pdm3-1 introduction to classifying data

Probability & Data Management Teacher’s Guide Workbook 3:1 1 Copyright © 2007, JUMP Math For sample use only – not for sale.

PDM3-1 Introduction to Classifying Data

Goals: Students will group data into categories. Students will identify attributes shared by all members

of a group.

Prior Knowledge Required: The difference between “and” and “or”

Vocabulary: data, classify, attribute, and, or

Have eight volunteers stand up. Ask the students to suggest ways in which to classify them (for example,

long or short hair, boy or girl, nine or ten years old, wearing jeans or not wearing jeans, wearing yellow or

not wearing yellow). Then have one student classify the eight volunteers into two groups without telling the

class how he or she chose to classify them. The student tells each of the eight volunteers which side of the

room to stand on. Each remaining student then guesses which group he or she belongs to. (If the student

guesses incorrectly, the student who classified the volunteers moves that student into the right group but

does not reveal the classification.) Stop when five consecutive students have guessed correctly. The last

student to guess correctly appoints each remaining student in the class to either of the two groups and is

told if they’re right or not.

Repeat this exercise several times, with different students doing the classifying. Note that the student

doing the classifying never reveals the classification. To make guessing the classification harder, students

may decide to combine attributes, such as grouping “boys not wearing yellow” and “boys wearing yellow

and girls.”

Write the following words on the board:

J.K. Rowling lion Alberta Ottawa Anna Klebanov

dog cat Canada mouse Rita Camacho

Ask students to put the words into the following categories:

People Places Animals

Have students add more words to each category. Then tell students that the category “People” could be

divided further. For example: adults and children, girls and boys, first language English or first language

other. Have students suggest other ways to categorize people and have volunteers put their own names in

the appropriate categories. Then do the same for Places and Animals.

Have students think of categories for the following data:

Weather (e.g., sunny, cloudy, rainy)

Time of day (e.g., morning, afternoon, evening, night)

Foods

Fruits

Vegetables


Have students identify attributes shared by all members of the following groups:

a) grey, green, grow, group (EXAMPLE: starts with “gr,” one-syllable word)

b) pie, pizza, peas, pancakes (EXAMPLE: food, starts with p)

c) 39, 279, 9, 69, 889, 909 (EXAMPLE: odd number, ones digit 9, less than 1000)

d) 5412 9807 7631 9000 9081 (EXAMPLE: number, 4 digits, greater than 5000)

e) hat, cat, mat, fat, sat, rat (EXAMPLE: three-letter word, ends in “at”) Have students write 2 attributes for the following groups:

a) 42, 52, 32, 62, 72 b) lion, leopard, lynx

Activity: Show students cards from the game SetTM

and ask students to say what categories can be used

to sort the cards (e.g. shape, colour, number, shading) and then to sort the shapes using those categories.

Have groups of students play the card game SetTM

. Include only the solid shapes (no stripes or blanks) until

students are very comfortable finding sets.

Extensions:

1. Which 2 attributes could have been used to sort the items into the groups shown?

Group 1:

Group 2:

� at least 1 right angle � 4 sides or more � 2-D shapes � quadrilaterals

� no right angles � 3-D objects � 3 sides � hexagons

Which categories do all shapes in both groups belong to? Which categories do no shapes in either group

belong to? What categories do some shapes in group 1 and some shapes in group 2 belong to? What

category do all shapes in group 1 and no shapes in group 2 belong to? What category do no shapes in

group 1 but all shapes in group 2 belong to? How were these groups categorized?

2. Give pairs of students the BLM “Shapes” (it shows 8 shapes that are either big or small, triangles or

squares) or the Set™ card game. The BLM has 2 of each shape, so that students can work individually.

Ask students to separate the small triangles from the rest of the shapes, then challenge them to

describe the remaining group of shapes (big or square). Encourage them to use the words “or” or

“and” in their answers, but do not encourage use of the word “not” at this point since, in this case,

“not small” simply means “big.” If students need help, offer them choices: big or triangle, big and

square, big or square.

Challenge students to describe the remaining group of shapes when they separate out the:

a) small squares e) shapes that are big or triangular

b) big squares f) shapes that are square or big

c) big triangles g) shapes that are both square and big

d) shapes that are small or triangular h) shapes that are both triangular and small


PDM3-2 Venn Diagrams

Goals: Students will sort data using Venn diagrams.

