Preparing to Teach Unit Four & December and January Number Corner

Transcription

1 Facilitator-Led Implementation Guide 1 Meeting 3 Preparing to Teach Unit Four & December and January Number Corner Recommended Timing 2 hours in late November Materials You ll Need for the Meeting Participants will need to bring: Getting Started Bridges Teachers Guide, Volume Two Number Corner Teachers Guide, Volumes One and Two pen or pencil highlighter and scissors notebook or scratch paper list of questions or concerns The facilitator will need to bring: this Implementation Guide Getting Started Bridges Teachers Guide, Volume Two Number Corner Teachers Guide, Volumes One and Two Number Corner Student Book chart of Professional Agreements you created for Meeting 2 compiled concerns and questions that participants ed (Group them into categories and present them in such a way that you can display them on an overhead.) Blackline NC 4.2 (Quarter Grids), 1 copy on yellow paper and 1 copy on white paper Blackline NC 4.3 (Dollar Grids), 4 copies on green paper Blacklines NC 4.6 and Quarters a Day Record Sheet), trimmed and glued 3 pieces of 6 by 12 white paper glue and tape Calendar Grid January Calendar Grid Markers Blackline NC 5.1 and 5.2 (January Calendar Grid Record Sheet) trimmed and glued Overhead NC 5.1 (Quick Facts Worksheet) Multiplication Facts Class Checklist (Blackline NC 5.5) about 6 blank overhead transparencies if you are using an overhead projector NC A 5.5 & 5.6 (Checkup 2 Class Checklist) Word Resource Cards Student Book page 89 Overhead 4.12 (Rotational Symmetry) Overhead 4.13 (Pattern Block Symmetries) Overhead 4.16 pattern blocks, several for each participant geoblocks centimeter cubes Challenges & Solutions, Handout 1 (Available for download on the MLC Website: materials/implementation/implement4.asp) sticky notes index card for each participant Copies the facilitator will need to make: December and January Planners, downloaded from Math Learning Center Web site (1 copy of each for each teacher) erials/grade-four.asp Teachers Guide, page 466 (1 copy to display on the projector) Meeting 3 Agenda, Sheet 3.1 (1 copy for each participant or 1 copy for the projector) Unit Four Planner, Teachers Guide, page 434 (1 copy for use on the projector) Student Book pages 73, 74, 77, & 79, 1 for each participant an overhead (if you are using an overhead projector) or a copy of Student Book pages 79, 80 & 89 giveaway for each participant (See page 3 of this guide for giveaway options.) Sharing Responsibilities for Unit Four, Sheet 3.2 (1 copy for each participant) Sharing Responsibilities for December, Sheet 3.3 (1 copy for each participant) Sharing Responsibilities for January, Sheet 3.4 (1 copy for each participant) Note: Overheads, blacklines, and student pages from the Bridges kit are included at the end of this guide.

2 Facilitator-Led Implementation Guide 2 Advance Preparation for the Meeting About two weeks before the meeting, and again a day or two before the meeting, send a reminder to your participants. Ask them to bring the materials listed on the previous page and to you their questions and concerns to you so that you can address them during the meeting. Remind them who signed up for snacks. Compile, categorize, and display the questions and concerns participants ed to you. Format them in such a way that you can display them in this meeting. Review the activities from the Teachers Guides that you ll model in this meeting. Meeting Setup Immediately prior to the meeting, set out the following items for each table group: sticky notes any sheets or handouts you have pattern blocks copies for participants an index card for each participant centimeter cubes geoblocks tape Post the agenda on the overhead or on chart paper. Glue 3 Dollar Grids (Blackline NC 4.3) across the top of each of the 3 pieces of 6 by 12 white construction paper, leaving room for notes underneath the grids. Cut out the Quarter Grids from Blackline NC 4.2 and glue three white quarters on the first dollar grid on one sheet of paper. Then glue 3 yellow quarters and 3 more white quarters as shown on page 158 of the Number Corner Teachers Guide. Store the remaining Quarter Grids in an envelope or re-sealable plastic bag. Post the paper with the Dollar Grids on the wall and post the 3 Quarters a Day Record Sheet (Blacklines NC 4.6 and 4.7) in your Number Corner Display. Hang the Calendar Grid on the wall with the first seven January calendar markers showing. You can either have the rest of the markers turned over in the grid or just have them available to add as you model the Calendar workout. Post the January Calendar Grid Record Sheet (Blacklines NC 5.1 and 5.2) next to the Calendar Grid. Cut figures c and d out of your copy of Student Book page 89. Follow Up After this meeting is over, try to do the following things within about a week: a list of participants concerns/questions and solutions if you have sufficient notes to do so. If you ran out of time, be sure to possible solutions for unresolved concerns to all participants. participants a link to the parent materials on the Math Learning Center Web site. This page includes the FAQ and links to grade-level resources, including unit overviews with sample problems and vocabulary lists. They may find the materials, particularly the FAQ, useful for parents questions during conferences.

