Download Statistics and Probability 15_Guided and

Statistics and Probability 15_Guided and Independent Investigations
(Year 5) ACMSP118, ACMSP119, ACMSP120, ACMSP116, ACMSP117 NSW MA1 11MG
Pose questions, construct column and line graphs, dot plots and tables, identifying best representation for each investigation, make decisions.
GUIDED INVESTIGATION
Children learn how to investigate the concept by following teacher’s
instructions until they are ready to investigate the concept independently.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their current level of
understanding informing both themselves and the teacher of their current level of understanding
Resources: graphs, pencil, paper, ruler, spreadsheet computer program
What could we do?
What language could we use to ask
questions and explain?
What could we do?
What language could we use to explain?
Children:
 How could we collect data?
 I collected data by observation or survey
by …
1. sit in pairs
 How could we construct a
column graph?
 I constructed a column graph …
2. collect data through observation or
survey
as
guided
by
the
teacher
 How could we construct a dot
 I constructed a dot plot …
plot?
3. construct a picture or column graph
 The advantages of the column graph are …
or dot plot
 What are the advantages of
 The advantages of the dot plot are …
4. explain their choice of graph
the column graph?
 The data is the line graph is …
5. interpret line graphs as guided by the
 What are the advantages of
 I can use the data in the graph to make
teacher
the dot plot?
decision by …
6. use the data to make decisions
 What data is recorded in this
line graph?
 How could we use the data in
the graph to make decisions?
• How are column graphs and dot plots different?
REFLECTION Before, during and after • What data can we collect through survey?
•
What
data
can
we
collect
through
observation?
• When is a dot plot a useful representation of data?
lessons, children discuss then record
• What is a graph?
• When is a dot plot not a useful representation of data?
responses to reflection questions to
•
What
is
a
column
graph?
• What is a line graph?
inform themselves and the teacher of
•
What
is
a
dot
plot?
• When is a line graph a useful representation of data?
their current level of understanding
• How are column graphs and dot plots similar?
Children:
1. sit in pairs
2. collect data through
observation or survey as
guided by the teacher
3. construct a picture or column
graph or dot plot
4. explain their choice of graph
5. interpret line graphs as
guided by the teacher
6. use the data to make
decisions
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative assessment
data for both the child and the teacher.
‘Doing’ mathematics is not enough and is not a good indicator of understanding.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,
Collect data,
select best data
representation.

In pairs or small groups, children collect data by either observation (for example, cars driving past the school, temperature
across time, children wearing full school uniform in each class) or survey (favourite fruit / animal, number of children in
family, types of pets, country of birth, parents’ country of birth, languages spoken). They decide which type of graph to use to
represent the data. They construct the graph, justifying their choice. They make 3 interesting statements about the data. They
use the data to make decisions. They identify whether their data collection method and whether their survey question was
effective for gathering the data.
Construct and
interpret line
graph.

In pairs or small groups, children collect data that changes over time, for example, temperature, pulse rate before exercise,
immediately after exercise, then at 1 minute intervals (count pulse for 10 seconds and multiply by 60 for rate per minute).
They identify a line graph to use to represent data that changes over time. They construct the line graph. They identify data
between measurement times. They make 3 interesting statements about the data. They use the data to make decisions. They
identify whether their data collection method was effective for gathering the data.
Construct dot
plots based on
statements.

In pairs children record interesting statements about animals, for example, ‘there are 6 more cats than dogs and 4 more dogs
than guinea pigs’. Children create a number of different dot plots to represent the data.
M&M dot plots.

Children each have a small packet of Smarties or M&Ms. They create dot plots by placing colours into stacked columns on a
base line. They record their dot plots and compare them with other children’s dot plots. From the data, identify which colour
they would be most and least likely to find in a random packet.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Make decisions
using data.

Internet data
representations.

Children collect column and line graphs and dot plots from the Internet, including newspapers on-line. In pairs or small
groups, children discuss the advantages and disadvantages of each type of graph, whether the data is best represented in the
type of graph.
Line graphs on
Excel.

Children use a spreadsheet program (for example, Microsoft Excel) or a word processing program (for example, Microsoft
Word) to construct line graphs. See Statistics (Data) and Probability (Chance) 8.
Children read through information related to fitness in the teen years posted on the Bureau of Statistics website:
http://kidshealth.org/parent/nutrition_center/staying_fit/fitness_13_18.html# identifying the recommended number of
hours of physical activity per week. Children use the data to make decisions about the amount and type of exercise they will
do.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Collect data by either observation (for example, cars driving past the school, temperature across
time, children wearing full school uniform in each class) or survey (favourite fruit / animal, number
of children in family, types of pets, country of birth, parents’ country of birth, languages spoken).
Decide which type of graph to use to represent the data.
Construct the graph, justifying your choice of graph.
Make 3 interesting statements about the data.
Use the data to make decisions.
Identify whether your data collection method and whether your survey question was effective for
gathering the data.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Collect data that changes over time, for example, temperature, pulse rate before exercise,
immediately after exercise, then at 1 minute intervals (count pulse for 10 seconds and multiply by
60 for rate per minute).
Identify a line graph to use to represent data that changes over time.
Construct the line graph.
Identify data between measurement times.
Make 3 interesting statements about the data.
Use the data to make decisions.
Identify whether your data collection method was effective for gathering the data.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Record interesting statements about animals, for example, ‘there are 6 more cats than dogs and 4
more dogs than guinea pigs’.
Create a number of different dot plots to represent the data.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Have a small packet of Smarties or M&Ms.
Create dot plots by placing colours into stacked columns on a base line.
Record your dot plot and compare them with other children’s dot plots.
From the data, identify which colour you would be most and least likely to find in a random
packet.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Read through information related to fitness in the teen years posted on the Bureau of Statistics
website:
http://kidshealth.org/parent/nutrition_center/staying_fit/fitness_13_18.html#
identifying the recommended number of hours of physical activity per week.
Use the data to make decisions about the amount and type of exercise you will do.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Collect column and line graphs and dot plots from the Internet, including newspapers on-line.
In pairs or small groups, discuss the advantages and disadvantages of each type of graph, whether
the data is best represented in the type of graph.
http://www.alearningplace.com.au
Investigating Pose questions, construct column graphs, line graphs, dot plots and
tables, identifying best representation for each investigation.
STATISTICS AND PROBABILITY 15 Pose questions, construct column graphs, line graphs, dot plots and tables, identifying best
representation for each investigation.
Use a spreadsheet program (for example, Microsoft Excel) or a word processing program (for
example, Microsoft Word) to construct line graphs.
http://www.alearningplace.com.au