Prior Knowledge Required: Identifying attributes

Classifying according to attributes The words “and,” “or,” and “not”

Vocabulary: Venn diagram, or, and, not

Label a cardboard box with the words “toy box,” then ask individual students if various items (some items

toys and some items not toys) belong inside or outside the box. Then tell students that you want to classify

items as toys without having to put them in a box. Draw a circle, write “toys” in the circle, and tell your

students that you want all of the toy names written inside the circle and all of the other items’ names written

outside the circle. Ask your students to tell you what to write inside the circle. Make sure to crowd the words.

ASK: Is there a way we can save space and not write the whole word in the circle? If students suggest you

write just the first letter, ask them what will happen if two toys start with the same letter. Explain to them that

you will instead write one letter for each word. (EXAMPLE: A. blocks B. bowl C. toy car D. pen)

ASK: Which letters go inside the circle, and which letters go outside the circle?

Draw several shapes and label them with letters.

A. B. C. D. E. F.

Draw:

shapes

ASK: Do all the letters belong inside the box? Why? Which letters belong inside the circle? Which letters

belong outside the circle but still inside the box? Why is the circle inside the box? Are all of the triangles

shapes? Students should understand that everything inside the box is a shape, but in order to be inside the

circle the shape has to be a triangle. Change the word inside the circle and repeat the sorting exercise.

triangles

toys


[Suggested words to use include: dark, light, quadrilaterals, polygons, circles, dark triangles, dark circles.]

Ask your students why the circle is empty when it’s labelled “dark circles.” Can they think of another property

that would empty the circle of all the shapes? Remind them that the word inside the circle should reflect the

fact that the entire box consists of shapes, so “rockets” probably isn’t a good word to use, even though the

circle would still be empty.

Lay two hula hoops on a table or on the floor. Clearly label one hula hoop “pens” and another “blue,” then

ask your students to assign several coloured pens (black and red) and pencils (blue, red, and yellow) to the

proper position—inside either of the hoops or outside both of them. Do not overlap the hoops at this point.

Then present your students with a blue pen and explain that it belongs in both hoops. ASK: How can we

move the hoops so that the blue pen is circled by both hoops at the same time? Ask a student volunteer to

show the others how it’s done. If the student moves the hoops closer together without overlapping them, and

positions the blue pen such that part of it is in the “blue” hoop and part of it is in the “pens” hoop, be sure to

ask them if it makes sense for part of the pen to be outside of the “pens” hoop. Shouldn’t the entire pen be

circled by the “pens” hoop?

Draw:

A. B. C. D. E. F.

And draw:

Dark Triangles

Explain to your students that this is called a Venn diagram. Ask them to explain why the two circles are

overlapping. Have a volunteer shade the overlapping area of the circles and ask the class which letters go in

that area. Have a second volunteer shade the area outside the circles and ask the class which letters go in

that area. Ask them which shape belongs in the “dark” circle and which shape belongs in the “triangle” circle.

Change the words representing both circles and repeat the exercise. [Suggested words to use include: light

and quadrilateral, light and dark, polygon and light, circles and light.]

This is a good opportunity to tie in concepts from other subjects. For example, students can categorize words

by the beginning or ending letters, by rhyme patterns, or by the number of syllables. (EXAMPLE: “rhymes

with tin” and “2 syllables”: A. begin; B. chin; C. mat; D. silly). Start with four words, then add four more words

that belong to the same categories. Encourage students to suggest words and their place in the diagram.

[Cities, provinces, and food groups are also good categories.]

Activity: Create a big circle on the floor with masking tape and label it “8 years old”. Have students stand

in the circle if they are 8 years old and have them stand outside the circle if not.


Repeat with several other properties:

Wearing Girl Blue Takes the

yellow eyes bus to

school

Have your students stand inside the circle if the property applies to them. Have them suggest properties and

try to move appropriately (either to the circle or away from it) before you finish writing the words. Students

should learn to strategically pick properties that take a long time to write. Repeat the activity by overlapping

two circles.


PDM3-3 Introduction to Tallying Data

Goals: Students will switch between numbers and their corresponding tallies.

Prior Knowledge Required: Ability to count

Number recognition

Counting by 5

Vocabulary: tally marks, tallies, diagonal, vertical

Explain to students that experts in mathematics and other subjects often use tally marks to keep track of

what they are counting. Tell students that you want to count the number of boys in the room. Draw a vertical

stroke each time you say a boy’s name:

IIIIIIIIII

Then repeat using diagonal lines for each fifth boy:

IIII IIII

ASK: Which set of marks is easier to read? Explain that in a tally, each vertical stroke represents one, but

every fifth stroke is drawn diagonally across the first four. This makes it easy to count by fives.