3 Facilitator-Led Implementation Guide 3 Giveaway Options Your group size and the amount of time and assistance you have will determine which giveaway option(s) below makes the best sense for you. Option 1: Half-class set of illustrated directions for a building project such as bookshelves or toy boxes. Students will use these in Session 14 to understand the relationship between 2- dimensional and 3-dimensional shapes. What you will need illustrated directions for a building project Ikea has pdfs of directions for various projects: ms/en_us/customer_service/ assembly_instructions.html#2 white copy paper stapler What you will do Run a half class set of the directions. You can find more than one type of directions for variety. Staple pages together if they are more than one page. Requirements for a Group of 20 Teachers Assuming 30 students per class for a total of 600 booklets: number of sheets of paper varies, depending on how long the directions are 1,200 staples Option 2: One and one half class set of 2 ¾ by 2 ¾ paper squares for each teacher. Students will use these in Session 6 when they study translations What youʼll need good quality white paper ruler scissors envelopes of plastic bags What youʼll do Cut a one and one half class set of paper squares for each teacher. Store them in an envelope of plastic bag. Requirements for a Group of 20 Teachers approximately 60 sheets of good quality white paper 20 envelopes or plastic bags 1 pair of scissors 1 ruler Option 3: A class set of Unit Four Assessment Blacklines for each teacher. Teachers will give the pre-assessment in Session 3 and the post-assessment in Session 21. What youʼll need Blacklines A white copy paper large paper clips or binder clips What youʼll do Run a class set of Blacklines A , A , A , and A Run 1 or 2 copies of Blacklines A 4.11 and A Clip class sets together for each teacher. Requirements for a Group of 20 Teachers 7,800 sheets of white copy paper paper clips or binder clips

4 Facilitator-Led Implementation Guide 4 Part I Welcome & Agenda (5 minutes) Draw participants attention to the Professional Agreements chart from the previous meeting. Explain that you ll keep it posted throughout today s meeting and will take some time at the end of the meeting to discuss it explicitly. Briefly review the agenda for today s meeting, and explain that you ll be focusing on December and January Number Corner, because you will not be meeting during the month of December. You ll also discuss Unit Four, although teachers aren t really expected to begin teaching Unit Four until they return from winter break. During the month of December, their goal is to teach Unit Three, which you reviewed in the previous meeting. At this point, you might ask one participant to act as timekeeper and another to act as recorder for the meeting. Quickly get a sense of how far along people are at this point by asking some questions like the following. Who has made it through Session 10 (Work Places 3A and 3B) in Unit Three? Who has played Round & Add as part of the Number Line workout in the November Number Corner with their students? Part II December & January Number Corner Preview (25 minutes) As you are investigating two Number Corner months in this meeting, you may want to extend the meeting beyond the recommended two hours, if it is at all possible. Explain that you re going to spend some time looking over the December and January Number Corner workouts. As you model different workouts, be sure to be explicit about when (which month) each workout occurs as you are doing two months in this meeting. Invite participants to use the sticky notes you ve provided on their tables to flag key pages in their Teachers Guides as you go. Begin by asking participants to turn to pages 143 and 144 and then to pages 177 and 178 in their Number Corner Teachers Guides to get a quick sense of what they ll be doing in December and January. They will see with just a glance that these two months include work with money, decimals, and fractions as well as patterns, estimation, multiplication facts, telling time, and more. Explain that in this part of the meeting you will focus mainly on the November Calendar Collector and the January Calendar Grid. You will also look at the second Number Corner Checkup, which takes place in January, and go over the new format for Computational Fluency, which is an ongoing assessment for multiplication facts. Ask participants to mark pages 182 and 183 with a sticky note: these pages include information about the second Number Corner checkup and the Support Activities that teachers can use with students who show a need for more practice with a particular skill on this checkup. Take a moment to remind participants that the blacklines for the Support Activities are located in the back of the packet of Number

