correct? What does it tell you?Do you think this is an appropriate graph to compare two sets of related data? Why or why not?

What might you do if your data is expressed as a decimal?Can students explain the stability of the median as compared to the mean or can they explain what effect extreme values in a set of data have on the median?

Sub Task #9Culminating Task -

Students will graph data for 5 countries using the United Nations social indicators data on:-Literacy-Education expectancy-Life expectancy-Adult

unemployment

Students will look at all 5 graphs they created and rank the countries from 1 to 5 in terms of Living Conditions. Then they will draw conclusions from all the data examined by answering questions.

See Culminating Task outline

School Board: TDSB School: Grade:

Name: Debbie Stockton Givins/Shaw P.S. JuniorLesson Title: Conducting a Survey Date: Learning Goal – Big Idea and Curriculum Expectations: (Process, Overall, Specific)Big Ideas: collection and organization of data

Curriculum expectation: : collect data by conducting a survey or an experiment (e.g., gather and record air temperature over a two-week period) to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurementsMaterials: computers, pencil and notebooks, class list, Excel, chart paper and markersLesson Components Anticipated Student

ResponsesBefore 3 - 5 minutes – Activation/Minds OnPut the following graph on the board. Ask the students to identify the elements of a bar graph. Ask them what conclusions they can draw from the data.

Cuba Namibia India Portugal Finland0

20

40

60

80

Unemployment Rates

CountriesPerc

enta

ge o

f Une

mm

ploy

ed

Adul

ts

TitleAxis labelsNumbers and names of countriesLines Starts at zeroScale (intervals)Various answers to conclusions drawn

During 20 – 25 minutes – Working On It/ActionDiscuss with students why the unemployment rates might be so different in various countries. Talk about how the types of jobs available are different depending on the country in which one lives. Pose the following problem:You have been tasked with developing a plan for future employment opportunities in Canada for the year 2025. Canadian officials are interested in knowing the interests of students in 2014 in order to prepare college and university courses, apprentice placements, and workplace entry positions required for successful employment opportunities. With your math partner, write a survey question which will provide the government with the information they need, survey your classmates, graph your results, and draw a conclusion in response to your question. Students may work on chart paper or on the computers using Excel.(Modify the question for grade level.)Ensure the students have a good survey question before they complete the rest of the activity.

Students may have difficulty developing the question – guiding questions:What do you think is important now that might have an influence on your choice of job?Are skills and interests important for choosing a job?What kinds of classes will you take to become what you want when you grow up?Should choose a bar graph but may try a circle graphStudents conclusions may have to do with many students chose different categories rather than prospects for the future – guiding question – how can the government use your graph to plan for the future?

After (Consolidation) 15 minutes Bansho – looking for good questions, accurate graphing procedures (titles, labels, numbers, clear information). Order the graphs according to the conclusions drawn and discuss the most helpful type of information.

There may be missing information in the graphs. The conclusion may be unclear or unhelpful.

After (Highlights and Summary) 5 minutes - What math did we learn today?What was the most important part of the activity? How do you know?What challenges did you face? What would you do differently next time?Why is it important to label graphs correctly?After – (Practice) 15 minutes Word Problems for homework: List the components of a good bar graph.

Data Management Unit – Subtask #3 – 3 Part Lesson Plan Laura Segreto

TDSB – Data Management Unit Dewson St. PS

Grade 5

Sub Task # 3 – Read, Interpret and Draw Conclusions from Broken-Line Graphs

Date

Learning Goal (Curriculum Expectations)

-read, describe, and interpret primary data and secondary data presented in charts and graphs,including broken-line graphs

- Students will look at a broken-line graph and be able to read, interpret and draw conclusions from dataLesson Components Anticipated Student

ResponsesPart 1: Minds On (10 minutes)

Show the above broken-line graph (see Subtask #3-Minds on attachment) on the board as students walk in. This broken-line graph shows this week’s temperature forecast in Toronto. Have the following questions written on the board for the students to answer: What does this graph tell you? How do you know? Ask the students to answer using vocabulary from the math word wall and to explain their thinking as best as they can. Students share their sentences with the class.

