Unit Plan Prepared by: Kisrene McKenzie, Leslie Jennings and Jonathan Ball
Mathematics Part 1, AQ
Instructor: Coleen Bellehumeur
Date: May 1, 2014
Grade 6 Data Management and Probability
Overall Expectations:
 determine the theoretical probability of an outcome in a probability experiment, and use it to predict the frequency of
the outcome
 read, describe, and interpret data, and explain relationships between sets of data
 collect and organize discrete or continuous primary data and secondary data and display the data using charts and
graphs, including continuous line graphs
Specific Expectations:
 represent the probability of an event (i.e., the likelihood that the event will occur), using a value from the range of 0
(never happens or impossible) to 1 (always happens or certain)
 predict the frequency of an outcome of a simple probability experiment or game, by calculating and using the
theoretical probability of that outcome
 read, interpret, and draw conclusions from primary data and from secondary data presented in charts, tables, and
graphs
 collect data by conducting a survey or an experiment
 select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the
choice of graph
 display the data in charts, tables, and graphs (including continuous line graphs) that have appropriate titles, labels
(e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and
distribution of the data, using a variety of tools (e.g., graph paper, spreadsheets, dynamic statistical software)
Success Criteria and Misconceptions
Success Criteria:

I know that probability is a measure of the likelihood
Misconceptions:

of an event occurring

I understand that the probability of an event is
measured on a continuum from 0 (impossible/ never)
to 1 (certain/ always), therefore I can express
probability as a fraction or as a percentage


I know that the larger the sample or number experimental
trials conducted, the more reasonable are my predictions
of the outcome
I know that experimental probability measures the
probability of an outcome in an experiment

Students may think that previous events affect future ones
even though the events are independent. For example,
students may think that if a coin is flipped and lands on heads
5 times in a row then it is likely to land on heads the next time.
The fact is once students understand theoretical probability
they will use logic to understand and predict that the coin has
an equal chance of resulting in heads or tails each time it is
tossed and that the probability is always 1/2
Students own cultural or personal beliefs or intuition about
chance can sometimes influence their predictions. For
example a student may think that 3 is their lucky number so
they will likely roll a 3. Encourage students to understand that

I know that experimental probability is expressed as:
P = Number of favourable outcomes
Total Number of Trials



I know that theoretical probability predicts what is likely to
happen in advanced of an event that has a fair (equal)
chance of occurring
I know that theoretical probability is expressed as:
P = Number of favourable equally likely outcomes
Number of equally likely outcomes





I know that data are pieces of information.
There are many different ways to display data.
Depending on the data, some of these are more or less
effective.
Line graphs are effective when pieces of data are
connected, for example a change over time.
We can use line graphs to display trends and to predict
future events.
Success Criteria for Problem Solving:






I will highlight the important information in the word
problem
I can make a K/W/H chart to help me find out what the
question is asking me to solve
I will choose a strategy to help me solve the problem
I will try my strategy (carry out the plan)
I will check to see if my answer is reasonable
I will use math language to justify my thinking/answer