5 Facilitator-Led Implementation Guide 5 Corner Blacklines. Also have participants mark pages 180 and 181, which give an overview of the Quick Facts routine used in the Computational Fluency workout. Introduce the December Calendar Collector with a question ask participants to imagine that someone has offered to give them $10 on December 20 th or 3 quarters a day, starting on December 1 st and ending on December 20 th. Let them know that the money can t be spent before the 20 th and then ask them which they would choose. Have participants discuss the thinking with a partner and then invite a few people to share their choice and the reason for their selection. Then, let participants know that in the December Calendar Collector, students will collect 3 quarters a day. The quarters are paper squares with a picture of a quarter on a 5 by 5 grid and are glued on to dollars which are 10 by 10 grids with pictures of dollars on them. Hold up or point to the example you created for the first few days. Ask a few volunteers to share what they notice. Elicit thoughts on patterns, the relationships between decimals and fractions seen here, and parts and wholes. Ask the group how many days it will take to have a whole number of dollars and then ask when they will see a whole number of dollars again. Then, take a moment to show the Calendar Grid Record Sheet (Blacklines NC 4.6 and 4.7). You can have a volunteer come up to call on other participants for what should be filled in on the record sheet, or you can call on participants and fill in the chart yourself. At the same time, have another volunteer add a few more days worth of quarters to the dollar sheets, continuing the pattern of 3 yellow quarters and 3 white quarters. After a few more days have been filled in on the record sheet, ask the group to discuss in partners what patterns they are seeing on the record sheet and on the dollar grids as more and more quarters are added. Invite a few participants to share what they talked about with their partners. Listen carefully to make sure that participants are seeing the big ideas of the workout that students will be conceptualizing fractions, looking at equivalent forms of fractions and decimals, adding fractions and decimals, and using a table to analyze and represent patterns and add any necessary information after they have shared. Conclude this part of the session by showing or having participants look at Number Corner Student Book page 45, which goes along with this workout. Next, direct participants attention to the January Calendar Grid where you have posted the first seven calendar markers. Ask them to study the grid quietly for a minute and then ask for a few observations. Then, invite a few participants to share predictions they have about what the next marker will look like. After you have heard a few predictions, post or turn over the next six markers and ask participants to make more observations. Ask them if the markers match their predictions, what was surprising, if anything, and if they are more able to predict what the next marker or several markers will look like. After a few minutes of discussion, direct participants attention to the Calendar Grid Record Sheet (Blacklines NC 5.1 & 5.2). Emphasize the columns on the right, which look at the elapsed time between each day and the day before and the total elapsed time since the first day of the month. The term elapsed time will confuse some students at

6 Facilitator-Led Implementation Guide 6 first, but as they fill in the record sheet, they will begin to develop an understanding of its meaning. You don t have to take time to fill out the record sheet now. Let participants know that there are four Number Corner Student Book pages to go along with this routine, and the first two, pages 47 and 48, need to be done before the 13 th calendar marker is revealed. Conclude this activity by having participants look at the list of questions on page 189 of the Number Corner Teachers Guide. These questions will help students deepen their thinking and understanding and encourage them to justify their thinking and explain their reasoning. Give participants a quick overview of the January Quick Facts workout used in the Computational Fluency workout for the next few months. Students will have a certain amount of time to solve a series of multiplication facts. They will be able to choose the multiplier they want to work with and use that multiplier in forty different multiplication problems. Ideally, everyone will start with 2 as their multiplier and as they achieve mastery with each number, they will move on to another number. Show Overhead NC 5.1, taking care to cover the division problems on the bottom of the sheet. Point out the cell in the table where students put the multiplier they are working with. Then, point to the chart below the table and explain that rather than using a more standard notation for multiplication facts, students will multiply their multiplier by the number in each box and put the product in the box. Let teachers know that they have some flexibility in how they want to conduct the timing for these Quick Facts. Bridges recommends giving students four minutes to complete the chart. This will be too much time for some students and not enough time for others. Have participants read the paragraph on the bottom of page 198 in the Teachers Guide to see how they can keep track of the time it takes for students to complete the chart. When most participants are finished reading, take a moment to ask if there are any questions about the workout. After answering any questions, move on to explain how teachers and students will keep records of progress with multiplication facts. Each teacher will have a Class Checklist where he or she will mark off the multiplication sets that each student has mastered. Hold up the checklist (Blackline NC 5.5) or show it on a document camera so participants will know what to look for. Students will keep track of their own progress by filling out the Quick Facts Tracking Sheet on page 50 in their Number Corner Student Books. This way, both students and teachers will know how they are progressing with their facts. Once participants understand how to use the Quick Facts sheets for multiplication, show the bottom portion of the overhead on division. Explain that students will select any ten products from the box above and write them in the division boxes. Then, they write whatever multiplier they used that day as the divisor and they solve the problems. This part of the sheet is not timed. Wrap up your exploration of this workout by showing participants two important sections in the Teachers Guide. First, have participants look on page 201 to see a challenge opportunity for

