Download Unpacking the Learning Progressions

2014-15 K-5 QM # 2 K-5 Plans
Session I: Unpacking the Learning Progressions
Time Allotment
90 minutes
Outcomes(s)
Participants will:
 Reflect on Next Steps from QM #1
 Review and deepen understanding of the Algebra Learning Progression and how
the content is sequenced within and across the grades (coherence)
 Illustrate, using tasks, how math content develops over time
 Discuss how the progressions in the standards can be used to inform planning,
teaching, and learning
Slides
Lesson Flow
1 minute
Welcome participants to 2nd
Quarterly Meeting for 20142015 school year.
5 minutes
Say, “you are all here today for
specific professional learning.
Let’s not forget that today’s
learning aligns with the Alabama
Quality Teaching Standards.
Grounded on the five Alabama
Quality Teaching Standards, the
Continuum is based on two
assumptions: (1) that growth in
professional practice comes from
intentional reflection and
engagement in appropriate
professional learning
Research/Helpful Hints
For facilitators only
(Do not read to participants!)
2014-15 K-5 QM # 2 K-5 Plans
opportunities and (2) that a
teacher develops expertise and
leadership as a member of a
community of learners focused
on high achievement for all
students, which we are doing in
the CCRS quarterly meetings.”
2 minutes
Emphasize “locally”
Support samples (Sample lesson
plans and supporting resources
found on ALEX, differentiated
support through ALSDE
Regional Support Teams and
ALSDE Initiatives, etc.)
Assessments - (GlobalScholar,
QualityCore Benchmarks, and
other locally determined
assessments)
1 minute
Good Morning, the outcomes for
the QM #2 is: (read slide).
As always, the CCRSImplementation Team is
representing the administrators
and teachers that are not able to
receive this training, and will
think about ways in which the
information, strategies, and
resources from QM #2 can be
2014-15 K-5 QM # 2 K-5 Plans
taken back to benefit the system,
school, and students.
1 minute
Read slide.
15 minutes Have participants
reflect first and then share out
at table.
Give participants some time to
write individually, then facilitate
a discussion around some or all
of the questions listed on the
slide.
2 minutes
In this table, related domains are
grouped together. Each “colored
row” identifies how domains at
the earlier grades progress and
lead to domains at the middle
and high school levels. The
right side of the chart lists the
five conceptual categories for
high school: Number and
Quantity, Algebra, Functions,
Geometry, and Statistics and
Probability. You will need to
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emphasize the Algebra
conceptual category because it
is the main idea of this CCRS
meeting. If you select one
conceptual category and move
left along the row, you’ll find the
domains at the middle and
elementary school levels from
which this concept builds.”
Say, “Notice that the K-8
horizontal organization
demonstrates grade level
progressions of mathematics
content. In High School, the
mathematics content is
organized into five conceptual
categories which progress over
multiple high school courses.
Notice in K-8 that the domains
change as students move through
their school years. These
domains provide foundational
knowledge for each high school
conceptual category. The new
emphasis on “college and career
readiness” for all students
implies that it is everyone’s
responsibility to help prepare
students for mastery of
foundational mathematics
content.
There is a sixth conceptual
category of Modeling which
does not have separated
standards, but there are specific
standards designated throughout
these five conceptual categories
Facilitator should monitor when
participants are sharing at their table
(step 3), select participants to share
out (making participants aware of
what they said that you want them to
share whole group). Facilitator should
sequence the order in which
participants should share out. The
facilitator should make the connection
of what each person shared.
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as modeling standards. These
standards are identified with a
(*) in the CCRS.
4 minutes
Today we are focusing on the
Operation and Algebraic
Thinking, Expressions and
Equations, and Algebra
Progressions which can be found
at
http://ime.math.arizona.edu/prog
ressions/
The Common Core State
Standards in mathematics were
built on progressions: narrative
documents describing the
progression of a topic across a
number of grade levels,
informed both by research on
children's cognitive development
and by the logical structure of
mathematics.
1 min
Because of structural differences
between the disciplines of
mathematics and English
Language Arts, the mathematics
standards do not support such
2014-15 K-5 QM # 2 K-5 Plans
easy analysis of the progression
of standards across grades.
This diagram depicts some of the
structural features of the
mathematics standards, where
several different domains from
grades K-8 converge toward
algebra in high school. This
diagram does not include other
“flows,” such as from Number
and Operations—Fractions in
grades 3-5, to Ratios and
Proportional Relationships in
grades 6 and 7, to Functions in
grade 8 and high school, with
connections to geometry and
probability.