Then write the numbers 1–5 on the board, making sure they are well spaced out. Under the number 1, draw

the corresponding tally: one vertical stroke. Ask students what they think the tally for the number 2 will look

like. Have a volunteer write that on the board. Repeat with the numbers 3 and 4. For number 5, remind

students that tally marks are grouped in fives and we draw the fifth line diagonally across the other four—the

fifth line “bundles” the other four together.

Next, write the numbers 6–10 and show students the tally for the number 6. Ask volunteers to write the

tallies for the numbers 7–9. For the number 10, ask students to predict what the tally will look like and then

show them.

Repeat the process with numbers 11–15 and then 16–20.

Now show students the tally for the number 4 and ask them to identify it. Then do 5, 8, 12, 15, and others

until all students can quickly and easily read the tallies.

Next, draw 5 apples on the board and remind students that tallies are useful for tracking data. Cross out an

apple, and draw a tally mark. Ask a volunteer to continue the process. Repeat with an array of 12 circles.

Bonus Questions: Who can count quickly? Show 15 as a tally. Then show 20, 25, 35… and 100!


Activity:

Paper Clip Search. Place enough paper clips around the room to average about 10 per student. Have

students find and collect as many paper clips they can. Show students how to use 1 paper clip to bundle

another 4:

Ask students how many paper clips they have in total. They should use the bundles of 5 to count by 5s. Then

have students pair up and find out how many the pair has in total; they may need to bundle once more.

Extension: Show students a penny and ask them to show what the penny is worth with tally marks.

Continue showing tallies for a nickel, a dime, a quarter, a loonie, and a toonie.


PDM3-4 Reading Data from a Tally Chart

Goals: Students will compare, order, add, subtract or multiply data to find new information

Prior Knowledge Required: Tallies

Addition, subtraction, and multiplication by small numbers

Vocabulary: add, subtract, multiply, twice as many, three times as many

Take a survey of your students and ask what type of fruit is their favourite among: apples, bananas,

oranges, grapes, and peaches. Record the tallies yourself and have students complete the chart by writing

the appropriate number for each tally.

Fruit Apples Bananas Oranges Grapes Peaches

Tally

Number

Ensure that students can read the data directly from the tally chart. ASK: How many students like grapes

best? How many like apples best? Oranges? Bananas? Peaches?

Tell students that they can compare and order the data to find new information. ASK: Did more people

like oranges or bananas better? Which fruit was the most popular? Which fruit was the least popular?

Working independently, have students list the fruits in order from most popular to least popular. Ask them

to explain their thinking. (PROMPTS: How did you know which fruit to put first? How did you decide which

one came next?) Tell students that they can add the data values together. ASK: How many students

answered the survey? Was it everyone in the class? How many students are in the class? How many

students liked either apples or grapes best? Bananas or oranges? Peaches or oranges or apples?

Bonus: Combine comparing and ordering with addition. For example, ASK: Did more people like bananas

best than liked peaches and grapes best?

Tell students that sometimes they need to subtract data to find new information. ASK: How many more

students liked apples best than peaches best? (Or “peaches best than apples best” if appropriate). Make

more such comparisons. Then ASK: Of all the people who answered the survey, how many did not choose

oranges? What number do we need to subtract from what to figure this out? How many students did not

choose bananas? Can we answer these questions without using subtraction? (Yes, we can add the other

four data values.)

Bonus: How many chose students neither bananas nor oranges? Did you use addition or subtraction or both?

Tell students that sometimes they need to multiply data to find new information. ASK: Is any fruit twice as

popular as another fruit? Is any fruit three times as popular (or almost three times as popular) as another

fruit?


PDM3-5 Introduction to Pictographs

Goals: Students will read and interpret pictographs that have a scale of 1.

Prior Knowledge Required: Ability to count

One-to-one correspondence

Understanding of symbols

Comparing and ordering numbers

Addition, subtraction, multiplication

Vocabulary: pictograph, key, symbol, more, less, least

ASK: What is a symbol? Allow students to discuss this in pairs and then debrief as a class. If students need

hints, remind them of maps—what pictures/symbols they have seen there? What are some of our country’s

symbols? (beaver, maple leaf, loon, etc.)

Tell students that they will learn how to show data in a pictograph today. Explain that pictographs use

symbols which represent the data in order to show how many of each set of data there are. Explain that the

symbol should match who is being asked the question or what is being asked about.

Display this data on the board:

What time do students go to bed during the week?