7 Facilitator-Led Implementation Guide 7 students who already know their facts and support suggestions for students who are struggling. Then, have participants turn back to page 197 to read the note about timed testing. If you don t have time for participants to read it right now, strongly encourage them to read it before beginning this workout. Finally, spend the last few minutes of the Number Corner Preview looking at the Number Corner Checkup 2. Remind teachers that these checkups are what they say they are a basic check to see what students can do at this point in the year. All of the checkups are optional, but it may be helpful for teachers to have a summary of student progress and ability at this midway point of the school year. The checkup will take the place of two full Number Corner sessions and should be completed toward the end of January. Give participants a minute to skim over pages 211 through 214 to see what skills and concepts Checkup 2 includes. Show them a copy of the class checklist (Blackline NC A 5.5 & 5.6) so they know what to look for and how to use it. Close this part of today s meeting by giving each participant a copy of the December and January Number Corner Daily Planners. Also give them a moment to flag pages 149 and 184 in the Number Corner Teachers Guide: these two planners show what to do each day of the week. Part III Sharing Successes (3 minutes) Ask participants to think privately for a minute about the successes they have had this past month. Then give them time to discuss their successes in table groups. In their discussions, ask them to talk about what they did to make their successes happen. While they talk, you might want to circulate around the room to listen in on their conversations to get a sense of how things are going in their classrooms. Finally, invite a representative from each table group to share a success from his or her group. Part IV Reviewing Questions & Concerns (7 minutes) Draw participants attention to the display of concerns and questions, and thank them for taking the time to send you these thoughtful responses. Give them a moment to read over the concerns and questions, and then address a couple of them one at a time. First invite others who have encountered the same problem to share how they have begun to solve it, and then ask others to offer some possible solutions. Finally, you can share some solutions of your own or refer to Handout 1: Challenges & Solutions. Also direct participants to sections of the Teachers Guide and Getting Started that might help them. When you have run out of time and need to move on, quickly refer to the agenda and point out that you ll brainstorm solutions to some more of their concerns in Part VIII of this meeting.

8 Facilitator-Led Implementation Guide 8 Part V Looking at the Unit Planner & Exploring Unit Four (10 minutes) Ask participants to turn to the Unit Four Planner on page 406 in their Teachers Guides and display your copy of the planner on the projector or overhead. Ask them to mark Sessions 3, 9, 12, 14, and 21 with a highlighter: these sessions require more advance preparation than usual. They can refer to pages 407 and 408 in the Teachers Guide to get more information about exactly what is required for these sessions. Give participants a few minutes to look over the Unit Planner quietly: you might invite them to find the different assessments and work samples included in this unit and make note of how many Work Places there are and when they are introduced. Give them a couple minutes to think of a way to summarize the unit in two or three sentences, based on what they gleaned from the planner. Then ask them to share their summaries with their neighbors. Next, ask participants turn to page 404 to see the Unit Four: Skills & Concepts Across the Grade Levels chart. This chart shows at which level (introduction, development, mastery, or extension) each skill is addressed in this unit. Give participants just a few minutes to look over the chart, and ask them to think about what it indicates about their goals for this unit. You might ask participants to give a silent thumbs-up when they re done scanning the chart. When most thumbs are up, ask volunteers to share what they learned from the chart, what surprised them about the chart, or how they expect the information on the chart will inform their instruction. Part VI Reading the Unit Introduction (10 minutes) Give teachers time to read the Unit Four Introduction in silence (Teachers Guide pages ). Before they begin reading, ask them to pay careful attention to what the learning objectives for this unit are and how they might determine whether students are meeting those objectives. Invite participants who finish early to spend the rest of this time skimming the sessions in the unit. Part VII Doing Key Activities from Unit Four (40 50 minutes) Note Read through this entire section before conducting the meeting. During the meeting, you might find the mini agenda for this section on page 15 useful. Begin this part of the meeting by explaining that, as they just read in the introduction, this unit focuses on helping students develop a more sophisticated understanding of geometry. Students will move from labeling shapes and parts to looking at relationships between them and being able to use them to make analyses and to draw informal deductions. They will review shapes, line, and angles, focus on motion geometry, and study three-dimensional figures. The main goal for