5 minutes
st
1 ) Read slide.
2nd) Have participants record
their definition of Operations
and Algebraic Thinking on
Journal Reflection hand-out.
3rd) Have participants share their
definition with members at their
table (participants should record
Facilitator should monitor when
participants are sharing at their table
(step 3), select participants to share
out (making participants aware of
what they said that you want them to
share whole group). Facilitator should
sequence the order in which
participants should share out. The
facilitator should make the connection
of what each person shared.
2014-15 K-5 QM # 2 K-5 Plans
this on their K-W-L handout
under the “K”).
4th) Have each person selected
while monitoring share out
whole group
5 minutes
1st) Say, “We are about to watch
a video (video is 1:50 in length)
to connect our background
Knowledge of Operations and
Algebraic Thinking to what one
of the writers of the standards,
Jason Zimba, says about it.
2nd) Jot down any information
you learn while Watching the
video.” (participants should
record this on their K-W-L
handout under the “W”).
3rd) Have participants share any
new knowledge gained with
members at their table.
4th) Have each person selected
while monitoring share out
whole group
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2 minutes
Say, “We have a whole group
overarching definition of
Operation and Algebraic
Thinking.”
(Divide the participants into 6 groups:
K, 1st, 2nd, 3rd,4th, 5th)
We’ve heard what Jason Zimba,
one of the writers of the CCRS,
has said about Operations and
Algebraic Thinking.
Now, we will go deeper. You
will deepen your content
knowledge of the specified grade
as you read the Learning
Progression for Operations and
Algebraic Thinking.”
Say, “As you are reading your
section, keep in mind the
fluencies required for this
domain, conceptual
understandings student’s need,
and different ways operations
and algebraic thinking can be
applied.”
Say, “Turn to the section of the
progressions document that
addresses the grade level you are
going deeper in.”
Say, “You have a purpose for
reading collectively: fluencies,
student’s conceptual
understanding, and application
of this domain. Because there is
Set a purpose for reading:
(have a participant restate the purpose
for reading)
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a wealth of information in this
document, because our
conceptual understanding of this
domain is at different levels, as
you read you will code the text.
15 minutes:
Go over slide of how
participants should code the text
as they read.
Once participants have finished
reading independently, have them
record what they learned about the
grade level they just read about. Have
them record this on their K-W-L
handout under the “L” column.
Allow 15 minutes for participants to
read the learning progression
independently.
10 mins
1st) Say, “Now that you have
read the Operations and
Algebraic Thinking Progression.
You will share with members at
your table and chart what you
Learned as it relates to our
purpose for reading the
progression document (3
purposes on this slide) on chart
paper.
2nd) Have 1 person from each
group share out what they
learned. (Starting with K, then
1st, 2nd, etc.) Participants can
record this on there K-W-L
(Even though 4th and 5th reads both
progressions, have the teachers chart
only for the grade they are sitting
with.)
Have them discuss with their group
and record and chart out the fluencies
that are required for their grade level,
and conceptual understanding students
need and how this learning can be
applied (situations, word problems,
other domains like geometry and
measurement, etc.)
(Note: Emphasize that OA can be
applied to Word problems if the
participants don’t bring out this point.)
Facilitator should monitor when
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handout.
Facilitator sums up the 3
purposes for reading by saying,
“these attend to the rigor in the
standards.”
participants are sharing at their table.
The facilitator should make the
connection of what each group
shared.
Possible Questions to ask as groups
share:
1.) How do the learning progressions
develop within this domain?
2.) How will/can students use this
knowledge in the next grade?
It is important that students learn to
solve all these different types of
problem as this will demonstrate a full
One way students can apply their understanding of the meaning of the
knowledge in Order of Algebraic addition and subtraction operations.
Thinking is through word
Practice with lots of examples is
needed but this should be done after
problems.
starting with plenty of hands-on
activities with concrete materials.
1 min
3 minutes
1st) Have participants write a
word problem for each equation
within the grade-band they read
on a different post-it.
9 minutes
1st) Have participants turn to
page 7 (if they read K-2) or 23
(if they read 3-5) of the
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progression document and
identify the type of problem they
wrote.
(While they are writing,
facilitate and ask questions.)
2nd) Have each table post their
problem on the K-2 or 3-5 story
problem poster.
3rd) Have participants take a
moment to look at the poster and
reflect on what they notice, then
share at their table, and finally
whole group discussion.
