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Alternate Assessment Curriculum FrameworkIntroduction
The D75 Alternate Assessment Curriculum Framework was developed in response to schools’
requests for instructional expectations connected to the Common Core Learning Standards
(CCLS) for students in Alternate Assessment classes. Groups of teachers, administrators, and
district content area coaches gathered for four weeks during the summer of 2013, and
participated in a collaborative process to create an Alternate Assessment Curriculum
Framework. The process included a workshop at the beginning of each week to train the group
in the leveled learner concept (Levels B, C, and D), resources available (developmental math
skills progressions, Webb’s Depth of Knowledge, Common Core Essential Elements and
Alternate Achievement Descriptors for Mathematics from the State Members of the Dynamic
Learning Maps Alternate Assessment Consortium and Edvantia, Inc.), and final product
expectations. Subsequently, small groups collaborated to develop the leveled learning plans
and activities, culminating performance tasks, and the introductory contexts for the different
modules.
The structure of the framework provides four modules in ELA, Math, Science, and Social
Studies created in grade bands (K-2, 3-5, 6-8, and High School). Four math modules have been
developed as grade specific modules for K-8, while High School modules reflect specific
conceptual categories.
Each module consists of:
a context overview
culminating performance tasks for each level
Common Core Learning Standards connections
Career Development and Occupational Studies (CDOS) standards connections
Content standards connections
essential questions
key vocabulary
lesson strands with leveled learning plans and activities for each
Resources list
materials lists
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Underlying the development of the activities included in this document is the profound
belief that students with significant intellectual disabilities need high standards that are
reasonable and achievable given sufficient and appropriate opportunities to learn. All students
who participate in Alternate Assessment classes are expected to be provided with access and
exposure to the content learning expectations of their general education peers at a reduced
depth, breath and complexity. The presented tasks, while not reflecting the degree of higher
order skills and comprehensiveness of expectations established for students participating in the
general assessment system, do reflect reasonable and achievable expectations for students
with significant intellectual disabilities. In addition, they maintain a necessarily broad
connection with the Common Core Standards through a concentrated focus on salient features
of specific Standards. These content area sample learning plans and activities are designed not
only to elicit performances of content area thinking skills/behaviors but also to provide
opportunities for students to engage with, read and/or use content understandings that are
imbedded within the tasks.
The sample learning plans and activities for each strand have been divided into three distinct
levels of student expectations based on cognitive abilities: Level D, Level C, and Level B.
Level D learning plans and activities are reflective of students who experience the most
significant cognitive disabilities within our district. These students are typically working at the
engagement level. Instruction is typically focused on developing the accessing skills that a
student needs to possess. It is understood that for additional information processing to take
place, engagement is a necessary first step. (Please refer to the Essential Thinking Skills and
Behaviors Explanatory Notes document for further information regarding the concept of
Engagement).
Level C learning plans and activities are reflective of students who demonstrate the
essential thinking skill of conceptualization. These students can form mental representations
of a concept and apply this knowledge. They exhibit intentional behavior in response to
situations. They rely heavily on objects, picture cues, a print rich environment, and an exposure
to content in multiple and modified formats to facilitate learning. These students typically work
within Level one and two in Webb’s Depth of Knowledge. (Please refer to the Essential
D75 Alternate Assessment Curriculum Framework 7th Grade Math Module 4: Statistic and ProbabilityPage 2
Thinking Skills and Behaviors Explanatory Notes document for further information regarding
the concept of conceptualization, and Webb’s Depth of Knowledge).
Level B learning plans and activities are reflective of students who demonstrate skill abilities
closest to meeting the CCLS and content standards expectations as they are written. These are
typically students who may participate in inclusion settings and students who may return to
community based instruction programs. These students would be expected to work in all levels
of Webb’s Depth of Knowledge.
The Revision of Modules
The Alternate Assessment Curriculum Framework was developed to serve as a guide for
schools. It is expected to be modified and adjusted in order to meet school-specific instructional
goals and objectives.
To assist schools with understanding what the revision process entails, the district gathered
a small group of teachers and administrators during the summer of 2014 to revise Math module
2 for third grade, sixth grade, and High School. These modules serve as guiding examples for
schools to refer to as they consider revisions to the additional modules in all content areas.
Along with these examples, a general revision protocol and a sample reflections document
from the summer revision group regarding the revision process can be found at the end of this
introduction.