Before 8:30 x

8:30 x x x x

9:00 x x x x x x x

9:30 x x x x

After 9:30 x x

Ask students what symbols they could use to show the above data and choose one. (Suggestions include: a

stick person, a pillow.) Invite a volunteer to replace the Xs with the new symbol.

Next, introduce the word “key” to students. Draw the symbol chosen for the above example and an equal

sign next to it. Ask students what each symbol in the chart represents (one student). Write the number 1 next

to the equal sign. Explain that this is the key and it tells us what each symbol represents. In this case, each

symbol represents or is equal to one student. Tell students that all pictographs usually include a key.

Encourage students to talk about what the data tells us. Encourage them to make comparisons and to ask

questions. ASK: How many students go to bed at 8:30? How many go to bed after 9:30? What is the most

popular bedtime? How many students were surveyed? (Show students how to count the symbols to find out.)

How many more students go to bed at 9:00 than after 9:30? How many more students go to bed at 9:00 or

earlier than at 9:30 or later? How many students go to bed at 8:30 or later? To answer this last questions, did


they add all the data values or did they subtract from the total number of students surveyed that they found

earlier?

Discuss good symbols to show various data. Have students first choose the best possible symbol from a list

and then move to having them choose their own.

a) Number of books Tanya read in each season:

b) Number of sunny days in each season: c) Number of rainy days in each season. d) Number of people whose favourite fruit is apples, bananas, oranges, grapes or peaches.

ERRATA NOTE: The chart in the workbook should say “Number of Rainy Days,” not “Number of Sunny Days.”

Activities:

1. Have students create concrete graphs by collecting small items (e.g., leaves, shapes, beads, buttons)

and sorting them. A partner can interpret the data and write a few sentences about the items collected.

(EXAMPLE: Most of the buttons are big. There are more red beads than blue beads.)

2. Place students into small groups and give them a package of Smarties, M&Ms, or jelly beans. Ask

students to sort the candies (you can choose categories or they can), count how many are in each

group, record the data, and display it. Encourage students to analyze the data—what does it tell them?

What are there more of and less of? Why do they think that happened?


PDM3-6 Pictograph Scale

Goals: Students will read pictographs that have a scale larger than 1.

Prior Knowledge Required: Pictographs that have scale 1

Vocabulary: symbol, key, scale, pictograph

Tell your students that you have a garden but you are very secretive about how many flowers are in it. You

want to make a pictograph of how many of each kind of flower you have. ASK: What is a good symbol to use

for the key? Tell your students that instead of using one symbol to mean one flower, you will use one symbol

to mean many flowers—that way, your students won’t know exactly how many flowers you have without

knowing your key.

Draw on the board:

Daffodil F F F F

Buttercup F F F F F

Daisy F F F

Tell your students that each symbolic flower could mean any number of actual flowers, but it’s always the

same number for each symbol. If the first symbol means 2 flowers, then all the symbols mean 2 flowers.

ASK: If each symbol means only 1 flower, how many flowers do I have in my garden? What numbers did you

add together to find the answer? What if each symbol means 2 flowers—then how many flowers would I

have? What strategy did you use to find the answer? (Allow several students to explain how they found the

answer, to illustrate the diversity of strategies. ) What if each symbol means 3 flowers? 4 flowers? 5 flowers?

ASK: If each symbol means 3 flowers how many daisies do I have?

If each symbol means 100 flowers, how many buttercups do I have?

If each symbol means 5 flowers, how many daffodils do I have?

If each symbol means 4 flowers, how many daisies do I have?

Bonus: “Accidentally” tell your students that you have 12 daffodils. Can they figure out the key?

Ask students whether or not it would make a difference if the data in the pictograph was presented vertically

instead of horizontally. Re-create the graph so that the symbols are stacked vertically, starting from the

bottom and moving upwards. Then erase each flower and draw an “x” in its place.

Ask students if this reminds them of any type of graph they saw last year. It should remind them of line plots.

Remind your students that they learned pictographs and line plots last year, but they always used the symbol

to mean only one object. Now they are using a symbol to mean more than one object.


Tell your students that sometimes people will pick a symbol just because it’s easier to draw, and circles are

often a good choice. Draw the following pictograph and tell students that each circle means 4 flowers:

Number of Flowers

Daffodil

Buttercup Key: 1 means 4 flowers

Daisy

ASK: How is the circle easier to draw than the flower? Use the following questions to address the half circle:

If means 4 people, how many people does mean? What if means 6 people—then how many people

does mean? Repeat with the circle meaning a variety of even numbers. Then return to the pictograph

above and ask how many flowers of each type there are.

