ESD 123 Addition & Subtraction Content Training Developed by Valerie Adams, Math Coach, Intervention Specialist Virgie Robinson Elementary School, Pasco School District February 2009 ESD 123 Mathematics Content Training Package ESD 123 has developed mathematics content training packages for use throughout the region. These packages were developed by educators under contract with ESD 123 and are the property of the ESD. They are to be used by trained facilitators under the direction and coordination of ESD 123. For more information, please contact: Cathey Bolson Debi DePaul Regional Mathematics Coordinator Regional Mathematics Coordinator firstname.lastname@example.org email@example.com 509-544-5736 (Office) 509-544-5737 (Office) 509-492-6230 (Cell) 509-492-0222 (Cell) ESD 123 Mathematics Content Training Package Addition and Subtraction Materials Technology Chart paper Computer Markers Projector Table Boxes Document camera sticky notes PowerPoint index cards highlighters markers Masking tape or sticky labels Blank paper for participants to write on K-8 Mathematics Standards Document OR K-8 Mathematics Strands Document (brought by participants) Rekenrek Demonstration Model. Cord and 10 red and 10 white beads for each participant Round Counters. You will need enough for each participant to have 20. May use cubes, tiles or any other small objects Handouts Parking Lot for each table (or use Chart) Group norms table tents (or posted in room) Handouts for Participants (One per participant, unless otherwise noted.) Problem Type Framework and Cut up Problems Five and Tens Frame o Five and Tens Frames can come from many sources. An online source can be found here: www.ablongman.com/vandewalleseries/volume_1.html o Choose BLM 1,2,17,18 Evaluation Form ESD 123 Mathematics Content Training Package Introduction to the Facilitator Notes All of the Facilitator Notes are organized in a three-column format. The left column provides a sequence of activities, along with estimated time allocations for each activity. Times may need to be adjusted, depending on the needs of a particular group of participants. The middle column shows the slides that should be projected. A separate PowerPoint file of these slides is provided. The right column contains notes for facilitators (e.g., suggestions on how to introduce an activity, background information, answers to some of the questions, etc.) There is also blank space in this column for making additional notes and comments. Logistics These professional development materials were designed with the following assumptions about logistics for the meetings. 1. Participants will primarily be classroom teachers of mathematics from grades K-12. Modifications may need to be made if the grade range of participants is more restricted or if there are significant numbers of ELL teachers, special education teachers, or preservice teachers. 2. Ideally, participants should be seated at tables of 3-6 people each. As indicated in the Facilitator Notes, these small groups (or table groups) are sometimes mixed across grades and sometimes restricted to a single grade. 3. It is helpful to have supplies on the tables ahead of time. Some presenters like to use table boxes (see materials section above) that have basic supplies in them. However, you may also just place the materials in the center of the tables before you begin. You can pass out the handouts as you need them. 4. It highly recommended that you test any equipment that you plan on using during your presentation well before the start time, especially if you are using equipment other than your own. It is dangerous to assume that any piece of equipment will always perform the same way, no matter how familiar you are with it. ESD 123 Mathematics Content Training Package Slide# Slides Notes This is the time for general statements from the host of the event. It would also be a good time to mention that the ESD is sponsoring several of these content workshops and that they can get Slide 1 more info on the ESD 123 website or by contacting Cathey or Debi. This You, or the host, should take care of any housekeeping items like clock hours, restroom section locations, dinner time, etc. takes 20 min Enter each facilitator name and affiliation. You may also want to add your title after your name and before your affiliation. BRIEFLY share information about yourself, such as grade level, PD experience, experience in the content area, etc. No need to give your life story but try to establish rapport with group. Slide 2 ESD 123 Mathematics Content Training Package Slide# Slides Notes Purpose: Develop an understanding of addition and subtraction concepts for your grade level. Develop an understanding of different problem types. Slide 3 Learn a variety of strategies for solving addition and subtraction problems. Experience different models that support students thinking about addition and subtraction strategies. This is the standard list of Group Norms established by the ESD. It may