Possible student Responses:-This graph tells what the temperatures this week will be. I know because I looked at the titles.-This graph tells me that the temperature will go up (increase) and then down (decrease) because the lines go up and down.-This graph tells me the temperature will stay about the same, around 12.5 C, after April 27.-This graph tells me that the temperature tomorrow, April 25th, will be 15C and it will be the warmest temperature of the week. I know because the highest point of the graph is April 25th.

Success criteria:-I can read, discuss and analyze the data in a broken-line graph

Part 2: Hands On (25 minutes)Students will work in groups to analyze 2 broken-line graphs (see Subtask #3-Hands On attachment). The 2 broken-line graphs have no titles or axis titles. Groups

Strategies: Guess & Check-guess

a scenario and check

will work together will come up with 1 scenario that each of these graphs could represent. The students must come up with the necessary titles and they must be prepared to explain their scenario. They must also be able to explain the trend that they see. Students are encouraged to describe one graph in terms of literacy rates. The teacher will explain what literacy rates represent. Possible scenarios: Broken-Line Graph A represents the number of missed school days for a student from Grade 1 to 8. The student went on a big trip in Grade 4 & 5 and missed a lot of school those years.

if it works Write on titles Brainstorm with

group members

Tools: 2 graphs & markers

Part 3: Consolidation (20 minutes)

Bansho – Each group is going to post one of their broken-line graphs scenarios on the board. They need to make sure their broken-line graph has all the necessary titles (a main graph title, and a y axis title and a x axis title). Each group will select 1 group member to describe the scenario that their group invented.

Each group shares their scenario and teacher asks the following questions to each group:

1) Why did your group choose to have time along the x axis?

2) Does a broken-line graph work best to show change over time? Why?

3) Do you think the broken-line graph clearly tells the story about what is happening in your scenario?

4) Did you include a descriptive title on the top and titles for both the x and y axis?

Misconceptions:- Students may not

understand that broken-line graphs show change over time

- Students may not know how to add appropriate titles to their graphs

- Students are missing one of the titles for the x or y axis

- Students may have chosen data that does not fit well with a broken line graph (i.e. what is your favourite colour: red, blue, green)

After (Practice)All the student scenarios are posted on the wall for further examination. Students are encouraged to take a look at all the examples later on during the day. Students are also asked to look at home in the paper or in magazines for examples of broken-line graphs and to bring them into the class.

Data Management Unit – Subtask #4 – 3 Part Lesson Plan

TDSB – Data Management Unit Dewson St. PS

Grade 5

Sub Task # 4 –Create Broken-Line Graphs and Draw Conclusions

Date

Learning Goal (Curriculum Expectations)

-read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs

- Students will read and interpret data (UN Literacy statistics) then create a broken-line graph with this data

Lesson Components Anticipated Student Responses

Part 1: Minds On (10 minutes)

On the Board, show the table with the data on Pakistan Youth Literacy Rates (see Subtask #4-Minds on attachment).

Ask students the following questions: Does looking at this table give you an idea of what the data is telling you/showing you? What type of graph would you use to show how literacy rates have changed over time?

Possible student Responses:-the table of data doesn’t show me much-its hard to really “see” what “story” the data is telling me

-I think a broken-line graph would help me see what the data is telling me

-I know that I should show this data in a broken-line graph because the data is over many years

Success criteria:-I can analyze data in a table -I can create a broken-line graph with data I find from various sources

Part 2: Hands On (40 minutes)Students will build their own broken-line graphs (Using Excel) by choosing one of the countries from the U.N. statics database (www.data.un.org). Before students begin, show them the graph that the teacher created with the data from the Minds On activity (see Subtask #4-Minds on attachment). Ask students if anyone can explain what they see in terms of the difference between boys and girls, increase or decrease in literacy rate, ect. Explain that they will be making their own graph similar to this one. Students will graph the data for their chosen country, showing the boys’ literacy rates and the girls’ literacy rates over time. Students follow the step by step instructions on the handout (See Subtask #4 Graphing Instructions). Modify/Accommodate:

Strategies: Analyze data Make a graph

Tools: MCS 2.0 Laptop

Trolley MS Excel & MS Word Printer Graphing/grid paper

Students who will struggle with the Excel graphing can make the graph on grid paper.