Draw the following pictograph, and ask how many people like each colour:

Number of People with Each Favourite Colour

Red

Blue

Yellow

Orange Key: 1 means 10 people

Green

Purple

Other

Write the number of people who like each colour as students tell you the answers. Then have students draw

a pictograph of the same data using a different key: 1 means 5 people. Discuss the similarities and

differences between the two pictographs. How would you tell from each graph which colour was most often

picked as favourite?

Explain that the data sometimes makes it easy to choose a scale. Ask students to choose a scale of two, five, or ten for the following data:

a) 12, 4, 10 b) 5, 25, 35 c) 40, 20, 70 d) 35, 50, 20 e) 16, 8, 14

Choose a scale of two, three, or five for the following data:

a) 3, 9, 18 b) 20, 10, 25 c) 6, 12, 15 d) 8, 18, 6 e) 40, 25, 30

Bonus:

f) 18, 15, 9, 21, 27, 30 g) 40, 105, 35, 70, 60, 95, 35 h) 40, 20, 36, 18, 24, 16, 32


PDM3-7 Displaying Data on a Pictograph

Goals: Students will select a symbol for a pictograph that is easy to draw based on the choice of scale.

Prior Knowledge Required: The symbol on a pictograph can mean more than one object.

Vocabulary: scale, key, pictograph, symbol

Take a survey of your students’ favourite colours among the choices: blue, red, or yellow. Tally the results on

the board and then write:

Favourite Primary Colour

Blue

Red

Yellow

1 means 2 students

Have a volunteer complete the pictograph, then demonstrate how difficult it would be if you chose the same

symbol to mean 5 students—it is hard to draw one fifth of the happy face!

Brainstorm symbols that are easy to draw when you need to draw half a symbol and symbols that are easy

to draw when you need to show a fifth of a symbol. (EXAMPLES: flower with 5 petals, star with 5 points)

As in the last lesson, ask your students which scale they would use (5 or 10) for each data set below:

a) 80, 90, 95 b) 20, 10, 25 c) 120, 45, 90 e) 40, 25, 30

To guide your students, ASK: For the scale you used, do you need to draw a half symbol? How many whole

symbols would you need to draw? Emphasize that students don’t want to have to draw too many symbols.

It’s okay to use half symbols! Students should choose the symbol carefully so that they can draw half of the

symbol easily. Have students practice drawing a pictograph using the data from part c) above, a scale of 10,

and the symbol of their choice.

Discuss with your students what is wrong with the following pictograph:

Tell your students that one happy face represents one

student who picked that sport as their favourite.

ASK: Which sport is the most popular? Which sport has

the longest row of faces? Why is it easier to read the

graph when all the faces are the same size?

Tell your students that it is easier to make all the happy

faces the same size if they draw on grid paper. That

way, they can draw each happy face in one grid square.

Students should use 2 cm grid paper to make drawing

the objects easier.

Favourite Sport of Students in Class A

Soccer

Hockey

Basketball


PDM3-8 Introduction to Bar Graphs

Goals: Students will read and interpret bar graphs.

Prior Knowledge Required: Pictographs

Scale of a pictograph

Vocabulary: bar, graph, bar graph, common

Review pictographs. Tell your students that there are other ways, besides pictographs, to show data. Write

the words ‘bar graph’ and ‘pictograph’ on the board side by side. Underline the word ‘graph’ in each. A

pictograph uses pictures to display data. Ask students how they think a bar graph will display data.

Create a pictograph and a bar graph for the same data ahead of time, or use the examples below. Identify

the parts of the bar graph: the two axes (vertical and horizontal), the scale, the labels (including the title), and

the data (shown in the bars).

What time do students go to bed during the week?

Before 8:30 x

8:30 x x x x

9:00 x x x x x x x

9:30 x x x x

After 9:30 x x

1 x = 2 students

Student Bed Times During the Week

0

2

4

5

8

10

12

14

16

Before

8:30

8:30 9:00 9:30 After 9:30

Times

Nu

mb

er

of

Stu

de

nts


Remind students that a pictograph can be drawn vertically as well and have a volunteer draw a vertical

pictograph that shows the same data as the horizontal pictograph.

Allow your students to compare the bar graph and the vertical pictograph, then ask them if they think the

graphs show the same data. Explain to them that the scale of the bar graph expresses how much each

mark on the grid represents. Ask them what scale was used for the bar graph. Was the same scale used in

their pictograph? Instead of using a symbol, how does the bar graph represent two students? How would

the bar graph represent one student? How does the pictograph represent one student? Emphasize that a

bar graph is like a pictograph that uses one grid square as a symbol, and that grid square can mean any

number of objects, just like the symbol on a pictograph. The nice thing about the grid square as a symbol, is

that it is easy to draw half a symbol, or a third of a symbol, or a quarter of a symbol—just use a ruler to

measure half the height or a third of the height or a quarter of the height.