Possible Questions to ask:
Were there any problem types
not shown?
Say, “The same story problem
handout that you are looking at
is found in the appendix section
of ALCOS.
3 minutes
Say, “However that handout
isn’t as explicit as the handout in
the learning progression
document.”
Have participants turn to page 9
of the OA progression
document.
Go over which grade level
requires mastery of which
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problem types/subtypes.
Say, “Van de Walle describes
four types of
addition/subtraction problems &
four categories of
multiplication/division
problems.” (Noted in pink
vertically)
Say, “Each of these main
types/categories have two or
three subtypes/subcategories.”
(noted in pink horizontally)
Say, “Kindergarten has some
Problem types to be mastered by
the end of the Kindergarten year
(yellow).
Ask, “What is the difference in
the Add To/Take From and Put
Together/Take Apart problem
types?”
Say, “ Add To/ Take From
problem types require movement
and Put Together/Take Apart
problem types require no
movement (total items
mentioned in word problem are
already visable).
1st: Problem types to be
mastered by the end of the First
Grade year (yellow and white).
However, First Grade students
should have experiences with all
12 problem types.
2nd: Problem types to be
mastered by the end of the
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Second Grade year (yellow,
white and green).
The green shaded problems are
the four difficult subtypes that
students should work with in
Grade 1 but need not master
until Grade 2.
Say, “So when you look at the
story problems in your
curriculum, think about the rigor
in the problems.
It depends on the content in the
problem to determine the type of
problem.
2 minutes
Have participants turn to page 23
of the OA progression
document.
Go over which grade level
requires mastery of which
problem
categories/subcategories.
3rd Grade has some problem
types that must be mastered by
the end of the 3rd grade, they are
highlighted in yellow. They
include Equal Groups and
Arrays (Multiplicative)
4th Grade has some problem
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types that must be mastered by
the end of the 4th grade, they are
the yellow and white sections on
the chart. They include Equal
Groups, Arrays, Area, and
Multiplicative Comparison
problems using whole numbers.
5th Grade has some problem
types that must be mastered by
the end of the 5th grade, they are
the yellow and white sections on
the chart. They include Equal
Groups, Arrays, Area, and
Multiplicative Comparison
problems using whole numbers
and fractions.
3 minutes
Have participants turn to this
Journal Reflection Hand-Out in
their Participants Packet.
Read Slide
Give participants some time to
write individually, turn and talk,
then facilitate a discussion.
Tell participants to enjoy lunch
and you will see them after
lunch.
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While you are waiting for
participants to return:
Recommend that participants
collect their thoughts from this
morning and record them on the
“Professional Development
Transition Plan” that they will
use later on in their district
planning meeting.
Welcome participants back from
lunch.
1 min
Take a moment to read the
question and quote and reflect on
the implications for your role as
a CCRS Team member. How
has discussing and reflecting on
the Number progression from the
last CCRS meeting impacted
your practice?
2 mins
This is just a transition slide to
frame the next activity. Give
them time to read it and advance
to the next slide. Now that you
have reflected on the effect of
progressions on your practice,
discuss these two questions and
give specific examples about
how student learning in your
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classroom was impacted.
3 min
Show video. This diagram
depicts some of the structural
features of the mathematics
standards, where several
different domains from grades
K-8 converge toward algebra in
high school. BE SURE TO
START AT 16 SECONDS!!
3 mins
Give them time to read the slide.
Give them the handout
containing Zimba’s Wire
Diagram for their grade level.
Ask them to read the handout
and think through the questions
and comments on the handout.
Say, “In the morning session,
you read through how algebra
concepts are connected across
grades. This afternoon, you will
see a diagram designed by Jason
Zimba, one of the original
writers of the College and Career
Ready Standards that also shows
how standards progress.”
Allow time for each person to
have a discussion with someone
at or adjacent to their grade level
about what kind of conversations
2014-15 K-5 QM # 2 K-5 Plans
a team should have to organize
Algebra instruction within and
across years.
2 mins
To be even more specific, these
are cluster headings from the
CCRS: Mathematics in grades K
- 8. These cluster headings are
the foundational topics for each
of the grades that lead to the
conceptual category of algebra.
Note that in the middle grades,
there are more clusters that begin
with “apply and extend” as
students build on what has been
previously learned. Today’s
discussion is not about an
Algebra 1 class, but is about
algebra as a critical strand of
mathematical thinking and
reasoning.