Part 3: Consolidation (10 minutes)

Gallery Walk- Students print off and post up their broken-line graphs around the class. Then as a class we discuss the trends and we noticed and how the broken-line graph helped us to see the trends. Students are asked to share what “story” they found by examining the UN Data. Teacher asks:

5) How did the broken-line graph help you see the trends?

6) What does it mean if the line is going up? What does it mean if the line is going down? What does it mean if the line stays flat?

7) Do you think it’s easier to interpret the data in a table or in a graph?

8) What does this graph tell you about literacy rates in the country you selected?

9) Was there a difference between boys and girls’ literacy rates? Why do you think there was this difference?

Misconceptions:- Students may not

understand that broken-line graphs show change over time

- Students may not be able to analyze what the data is telling them about literacy rates

- Some students may not connect that the line going up means increase in literacy rates, and the line down means decrease in literacy rates

- The differences between boys and girls literacy rates may not be clear for some countries

After (Practice)Students are encouraged to examine the graphs other students posted on the walls. At home, students can research what may have happened (war, peace, government change, ect) in the country they examined to cause the changes in literacy rates. The students who are interested in looking at www.data.un.org at home are encouraged to look at other data on the site. They will need to be familiar with this site for when they work on the culminating task of the unit.

Lesson Plan 5Big Idea: Graphs are powerful data displays because they quickly reveal a great deal of information. (Dr. Marian Small)Curriculum Expectations: Overall: Collect and organize discrete or continuous primary and secondary data and display the data using charts and graphs, including broken line graphs.

Specific: Collect and organize discrete or continuous primary and secondary data and display the data using charts, tables and graphs that have appropriate titles, labels and scales that suit the range and distribution of the data.

Task/ProblemCollect information about urban populations and display the information effectively using a graph.

Learning Goal:I will be able to collect information about urban populations and display it effectively using a graph.

Part 1 Before, Minds On or Activate Prior Knowledge

Having placed land-mass labels on the carpet (Europe, Asia, Africa, South America, North America) students are asked to line up in front of the land-mass label their family comes from forming a 3-D bar graph. Give each student in a “bar” a sticky note (different colours for boys and girls) and ask the bars to place their stickies in the correct column on the white board to form a bar graph.

Questions:Is the class demographic clearly illustrated by this display?What might we add so that someone not in the class would understand the information? (title, scale)What information can we draw from this graph?Do you think the data would be similar for other classes in the school? Why?

Student Success Criteria: I can collect information from the World

Bank web site I can select and use a graph that will clearly

display my data I am able to choose a scale for my graph that

gives a clear snapshot of the information collected.

I understand that titles and labels will give meaning to the data.

I can explain why the graph I chose to use is appropriate for the data.

Part 2- During, Work on It or Hands OnIn Canada about 81% of people live in an urban setting. How might this compare with other countries? Work with your math partner. Use the World Bank website (http://data.worldbank.org/indicator/SP.URB.TOTL.IN.ZS) to gather data for one country from each of the following continents (total of four countries):Europe AsiaAfricaSouth AmericaMake one or more graphs to illustrate the data you have collected along with the data for Canada.Questions:What might you do if your data is expressed as a decimal? (round to the nearest whole number)Percents refer to parts of 100. How could this help determine your scale?

Strategies: Make a table Use a bar graph

Tools: Paper/pencil Grid paper Atlases Computers

Part 3 – After, Gallery Walk

Questions:What made you choose to use a ___ graph?How did you decide on a scale for your graph?

Misconceptions: When students have chosen a scale they

may have difficulty relating the data to the scale.