Half a symbol A third of a symbol A quarter of a symbol

Just as there is usually space between the pictures on a pictograph, there is always a space between bars

on a bar graph.

Draw students’ attention to the height of the bar and the number where the bar stops. Explain that this shows

how many students answered in each of the categories. Ask students how many students responded in each

category. Change the data and repeat to ensure that students are able to read the vertical axis correctly.

Then move on to information that follows more indirectly from the bar graph, such as: How many students go

to bed at 9:00 or earlier? How many students do not go to bed before 8:30? How many more students go to

bed at 9:00 than at 9:30? Have students indicate the concepts and/or operations they used to answer the

questions—addition, subtraction, comparing, and/or ordering. Challenge students to think of a question that

would require multiplication.

Next, introduce ‘common’ by writing it on the board and ask students to define it. Then, ask them what the

most and least common answer was to the question “What time do you go to bed?” Prompt discussion by

asking why 9:00 is the most common bedtime? In other cases, students may use the word ‘popular’ to

describe data such as favourite foods or sports. Discuss this as a group and explain why it would not be

accurate to say that the most common bedtime is the same as the most popular bedtime.

Activity: Ask students to discuss, and then write everything they can about, the data displayed in the

following bar graph. There is no title on the graph. This is done on purpose, so that students may interpret

the data in different ways. Discuss the importance of a title on a graph and how it clarifies what the data

represents even further than the labels on the bars.


0

1

2

3

4

5

6

7

8

dogs cats fish none

Literature Connection:

Tikki Tikki Tembo by A. Mosel

(This is a Chinese folktale with a moral which lends itself well to student participation through chanting.

A boy’s long name causes a dilemma.)

Survey the class about how many letters there are in each of the students’ names. Graph the data.


PDM3-9 Bar Graphs and PDM3-10 Bar Graphs (Advanced)

Goals: Students will read, interpret, and create bar graphs.

Prior Knowledge Required: Bar graphs and pictographs

Scale

Vocabulary: data, bar graph

Using a scale of 10, draw a bar graph for the following data:

Skis sold by a sports store during each season

Fall: 120 Winter: 60 Spring: 45 Summer: 15

ASK: In which season did the store sell 3 times as many skis as in another season? In which season did

the store sell twice as many skis as in another season? In which season were there 15 more skis sold than

in Spring?

Then draw a partially completed bar graph, with only the “tennis” bar shown:

Favourite sports of people in a Grade 3 class

Tennis: 4 Hockey: 5 Basketball: 12 Soccer: 10

Tell your students that hockey was chosen one more time than tennis was and have a volunteer draw

the bar. Then tell them that basketball was chosen three times as often as tennis and have a volunteer add

that bar. Finally, tell them that soccer was chosen twice as often as hockey and have a volunteer add the last

bar. Ask students what other conclusions they can draw from the graph.

Activities:

1. You will need a large open space for this activity. Create a ‘human’ birthday graph. Place cards with the

names of the months of the year along a horizontal line. Students should line up in rows behind their

birth month. If a camera is available, take a photo of the graph. After determining which months have the

most and least birthdays, ask students why it is easy to tell this. (The ‘bars’ are the rows of students—

some rows are long and some are short.) Students can then transfer the data into a graph on paper.

2. Give students a paragraph of text and ask them to create a graph that shows the number of words on

each line.

3. Some students might enjoy the Internet game found at:

http://pbskids.org/cyberchase/games/bargraphs/bargraphs.html

Students need to be quick with their hands to catch bugs. A bar graph charts the number of each colour

caught. The game gives practice at changing scale.


4. Encourage students to look at bar graphs in books, in magazines, on the Internet, or on television

(such as on The Weather Network). Have them record the number of markings on the scales and the

number of bars. About how many markings do most bar graphs use? About how many bars do most bar

graphs use?


PDM3-11 Collecting Data

Goals: Students will ask good survey questions.

Prior Knowledge Required: Ability to distinguish between a statement and a question

Ability to distinguish between “and” and “or”

Vocabulary: survey, other, none

Explain to the class that the quality of a survey question determines the quality of the data collected. For

students to be successful at conducting surveys and collecting data, they must learn how to ask a good

question.

Conduct a survey with your students by asking them what their favourite flavour of ice cream is—do not limit

their choices at this point.

