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7-10 Breakout 2 PR: Learning Goals & Consolidating Questions
Math Learning Goals
We will use Learning Goals to interpret important mathematics and target the mathematical
thinking we want to expose and evoke with students.
We will recognize the link between Learning Goals, Curriculum Expectations, Consolidation
Questions, and Big Ideas and the purpose of attending to these prior to a lesson activity.
MO:10
A: 40
C: 20
Minds On…
Pairs/Elbow partner  Discussion
(Displayed on PPT only)
Here are 6 different actions. Discuss and decide with a partner at your table what the goal of
each action might be?
Small Group (3)Complete 2 of the 3 activities
DI based on readiness & interest
2.
3.
Sets from BLM 2.1.2 are placed in invoice envelopes (7/8 & 9/10) with 2.1.1
stapled(glued) to front of each envelope. 2 sets of each per table. Participants
consider which problem meets the learning goal best, using the probing questions
provided.
Each table would have 2 sets of BLM 2.2.1 – 2.2.4 in manila envelopes, with 2.2
(instructions) stapled or glued onto the front of envelope. Participants discuss
whether the Consolidation Question meets the Learning Goal using the lens of the
Big Idea. They will provide a better consolidating question for those they feel need
improving.
Two copies of BLM 2.3 per table. Instructions included on BLM.
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PPT Breakout #2
2.1.1 & 2.1.2
2.2, 2.2.1 – 2.2.4
2.3
Big Ideas for PR
eduGains Viewing Guide
Appendix E, p. 45; LG
definition from wiki & GS
Journal/Post-Its/Buttons
&Bandana
Idea to impart:
The intended goal of these
actions lends clarity to where
they will lead or to what the
person will do next
Note: Probing questions for
campers to consider while
doing these activities are
supplied on intro BLM with
each activity
Activity 1 & 2: Justification
should include what a good
answer would look like
(success criteria)
Scaffold Activity 3, if needed provide definition for LG
provided on Wiki; could also
use criteria for LG offered on
eduGains in the Viewing
Guide for LG & SC,
Appendix E p.45
http://www.edugains.ca/newsit
e/aer2/aervideo/learninggoals.
html
Whole Group Sharing
Selected participants share results/decisions for an activity using the document camera.
Invite thoughts, ideas, and questions from whole group.
Questions to Consider
 What was challenging about these tasks? What did you find useful?
 What is the difference between a learning goal and a curriculum expectation?
(offer/read def’n from Growing Success and also one by Marian provided on wiki)
 When/why might you choose not to reveal the LG at the beginning of the lesson?
 Why is it important for us to consider what a good answer will look like?
Reflection


1.
Consolidate
Debrief
Materials
We will know the purpose of considering what a good answer would look like.
 Husband buys his wife a dozen roses
 You buy a turtle from the pet store
 You apply to law school
 A new graduate enrols in Spanish lessons
 An employee asks for and accepts extra hours of work
 Your son cleans your car without being asked
Whole Group  Sharing
Sharing of ‘intended goals’ implied by actions above
Conclusion: ‘For every action we take we have a goal in mind’
Action!
Grade 7-10
Home Activity or Further Classroom Consolidation
Individual Journal Entry
How are you providing Learning Goals for your students?
Consider the interconnectivity of Learning Goals and Consolidating Questions.
*Button activity - recording of a new strategy I learned about this breakout
(optional) Participants invited to post a question or a comment about LG and CQ’ns
Questions could be posted on
the PPT or provided orally by
facilitator
(self-assessment)
Why might it be useful to
consider the Consolidating
Questions to be used at the end
of a lesson once you have
determined the Learning Goal?
BLM 2.1.1 Which is Best?
Probing Questions to consider:
1. What mathematical thinking does each problem evoke?
2. Would our goal for using each problem be the same? Why or why
not?
3. In your opinion, which problem meets the Learning Goal best? Why?
What would you expect to see in a good answer?
BLM 2.1.2 Which is Best?
Set 1: Grade 7/8
Learning Goal: Students can use an alternate representation for percent to solve a
problem.
Problem 1: In many North American regions, 60% of frogs are born with some kind of
malformation, (missing or extra limbs, etc.). How many frogs, in a population of 1175, might
you expect to be deformed?
Problem 2: How could a number line help you solve this problem: “60 is what percent of
300?” How might a 100 grid help you solve this problem?
Problem 3: Write 76% using two other representations. Justify your representations.
Set 2: Grade 9 Applied
Learning Goal: Students will use a variety of methods to show that ratios give us
information about quantity
Problem 1: A vase holds red and white roses only. For every three red roses, there are two
white roses. How many flowers might be in the vase? *
Problem 2: Sarintino’s restaurant advertises that it offers two food servers for every nine
guests. Zapoteka restaurant seats 135 guests and boasts a better food server-to-guest ratio.
How many food servers might it have? *
Problem 3: Use ratios to show that one kind of cereal is less sweet than another.
*Question from Good Questions for Math Teaching, Schuster & Anderson
Set 3: Grade 10 Academic
Learning Goal: Students will be able to illustrate their understanding of the primary trig
ratios as the ratio of two sides in a right triangle
Problem 1: In ∆ABC, sin A = ½. Draw and label two possible triangles that could represent
∆ABC.
Problem 2: Melissa states the measure for <X will be the same as <A, given the information
below. Moira states there is not enough information to determine this. Who do you agree with
and why?