Students may start at the first number in the

Which type of graph displays the data most effectively? Why?What might you add to let someone not from our class make meaning of this graph? How does the data compare for each continent?How do the various continents compare with Canada?

data rather than at zero for their scale. Students may not have equal intervals on

the scale (either the actual numbers or the physical space between each number).

Lesson Plan 5Big Idea: Data are gathered and organized inorder to answer questions (Van de Walle)Curriculum Expectations: Overall:

Collect and organize discrete or continuous primary and secondary data and display the data using charts and graphs, including broken line graphs.

Read describe and interpret secondary data presented in graphs.

Specific: Collect and organize discrete or continuous primary and secondary data and display the data using charts,

tables and graphs that have appropriate titles, labels and scales that suit the range and distribution of the data, using a variety of tools.

Compare similarities and differences between two related sets of data using a variety of strategies (double bar graph).

Task/ProblemCollect information about the number of years boys and girls attend school, use Microsoft Excel to display the information in a graph and compare the two sets of data.

Learning Goal:I will be able to collect information about schooling for boys and girls, create a graph using Excel to illustrate the information and compare the similarities and differences.

Part 1 Before, Minds On or Activate Prior Knowledge

Draw children’s attention to the bar graph made in the previous lesson. Each bar is made up of both green and yellow stickies. The green stickies represent boys and the yellow girls.

Questions:If we wanted to show the difference in data for boys and girls how might we rearrange each bar? Is there another way that the stickies could be arranged to show the difference between girls and boys?

Student Success Criteria: I can collect data and enter it into an

electronic spread sheet. I can select the information needed to

form a graph. I can use colours effectively to illustrate

my data. I understand that a double bar graph

helps to compare two sets of data. I can find similarities and differences

when considering the data for different countries

Part 2- During, Work on It or Hands OnIn Canada boys stay in school for an average of 15 years and girls for 16 years. How might this compare with the countries you chose in the last class? Using the UN data website (http://unstats.un.org/unsd/demographic/products/socind/) work with your math partner to collect and organize information on the years of education that men and women achieve in those countries, and use Excel to display the data in a bar graph.

Strategies: Use a table to enter data Compare data with a double bar graph

Tools: Sticky note bar graph from previous

class Grid paper from previous class Computers

Extension: If we look at all the data collected from the last class, how might we arrange it in one graph? (Group countries by continent.)Questions:How might you display the data for men and women on the same graph?How does the material you highlight change the appearance of the graph you create.What information might you need to add to your graph to better understand your data?How might you use colour more effectively in your graph?

Part 3 – After: CongressChose three or four graphs to display for discussion. Post them alongside the students’ work from the previous class.

Congress Questions:What were some of the challenges in using Excel to create your bar graph?How did Excel make your job easier?Why might children in other countries not get the same education as children in Canada?What do you notice about the number of years of education a boy gets and the years a girl goes to school?Why might there be a difference?

Follow-up:What conclusions might you be able to draw from comparing for each country the percent of the population that lives in an urban area and the average number of years of schooling.

Misconceptions: Data is not entered consistently into the

correct columns in Excel Information is missing in Excel

spreadsheet Student selects more or less data than

is needed for the graph Titles and labels are missing

Big Idea: Sometimes a large set of data can be usefully described by using a summary statistic, which is a single meaningful number that describes the values of individual pieces of data or how the data are distributed or spread out.Lesson Plan on how to calculate the mean and the mode for a small set of data.Curriculum Expectations: Overall: Grade 5: read, describe, and interpret primary data and secondary data presented in charts and graphs, including double bar graphs.Specific: Grade 5: calculate the mean and the mode for a small set of data across its range of values, using charts, tables and graphs.

Task/ProblemTo calculate the mean and the mode for a small set of data across its range of values.

Learning Goal:I will learn how to calculate the mean and the mode for a small set of data.

Part 1 Before, Minds On or Activate Prior Knowledge (10 minutes)

To help them understand the concept, they will first practice finding the mean with the help of linking cubes.

