Module Focus: Grade 2 – Module 6
Sequence of Sessions
Overarching Objectives of this February 2014 Network Team Institute

Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate
how these modules contribute to the accomplishment of the major work of the grade.

Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom
teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.

Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding
how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.

Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the
mid-module assessment and end-of-module assessment.
High-Level Purpose of this Session
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●
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Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons.
Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the
module addresses the major work of the grade.
Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module.
Related Learning Experiences
●
This session is part of a sequence of Module Focus sessions examining the Grade 2 curriculum, A Story of Units.
Key Points



Module 6 focuses on using repeated addition to find the total number of objects arranged in rectangular arrays (2.OA.4), partitioning
rectangles into rows and columns of same-size squares (2.G.2), and determining numbers as even and odd (2.OA.3).
This foundational understanding is crucial, since multiplication and division is the major work of Grade 3.
Module 6 also supports the required fluency of Grade 3: Fluently multiply and divide within 100, using strategies such as the
relationship between multiplication and division or properties of operations.
Session Outcomes
What do we want participants to be able to do as a result of this
session?
 Participants will develop a deeper understanding of the sequence of
mathematical concepts within the specified modules and will be able to
articulate how these modules contribute to the accomplishment of the major
work of the grade.
How will we know that they are able to do this?
Participants will be able to articulate the key points listed above.
 Participants will be able to articulate and model the instructional approaches
that support implementation of specified modules (both as classroom
teachers and school leaders), including an understanding of how this
instruction exemplifies the shifts called for by the CCLS.
 Participants will be able to articulate connections between the content of the
specified module and content of grades above and below, understanding how
the mathematical concepts that develop in the modules reflect the
connections outlined in the progressions documents.
 Participants will be able to articulate critical aspects of instruction that
prepare students to express reasoning and/or conduct modeling required on
the mid-module assessment and end-of-module assessment.
Session Overview
Section
Time
Overview
Prepared Resources
Facilitator Preparation
Introduction to the
Module
15 mins
Establish the instructional focus of
Grade 2 Module 6
 Grade 2 Module 6 PPT
 Faciliators Guide
Review Grade 2 Module 6.
Topic A Lessons
20 mins
Examine the lessons of Topic A.
 G2 M6 Lesson Excerpts
 G2 M6 Problem Set Excerpts
Review Topic A.
Topic B Lessons
30 mins
Examine the lessons of Topic B.
 G2 M6 Lesson Excerpts
 G2 M6 Problem Set Excerpts
Review Topic B.
Topic C Lessons
30 mins
Examine the lessons of Topic C.
 G2 M6 Lesson Excerpts
Review Topic C.
 G2 M6 Problem Set Excerpts
 G2 M6 Lesson Excerpts
 G2 M6 Problem Set Excerpts
Topic D Lessons
30 mins
Examine the lessons of Topic D.
Summary
15 mins
Reiterate the key points of Grade 2  Grade 2 Module 6 PPT
Module 6 and facilitate discussion  Faciliators Guide
Review Topic D.
Session Roadmap
Section: Grade 6 Module 2
Time: 135 minutes
[135 (143) minutes] In this section, you will…
Materials used include:
Time Slide Slide #/ Pic of Slide
#
Script/ Activity directions
30
sec
Welcome! In this module focus session, we will examine
Grade 2 – Module 6.
1
GROUP
1 min
2
The ultimate objective is to prepare you to implement
Module 6. To do this we will:
•Examine the development of mathematical understanding
across the module using a focus on Concept Development
within the lessons.
•Introduce mathematical models and instructional strategies
to support implementation of A Story of Units.
30
sec
3
We will begin by exploring the module overview to
understand the purpose of this module. Then we will dig in
to the math of the module. We’ll lead you through the
teaching sequence, one concept at a time. Along the way,
we’ll also examine the other lesson components and how they
function in collaboration with the concept development.
Finally, we’ll take a look back at the module, reflecting on all
the parts as one cohesive whole.
Let’s get started with the module overview.
30
sec
4
The sixth module in Grade 2 is Foundations of Multiplication
and Division. The module includes 20 lessons and is allotted
24 instructional days.
10
min
5
Take 8 minutes to read the descriptive narrative of the
Module 6 Overview. As you read, highlight language that
shows the progression of learning in this module.
Summarize the sequence of the major learning in Module 6.
(After 8 minutes)
Share with others at your table: What is new and different
about the way these concepts are presented? (students are
not multiplying or dividing; the focus is on conceptual
understanding, building from their work with addition and
subtraction.)
Note that most of the fluency focuses either on a review of
core fluency or skip counting, leading students towards
