By: Laura Segreto
April 12, 2014
Manipulative Assignment
Manipulative: Spinners
(NLVM Spinner example)
Description of manipulative: The spinner is a circle divided into sections. In the
middle of the spinner there is an arrow, which shows you where the spinner “lands”
when it stops spinning. The spinner is used for probability experiments. The sections
on the spinner can be any size and there can be any number of sections. In the
middle of the spinner there is usually an arrow, which spins around, or you can use a
paper clip and a pencil for the arrow. The spinner usually has several colours or
numbers on it and the students can predict the outcome of spinning the spinner
several times.
Uses of manipulative:
Probability experiments: The spinner can be used to test predictions about the
likelihood of the arrow falling on a specific section. Students can predict how many
times the spinner will stop on each section if they spin it 10 times. Then the student
can spin the spinner 10 times, record the results in a tally chart and compare their
predictions to the actual results. Students are therefore able to compare the
theoretical probability to experimental probability.
Build your own spinners:
Students can experiment with the size of the sections in spinner to see how the size
of the section can influence the outcome. Through using the spinner they will see that
the larger the section, the more likely the arrow will fall on that section. Students can
build their own spinners on paper or using the NLVM Spinner manipulative.
Fractions link: Spinners are a great way for students to visualize fractions. The
students can decide what fraction of the spinner is a specific colour. For example,
there are 5 equal sections, and 3 are blue so 3/5 of the spinner is blue. Students can
also calculate the % of the circle that is a specific colour.
Show a probability continuum: Use spinners on a continuum to show a probability
continuum. In Van de Walle’s book “ Elementary and Middle School Mathematics,
By: Laura Segreto
April 12, 2014
Teaching Developmentally” Figure 23.4 shows how spinners are used as a visual to
show the difference along the continuum from impossible to possible.
Discover how probability outcomes change based on number of spins: Using
the NLVM Spinner, students can compare the outcomes on a spinner after 10 spins
to 100 spins. It would be unrealistic to ask the students to spin a paperclip 100 times
on a spinner, but with the NLVM spinner, with 1 click, the results up to 999 spins
can be shown. Students can record the results after 10 spins and then after 100 spins
and compare. They will notice that the more times you spin, the closer the results are
to the theoretical probability.
3 Part Lesson for Probability –Spinner
TDSB
Dewson St. PS
Lesson Title – Using Spinners To Explore Probability
Date
Grade(
s) 5
Learning Goal (Curriculum Expectations)
– represent, using a common fraction, the probability that an event will occur in
simple games and probability experiments (e.g., “My spinner has four equal sections
and one of those sections is coloured red. The probability that I will land on red is ¼)
– pose and solve simple probability problems, and solve them by conducting probability
experiments and selecting appropriate methods of recording the results (e.g., tally chart, line plot,
bar graph)
Lesson Components
Anticipated Student
Responses
Part 1: Minds On (10 minutes)
Possible student Responses:
Show a spinner with unequal sections like the one
above. Ask the students to write 2 sentences about
the spinner using the probability vocabulary from the
math word wall and to explain their thinking.
-Red is more likely than blue.
-Blue is more likely than green.
-There are 3 colours
-The probability that the spinners lands on
red is ½ because half of the spinner is red
- The probability that the spinners lands
on Green is 1/6 because if you divide the
spinner into 6, the sections would be the
same size as the green section
- The probability that the spinners lands
on Blue is 2/6 because green is 1/6 and
blue is 2 greens
By: Laura Segreto
Students share their sentences with the class
April 12, 2014
-Blue is twice as likely as green
Success criteria:
-I can find the fraction to represent each
section on the spinner
-I can predict the possible outcomes of
spinning a spinner 10 times
Part 2: Hands On (25 minutes)
Strategies:
 Make a picture
 Keep track using
a tally chart
Students are sent in partners onto the computers to the Spinner on
the National Library of Virtual Manipulatives
(http://nlvm.usu.edu/en/nav/frames_asid_186_g_2_t_5.html?open=act
ivities&from=category_g_2_t_5.html)
Tools:


Students are to click on “Change Spinner” to change the size of the
sections in their spinner. They are allowed to change the sections any
way they want. Students replicate the virtual spinner they have just
designed by drawing it into their workbook. Students must make a
prediction for the outcome based on spinning the spinner 10 times.
Students are asked to write down the fraction for each section.
Students click on “Record Results” to have the results of their 10 spins
tabulate in a chart. Students click “Spin” 10 times. Students write
down the outcomes in a tally chart in their notebooks. Students could
also print out their spinner and the table that was automatically
tabulated.
Paper/pencil
Computers &
NLVM link in
shared file
Once the students have hit spin 10 times, students can change the
number of turns to 100 and watch the results appear. Students are to
compare the results from 10 spins to the results of 100 spins.
If time permits, students can reset the spinner and change the sizes of
the sections and re-spin for 10 and 100 spins.
Part 3: Consolidation (20 minutes)
Bansho – Students are going to post up their drawings of their
spinners and their results on the board and share their findings
with the class. (Students could also print their spinners out and
print out the computer-generated table).
Questions the teacher will ask each group:
1) Describe your spinner (Possible answer: there are 4
equal sections)
2) What did you look at to help you make your
predictions?
3) Were your predictions close to what actually
happened?
Misconceptions:
- Do not understand
probability as a fraction
-
-
may not see the link
between the size of the
section and the increase
in likelihood of the
spinner stopping on the
section
may not understand the
difference between
By: Laura Segreto
4) Were you surprised by the outcomes? At 10 turns? At
100 turns?
After (Practice)
Students are provided with the link to the Spinner via the NLV for
further experimentation / exploration at home
A similar spinner is available at
http://illuminations.nctm.org/adjustablespinner/. The spinner on the
illuminations website can go up to 99 999 spins! As a practice,
students could show their parents at home how they can build the
spinner and predict the outcomes.
April 12, 2014
theoretical probability
and experimental
probability yet