9 Facilitator-Led Implementation Guide 9 students in this unit is to consider relationships between shapes and their properties. If you spent little or no time on the Word Resource Cards in the previous meeting, you will want to devote some time to them in this meeting, as there are so many geometry terms in this unit. Check to see if participants have been using their cards. If they have not really started using the cards, hold up at least two cards (rotational symmetry and net would be good examples for this unit) for participants to see. Show them that the card provides the term and an illustration on one side and the definition on the other side. Students will add the definitions to the glossary in the back of their Student Journals. Encourage participants to make use of the cards and the process of having students build their glossary. Rotational Symmetry (Session 8, pages ) 15 minutes Introduce the idea of Rotational Symmetry by showing Overhead 4.12 with pattern blocks placed in the frame. Take one minute to ask participants for observations. Then, remove the pattern blocks and ask participants what they notice now. Let participants know that what they are looking at is going to be called a frame. Then, return the pattern blocks to the frame and tape the pieces together. Ask participants if it is possible to rotate the pattern block figure to a new position so that they fit exactly back into the frame. Give participants a minute to discuss the question with a partner. Interrupt their talk to ask them if there is more than one way that the pattern block figure can fit back into the frame and have them continue talking. Then, invite a participant to come up and rotate the pattern block figure, pausing each time it fits perfectly back into the frame. Ask the group how many times the figure fit perfectly into its frame. Then, let the group know that they have been exploring the concept of rotational symmetry. Invite a few participants to see if they can come up with a definition of rotational symmetry. After hearing a few thoughts, clarify if necessary by explaining that rotational symmetry is the number of different positions in which a figure is indistinguishable from the figure in its original position. In other words, rotational symmetry is the number of times a figure can be rotated and fit perfectly into its frame. Let participants know that the exact number is referred to as the order of rotational symmetry. Write order of rotational symmetry 4 near the pattern block figure and tell participants that because they could rotate the figure and have it fit in the frame 4 times, it has order of rotational symmetry 4. There will probably be discussion and confusion in your meeting and back in the classrooms about whether to count the original position once or twice. If it comes up, let participants discuss and debate the issue for a minute or so and then clarify is necessary the original position should be counted first and when the figure is returned to the original position should not be counted. Thus, the figure they looked at has order of rotational symmetry 4 and not 5.

10 Facilitator-Led Implementation Guide 10 There will probably also be some discussion about the number of degrees in each turn. While adults will know that the turns for this figure were 90, 180, 270, and 360 degrees, students are not expected to know this at this time. However, you might let participants know that some students will have this knowledge, especially if they have a lot of experience with skateboarding or other sports. This is a great opportunity to connect math with other areas and a great opportunity for kids to share their background information. These terms are probably new to participants (and students) and it will take some time for them to become familiar. Even more confusing is that order of rotational symmetry is sometimes called rotational symmetry of order. Let participants become more familiar with the words and concepts with some practice. Have them complete Student Book pages 73 and 74 by themselves or with a partner. When most participants have finished pages 73 and 74, bring the group back together for a quick discussion. Ask them what surprised them, if anything as they completed the problems. Ask them to think about teaching this lesson in the classroom what might be challenging? What could they do to make the lesson go smoothly? Pattern Block Symmetry (Session 9, pages ) (10 minutes) Show Overhead 4.13 (Pattern Block Symmetries). Ask participants for strategies that their students would use to find the number of lines of symmetry in any of the pattern block frames shown on the overhead. After collecting a few ideas, ask participants to complete at least 4 of the problems on Student Book page 77, using the pattern blocks and any other helpful resources on their tables. As they work, circulate around the room to help out, answer questions, and listen as participants work further with symmetry. Once most participants have finished 4 problems, bring the group back together. Ask them what they discovered as they found the number of lines of symmetry and the rotational symmetry of order. If the idea does not emerge on its own, ask participants if figures always have the same number of lines of symmetry and rotational symmetry of order. If participants have different ideas, let them debate for a minute or two. Then, have participants read page 457 in their Teachers Guides before moving on to the next activity. 3-Dimensional Views (Session 14, pages ) (10 minutes) Get participants busy by showing them Overhead 4.16 (3-Dimensional Views). Ask them to study the overhead for a moment. Ask them what they see and make sure that they see how the views match the structure toward the top. Ask a participant to explain why the top view represents this structure. Ask participants to think about why and how this top view might be confusing for students and how they can help students see that it is an accurate representation. If no one mention s a bird s eye view of buildings, bring up the idea yourself and ask participants how buildings would look if we could look down on them from above.

