Math Facilitator Meeting Tuesday, March 5, 2013

Agenda Welcome, Goals, and Agenda Geometric Measurement LUNCH Linear Measurement Area LUNCH Leadership Data Taking the work back to your school

Goals for the year In order to develop mathematically proficient students, we will: Deepen our understanding of the practice and content standards in the MCF 2011 Articulate how BPS curricular resources support implementation of the standards Support communication among district staff, school leaders, and classroom teachers

Objectives Consider how geometric measurement connects the two critical domains of number and geometry. Develop an understanding of measuring attributes such as length and area. Learn about the achievements of our colleagues, consider ways to address facilitator challenges, and plan for upcoming facilitation opportunities.

How tall do you think this is?

K-5, Geometric Measurement Geometric measurement connects two critical domains, number and geometry. In what ways does each domain provide conceptual support to the other?

Focus Questions, jigsaw Geometric measurement connects two critical domains, number and geometry. As you read the progression, note ways each domain provides conceptual support to the other. How do the authors of the progression distinguish between a continuous attribute and a discrete attribute? How does this distinction relate to students’ understanding of the number line? The authors of the progression provide four reasons why length is a core concept. What are the reasons? How do these reasons support students’ work in the number domain? Describe the differences between the measuring attributes (length, area, and volume). The central characteristics of measurement are the same. Examine the side-by-side comparison of the grade 3’s area cluster and the grade 5’s volume cluster. What is the same?

Individual (15 minutes) Jigsaw (20 minutes) Whole group (10 minutes)

Jigsaw Identify a timekeeper and facilitator Partner up with the other person who focused on the same question. Name and finalize what you want to share with your small group. 5 minutes Share findings with whole group. (4 × (2 minutes per question + 1 minute to discuss question as a small group)) Synthesize in small group. 3 minutes Whole group. Green (move on) Red (questions)

K-5, Geometric Measurement Geometric measurement connects two critical domains, number and geometry. In what ways does each domain provide conceptual support to the other?

Math Activity Length, Part 1 A 11 inches B 4 5/8 inches C 5 3/8 inches D 8 ½ inches E 6 ¼ inches F 7 inches G 15 inches H 13 ½ inches

Geometric Measurement Progression Grade 1 Grade 2 Read pages 8- 9 Length comparisons Seriation Measure lengths indirectly and by iterating length units at the end of the first full paragraph on page 9. Read pages 12- 14 Measure and estimate lengths in standard units at the top of page 14 right before the first new paragraph.

Quick Write In what ways does the Measurement Domain provide conceptual support to the Number and Operations Domains?

Smoots

A nonstandard unit of measure One smoot is equal to Oliver Smoot's height at the time of the prank (five feet and seven inches ~1.70 m).[1] The bridge's length was measured to be 364.4 smoots (620.1 m) plus or minus one ear, with the "plus or minus" intended to express uncertainty of measurement.[2] Over the years the "or minus" portion has gone astray in many citations, including the markings at the site itself, but has now been enshrined in stone by Smoot's college class.

Break

How long is this line segment? How do you know?

Percentages of Students in Grades 3 and 7 Responding to an Item of the National Assessment of Educational Progress

Math Activity Length, Part 2

Grade 2 Relate addition and subtraction to length 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

Geometric Measurement Progression Read pages 14-15. at the top of page 15, right before the first new paragraph. Geometric Measurement Progression Grade 2

“Measurement activities can also develop other areas of mathematics, including reasoning and logic.” How might these tasks develop reasoning and logic? What are the implications for teaching?

Turn and Talk In what ways does the Measurement Domain provide conceptual support to the Number and Operations Domains?

Math Activity Distinguishing between perimeter and area

Math Activity Draw a rectangle to scale with the dimensions of inches and inches. Find the perimeter and area of this rectangle. Illustrate your solution on the rectangle and show any equations you use. Share your solution with a partner. Read page 21- 22. “Understand concepts of angle and measure angles”.

Whole group Looking at the representation, how can we see “Area as entailing two lengths, simultaneously”?