Given Information: Tan X = 5/12
A
26
C
10
B
Problem 3: Determine the primary trig ratios for <A in each of these triangles: (students
would be given 2 right-triangles in different orientations)
BLM 2.2 The ‘Learning Goal – Consolidation’ Connection
You have been supplied with a selection of lessons partially completed:
Each lesson identifies a Learning Goal, a Curriculum Expectation, a Big
Idea, and a Consolidating Question. (the Minds On and Action are blank as
our focus for this activity is not on these sections)
Your task:
With your partners, discuss whether the Consolidating Question meets
the Learning Goal using the lens of the Big Idea. Provide a better
consolidating question for those you feel need improving.
Questions to consider:
1. What mathematical thinking does the Learning Goal and Big Idea
indicate is important?
2.
What would you expect as a good answer for the Consolidating
Question?
3.
Does the Consolidation Question link back to the Learning Goal and
Big Idea appropriately, exposing that mathematical thinking? Why?
If not, improve or provide a better Consolidating Question.
BLM2.2.1
Posing Powerful Questions
Lesson Title: Understanding Constant Rate of Change
Grade/Program: 9 or 10 Applied
Curriculum Expectations
Gr. 9: determine, through investigation, that the rate of change of a linear relation can be
found by choosing any two points on the line that represents the relation, finding the vertical
change between the points (i.e., the rise) and the horizontal change between the points (i.e.,
the run), and writing the ratio rise/run
Gr. 10: Connect the rate of change of a linear relation to the slope of the line, and define the
slope as the ratio m = rise/run
Big Idea(s) Addressed by the Expectations
Comparing mathematical relationships helps us see that there are classes of relationships with
common characteristics and helps us describe each member of the class.
Groups of functions or relationships go together because they behave in similar ways. Knowing
about the group helps us know a bit about each member of the group.
Goals(s) for a Specific Lesson
Students will make the connection between constant rate of change and the proportionality of
the rise/run between any two points on a line
Mathematical Process Focus: Connecting
Minds On
Action!
Scaffolding Questions (posed to individuals as needed)
Consolidating Question
What does a slope of
tell you about a straight line?
BLM2.2.2
Posing Powerful Questions
Lesson Title: Which is best and why?
Grade/Program: 7
Curriculum Expectations
Determine, through investigation, the relationships among fractions, decimals, percents, and
ratios.
Big Idea(s) Addressed by the Expectations
There are many equivalent representations for a number or numerical relationship.
Each representation may emphasize something different about that number or
relationship.
There is usually more than one way to show a number or relationship and each of those
ways might make something more obvious about that number or relationship.
Goals(s) for a Specific Lesson
Students will learn to recognize which representation – fraction, decimal or percent – is more
useful in which situation.
Mathematical Process: Representing & Reflecting
Minds On
Action!
Scaffolding Questions (posed to individuals as needed)
Consolidating Question
Describe a situation when it might be useful to know that ½ can be written as:
 50%
 an equivalent fraction.
 0.5
BLM2.2.3
Posing Powerful Questions
Lesson Title: Comparison
Grade/Program: 8
Goals(s) for a Specific Lesson
Students will know when it is useful to convert to a unit rate and when it isn’t necessary
Curriculum Expectations
Solve problems involving rates
Big Idea(s) Addressed by the Expectations
Numbers are compared in many ways. Sometimes they are compared to each other;
other times, they are compared to benchmark numbers.
Numbers can be compared in different ways – sometimes to each other and sometimes to
benchmark numbers.
Minds On
Action!
Scaffolding Questions (posed to individuals as needed)
Consolidating Question
Compare these by calculating the unit rate.
Resting heart rates for animals:
 Lion – 40 beats in 60 seconds,
 Giraffe – 5 beats in 12 seconds
 Hummingbird – 41 beats in 10seconds.
What other method could you have used for comparison?
BLM2.2.4
Posing Powerful Questions
Lesson Title:
Grade/Program: 9 Essential
Goals(s) for a Specific Lesson
Students will investigate relationships between fractions, percentages, ratios, and rates both visually
and concretely
Curriculum Expectations
Determine relationships among fractions, percentages, ratios, and rates by constructing diagrams,
building models, and estimating measurements
Big Idea(s) Addressed by the Expectations
There are many equivalent representations for a number or numerical relationship. Each
representation may emphasize something different about that number or relationship.
There is usually more than one way to show a number or relationship and each of those ways might
make something more obvious about that number or relationship.
Minds On
Action!
Scaffolding Questions (posed to individuals as needed)
Consolidating Question
Is a 25% discount the same as a 10% followed by a 15% discount?
BLM 2.3 Improving Learning Goals
You have been provided with a selection of curriculum expectations and learning goals. Your task is to improve the
learning goal by choosing a Big Idea as a filter or lens for the goal.
Here are some prompts to assist you:
 What important math should the learning goal address?
 What Big Idea might help illuminate that important math?
 Think about the math you would like to observe (see & hear) students using
Curriculum Expectation
Learning Goal for student
Solve problems that involve
determining whole number percents,
using a variety of tools
(gr 7)
Demonstrate an understanding of rate
as a comparison, or ratio, of two
measurements with different units
(gr. 7)
Identify and describe real-life
situations involving two quantities
that are directly proportional
(gr. 8)
Solve problems involving similar
triangles in realistic situations
(gr 10)
Make comparisons using unit rates
(gr 9 Applied)
I will use a variety of tools to solve a
percent problem
Solve problems requiring the
expression of percents, fractions, and
decimals in their equivalent forms
(Gr 9 Applied)
Solve problems involving right
triangles, using the primary
trigonometric ratios
(gr 10 Applied)
I will convert between percents,
fractions, and decimals in order to
solve problems
I will be able to identify the two units
of measurement involved in a
specific rate
I will identify relationships that are
proportional
I can solve problems using similar
triangles
I will be able to compare prices using
unit rates
I will use the primary trig ratios to
solve for missing triangle information
Big Idea
Improved Learning Goal