events are random and equally likely so they must remain
objective.
Students may believe that the word likely means almost
always. This misconception can be cleared up discussing and
using (interchangeably) the vocabulary of probability (likely,
often, probable, sometimes, not probable , unlikely) and
place the results of an experiment along a probability line
between impossible and certain using a probability
Students may look for patterns to make predictions instead of
treating events as random
Students may fail to recognize when possible outcomes are
not equally likely. For example, when spinning a spinner with 4
unequal sections may think the probability is still 1 out of 4
Students may not identify all the possible equally likely
outcomes, particularly in compound events. For example,
students may only identify 3 possible outcomes in a double
coin flip. Encourage students to use a tree diagram or area
model to reveal “hidden” outcomes
*Based on Marian Small`s (2009) Making Math Meaningful to
Canadian Students, K-8
Strategies:
Tools: table, charts (tree diagram, area model), dice, spinner,
counters, coins, tiles, playing cards, paper bag
Lesson
Diagnostic: Grade 6 ONAP
LG: to determine what
students already know
about probability and
what they learned from
the previous grade
Minds-On
We know that probability
means making a prediction
about the possibility of an
outcome. We use probability
every day in our lives to
calculate the likelihood of
something happening.
Today you will be given a
Action: Hands On!
Task
ONAP Performance Task
activity:
For this task, students will
predict the outcome of a
simple probability experiment
and analyze the results.
Students consider the results in
the context of playing a
game.
Consolidation
(Part 1)
Gallery Walk:
Students showcase their mathematical
thinking by posting how they solved the
problem. Students circulate among the
gallery and engage in math talk about
strategies used.
Questions to develop class discussion:
How did you solve the problem? What
probability challenge to solve.
Try your very best to answer as
much as you can. I just want
to know and understand what
you already know about
probability.
Tell students they will 1) predict
who they think would win a
coin-toss game 2) toss two
coins ten times and record the
results. Give students the coin
toss activity sheet to complete.
strategy did you use to solve the problem?
Are there more possible outcomes? How
do you know?
Possible strategies/
Anticipated solutions:
Students could make a chart
to show their prediction
HEADS TAILS
HEADS
HH
HT
TAILS
TH
TT
Lesson #1: What are my
chances?
LG: to learn about
experimental probability
by conducting simple
probability experiments
Discuss with class how
probability is part of our
everyday lives. Ask: “how
many of you decided what to
wear today based on
predicting the weather? Did
you consider the chances of
rain, snow or sunshine? What
factors did you consider in
your prediction of the
weather?
Model a simple probability
experiment with the class:
show students the paper bag
and tell them the contents (5
red tiles and 5 yellow tiles); ask
students to predict the
probability that I will draw 2
tiles of the same colour. Ask
the class how many times I
should draw tiles out of the
bag (discuss number of trials
and sample size, ask whether
1 trial is enough to make a
prediction; do 10 trials). Ask
the class what I should do with
the tiles I have drawn (put
Playing Cards activity:
With a group of 3, use the
deck of cards to conduct a
probability experiment using
10 trials to predict the following
independent event: the
probability of drawing a King.
You must select an
appropriate tool to
demonstrate the results of your
experiment. (Provide students
with chart paper and markers
for their group). Express the
probability using words,
fraction, percentage or
probability line
Possible strategies/
Anticipated solutions:
Tool selected
 chart with Tally
 chart with Check marks
 tree diagram
 area model
Congress: Choose several students to
showcase their thinking. Have them show
how they solved the problem
Show students the experimental probability
formula which they must use to calculate
the fraction or percentage:
P = Number of favourable outcomes
Total Number of Trials
Questions to develop class discussion:
Lesson #2:
LG: to determine the
theoretical probability of
an outcome in a
probability experiment
them back in the bag why or
why not?) Return the tiles to
the bag after each draw so
the events are independent
(assess students’ knowledge of
dependent and independent
events). Ask students to
record the results of the
experiment on the blank sheet
of paper provided by
selecting an appropriate tool
to represent the experiment
(assess if students can
represent the experiment
using a chart with title, # of
trials, and title of outcomes
(same colour / different
colour)). Ask students to look
at the outcome of the
experiment and express the