also be helpful to have these printed on chart paper or at each individual table. You may also want to ask if participants have any to add. Slide 4 ESD 123 Mathematics Content Training Package Slide# Slides Notes Explain the use of the parking lot. There are two effective ways to use this feature. One is to post a piece of chart paper on the wall and provide sticky notes at each table. If someone has a question and doesn’t want to ask it at that time or if a participant thinks of a question that wouldn’t be appropriate to ask at that time, he or she can write it on the sticky note and put it on the Parking Lot paper when convenient. Facilitators should review those questions and Slide 5 address them after breaks for before the session ends. The second option is to provide one or two Parking Lot sheets of paper at each table. Participants can add questions or comments at any time. Facilitators must retrieve those papers in order to respond after breaks for before the session ends. This slide has been used in presentations for many years by OSPI. It is a reminder that all the content training in the world won’t be nearly as helpful to students unless they see a reason for it. Slide 6 ESD 123 Mathematics Content Training Package Slide# Slides Notes This is a very brief review of the Washington State K-8 Math Standards. Slide 7 This section takes 20 min The intent of this slide is to communicate that the current standards were designed to balance concepts, procedures, and processes throughout. If you need help in explaining this idea, refer to the Standards Training facilitator notes. Essentially, the idea is for students to have a strong understanding of mathematical concepts, know how to use appropriate mathematical procedures, and use mathematical processes to Slide 8 reason and solve problems. ESD 123 Mathematics Content Training Package Slide# Slides Notes This might be a good time to have participants open up their standards or strands documents. Briefly remind them of the structure and components of the standards. Slide 9 It is important to have participants look Operations Number Strand: through the documents to find where K..2.C, K.2.D K.1.C, K.1.H, 1.1.F the content for this session is located. 1.2.A, 1.2.C, 1.2.D, 1.2.E, 1.2.F, 1.2.G, Slide 10 Included to the right are standards in 1.2.H 2.2.A, 2.2.B, 2.2.C, 2.2.D, 2.2.E, 2.2.F, 2.2.G Number Strand addressing decomposing Numbers. ESD 123 Mathematics Content Training Package Slide# Slides Notes Slide 11 This section takes 30 min Participants model problem types with manipulatives. (tiles, cubes or any object) Remind them to model problem as it is written following semantic structure of the problem. Slide 12 ESD 123 Mathematics Content Training Package Slide# Slides Notes Participants use sheet of problem types and Problem type framework to determine where the problems fit on the framework. Monitor groups and provide clarification where needed. After table group discussion, share briefly whole group. Slide 13 During discussion, draw out importance of students having opportunity to work with all problem types. Participants describe how they modeled unknown change problem. They then describe what they would enter into calculator to solve the problem. Slide 14 How are those two alike? In both equations we know the parts and we are looking for the whole. 5 min Discuss the ability to use inverse relationship in order to solve with calculator. Experience with all problem types helps develop part-whole relationship. We can only use inverse if we understand part-whole relationship. ESD 123 Mathematics Content Training Package Have participants think about a short definition for each term. Discuss Van de Walle definition. Slide 15 How is that definition different from what we typically think of as addition and subtraction? 4 min Reflect back on problem types and developing part-whole relationship. If there is a meal provided, people need to move quickly since the break will only last 30 minutes. If no meal is provided, the break time can be cut to 15 minute (but don’t forget to change the time on the slide.) Slide 16 30 Min ESD 123 Mathematics Content Training Package This following section of presentation is about using physical and visual models of thinking for Addition and Subtraction. Slide 17 This section takes 30 min Composing and decomposing numbers helps develop part-whole relationship needed for addition and subtraction. Standards K.1.C and 1.1.F are about composing and decomposing numbers. Discuss variety of models, activities for developing composing/decomposing. Coverup, In/Out, Slide 18 etc. Amount of time spent on decomposing/composing dictated by grade levels in audience. Big idea here is that when we keep the quantity constant students are more likely to see part- whole relationship. ESD 123 Mathematics Content Training Package Discuss each strategy. If participants are unfamiliar with these strategies spend more time with examples on document camera. Slide 19 7 min There are two ways to approach development of Fact Strategies. One is to work with simple story problems with numbers chosen to lead toward a strategy. Another is to have short lessons using a focused collection of similar facts (Number String) or focused strategy. Slide 20 Example of a Number string would be: 4+4, 3+4, 4+5, 5+4, 6+6, 6+7, 5+6. The idea being to This build on the double to near doubles. 