Tally the answers, then ask students how many bars will be needed to display the results on a bar graph.

How can the question be changed to reduce the number of bars needed to display the results? (Remind

them of what they learned from Activity 4 in PDM3-9,10). How can the choices be limited? Should choices

be limited to the most popular flavours? Why is it important to offer an “other” choice?

Explain to your students that the most popular choices to a survey question are predicted before a survey is

conducted. Why is it important to predict the most popular choices? Could the three most popular flavours

of ice cream have been predicted?

Have your students predict the most popular choices for the following survey questions:

• What is your favourite colour?

• What is your favourite vegetable?

• What is your favourite fruit?

• What is your natural hair colour?

• What is your favourite animal?

Students may disagree on the choices. Explain to them that a good way to predict the most popular choices

for a survey question is to ask the survey question to a few people before asking everyone.

Emphasize that the question has to be worded so that each person can give only one answer. Which of the

following questions are worded so as to receive only one answer?

a) What is your favourite ice cream flavour?

b) What flavours of ice cream do you like?

c) Who will you vote for in the election?

d) Which of the candidates do you like in the election?

e) What is your favourite colour?

f) Which colours do you like?


Have your students think about whether or not an “other” category is needed for the following questions:

What is your favourite food group?

Vegetables and Fruits Meat and Alternatives

Milk and Alternatives Grain Products What is your favourite food?

Pizza Burgers Tacos Salad

Then ask students how they know when an “other” category is needed. Discuss which of the following questions would require an “other” category and why:

• What is your favourite day of the week? (List all seven days.)

• What is your favourite day of the week? (List only Friday, Saturday, and Sunday.)

• What is your favourite animal? (List horse, cow, dog, pig, cat.)

• How many siblings do you have? (List 0, 1, 2, 3, 4 or more)

• Who will you vote for in the election? (List all candidates.)

Then bring up the point that an “other” category may not be an option. For example, if the teacher wants to

bring 2 movies to show on the last day before Christmas holidays and she has only 5 movies at home, she

would give only those 5 movies as choices and would bring the 2 most popular ones to class.

Ask students what they think most people in the class would prefer to do for a party: go to a movie or go on

a skating trip. Ask students what kind of question you should ask to gather this data. Record all of their

suggestions on the board. Once this is done, review all the questions and determine all the possible answers

for each one.

Questions and answers might include the following:

1. Do you want to have a party? Yes/no

2. If you had a party, would you like to go to a movie? Yes/no

3. If you had a party, would you like to go on a skating trip? Yes/no

4. If you had a party, would you like to go to a movie or go on a skating trip? Movie/skating trip/neither/both

5. If you had a party, choose one of these things to do: go to a movie, or go skating? Movie/skating trip

Now, discuss with students which is the best questions to ask. Questions 1, 2, and 3 are limiting and will not

capture all data. Question 4 makes it difficult to make a decision (i.e., determine what is the most popular

choice) but Questions 5 makes it clear which activity is preferred. (NOTE: Make sure that you emphasize the

positive in each suggestion, showing how it’s a good start and demonstrating where to go from there to get to

the targeted question.)

Activity: Discuss the difference between ‘and’ and ‘or’ in a question and what they mean. For example,

the questions “Do you have a cat and a dog?” and “Do you have a cat or a dog?” will produce different

answers. For the first question, respondents can answer no (I don’t have a cat AND a dog) or yes (I have

both a cat AND a dog). For the second, respondents can answer yes and no but the meaning changes:

yes means I have a cat OR a dog; no means I don’t have either.

If possible, bring in pictures (perhaps cut from magazines) of people with cats and/or dogs: some with a cat

and a dog, some with only a cat, some with only a dog, and some with neither. Hold up the pictures one at a


time and ask students how each person would answer these two questions: Do you have a cat or a dog? Do

you have a cat and a dog? Tally the results. For example, depending on the pictures you brought, your tallies

might look like:

YES NO

I have a cat or a dog

I have a cat and a dog Then have students summarize the answers in a separate bar graph for each question.


PDM3-12 Practice with Surveys and PDM3-13 Blank Tally Chart and Bar Graph

Goals: Students will create a survey question, tally the data and present their data in a bar graph

Prior Knowledge Required: How to show data (graphs)

How to collect data

How to ask a question

What choices to give survey takers

How to analyze data

Vocabulary: survey, tallies, pictograph, bar graph

Tell students you want to find out what they will be doing on their summer holidays. Then discuss the

question and choices: What will you be doing over the summer holidays? Camp, family trip, summer school,

staying at home, other. (Modify the choices according to your students’ interests and activities.)