Each revised Math module 2 (grades 3, 6, and HS) now consists of:
a context overview
culminating performance tasks for each level
sample rubric designs for the performance task at the varied levels
An IEP goal tracking rubric format
Common Core Learning Standards connections
Career Development and Occupational Studies (CDOS) standards connections
Content standards connections
essential questions
key vocabulary
Sequenced lesson strands with leveled learning plans and sequenced activities
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Resources list
materials lists
A sample lesson written related to one activity in one strand
It is hoped that the D75 Alternate Assessment Curriculum Framework provides teachers and
schools with a resource to better understand how students can be provided with opportunities
to develop targeted skills through content-based instructional experiences that are also applied
in the context of functional activity experiences.
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Revision Protocol
The following is a step-by-step process that schools can reference when they
begin the process of revising a module for their own use. These are generic
expectations in the order they should occur to ensure an efficient and effective
revision of a module. This is by no means the only way in which a module can be
revised, but is intended to provide the essence of what the revision process
should include and be focused around.
1. Understand the standards for the learners in your class/school.
2. Ensure the connection between the standards, the learning strands and the
performance task.
3. Ensure that the learning strands and activities within the activities are
sequenced correctly for your students.
4. Ensure that the learning activities are appropriate for each level (B, C, and D).
5. Determine and agree upon the specific considerations that must be
accounted for when creating a rubric against the performance task for Level B,
C, and D.
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A reflection Sample on “How to” Revise an Alternate Assessment Curricular
Framework Module of Study (AACF) based on the guiding protocol. 1. How do you ‘unpack’ or understand the standards for the learners in your class?Read the standards listed in the module and isolated the key nouns and verbs. Determined what the standard asking the students to know and do. Came to consensus regarding what the performance of these standards would look like for the students in alternate classes. Finally, the group translated the standard into actionable skills for the learners.2. How do you ensure connection between the standards, the learning strands and the performance task?One method the participants used was to use color-coding to ensure a connection. First, the group members color-coded each standard. Second, they looked at each learning strand and checked off, using the color system, where elements of each standard were contained in the strand. Last, they looked at the performance task, and highlighted or checked, using the color system, where elements of each standard were contained in the task. (These key elements were translated into actionable skills accessed in the rubric. See #5)If connections were not achieved, group members made a decision to reorganize, omit, add, condense or adjust as needed. 3. How do you ensure that the learning strands and activities within the activities are sequenced correctly for your students?Several resources were used, such as the CCLS Skills Progression at a Glance, Wisconsin Early Learning Skills, Equals chapter/skills sequencing, etc. (Note: please remember that the use of available resources such as language skills progressions, other content curricular models from various states, reading skills checklists, etc. should be referenced when revising other content area modules)4. How do you ensure that the learning activities are appropriate for each level (B, C, and D)?Participants referred back to Piaget’s Cognitive Levels of Development, their own students IEPs, as well as, keeping the individual needs of the learners in alternate assessment classes at the forefront of their minds When developing the learning activities for all levels.5. What should you consider for creating a rubric against the performance task for Level B, C, and D?Isolated key skills were identified in the standards and translated to actionable learning targets for the students when developing the Level C and B rubrics. Content expectations played a significant role in establishing the rubrics. Aspects of the rubric quantified skills for the B and C level learners and included a simple rating system (4-1, 3-1, etc.).It was determined by the revision group that a specific rubric that could be used across the modules for the level D student would provide teachers with the ability to track skills related to engagement. This was determined to be the best approach to tracking progress for student who are cognitively young and require mastery of those skills related to engagement before any further content knowledge acquisition could be expected.
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District 75 Alternate Assessment Curriculum Framework 7th Grade Math Module 4
Statistics and Probability
CONTEXTUNIT TOPIC: Statistics and Probability
The fourth module of the 7th grade Math Frameworks centers on statistics and probability.
Students should have ample opportunity to experience these concepts through real-life, social, hands-
on activities. Some key concepts that should be focused on include data collection, organization and
representation of the data, analyzing data and using the information to make informed decisions and
predictions.
Although the use of statistics is relatively new, no one can argue its’ importance in everyday life. The
great cholera outbreak in London, England in 1854 is a perfect example of how data collection has
influenced the population as a whole. Florence Nightingale was a pioneer in the field of gathering and
analyzing data, and used this information to determine that the outbreak originated with one well. This
helped to eradicate the disease. In present day, statistics and probability play a great role in industry,
affecting quality control. Advertising, political campaigns, and television all use statistics and
probability to make decisions which influence what is seen by the public.
The sample learning plans and activities outlined are designed not only to elicit performances of
mathematical thinking and behaviors, but also to provide opportunities for students to acquire a
concrete understanding of how probability works. Teachers should emphasize that data can be utilized
to make decisions and predictions.
The activities in this unit should be reinforced by having students work with the concepts being taught
in this unit throughout the day, and in various situations. In supporting PBIS, students can be reminded
that the probability of a desirable event occurring is highly unlikely if they display negative behaviors.