Provide students with a set of data (6, 10, 10, 5, 9) and interlocking

Student Success Criteria:

I can read and understand the data.

I can use

cubes that they can use to make towers to represent each of the values.Ask: “Can you rearrange the cubes so that all the towers have the same number of cubes?” Allow students sometime to work on this problem, then, in a whole class setting, ask them to share and discuss the strategies they used.

Questions:1. Can you solve the problem using a variety of strategies? 2. Is there more than one solution? How do you know?3. What is the relationship between the number of values in the

set and the sum of the data values?

Record the answers of the students on the board and then point out how, in each case, the sum of data values is a multiple of 8. Infact, the multiple of 8 that the data values total equals the number of values in the set. For. Example, the sum for (6,10,10,5,9) is 40, which is 5x8 (i.e. the number of values in the set x the mean value for the set).

Mean: Mean is often referred to as the “average”, the mean is one of the three ways to express average or central tendency. Other two are median and mode.Mode: The mode is the number that occurs most often in the data. In the above data, the number 10 occurs twice so the mode is 10.

manipulatives (linking cubes) to find the mean.

I can find mean by adding all the values and then dividing by the number of terms.

I can interpret and write about the information which I am able to gather from the graph.

I can use comparative language (example: worse, better, best) in describing the trends in the data.

Part 2- During, Work on It or Hands On (20minutes)Life Expectancy at age 60 yearsCountries Women MenAustralia 26 23

Afghanistan 15 14France 27 22

Mali 14 13Trinidad and Tobago 21 16

Canada 26 22

Australia

Afghanistan

France

Mali

Trinidad and Tobago

Canada

26

15

27

14

21

26

23

14

22

13

16

22

Life Expectancy at age 60 years MenLife Expectancy at age 60 years Women

Source: http://unstats.un.org/unsd/demographic/products/socind/Provide the table and the double bar graph to the students that shows ‘life expectancy rates’ among men and women in 6 countries including Canada. Give the definition of ‘life expectancy rate’ to the students.

Strategies: Find mean by

using manipulatives (linking cubes).

Find mean by adding all the values then dividing by the number of terms.

Interpret the data results using comparative language.

Tools: Paper/pencil Linking cubes Grid paper

Students will work with their Math partner to analyze the table and the graph to answer the following questions.

Questions:1. What trends do you see in the data?2. How could you use the bar graph to find the mode? Explain.3. Calculate the mean:

life expectancy rate in men life expectancy rates in women

4. Which country do you think is the best in life expectancy rate? Why? Explain your thinking.

5. How can we use this data?

Part 3 – After, Consolidation, Congress, Bansho or Gallery Walk (20 minutes)Math Congress: Highlight three chosen pieces of work where students explain their findings from the data. Have students offer descriptive feedback about their findings.Congress Questions:

1. What is the general trend you see in life expectancy rate in women as compared to men?

2. What is interesting about the data?3. Is the mean the most effective measure of ‘average in this case?

Why or why not?4. Can you explain how the extreme values in the set affect the

mean but not the mode?

Practice: Create a set of five pieces of data with a mean of 6. No more than one of the values can be 6.

What is a mean? How do you know that your mean is correct? How did you figure out the other numbers?

Misconceptions: Students can get

confused between mean, median and mode

Computational error in calculating mean

Students have difficulty comparing data using comparative language (worse, better, best)

Extension: Grade 6: Students can cut out examples of graphs from newspapers, magazines and write notes about the kinds of information the graphs give them. Find the mean and mode in each set of data in the graphs. This activity will allow them to make connections between the real world and what they are doing in their class.

Differentiation: Use of manipulatives like linking cubes to find mean is good for all students and can provide valuable scaffolding for differentiated instruction.

