Addition _ Subtraction by pengxiang


									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


              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
     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:
                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.


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

                           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

                           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

                           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

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

takes 20

                           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

ESD 123 Mathematics Content Training Package
Slide#        Slides                                                   Notes

Slide 11

takes 30

                           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
 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

takes 30

                           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

                           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
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.
  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.
takes 20
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.
 section                   You will need Tens frames with preprinted dots for this slide.
takes 10

                           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.

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.
                           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

Slide 29                   You may ask participants to share in groups if time.

takes 10

                           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

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


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