2 mins
Our next step in understanding
the algebra progression and its
effect on student learning, leads
us to explore these high-level
tasks from K - 12. The tasks
chosen for this activity were
grouped together to represent
one interpretation of a learning
**Note: Refer to the learning
progression discussed this morning.
The learning progression graphic is in
their participant packet.
2014-15 K-5 QM # 2 K-5 Plans
progression. There are other
pathways that are different, this
is only one interpretation.
10 mins
In this section, you will track the
progression of how an idea
develops from kindergarten to
high school. View a high school
standard and then see how we
start preparing for high school in
kindergarten. Have a whole
group discussion about what the
standard encompasses. Student
expectations should be included
in this discussion. Participants
should discuss topics such as:
Vocabulary including the word
“complicated”, simplifying
expressions, evaluating
expressions, exponential
expressions, etc. Allow
participants to share, but don’t
spend too much time dissecting
the standard. Focus on the
general big ideas.
Participants have the tasks in
their packet. You may hide
them if you would like.
Directions on how to distribute
the tasks:
Each table (or person) gets one
or two (depending on group
size/structure). After studying
2014-15 K-5 QM # 2 K-5 Plans
the standard and illustration,
table/person discusses how their
standard and task is a building
block toward the high school
standard (and task) shown –
structure, parts of an expression,
context, interpreting in context,
quantities, etc.
12 mins
In this task students have to
interpret expressions involving
two variables in the context of a
real world situation. All given
expressions can be interpreted as
quantities that one might study
when looking at two animal
populations. For example,
PP+Q is the fraction that
population P makes up of the
combined population P+Q .
Although the context is quite
thin, posing the question in terms
of populations rather than bare
numbers encourages students to
think about the variables as
numbers and provides avenues
for them to use their common
sense in explaining their
reasoning. This encourages them
to see expressions as having
meaning in terms of operations,
2014-15 K-5 QM # 2 K-5 Plans
rather than seeing them as
abstract arrangements of
symbols.
This is for reference only:
Solution: Comparing expressions
The expression P+Q is larger.
The expression P+Q gives the
total size of the two populations
put together.
The expression 2P gives the size
of a population twice as large as
P.
Putting the smaller population
together with the larger yields
more animals than merely
doubling the smaller.
Another way to see this is to
notice that 2P=P+P, which is
smaller than P+Q because
adding P to P is less than adding
Q to P.
The expression P+Q2 is larger.
The total size of the two
populations put together is P+Q,
so the expression PP+Q gives
the fraction of this total
belonging to P. Since P<P+Q,
this will be a number less than 1.
For instance, if P=100 and
Q=150, this fraction equals
100/(100+150)=0.4=40%.
The average or mean size of the
two populations is their sum
divided by two, or P+Q2. This
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will be a number between P and
Q, so it is larger than 1 (since P
and Q describe animal
populations). For instance, if
P=100 and Q=150, the average
is (100+150)/2=125.
The expression Q−P/2 is larger.
The expression (Q−P)/2 gives
half the difference between P
and Q. For instance, if Q=150
and P=100, half the difference is
(150−100)/2=25.
The expression Q−P/2 gives the
difference between Q and a
population half the size of P. For
instance, if Q=150 and P=100,
this difference equals
150−100/2=100.
To see why the second of these
is bigger, write
(Q−P)/2=Q/2−P/2
In the expression Q−P/2, we
subtract P/2 from Q. But in
(Q−P)/2, we subtract the same
value, P/2, from a smaller
amount, Q/2.
The expression Q+50t is larger.
In both expressions, the same
value, 50t, is added to the
population.
Since P<Q, adding 50t to P
results in a smaller value than
adding the same amount to Q.
2014-15 K-5 QM # 2 K-5 Plans
The expression 0.5 is larger.
The total size of the two
populations put together is P+Q,
so the expression PP+Q gives
the fraction of this total
population belonging to P. Since
there are fewer animals in
population P than Q, this
fraction is less than 12. For
instance, if P=100 and Q=150,
this fraction equals
100/(100+150)=0.4.
PQ and QP can be interpreted in
two different ways.
PQ can be interpreted as a unit
rate, namely, the number of
animals in population P for
every 1 animal in population Q.
Similarly, QP can be interpreted
as the number of animals in
population Q for every 1 animal
in population P. Since there are
more animals in population Q,
the unit rate QP will be greater
than the unit rate PQ.
For example, if P=100 and
Q=150, then 100150=23, so
there would be 23 of an animal
in population P for every 1
animal in population Q, while
150100=32, so there would be
32 of an animal in population Q
for every 1 animal in population
P.
