Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Lesson Study Group Members: Stacey Tiger (John Wash), Kim Labosky and Chris Gulbronsen (Quail Lake), Matt
Canaday (Centerville), Bobby Mullins (Sanger Academy)
Facilitator: Matt Canaday
Outside Observer: Jeff Brown, Dr. Rajee Amarasinghe
Lesson Study Goal: We will enable all students to become critical thinkers while collaborating in cooperative groups to
successfully complete the given task.
Chapter Goal: Chapter 6 – Macmillan/McGraw-Hill Glencoe – Ratios and Proportions
Lesson Goal: Solve for the missing quantity with proportions using cross-multiplication
6th Grade California Mathematics Standard(s):
NS 1.3 – Use proportions to solve problems
Manipulatives, materials required:
4 different sizes of regular skittles:
32 fun size bags, 1 regular size bag per group, 1 medium size bag and 1 large bag
for the class.
Poster Paper
Flip Chart Markers – at least one for each group
Overhead transparencies and pens
White Boards and white board markers
Rationale for lesson: (what is it that you want students to learn that they didn’t know before the lesson? Why?)
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
We want students to use cross-multiplication to solve proportions.
Time
Steps, Learning Activities, Teacher’s questions
5 mins
Expected Student Responses
Points of
Evaluation
These answers could be
varied. They should mention
something about equivalent
fractions or ratios depending
on background knowledge.
Sharing,
Volunteers,
Non-volunteers
Teacher says: “Use a proportion to calculate the number of orange skittles in the
large bag (41 oz, 1,162 grams) of skittles. Use the smaller bag (2.17 oz, 62 grams)
to help you.” Tell them to stick with what they know, not what they don’t know. If
they get finished before the time allotted, see if they can find another way to do
the problem.
Watch for correct use of a
proportion
May guess the number in the
big bag and use that number
in the proportion.
See if any
group
recognizes that
this could be
multiplication
At the end of 10 minutes you will have 5 minutes to put your group answer on poster
paper. A randomly selected student from each group will be called upon to present.
"Do we get to eat them?”
Students present their predictions.
Perhaps not able to explain
the prediction.
They may have a non-integer,
which will not make sense.
Goal:
Tell students that they are going to be working with proportions today to make
predictions for the missing number.
Talk to your neighbor for 30 seconds about what a proportion is. Share out Volunteers as needed, then pick 3 non-volunteers
23 mins
10 mins
Tell the students that they will be challenging each other to see who can come the
closest to the actual number of orange skittles in a large bag by using a smaller size
bag.
Ask clarifying questions to all group members after the presentation is over. Why
did they use the chosen numbers?
10 mins
Reveal the number of orange skittles actually in the large bag. Instructor
summarizes what proportions are using the group answers. Use a visual model with
small bag info (# orange skittles, oz, grams, total # of skittles) on the left and big
bag info (same) on the right. Show how different proportions could be set up, using
what we know for sure, to solve for the number of orange skittles we would expect
to find in the large bag. Demonstrate on overhead or whiteboard.
Students ask clarifying
questions
Group Poster
Presenter’s
Explanation
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Time
Steps, Learning Activities, Teacher’s questions
Expected Student
Responses
Points of
Evaluation
5 mins
Individual:
The instructor will hand out the fun size skittle bags (0.35 oz, 10 grams) for each
student.
Clarifying questions
Student
responses
Teacher
Observation
The instructor will show the class the medium size bag (16 oz, 454 grams).
Individually, the students will use a proportion to calculate the number of orange
skittles we would expect to find in the medium size bag.
Pass out paper for student responses that will be collected.
7 mins
Closure:
After collecting, reveal the amount of orange skittles in the medium bag.
Depending on the time, discuss why the answers are different, or write a response.
Hand out reflection papers.
Why are there different
amounts of orange skittles in
the bags?
Student
Responses
Teacher
Observation
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
With your group, use a proportion to calculate the
number of orange skittles we would expect to find in the
large bag (41 oz, 1,162 grams) of skittles. Use the
number of orange skittles in the small bag (2.17 oz, 62
grams) to help you.
Stay focused on what you know, not what you don’t know!!
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
On your own, use a proportion to calculate the number of
orange skittles we would expect to find in the mediumsize bag (16 oz, 454 grams) of skittles. Use the number
of orange skittles in the fun-size bag (0.35 oz, 10 grams)
to help you.
Stay focused on what you know, not what you don’t know!!
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Please write about the new things you learned today:
Please tell us what you thought about today’s lesson:
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Observation of students attempting to define a proportion with partner.
Observation of students during group work time – calculating the number of orange skittles in the large bag from the regular size bag.
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Observation of group presentations
Observation of students during individual work time – calculating the number of orange skittles in medium size bag
Observation of students during closure
Sanger Unified School District
Central Valley Math Project
6th Grade Lesson Study 08-09
Fall 2008
Other observations
Small Bag
Big Bag
Number of
Orange Skittles
Number of
Orange Skittles
Weight in oz.
Weight in oz.
Weight in
grams
Weight in
grams