multiplication work in Grade 3.
30
sec
6
Now that you have a broad view of the module, we will
examine the sequence of learning, topic by topic.
3-4
min
7
Take 1 or 2 minutes to think about these questions and
discuss them at your table. (Allow a minute to share out.)
In Topic A, students follow the concrete-pictorial-abstract
path, first arranging objects to form equal groups, then
drawing pictorial representations of equal groups and
relating their drawings to the corresponding repeated
addition number sentences. By the end of the topic, students
draw tape diagrams to represent the number of groups, the
number in each group, and the total.
5 min
8
Topic A begins at the concrete level as students use objects to
create equal groups, providing a foundation for the
construction of arrays in Topic B.
First, students distinguish equal from unequal. Then, as they
manipulate objects, they discover that there are different
ways to arrange a given number of objects into equal groups,
e.g., 3 equal groups of 4 or 4 equal groups of 3.
**Guide participants through the lesson excerpt.**
2-3
min
9
Complete these problems from the Problem Set, then discuss
the questions with a partner. (Allow 2-3 minutes.)
The Problem Set reinforces the day’s concept development,
as students independently form equal groups. Working with
a static image moves them a step beyond their work with
objects. The debrief questions are designed to encourage the
articulation of their understanding. Note that the second
question sets the stage for Lesson 2, in which students will
relate equal groups to repeated addition.
5 min 10
Lessons 2 and 3 move to the pictorial level, introducing math
drawings to represent equal groups. Students are asked to
show groups: “Show me 3, now 3 more. Add 3 more, now 3
more than that.” They then determine the number of objects
and write the corresponding repeated addition number
sentence.
Lesson 3 extends this understanding as students look for and
practice a more efficient way to add, by bundling. For
example, for 4 groups of 3, the student might say, “I bundled
2 threes to make sixes, so 6 + 6 = 12.” They begin to see that
they are adding units of 3.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner A is the teacher
and Partner B is the student. In the following lesson, they will
switch roles.**
2-3
min
11
In this lesson, students continue working at the pictorial
level, using math drawings to represent equal groups and
relating those groups to repeated addition. They also use
addition strategies, such as doubles, to add more efficiently.
Complete the first page of the Problem Set to get a feel for
this work.
Note: A Rekenrek is an excellent way to show repeated
addition. Show the same number of beads in each row, and
then show the repeated addition sentence that goes with the
beads. For example, show 3 rows of 4 beads, and write 4 + 4
+ 4 to show the addition.
Also, some students may make the connection between
repeated addition and multiplication. Praise their
observation, but keep the focus on repeated addition for the
lessons and assessments. Multiplication will be taught in
Grade 3.
5 min 12
As students work with equal groups, they begin to
understand that numbers other than 1, 10, and 100 can serve
as units. In Lesson 4, students represent the total of a given
number of units with tape diagrams.
**Guide participants through the lesson excerpt.**
2-3
min
13
Lesson 4 is an example of when the Application Problem
might follow the Concept Development. This problem gives
students the chance to apply their learning in a real world
context.
Note that students follow the same procedure of moving from
concrete to pictorial to abstract when working with tape
diagrams. In the lesson, they filled their tape diagrams first
with objects, then drawings, and finally abstract numerals.
Take a moment to complete the Application Problem
posted, then share your work with a partner.
3 min 14
Topic B focuses on spatial relationships and structuring as
students organize equal groups (from Topic A) into
rectangular arrays. They build small arrays (up to 5 by 5)
and use repeated addition of the number in each row or
column (i.e., group) to find the total.
Take a moment to think about and share at your table why
the array is a useful model for representing equal groups.
(Organized rows and columns makes it easy to add on; this
leads to running totals in G3. Also, commutative property.)
Ask Grade 3 teachers to share how this work might be
beneficial to the study of area in Grade 3.
3 min 15
Take a moment to read this excerpt from the Grade 2 section
of the Geometry Progression. It helps explain both what
spatial structuring is and why it’s important.
It also gives insight into how the work of Topic B, and then
Topic C, lays the foundation for later work with multiplication
and area in Grade 3.
5 min 16
In Lesson 5, students compose arrays either one row or one
column at a time and count to find the total, using the
scattered sets from Topic A.
Students observe that each row or column contains the same
number of units. Thus, for 4 rows of 3, a student might
observe that there are 4 equal groups of 3. This is
foundational to the spatial structuring students will need to
discern a row or column as a single entity, or unit, when
working with tiled arrays without gaps and overlaps in Topic
C.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner B is the teacher
and Partner A is the student. In the following lesson, they will
switch roles.**
5 min 17
In Lesson 6, students compose arrays and then decompose