Some people think it is awkward
to talk about fractions of
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animals, so here is another way
to think about it:
PQ can also be interpreted as the
fraction that population P is of
population Q. Since there are
fewer animals in population P,
as a fraction of the population of
Q it will be less than 1.
Similarly, QP can also be
interpreted as the fraction that
population Q is of population P.
Since there are more animals in
population Q, as a fraction of the
population of P it will be greater
than 1.
For example, if P=100 and
Q=150, this fraction equals
100150=23, so there are 23 as
many animals in population P as
there are in population Q, while
150100=32, so there are 32 as
many animals in population Q as
there are in population P.
50 mins
DIRECTIONS FOR
ACTIVITY: Each table (or
person) gets one or two grade
level standards and task
illustrations (depending on group
size/structure). After studying
the standard and illustration,
table/person discusses how their
standard and task is a building
block toward the high school
2014-15 K-5 QM # 2 K-5 Plans
standard (and task) shown –
structure, parts of an expression,
context, interpreting in context,
quantities, etc. Make sure each
group has a quality discussion
about the task before you give
them half of a piece of chart
paper. Each grade should chart
the discussion points from the
slide. After posting the chart
papers, bring the group together
as a whole. Have each group
share their discussions about the
task. Be sure to connect the
groups’ discussions as they
present. The big picture should
be how each grade builds to
develop this algebra
progression as seen in the
documents in the morning
session.
Below are sample responses:
K – decomposes numbers using
drawings or equations
1 – meaning of equal sign (does
not mean output or “give me an
answer”)
2 - Begin using, <, >
3 - Properties of operations –
commutative, associative,
distributive
4 – four operations with
remainders , equations with
letters
5 – simple expressions, interpret
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without evaluating them
6 –Identify when two equations
are equivalent (Sixth grade also
learns order of operations)
7 – rewriting expressions in
different forms
Because of the limited reading
skills of kindergarten students,
this task should be introduced by
the teacher, followed by the
students carrying out the
activity. Teachers should have
counters on hand for students to
use.
Any number between 2 and 10
can be used in place of 9 to
address K.OA.3.
The purpose of this task is to
help broaden and deepen
students understanding of the
equals sign and equality. For
some students, an equals sign
means "compute" because they
only see equations of the form
4+3=7.
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In this task, students must attend
to the meaning of the equal sign
by determining whether or not
the left-hand expression and the
right hand expression are equal.
This task helps students attend to
precision (as in Standard for
Mathematical Practice 6).
This task requires students to
compare numbers that are
identified by word names and
not just digits. The order of the
numbers described in words are
intentionally placed in a different
order than their base-ten
counterparts so that students
need to think carefully about the
value of the numbers. Some
students might need to write the
equivalent numeral as an
intermediate step to solving the
problem.
This task is a follow-up task to a
first grade task:
http://www.illustrativemathemati
cs.org/illustrations/466.
On the surface, both tasks can be
completed with sound
procedural fluency in addition
2014-15 K-5 QM # 2 K-5 Plans
and multiplication. However,
these tasks present the
opportunity to delve much more
deeply into equivalence and
strategic use of mathematical
properties. These tasks add
clarity to the often
misunderstood or neglected
concept of equivalence. Students
often understand the equal sign
as the precursor to writing the
answer. Class discussion should
be carefully guided to ensure
that students come to the
understanding that the equal sign
indicates equivalence between
two expressions. Though these
tasks can be completed by
evaluating each expression on
either side of the equal sign, they
present deliberate next levels of
reasoning that invite students to
look for different approaches.
Anyone facilitating a
conversation about this task
should constantly ask, "Is there
another way to know whether
this equation is true?" Consider 5
x 8 = 10 x 4. Students will likely
know these facts relatively
quickly and come to the
conclusion that both sides are
equal to 40, thus this equation is
true. When pressed to see other
options, students may reason that
the 8 can be broken down into 4
x 2. The equation becomes 5 x (2
x 4) = 10 x 4. Through the
associative property, this
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becomes (5 x 2) x 4 = 10 x 4.
We can see that these
expressions are equivalent
because we know that 5 x 2 has
the same value as 10. The same
opportunity presents itself in part
f. Part g presents an opportunity
for students to think critically
about the meaning of
multiplication.
Third graders interpret
multiplication as equal sized
groups. Students might reason
that 8 x 6 means 8 groups of 6.