probability: Ask them to finish
this sentence “The probability
of drawing 2 tiles of the same
colour is___________.”
Expressing probability
 words ; e.g. 2 out of 10
 fraction; 2/10
 percentage ; 20%
 probability line
Remind the students of the
work they did yesterday on
probability. Revisit the success
criteria big ideas anchor
chart. Tell students they will
learn about theoretical
probability. Give pairs of
students a coin and ask them
to make a prediction 9head
or tail) then take turns tossing
the coin for 20 tries and record
their results.
Spinner activity:
Students are partnered up and
are given two different types
of (four-sector) spinners with
each section labeled by letter,
colour, or number. Tell them to
do two separate experiments
for each type of spinner and
to predict the outcome.
Students must record their
results using any tool. They
must answer the following: 1.
What is the probability of
spinning each outcome? 2.
Write the probability as a
fraction. Which spinner shows
a fair/equal chance of getting
the desired outcome?
Ask students to share the
results. Ask class to tell you
what all the possible
outcomes are. Point out that
the coin has 2 faces (heads or
tails). Then ask students to
what is the likelihood that they
Congress: Choose several students to
showcase their thinking. Have them show
how they solved the problem
Show students the theoretical probability
formula which they must use to calculate
the fraction or percentage:
P = Number of favourable equally likely outcomes
Number of equally likely outcomes
Questions to develop class discussion:
Why it is difficult to predict when the
probability tool you use is not equally
portioned?
would get the face they
predicted? Prompt students to
say ½ or 50%.
Share definition of theoretical
probability: predicts what is
likely to happen in advanced
of an event that has a fair
(equal) chance of occurring.
Lesson # 3
LG:
Lesson #4
LG: Students will represent
as a fraction the
probability that a specific
outcome will occur in our
sock experiment using lists
and tables.
Lesson adapted from A
Guide to Effective
Instruction- Data
Management and
Probability
(see attached lesson)
Minds on- Talk about the
relatable experience of pulling
clothes out of a dryer hopeful
to find a shirt and instead
grabbing a kitchen towel. Do
the chances seem likely or
unlikely they’d grab their
desired item? Brainstorm
events at home/school when
they think and use probability.
Present problem: You will
place 3 pairs of socks in a
paper bag. Each group will
perform 20 trials and record
their data in lists and present
findings in fractional form. Ask
students to quickly think, pair,
share about the problem and
make their own prediction
and explain their reasoning to
their partner. Get a show of
hands to hear different
predictions. These could be:
How many think socks will 1.
Match more likely? 2.
Students make groups of 2.
Have coloured socks, paper
bags and paper and pencil.
Perform 30 trials. Students #
socks from 1-6. Start trials and
record results on charts they
have created. Each trial
should be recorded. What was
the outcome and what was
the frequency? Once trials
have been completed ask
students to examine results
and reconsider their earlier
predictions during think, pair
and share. What observations
can they bring to class
discussion? Put results in
fractional form and bring to
class discussion.
Reconvene students and show results in
gallery walk. Let them share their groups’
results and discuss methods of recording
data, and final outcomes which should
show fractional amounts for results.
Questions?- How did your earlier prediction
compare with your experimental
outcome?
How many outcomes did you have? How
did you know these were all the outcomes
you could have? How did the frequencies
compare? What do you think helped
determine the outcome?
Mismatch more likely? 3. Both
equally likely? Allow this to set
stage for experiment and
show one method of
recording above with tallies.
Lesson #5
LG: Practice working with
probability by playing
different games in a
rotation. Show how the
experimental probability
compares with the
theoretical probability by
using percentages,
fractions or tree diagrams.
Compare your actual
experimental results to your
predictions.
Review difference between
experimental and theoretical
probability. Draw on previous
lessons and examples. Review
method for recording trial
results and fractional/percent
wins. Tell them they will rotate
and play several games once
and then be expected to
record findings through trials
and put final results in fractions
or percent.
Students play following games:
Taken from Math Makes Sense:
1. Counter Toss: Place 10
counters, 2 different coloured
randomly on a plate. Tip the
plate so the counters fall to the
floor. Count # of counters that
land red side up. Do 10x. Total
your result. Find the
experimental probability of a
counter landing red side up.
