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
● 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? / How will we know that they are able to do this?· 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. / Participants will be able to articulate the key points listed above.
Session Overview
Section / Time / Overview / Prepared Resources / Facilitator PreparationIntroduction 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
· G2 M6 Problem Set Excerpts / Review Topic C.
Topic D Lessons / 30 mins / Examine the lessons of Topic D. / · G2 M6 Lesson Excerpts
· G2 M6 Problem Set Excerpts / Review Topic D.
Summary / 15 mins / Reiterate the key points of Grade 2 Module 6 and facilitate discussion / · Grade 2 Module 6 PPT
· Faciliators Guide
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 / GROUP
30 sec / 1 / / Welcome! In this module focus session, we will examine Grade 2 – Module 6.
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.