Thus 7 x 6 + 6 would mean 7
groups of 6 with another group
of 6. Students might recognize
that extra 6 as the "8th group of
6," thereby making the two
expressions equivalent.
The purpose of the task is for
students to solve a multi-step
multiplication problem in a
context that involves area. In
addition, the numbers were
chosen to determine if students
have a common misconception
related to multiplication. Since
addition is both commutative
and associative, we can reorder
or regroup addends any way we
like. So for example,
20+45 =20+(5+40)=(20+5)+40=
25+40
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Sometimes students are tempted
to do something similar when
multiplication is also involved;
however this will get them into
trouble since
20×(5+40)≠(20+5)×40
This task was adapted from
problem #20 on the 2011
American Mathematics
Competition (AMC) 8 Test.
Observers might be surprised
that a task that was historically
considered to be appropriate for
middle school aligns to an
elementary standard in the
Common Core. In fact, if the
factors were smaller (since in
third grade students are limited
to multiplication with 100; see
3.OA.3), this task would be
appropriate for third grade:
"3.MD.7.b Multiply side lengths
to find areas of rectangles with
whole-number side lengths in the
context of solving real world and
mathematical problems, and
represent whole-number
products as rectangular areas in
mathematical reasoning." For
example, we could use a 5 ft by
12 ft garden, and a 7 ft by 10 ft
garden to make this appropriate
for a (challenging) third grade
task. This earlier introduction to
the connection between
multiplication and area brings
states who have adopted the
Common Core in line with other
2014-15 K-5 QM # 2 K-5 Plans
high-achieving countries.
The purpose of this task is to
generate a classroom discussion
that helps students synthesize
what they have learned about
multiplication in previous
grades. It builds on
3.OA.5 Apply properties of
operations as strategies to
multiply and divide
and
4.OA.1 Interpret a multiplication
equation as a comparison.
In this problem we have to
transform expressions using the
distributive, commutative and
associative properties to decide
which expressions are
equivalent. Common mistakes
are addressed, such as not
distributing the 2 correctly. This
task also addresses 6.EE.3.
The purpose of this instructional
task is to illustrate how different,
but equivalent, algebraic
expressions can reveal different
information about a situation
2014-15 K-5 QM # 2 K-5 Plans
represented by those
expressions. This task can be
used to motivate working with
equivalent expressions, which is
an important skill for solving
linear equations and interpreting
them in contexts. The task also
helps lay the foundation for
students' understanding of the
different forms of linear
equations they will encounter in
8th grade. In part (b), the task
asks students to interpret pieces
of the expression that arise by
parsing the expression from
different algebraic perspectives.
In particular, it requires students
to think about the difference
between interpreting −2x as −2
times x vs. subtracting 2x from
14. Note that the meaning of the
2 in the expression 2(7−x) is
slightly different than the
meaning given in the problem
statement because of the role it
plays in the expression. The
class will probably need to have
a whole-group conversation to
grasp this subtlety.
5 mins (for next 8 slides)
Summarize the big ideas
discovered during the whole
group discussion of both the
2014-15 K-5 QM # 2 K-5 Plans
morning and afternoon sessions.
Note: Remember to refer to
the equip rubric in past CCRS
meetings.
Some sample responses:
Supports remediation and
differentiation – teachers can
know better how to identify and
address gaps in unfinished
learning from previous grades
Teachers build on previous
understandings – this will result
in greater focus because teachers
can spend less time reviewing.
Teachers can understand how
their grade level content fits into
the larger picture of a student’s
mathematical trajectory and help
ensure success in future grades
If teachers’ own knowledge of
the content and how
mathematical ideas are
developed over time in stronger,
their instruction can be stronger
To summarize the session, allow
participants to read the slide.
Ask the participants if they are
truly connecting the progressions
in their practice in order to
develop deep conceptual
understanding.
2014-15 K-5 QM # 2 K-5 Plans
At our last CCRS meeting, we
explored the three instructional
shifts. Tell participants to look in
their packet for the page that
contains the instructional shifts.
Ask participants to bring student
work from their next steps
assignment to the 3rd quarterly
meeting.
Have participants read the slide.
The Special Education
curriculum is hyperlinked to the
symbol.
Plan with your table group on
how you will use today’s
learning to inform your teaching
and learning. Be sure to share
these ideas with the group, your
colleagues, and your
administrators.
With your district team think
about your next steps.
Record your thoughts on this
template and share with the rest
of your team when you join them
2014-15 K-5 QM # 2 K-5 Plans
in a few minutes.