11 Facilitator-Led Implementation Guide 11 Then, show the overhead you made of Student Book page 79. Ask participants to find the same page on their tables and draw the front, right, and top views of the first Building. They can use the centimeter cubes on their tables and can choose to work with a partner or alone. After they have worked for a few minutes, stop participants to reflect on the practice of drawing views. Ask them what is challenging about drawing 2-dimensional views based on 3-dimensional figures. Invite different participants to come to the overhead to draw their representations of the front, right, and top views of the building. If there is disagreement about what the views should look like, encourage a discussion to help resolve the differences. Participants may have to make the buildings out of cubes if they haven t already done so. When everyone agrees on what the views should look like, take a moment to show the overhead you made of Student Book page 80. Participants don t have to solve the problems now, let them now you are just showing them the next phase of the lesson. After participants have had a minute to think about the opposite challenge, constructing buildings from views, move on to the next activity. Geoblock Nets & Surface Area (Sessions 17 & 18, pages ) (10 minutes) Let participants know that after students construct views from buildings and buildings from views, they go on to figure out methods for finding the volume of cubes and rectangular prisms and begin to look at the surface area of cubes. Spend whatever time you have remaining exploring Session 17, Geoblock Nets and Session 18, Nets & Surface Area. Show the overhead you made of Student Book page 89. Check with the group to make sure that everyone knows what a net is. If not, bring out the Word Resource Card for net or just explain that it is a set of connected 2-dimensional shapes that fold together to become a 3-dimensional shape. Ask participants to imagine what 3-dimensional shape they would create if they could cut and fold figure c. As participants explain their answer, be sure to ask follow questions, such as what makes you think that? and how do you know? Participants can look at and use the geoblocks on their tables as they consider these questions. Repeat the process with figure d. Once participants have predicted which geoblocks fit into which nets, invite two participants to come up and test the predictions by folding the nets you already cut out around the predicted geoblocks. After the participants have shown how the nets fit over the geoblocks, let participants know that students will look at five nets, including these two, predict what 3-dimensional shape the net will, cut and tape the nets into 3- dimensional shapes, and then compare them to actual geoblocks. If you re running out of time: Skip the adapted activity from Session 18 below and wrap up this section of the meeting as described in the last paragraph before Part VIII. To provide a preview for Session 18, ask participants what tools they could use to measure the surface area of figure c in square centimeters (rulers, base ten pieces, cm cubes, cm grid paper). Then ask them to work with a partner to think about how students would use one or more of these tools to figure out the surface area of figure c. What strategies might they use or develop? Encourage participants to

12 Facilitator-Led Implementation Guide 12 think like their students, which might mean getting creative and moving beyond more traditional methods of finding area. Connect the question back to the different tools for example, if they use centimeter cubes, how would they use them to find the area? After participants have worked for a few minutes, invite one or two of them to share their ideas about how they or their students would find the surface area of figure c. Recommend that they come to the overhead to sketch and write their ideas for the group. Conclude this part of the meeting by reminding participants that there are four games played in this unit. These games are first introduced in sessions and then revisited as Work Places and participants should be sure to take advantage of these opportunities to observe and assess students and even to coach in and provide mini-lessons based on observations and assessments. Part VIII Brainstorming Solutions to Challenges (10 minutes) If you re running out of time: Remind participants that you ll have a discussion and brainstorming session similar to this one in every meeting. Offer to everyone with possible solutions to the unresolved concerns. When you send the , invite participants to offer ideas about other solutions as well. Move on to Part IX when you have about 10 minutes left. Once again, display the list of concerns you collected from participants via . Select one concern at a time and invite participants to think for a moment about how they would address this issue. Then ask participants who have encountered the same issue to describe how they are working to solve it, and invite others to share ideas about how they might resolve the problem or address the concern. After participants have shared some ideas, you might offer a solution based on your own experience or on the Challenges & Solutions chart (Handout 1). Also try to direct participants to key pages in the Teachers Guides and Getting Started that can help. You might want to ask one of the participants to make notes about the concerns and solutions during this time. If you have the time, type up these notes and them to participants so they can use them as a helpful reference. Part IX Wrap Up (10 minutes) Draw participants attention to the Professional Agreements chart, and invite them to think for a moment about your meetings. Invite them to suggest additions or changes to the chart. Also ask them to think about whether these meetings are consistent with these professional agreements. Invite them to contact you by sometime before your next meeting in January if they feel you need to change anything about the meetings to make them consistent with this set of agreements. They could also write their ideas on their exit cards (see the paragraph below).