them by both rows and columns. For example, they see that
an array of 4 rows of 3 beans can be pulled apart to show 4
rows of 3 or 3 columns of 4. Also, students see that when
another row or column is added or removed, so is another
group or unit.
As the lesson progresses, students move the objects in the
array closer together so there is no gap or overlap, forcing
them to discern the rows and columns without the visual aid
of spacing. Initially, students work with beans and then
transition to square tiles, which builds the foundation for the
area model in Grade 3. Students will do more extensive work
with square tiles in future lessons.
**Guide participants through the lesson excerpt.**
2-3
min
18
Complete these problems from the Problem Set, then discuss
the questions with a partner. (Allow 2-3 minutes.)
5 min 19
In Lesson 7, students move to the pictorial as they use math
drawings to represent arrays and relate the drawings to
repeated addition. They use their personal white boards and
markers to draw horizontal or vertical lines to show the rows
and columns within the array.
Note that students may naturally skip count to find the total.
Praise the observation, and perhaps allow the student to
explain the connection between skip counting and repeated
addition. However, the focus is on establishing a strong
connection between the array and repeated addition.
**Guide participants through the lesson excerpt.**
3-4
min
20
In Lesson 8, students work with square tiles to create arrays
with gaps, composing the arrays from part to whole, either
one row or one column at a time. They draw individual,
separated tiles as a foundational step for Topic C where they
will be working with square tiles without gaps. As usual,
students relate the arrays to repeated addition.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner A is the teacher
and Partner B is the student. In the following lesson, they will
switch roles.**
2-3
min
21
Take a moment to complete the Application Problem, then
share your work with a partner.
Discuss: How does solving this problem lead to deeper
understanding of the structuring and usefulness of arrays?
3-4
min
22
In Lesson 9, Solve Word Problems Involving Addition of Equal
Groups in Rows and Columns, students apply their
understanding of arrays to word problems that involve
repeated addition, interpreting array situations as either
rows or columns and using the RDW process. In addition to
drawing objects, they also represent the situation via more
abstract tape diagrams, just as they did in the final lesson of
Topic A.
Complete this posted problem from the Problem Set.
Which model made it easier to solve the problem, the tape
diagram or the array? Note that student responses to this
question can be an indicator of their level of understanding;
most struggling students rely on the array and counting all.
More advanced students will use the more abstract model,
the tape diagram.
2-3
min
23
In Topic C, students build upon their work with arrays to
develop the spatial reasoning skills they will need in
preparation for Grade 3’s area content. They work with
same-size squares to compose arrays with no gaps or
overlaps and then count to find the total number of squares.
After composing rectangles, students partition, or
decompose, rectangles, first with tiles, they with scissors and
paper, and finally, by drawing and iterating a square unit. In
doing so, they begin to see the row or the column as a
composite of multiple squares or as a unit, which is, in turn,
part of the larger rectangle.
Note that students are not multiplying or dividing in Grade 2,
rather, this topic lays the foundation for the relationship
between the two operations: As equal parts can be composed
to form a whole, likewise, a whole can be decomposed into
equal parts.
5 min 24
In Lessons 10 and 11, students compose a rectangle by
making tile arrays with no gaps or overlaps.
In Lesson 10, given a number of tiles (up to 25) students are
asked to create rectangular arrays that show equal rows or
columns (up to 5 by 5). Students build on their
understanding of manipulating arrays by either adding or
removing rows or columns to create various square arrays.
In Lesson 11, students build upon this understanding,
manipulating a set of 12 square tiles to compose various
rectangles (e.g., 1 row of 12, 2 rows of 6, and 3 rows of 4). As
students share their rectangles, they are encouraged to ask
themselves, “How can I construct this differently?”
**Guide participants through the lesson excerpt.**
5 min 25
In Lesson 12, students arrange square tiles into a specified
rectangular array without gaps or overlaps. Then they trace
to construct the same rectangle by iterating the square unit
much as they iterated a length unit in Module 2 to create a
centimeter ruler.
Next, students use spatial reasoning developed so far in the
module to draw the same rectangle without tracing, using
their understanding of equal columns and equal rows.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner B is the teacher
and Partner A is the student. In the following lesson, they will
switch roles.**
5 min 26
In Lesson 13, students use their understanding of number
bonds and part-whole relationships to decompose square tile
arrays.
This lesson develops the foundation for later work with the
distributive property beginning in Grade 3 Module 1.
**Guide participants through the lesson excerpt.**
3-4
min
27
In Lesson 14, the Problem Set is used during the Concept
Development. Students fold and cut paper models of arrays
to further develop their ability to visualize arrays. They see