Lesson Plan for comparing the related sets of data using stem and leaf plot and by determining the median and mode for the data.Curriculum Expectations:

Overall: Grade 5: Read, describe, interpret primary data and secondary data presented in charts, tables and graphs.Specific: Grade 5: Read, interpret, and draw conclusions from primary data and secondary data presented in charts, tables, and graphs, including stem and leaf plots.Compare similarities and differences between two related sets of data, using a variety of strategies (stem and leaf plots, by determining the median and the mode)

Task/Problem: To display the information about life expectancy

Learning Goal: I will be able to create a stem

rates in women and men in a stem and leaf plot and compare the two sets of related data by determining the median and the mode.

and leaf plot to illustrate the life expectancy rate in men.

I will be able to compare the similarities and differences in the two sets of related data by determining the median and the mode.

Part 1 Before, Minds On or Activate Prior Knowledge (10 minutes)

Life Expectancy at age 60 yearsCountries Women MenAustralia 26 23

Afghanistan 15 14France 27 22

Mali 14 13Trinidad and Tobago 21 16

Canada 26 22

Stem and Leaf Plot Life Expectancy at age 60 years for women

Stem Leaf 0   1 4, 5 2 1, 6, 6, 7

Source: http://unstats.un.org/unsd/demographic/products/socind/Students will look at the stem and leaf plot (displayed on the white board using Elmo) drawn from the table values on the life expectancy rate in women in the previous lesson.Questions:

Have the following questions written on the board for the students to answer:

What does this graph tell you? How do you know?

What is this graph called? How is it different from broken line graph, bar

graph and circle graph?Students share their answers with the class.

Teach students how to construct a new type of graph: the stem-and-leaf plot.Explain that stem and leaf plot is a visual representation of the data and how it gives a better sense of the shape of the data.

Show them how to determine the median by ordering the data from the least to highest value. The median is then the middle number of this ordered set of values. (The concept of median is introduced in Grade 4)Show them how to find median in the stem and leaf plot by following the steps:

Count the number of values in the data.

Student Success Criteria: I can read and understand the

data. I can select the information

needed to form a graph. I understand that a stem and

leaf plot helps to compare the two sets of related data.

I can find the similarities and differences when considering the data for different countries by determining the median and the mode.

I can understand that median is the the middle number of the ordered set of values. For an even number of data, the midway point (average) between the two numbers in the middle is the median.

If the values are odd numbers, then the middle value will be the median.

In the above plot, we have 6 values, take the middle values 3 and 4 (21 and 26) and find their average to determine the median.

Mode: Most repetitive number is 26 in the leaf so mode is 26.

Ask students to copy the table and the stem and leaf plot for the life expectancy rate in women in their notebook.Part 2- During, Work on It or Hands On (20 minutes)Work with your Math partner to create a stem and leaf plot for the life expectancy rate (at 60 years) in men from the above provided table.

Questions:

Compare the two sets of related data (life expectancy rates in women and men)

What have you noticed? What can you tell about the data?

Find the median and the mode for life expectancy rate of men and women.

Strategies: Use information from the table

to create stem and leaf plot Compare related sets of data

by determining the median and the mode correctly

Tools: Paper/pencil Manipulatives Grid/graph paper Elmo

Part 3 – After, Consolidation, Congress, Bansho or Gallery Walk (20 minutes)Choose three or four graphs to display for discussion. Students can display their stem and leaf plot under Elmo and explain their findings.

Congress Questions: How do you know your median is correct? What

does it tell you? How do you know your mode is correct? What

does it tell you? Do you know think this is an appropriate graph to

compare two sets of related data? Why or why not?

What might you do if your data is expressed as a decimal?

Practice: Assign questions on finding the median and mode from the text book.

Misconceptions: Organization of the data in the

stem and leaf plot Computational error in

calculating the median (if the number of the values in the data are even)

Extensions: Grade 4: Give students a number and identify it as the median from a set of data. Explain that their task is to describe what the values in the set might look like. Tell them that the set must have at least 10 values and that no value can be repeated. Students can choose to have an odd or an even number of values in the set. The same task can be set using the mode.Grade 6: For Grade 6 students, create a set of data in which the mean is greater than the median. The question is open in that it allows students to operate at their own comfort and knowledge levels to create either simple or complex sets of data.