Write the probability result as a
fraction and as a percent.
2. Alien Mix-up: Draw and
colour an alien on the
template given into 3 parts.
Make horizontal cuts along
solid lines. Do not cut past the
broken line. Fold on broken
line. Arrange all aliens from
your group into a booklet.
Staple inside the broken line.
You can create many different
aliens by flipping top, middle
and bottom sections of
booklet. Use a tree diagram
to show total possible alien
creations in your booklet.
3. Addison Wesley game- The
random removal game: 15
counters per player, 2 #cubes.
A) Each player makes a
number line from 2 to 12. B).
Each player makes a line plot
by placing 15 counters above
numbers on the line. C). To
play a player rolls the 2
Discuss game results in whole class.
Tabulate total counter wins and show
theoretical probability from combined
tosses in class. How did the experimental
probability in your small groups compare
to our theoretical probability? Which one is
more reliable, Why? Why does a larger
sample make a difference in results?
Questions: How did you record your data?
How did your prediction compare to
actual outcome?
Use the language of probability to
compare two games.
Lesson #6
Data Review
Learning Goals:
Data are pieces of
information. There are
different ways to display
this data and, depending
on the data, more and
less effective ways to
display it.
Lesson #7
Off to the Races
Learning Goals:
Line graphs are used
when different pieces of
data are connected, for
example change over
Show students
a T-chart of
student
birthdays by
season.
Question:
What are other
ways of
displaying this
data?
number cubes and states the
sum. Remove that position on
number line. D) Continue to
take turns until all of counters
by one player are removed.
Have groups of 2-4
Sort displays into like
create a simple
categories (e.g. all pie charts
survey to collect
together). Have each group
data from other
choose the one which best
students (e.g. How
represent their findings and
do you get to
explain their reasoning.
school? What pet do
you own?).
Have them record
the data on T-charts.
Whole group:
Have the
students list the
key
components of
a bar graph.
As they name
a component,
lay an
oversized visual
of it down on
the carpet to
create a large
graph. Use
wide masking
tape to create
the bars for
Fall, Winter,
Summer,
Spring.
Have each group
display their results in
as many ways
possible.
1. Show
students an
image of an
untitled line
graph.
Questions:
a) Describe
Small groups:
When might you use a:
- Pie chart?
- Bar graph (horizontal vs vertical)?
- Histogram?
- Pictograph?
- Text?
Can you display all data in a graph
(what about descriptive data)?
Possible strategies:
Textual methods
Graphical methods
Tabular methods
1.Weigh 10 or more
Matchbox cars.
Record in T-chart.
2.Drive them down a
1. Groups post findings on
board.
Follow up work:
Discrete vs. continuous data (see
appendix B)
2. Learning Discussion:
Think-Pair-Share T-Chart:
Did all groups
experience similar trends?
Data that ought to be displayed in
time or space. We can
also use line graphs to
predict events.
what this
graph might
be about? (M.
Small)
b) How are line
graphs
different from
other graphs?
What do they
show that
other graphs
don’t?
2. Weigh a toy
car and roll it
down a ramp.
Record the
distance in a Tchart (weight:
distance) and
plot that point
on a graph.
Lesson #8
Learning Goals:
Line graphs can be used
to predict future events.
3. State
Learning Goal
and explain
Hands On.
Set up several
lines 10 meters
away from a
target (hoop).
Have every
student
attempt to
throw a
beanbag into
the target.
Record the
results and
establish a
probability for
accuracy (e.g.
2 in 20).
Convert this to
a percentage
ramp. Record distances in
T-chart.
Can we develop a theory for
weight: distance experiments?
3.Plot points (y=weight:
x=distance)
3. Show a new heavy car to
the class. Weigh it and have
the students make a
prediction based on their
charts: Predictions are based
on PROBABLE results. How far is
it likely to go?
4.Connect points (broken
line graph)
5.Group question (write
on board):
Did you discover a trend?
Does your line graph
show you anything?
Small groups:
Record data at 10m,
9m, 8m, 7m ,6m
With tallies in a Tchart.
Convert data results
to probability
percentage for each
distance increment.
(ie: (success * 100) /
attempts = x)
Plot on graph.
Connect dots.
Create a rule (the
closer you get, the
higher the
probability).
a line graph
(e.g. speed of a bicycle as it goes
from 0 to 100 meters)
Vs.
Data thought should not be
displayed on a line graph
(e.g. different weights of cats in the
neighborhood)
Line graphs can be useful for
examining data that changes
through time/space. How was
this line graph useful to us as
scientists?
Present findings.
Have the class choose a
“reliable graph”. Post this
graph. Have the class try to
predict frequency probability
at 5 steps (by extending the
line). Test the prediction.
Possible strategies:
- Determine the line equation
(y= mx+b, where m=slope,
b=y-intercept)
- Sketch the line
An engineer is someone who
applies scientific knowledge and
mathematics to develop solutions
for technical problems. Engineers
design materials, structures, and
systems while considering the
limitations imposed by practicality,
regulation, safety, and cost. The
word engineer is derived from the
Latin roots ingeniare ("to plan,
invent") and ingenium
("cleverness"). (Wikipedia)
How might an engineer make use
of a line graph?
(e.g. 10%).
Question: How
can we
increase the
frequency (A:
widen target
or get closer).
Lesson #9
LG:
Independent
task for
assessment.
See appendix
A
Appendix A
Lesson #9 Independent task
1.a) Before planning a 5-day March Break trip to Thunder Bay, a family looked at the temperatures and rainfall from last year.
(Provide 2 T-Charts). Using the chart below, display this all of this data using line graphs.
1.b) Choose a 5-day range of dates to go on your holiday and explain your answer.
2. Design an experiment which ought to be displayed using a line graph. Carry out the experiment yourself and record the
results. Plot the results using a line graph.
Appendix B
Graphing Glossary
Glossary
Note: (A) indicates
definition from the ACARA Glossary
Bar graph
Categorical data
(See also column graph) In a bar graph or chart, the bars can be either vertical or horizontal. (A)
A categorical variable is a variable whose values are categories. Categories may have numerical labels, for example, fo
the variable postcode the
category labels would be numbers like 3787, 5623, 2016, etc, but these labels have no numerical significance. (A)
Column graph
A column graph is a graph used in statistics for organising and displaying categorical data. To construct a column graph
equal width rectangular
bars are constructed with height equal to the observed frequency. Column graphs are frequently called bar graphs or ba
charts. (A)
Continuous data
A continuous variable is a numerical variable that can take any value that lies within an interval. In practice, the value
taken are subject to
the accuracy of the measurement instrument used to obtain these values. (A)
Data
Data is a general term for a set of observations and measurements collected during any type of systematic investigation.
Primary data is data collected by the user. Secondary data is data collected by others. Sources of secondary data include
web-based data
sets, the media, books, scientific papers, etc. (A)
Data display
A data display is a visual format for organising information (e.g. graphs, frequency tables) (A)
Dependent
A dependent variable (response variable) is one whose value depends on the value of another variable. E.g. heigh
variable
depends on age
Discrete numerical A discrete numerical variable is a numerical variable, each of whose possible values is separated from the next by a definite
variable
'gap'. The most
common numerical variables have the counting numbers 0,1,2,3,… as possible values. Others are prices, measured in dollar
and cents.
Examples include the number of children in a family or the number of days in a month. (A)
Distribution
The pattern of variation of a variable
Dot plot
A dot plot is a chart where each data point is represented as a dot on a number line. Dots can represent more than one
observation.
Independent
An independent variable (explanatory variable) is one whose value does not depend on the value of another variable.
variable
Mean
The arithmetic mean of a list of numbers is the sum of the data values divided by the number of numbers in the list. (A)
Median
The median is the value in a set of ordered data that divides the data into two parts. It is frequently called the 'middle value'.
Where the number of
observations is odd, the median is the middle value. Where the number of observations is even, the median is calculated as
the mean of the two
central values. (A)
Mode
The mode is the most frequently occurring value in a set of data. When there are two modes, the data set is said to be
bimodal. (A)
Numerical data
Can be discrete, data can take specified values only; or continuous, data can take any value within a range. Also see note
above in ‘Categorical data’
Picture graph
A graph that use pictures to represent the frequency of categorical data. Each picture can represent one or more pieces o
data.
Stem and leaf
Stem and leaf plots are tables where discrete data e.g. the set of students’ height in cms, is represented (usually in order) by
plots
distinguishing values
(the leaf) within set intervals (the stem). Stem plots must include a key e.g. Key: 15|2 = 152 cms. Stem plots provide a visua
indication of spread.
Variable
Any characteristic of a person or thing. Univariate data has only one attribute e.g. eye colour. Bivariate data has two
attributes e.g. in a scatterplot a
single point can represent both height and age.
Australian Bureau of Statistics http://www.abs.gov.au/