13 Facilitator-Led Implementation Guide 13 Next, thank teachers for their participation and confirm the next meeting place, date, and time, as well as the names of those participants who will bring snacks. Next, give all participants an index card and ask them to write one thing they found useful about this class, as well as any additional questions or concerns. Give them a few minutes to write. Ask them to turn in these cards at a central place as they leave, but to stay seated for a few more minutes so that you can distribute some helpful materials. Finally, pass out any handouts, including the Sharing Responsibilities sheets (Sheets ), and the giveaway you ve prepared for them. If you have extra time or if you are able to linger for a few minutes, you might want to give participants time to fill out their Sharing Responsibilities sheets with their grade-level team members.

14 Facilitator-Led Implementation Guide 14 Appendix 1 Doing Key Activities from Unit Four Mini-Agenda You can use this mini-agenda to help guide your work during this section of the meeting, which will take about minutes altogether. Time 15 mins. 10 mins. 10 mins. 10 mins. Brief Overview Some details are not included. See pp for complete information. Rotational Symmetry Facilitator shows overhead 4.12 and illustrates the concept of Rotational Symmetry while asking questions and conducting a discussion with participants. Facilitator explains Rotational Symmetry of Order and makes a few points that will help in the classroom. Participants complete two Student Book pages. The group discusses the pages. Pattern Block Symmetry Participants look at an overhead and share ideas for how their students would find the number of lines of symmetry in a figure. Participants complete Student Book page 77. The facilitator leads a discussion about the page and then participants read Teachers Guide page Dimensional Views (Session 14) Facilitator talks about important skills and concepts associated with 3-dimensional shapes. Facilitator shows Overhead 4.16 and leads short discussion on views. Participants draw views based on a picture of a building. Participants share and discuss their work. Geoblock Nets & Surface Area Facilitator summarizes the next few sessions and then confirms everyone understands what a net is. Participants look at 2 nets and figure out what shapes they will become when folded into 3- dimensional shapes. Participants think about what tools they could use to measure the surface area of one of the nets. Then, they think about how they or their students would find the surface area with these tools. Participants share their ideas Facilitator wraps up this part of the meeting by referencing the Work Places in this unit. Teachers Guide Pages Pages Facilitator can preview Sessions 17 & 18, Pages

15 Facilitator-Led Implementation Guide 15 Sheet 3.1 Meeting 3 Agenda You can use this agenda as a guide while leading the meeting. You should also post some form of the agenda for participants; you might write a brief agenda on the whiteboard, display this page on a document projector, or distribute copies of this sheet to participants. Part Time Summary I Welcome & Agenda 5 minutes The group establishes a positive and professional environment and reviews the agenda and list of professional agreements begun in Meeting 2. The facilitator helps teachers preview key pages in the Teachers Guide related to planning and assessment for the II December & December & January Number Corner. The facilitator January Number 25 minutes models some activities, and teachers discuss the workouts Corner Preview with the big mathematical ideas and learning objectives for students in mind. Table groups share their successes, and then a III Sharing Successes 3 minutes representative from each group shares a success with the whole group. IV Reviewing Questions & Concerns V Looking at the Unit Planner and Exploring Unit Four VI Reading the Unit Introduction 7 minutes 10 minutes 10 minutes The facilitator and teachers review participantsʼ concerns submitted via and address one or two of them. Teachers develop a big picture of Unit Four while the facilitator helps them locate resources in the Teachers Guide that will be helpful in planning for and teaching the unit. Teachers read the unit introduction to consider the big mathematical ideas of the unit, as well as the flow of instruction and assessment. VII Doing Key Activities from Unit Four VIII Brainstorming Solutions to Challenges IX Wrap up minutes 10 minutes 10 minutes The facilitator helps teachers explore, discuss, and have hands-on experiences with key activities from Unit Four. The facilitator helps teachers brainstorm solutions to challenges they have encountered. The facilitator confirms the time, date, and location of the next meeting, collects teachersʼ exit cards, and shares giveaways with participants. Participants evaluate the efficacy of these meetings using the list of professional agreements.