Ask each student to identify their summer activity by raising their hand when you call out the choice. Record

the data in a tally chart with the choices listed.

Count the tallies for each category to determine how much space you will need for the bar graph. Draw a grid

with a fixed number of markings, say 8. ASK: What scale should we use?

Remind students that there is a space between the bars in a bar graph and have students independently

create a bar graph for the data collected. Remind them to include a title and labels on their graphs.

Analyze the data together. Ask students what the data is telling them. Record those statements.

Activity: Ask students to name some of their favourite authors. (Have a selection of books which are

popular during read alouds and independent reading time on hand for students to refer to.) Then, select

the top 3 authors as well as “other” for categories. Ask students to identify their favourite author (explain that

they can only raise their hand once when ‘voting’ and record data using tally marks) and collect the data

from the class.

When you’re finished, ask how students can tell if everyone voted or not. Do they think anyone voted twice?

Does the number of votes equal the number of students in the class? What would happen if someone didn’t

vote? If someone voted twice?

ASK: If we want no more than 5 markings on our graph (have a graph with 5 markings on the vertical axis on

the board), what scale should we use? Would it make sense to have only 1 marking on the graph? How

would that make the graph hard to read? Decide on the number of markings and the scale for the graph.

Then complete the graph.


Tell your students that they will be designing their own survey and then surveying their classmates.

Everyone can ask a different question, so suggest several topics if they have trouble getting started.

(EXAMPLES: How do you get to school? What is your favourite colour? How many people are there in your

family? What time do you wake up on weekdays? How long do you take to get ready for school? Does your

jacket have a hood? What pizza toppings do you like? What is your favourite meal? What is your favourite

cereal? What is your favourite season? Who is your favourite person? What type of home do you live in?

What is your favourite summer or winter activity?)

Extensions:

1. After completing their survey, students can transfer their graph data to KidPix to create a computer-

generated graph.

2. Ask student how they could find out the favourite colour of every teacher in the school. How would they

collect the data? How would they organize the data? Students can work on this in pairs or small groups

after they have a plan of action. After collecting and representing the data, students can report their

findings orally.

Literature Connection:

So you want to be president? by J. St. George

(A Caldecott winner. Anyone can be president, no matter what they look like or where they are from.)

After reading the book, have students work in small groups to collect data from their classmates. They can

ask the following question: What do you want to be when you grow up? Students should be encouraged to

organize the data in more than one way and be prepared to present their final work.


PDM3-14 Collecting and Interpreting Data

Goals: Students will understand when surveys are appropriate to find out information and when other

methods are required.

Prior Knowledge Required: Asking a good survey question

Vocabulary: survey, measuring, researching, observing

Conduct a survey of your students to determine how many of them were born before noon and how many of

them were born after noon. It is likely that very few, if any, students will raise their hands for either option.

Explain that deciding when to conduct a survey, or when to use another method to collect data, depends on

whether or not the people being surveyed can answer the question. Let’s look at the example above:

Question: When were you born?

Choices: Before or at noon / After noon

The question is very clear and there is no “other” category because no other choice is possible. But if

people don’t know the answer, the survey is pointless.

Have your students think about which topics from the list would be good survey topics:

• What are people’s favourite colours? (good)

• Are people left-handed or right-handed? (good)

• Can people count to 100 in one minute or less? (not so good)

• How many sit-ups can people do in one minute? (not so good)

• What are people’s resting heart rates? (not so good)

• What are people’s favourite sports? (good)

• How fast can people run 100 m? (not so good)

• How do people get to school? (good)

• How many siblings do people have? (good)

Is a survey needed for the following topics or can the data be obtained by observation?

• Do students in the class wear eyeglasses?

• Do students in the class wear contact lenses?

• What are adults' hair colours?

• What are adults' natural hair colours?

Sometimes a measurement or calculation is needed to obtain data. Have your students decide if

observation, a survey or a measurement is needed to obtain the data for the following topics:

• What are people’s heart rates?

• What are people’s favourite sports?

• How do people get to school?

• How many sit-ups can people do in one minute?

• How long are people’s arm spans?


• What colour of shirt are people wearing?

• How tall are people?

Sometimes students cannot find the information themselves but need to rely on measurements or

observations that other people have taken. Have students brainstorm examples of such situations (e.g.,

sports data from last year’s championships, world records, how fast different types of birds can fly, the time

of year that different animals hibernate, and so on).

pdm3-1 introduction to classifying data

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