that just as a rectangle is composed of equal rows or columns,
each row or column is composed of squares, or iterated units.
*Participants are given this description only. They do not
complete the PS.
5 min 28
In Lesson 15, students think more abstractly, using math
drawings to partition rectangles. They shade in rows or
columns and relate them to the repeated addition number
sentence. Then, given a rectangle with one row or column
missing, students draw in the remaining squares to complete
the array and find the total by relating their completed array
to repeated addition.
Give participants 5 minutes to complete the Problem Set and
discuss the Student Debrief questions with a partner.
5-6
min
29
In this lesson, students use the Problem Set during the
Concept Development to extend their earlier work of
composing and decomposing rectangles using tiles. Here,
they create tessellations, fitting their inch tiles together with
no gaps or overlaps to make patterns that could, theoretically,
extend indefinitely. This highly engaging activity serves the
important purpose of further developing students’ spatial
structuring ability, preparing them to work with area in
Grade 3, while generating work well suited for classroom
display.
**Guide participants through the lesson excerpt.**
(They iterate a core square, or unit. This builds spatial
structuring because students are iterating “units of units” and
reflecting on the resulting structures.)
3-4
min
30
Topic D focuses on doubles and even numbers, thus setting
the stage for the multiplication table of two in Grade 3. As
students progress through the lessons, they learn the
following interpretations of even numbers:
1.A number that occurs as we skip-count by twos is even.
2.When objects are paired up with none left unpaired, the
number is even.
3.A number that is twice a whole number (doubles) is even.
4.A number whose last digit is 0, 2, 4, 6, or 8 is even.
Armed with an understanding of the term even, students
learn that any whole number that is not even is called odd,
and that when 1 is added to or subtracted from an even
number, the resulting number is odd.
5 min 31
Lesson 17 introduces even numbers via doubles. In other
words, when we double any number from 1 to 10, the
resulting number is even, and any even number can be
written as a doubles fact.
They discover that doubles facts yield even numbers even
when the number being doubled is odd.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner A is the teacher
and Partner B is the student. In the following lesson, they will
switch roles.**
5 min 32
In Lesson 18, students pair up to 20 objects and see that
when objects are paired with none remaining, the number is
even. They see that objects arranged in columns of two also
create two equal groups. They count by twos up to 20 and
then back down. When they reach 0, the question is posed:
“Does this mean 0 is even? Can I write 0 as a doubles fact?”
As a result, students see that 0 is even. This practice lays the
foundation for the multiplication table of two in Grade 3.
Following the opening physical activity, students continue to
look for these patterns using counters.
**Guide participants through the lesson excerpt.**
3-4
min
33
In Lesson 19, students learn a faster way to identify even
numbers, by looking for 0, 2, 4, 6, or 8 in the ones place. They
circle the multiples of two on a number path and make the
observation that the ones digits are 0, 2, 4, 6, and 8. Then,
students revisit the number path: Would the pattern
continue past 20? They continue counting by twos and see
that the pattern continues.
They then discern whether or not a larger number is even,
and they prove their findings by using the interpretations
taught in the previous lessons. Once students work with
various interpretations of even numbers, they are ready to
name all other whole numbers as odd.
The lesson ends with students discovering that when 1 is
added to or subtracted from an even number, the resulting
number is odd.
2-3
min
34
5 min 35
Take a minute to complete the Homework excerpt and
restate the rule to a partner.
In Lesson 20, students use arrays to investigate even and odd
numbers. Students add even numbers to other even
numbers, odd numbers to other odd numbers, and even
numbers to odd numbers to see what happens to the sum in
each case: that the sum of two even numbers is even, the sum
of two odd numbers is even, and the sum of an odd number
and an even number is odd.
Through these explorations, students build an intuitive
understanding of prime, composite, and square numbers,
which will be foundational for later grade levels.
**Participants work with a partner and alternate the roles of
teacher and student. For this lesson, Partner B is the teacher
and Partner A is the student. **
30
sec
36
6 min 37
Now that you’ve had the chance to see and practice the
concepts, skills, and models of Module 6, let’s take a moment
to reflect back on the module overall.
Take 2-3 minutes to turn and talk with others at your table.
Share out for 2-3 minutes.
2 min 38
Let’s review some key points of this session.
Use the following icons in the script to indicate different learning modes.
Video
Reflect on a prompt
Turnkey Materials Provided




Grade 2 Module 6 PPT
Grade 2 Module 6 Faciliatators Guide
Grade 2 Module 6 Lesson Excerpts
Grade 2 Module 6 Problem Set Excerpts
Additional Suggested Resources
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

A Story of Units Curriculum Overview
How to Implement A Story of Units
A Story of Units CCLS Checklist
Active learning
Turn and talk