16 Facilitator-Led Implementation Guide 16 Sheet 3.2 Sharing Responsibilities for Unit Four Task Team Member Date Due to Others 1. Run off copies of Assessment Blacklines. Run a class set of Blacklines A , A , A , and A 4.15 for each class. Run 1 or 2 copies of Blacklines A 4.11 and A for each class. 2. Run Blacklines needed for Unit Four. Run two class sets of Blacklines 2.4 for each class. 3. If you have not purchased Bridges Student Books, run a class set of pages for each class. 4. If you have not purchased the Home Connections, run a class set of pages for each class. 5. If you have not purchased the Work Places Student Book, run a class set of pages for each class. 6. Make one and a half class sets of 2 ¾ by 2 ¾ paper squares for each class. 7. Find a copy of illustrated directions for a building project, such as bookshelves, a desk, or toy boxes Make a half-class set of these for session 14 for each class. If possible, find a few different sets of directions for variety. 8. For this unit, you will need to make sure that your geoblocks are labeled see page 409 for more information. 9. Each teacher will do independently N/A 10.

17 Facilitator-Led Implementation Guide 17 Sheet 3.3 Sharing Responsibilities for December Task Team Member Date Due to Others 1. Run copies of Number Corner Blacklines. Run 1 copy of Blackline NC 1.1, a third-class set of Blackline NC 1.9, 1 copy of Blackline NC 4.8, a class set of Blackline NC 4.9, and 1 copy of Blacklines NC 4.10 and 4.11 for each class. 2. Run 2 copies on yellow paper and 2 copies on white paper of Blackline NC 4.2. Cut them apart and store in an envelope or resealable bag for each class. 3. Run 4 copies of Number Corner Blackline NC 4.3 on light green paper, cut apart, for each class. Run copies of Number Corner Blackline NC 4.4, 2 copies per student for each class, and run copies of Number Corner Blackline NC 4.5, 3 copies per student for each class. 4. Run Number Corner Blacklines 4.6 and 4.7 for each classroom. Trim and glue 4.6 and 4.7 together to post on display boards. 5. If you havenʼt purchased Number Corner Student Books, run a class set of pages for each class. 6. Each teacher will need to have 5 pieces of 6 by 12 white construction paper. You will need to glue the dollar grids (NC blackline 4.3) across each of the 5 pieces of paper. See page 150 for more information. 7. Each teacher will do independently N/A 8.

18 Facilitator-Led Implementation Guide 18 Sheet 3.4 Sharing Responsibilities for January Task Team Member Date Due to Others 1. Run copies of Number Corner Blacklines. Run 1 copy of Blackline NC 1.1, a third-class set of Blackline NC 1.9, a one-third class set of Blacklines NC 1.10 NC 1.12, a few copies of Blackline NC 1.13, a class set of Blackline NC 4.9, 2 copies of Blackline NC 5.5 and 4 class sets of Blackline 4.6 for each class. 2. Run 1 copy of Blacklines NC 5.1 and NC 5.2 for each class. Run 1 copy of Blacklines NC 5.3 and NC 5.4 for each class. Trim and tape together Blacklines NC 5.1 and NC 5.2 and trim and tape together Blacklines NC 5.3 and NC 5.4 to show on the Number Corner display. 3. Run class sets of Number Corner Assessment Blacklines, NC A , and NC A 5.5 & 5.6 see page 150 in the Number Corner Teachers Guide for specific page numbers and quantities 4. If you havenʼt purchased a class set of Number Corner Student Books, run a class set of pages for each class. 5. Create a packet of Support Activities for each room. See p. 214 in the Number Corner Teachers Guide. The support blacklines are in their own subsection of the Number Corner blacklines. (Optional: You may not have time this year to use Support Activities. Use your judgment about whether to prepare these activities.) 6. Each teacher will need a paper lunch bag or a small paper bag for the Calendar Collector this month. 7. Each teacher will do independently. N/A 8. 9.

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