4+4 is 8, so 3 + 4 will be 1 less than 8 or 7. Or, 4 +5 will be section one more, 9. takes 10 min ESD 123 Mathematics Content Training Package This slide is intended to introduce the rekenrek model which builds on structures of 5. Model developed in Netherlands. Uses structure of 5 as it can be subitized. Model use of the rekenrek with problems for subitizing up to 5, then decomposing/composing numbers to 10 and then higher. Also model mental strategies. Slide 21 Model on board moving from rekenrek to open ended number line. 10-12 min See Minilessons for Early Addition and Subtraction, Fosnot, for more information on rekenrek or arithmetic rack. Participants make their own rekenrek strings and model each of the mental strategies on the next slide. Slide 22 Additional number strings for developing mental strategies are available in Mini-lessons for This Early Addition and Subtraction, Fosnot. section takes 20 min ESD 123 Mathematics Content Training Package Put this slide up as participants are working with beaded strings to help them see strategies. Circulate and elicit language used to model. Bring group together to discuss developing number strings to model. Number strings are small focused groups of related facts designed intentionally to build a particular strategy. Slide 23 Another model of 5 structure is the Fives frame. After showing slide, build several numbers with Fives Frame on document camera. Slide 24 Be sure to show composing and decomposing 5-8. [I need some examples.] Handout for Fives Frame ESD 123 Mathematics Content Training Package This slide shows using tens frame to compensate and make friendly tens strategy. After slide you model 2-3 tens frame problems with counters. Then use prepared tens frames Slide 25 with dots. Then pair equations with cards, then finally just equations. Remind participants to bridge from concrete to visual to symbolic. This section You will need Tens frames with preprinted dots for this slide. takes 10 min This slide is about using addition to solve subtraction. Again understanding part-whole relationship and inverse. Slide 26 Have participants solve a few subtraction problems at their table by thinking addition. Share. This section takes 3 min 17 – 8, 12 – 7, 14- 9, 15 - 8 ESD 123 Mathematics Content Training Package Strategies can be extended to use for 2 digit equations (and more). After this slide, use document camera. Write one problem at a time from the set of problems below. As participants solve mentally Slide 27 they put up a silent thumb. When everyone has had a chance to solve one way, participants This slide share their answers and their strategies for solving. You record their strategies. takes 10 As you record strategies point out strategies related to the ones discussed earlier. min 29 + 37, 53 -25, 46-28, 57 + 19 Explore these problems using the document camera. Allow participants time to ask questions. These will probably be about the last section you just presented but it could be about anything during the day. You may want to mention that you have some Parking Lot questions that you will be answering next (if you have any). Slide 28 ESD 123 Mathematics Content Training Package Have index cards or note paper available. Allow participants enough time to complete reflection. Slide 29 You may ask participants to share in groups if time. This section takes 10 min Answer these from the papers on the tables or the post-its (whichever format you chose for the day). You may also want to ask if there was a question that was posted but didn’t get answered. Slide 30 ESD 123 Mathematics Content Training Package Pass out the clock hour evaluation form to everyone. Stress that the ESD (and you) would love to have good feedback on this workshop so that we can improve it for the next time. You will want to be quiet during this time so that they can fill this out thoughtfully. After explaining the process they need to follow with the forms, mention that you will put up the next slide so that they will have the option of writing down resource information as they Slide 31 finish their evaluations. As the evaluations are done, display this final slide (with your own resources, of course) so that participants will have a list of the activities you used in the presentation and where you got them. It is also appropriate to give credit to the author of a particular game or activity. You may want to expand this to include resources for further study in case participants want to learn more on their own. Slide 32 Congratulations!!
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