LUNCH

Leadership

Math Facilitator Presenters Anthanette Nonye Julie Math Facilitator Presenters

Highlighting Achievements Small Group Sharing Achievements/Positives highlighted from logs Select a recorder, reporter and facilitator of the group. Recorder: Chart group members’ achievements, record group members’ names. Facilitator: Ensure each person has an opportunity to add his or her successes. Lead group to select 3 achievements to share. Reporter: Share out three achievements from your group with the whole group.

Building Capacity 1. Write down your biggest challenge. 2. Find your group by the color of your paper. 3. Sit 5 number 1s on one side, 5 number 2s on the other. 4. You have 1 minute to share your challenge and then 2 minutes to receive feedback on ideas to address/overcome the challenge. Record these opportunities on the document. 5. Switch and repeat the process. When the timer goes off, the number 2s move one place to the right.

Break

Planning Time Individual Math Facilitator Planning What will be your next leadership activity? What are the objectives of this session? When is your opportunity to facilitate? With whom will you be meeting? Create your agenda. Round table discussion One person is the recorder, each person has 1 minute to share what he or she is planning, recorder jot down each person’s idea on graphic organizer.

Math MCAS

Preparing for the Math MCAS Taking into account the number of items in each strand or domain assessed; Preparing for the level of rigor expected by the standards; Preparing for the kinds of strategies expected by the standards; Paying attention to focus and coherence needed at each grade level; and Preparing for short answer and open response items. Please be aware that our current scope and sequence pacing guides fully address the standards identified in the 2011 MCF for Mathematics.

Taking into account the strands or domains assessed There will be a number of items addressing measurement and data, especially at Grade 3. Many of these items in the measurement and data domain include area and perimeter (Grades 3 and 4) and volume (Grade 5) as well as angle measure (Grade 4). Perimeter, area, volume, and angle measure items are likely to require decomposing and recomposing computation strategies.

Preparing for the level of rigor expected by the standards (e. g. , 5 Preparing for the level of rigor expected by the standards (e.g., 5.NF.3) Students are expected to understand important concepts deeply enough to be able to fluently solve non-routine problems they have not seen or practiced solving earlier.

Preparing for the kinds of strategies expected by the standards

At Grade 5, this means building on the Grade 4 work with equivalence as follows:

It means not using strategies that do not build on prior work even when these are strategies that many of us were taught when we were learning this content.

Paying attention to focus and coherence at each grade level (e. g. , 4 Paying attention to focus and coherence at each grade level (e.g., 4.NF.4)

Note that 4.NF.4 does NOT address the multiplication of a fraction times a whole number. This is because the multiplication of a fraction by a whole number can be solved by repeated addition, while the multiplication of a whole number by a fraction is conceptually different and cannot be solved by repeated addition. The multiplication of a fraction times a whole number is addressed in 5.NF.4.

Preparing for short answer and open response items Please note the content of this open response item is from the earlier framework and no longer reflects a Grade 4 standard. This example is intended to communicate the demands of an open response item.

CAUTION!! Some standards that will not be assessed are embedded in standards that will be assessed!! Standard 5.NF.6 and 5.NF.7 are assessable: These standards include solving real world fraction problems with the operations of multiplication and division. Standard 5.NF.4 is NOT listed as assessable: This standard supports the knowledge required for 5.NF.6 and 5.NF.7 by exploring fraction operations through models and tiling. In this example of from grade 5, the assessable standards, 5.NF.6 and 5.NF.7 , cannot be fully understood by students without teaching the supporting concepts found in the unassessable standard of 5.NF.4 . Massachusetts Department of Elementary and Secondary Education Massachusetts Department of Elementary and Secondary Education

Recommendations As you continue to use the scope and sequence pacing guide for your grade level so you can be sure you are addressing the standards for your grade level, please . . . Keep in mind the level of rigor expected by the standards so students are prepared to do well on problems they have not seen before; Keep in mind the strategies specified by the standards so students can use and make sense of those strategies when asked to do so; Be sure to “focus where the standards focus” for your grade level including those standards that may not be directly assessed; and Provide opportunities for students to examine and discuss responses to sample items including why wrong answers are wrong, why correct answers are correct, and how sample solutions to open response items can be strengthened.

Closing Geometric measurement connects two critical domains, number and geometry. What are some ways each domain provide conceptual support to the other?