Similarly, the probability of having a special treat at the end of the day is likely if students earn all their
points for the week. In this way, students can personalize and internalize data and probability.
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ASSESSMENT
FORMATIVE ASSESSMENT EVIDENCE: Pictures of students participating in various classroom lessons and activities
Data collection
Student work samples, as appropriate
PERFORMANCE BASED ASSESSMENT TASK
Students are given a bag and a mixture of various types of clothing. Clothing can include but is not
limited to: hats, shirts, pants, unmatched socks, shoes, jackets, skirts, etc. There should be a mixture of
different colors/sizes and each piece of clothing should be a solid color (e.g. 2 blue t-shirts, 1 pair
yellow flip-flops, 3 red shirts, etc.).
LEVEL D:
Students engage with placing clothing in their bag. Students then engage in turn taking in order to pick
clothing out of the bag, one at a time. After 3 picks, students use PMC to predict what color will be
picked next. Teacher records results.
Students engage with yes (1)/no (0) paddle to answer various probability questions posed by the
teacher (e.g. Can you pick a blue shirt from the bag?-- yes(1), Can you pick a green turtle from the
bag?-- no(0), etc.).
*Extension – students engage in taking turns to pick up to 4 pieces of clothing from the bag. Students
use PMC to answer question: Can you make an outfit?
LEVEL C:In small groups:
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Before beginning, students count and record (on a chart, using PMC) the pieces of clothing (how many
of each color) they have received.
Students generate the probability of getting an item of clothing of each color (e.g. What is the
probability that you will pick a blue shirt? -- likely, What is the probability that you will pick a
purple monkey? -- impossible, etc.).
Students then place clothing into their bag and take turns picking a piece of clothing – recording
each selection on a graphic organizer.
After 3 picks, students predict and record (using a graphic organized and PMC) what color will
be picked next.
For each next piece of clothing, students test their predictions by picking next piece of clothing
and recording their results (on graphic organizer).
Repeat this until all items of clothing are removed.
Students then share their results with the class –How many did you guess right? How many did
you guess wrong?
*Extension – students take turns to pick up to 4 pieces of clothing from the bag. Students answer
question: Can you make an outfit?
LEVEL B: In pairs: Before beginning, students count and record the number of each color and piece of clothing
they have on a chart.
Students generate the probability statements based on their data (e.g. It is likely to pick a blue
shits, It is unlikely to pick red shorts, etc.).
Students then generate probability statements using fractions for each color of clothing they
have. Then again for each type of clothing they have. (e.g. the probability of picking a yellow
sock is 1/10, the probability of picking a hat is 4/10, etc.)
Students then place clothing into their bag and take turns picking a piece of clothing – recording
each selection on a graphic organizer.
After 3 picks, students predict and record what color will be picked next.
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For each next piece of clothing, students test their predictions by picking next piece of clothing
and recording their results (on graphic organizer).
Repeat this until all items of clothing are removed.
Students then write about their results using the following guiding questions:
1. How many did you guess right? Wrong?
2. How did you decide what prediction to make?
3. What did you notice as you were completing this project?
4. What could you have done to make better predictions?
*Extension – students take turns to pick up to 4 pieces of clothing from the bag. Students answer
question: Can you make an outfit? How can you increase your chances of making an outfit (e.g.
adding/removing a piece of clothing from the bag)?
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*See explanatory notes of “engagement” in The Essential Thinking Skills and Behaviors
Document.
STANDARDS
MATH COMMON CORE LEARNING STANDARDS:7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses
the likelihood of the event occurring.
7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that
produces it and observing its long-run relative frequency, and predict the approximate relative
frequency given the probability.
7.SP.7. Develop a probability model and use it to find probabilities of events.
7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and
simulation.
MATH COMMON CORE PRACTICE STANDARDS
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
MATH KEY IDEAS
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Summarize, represent, and interpret data on a single count or measurement variable. Summarize,
represent, and interpret data on two categorical and quantitative variables.
Interpret linear models.
CAREER DEVELOPMENT AND OCCUPATIONAL STANDARDS
2.1: Integrated learning encourages students to use essential academic concepts, facts, and procedures
in applications related to life skills and the world of work. This approach allows students to see the
usefulness of the concepts that they are being asked to learn to understand their potential application
in the world of work.
3a.1: Universal Foundation Skills Intermediate: Basic skills include the ability to read, write, listen, and
speak as well as perform arithmetical and mathematical functions.
ESSENTIAL QUESTION: 1. How can we use data to make decisions and/or represent patterns and trends in real world
situations?
VOCABULARY:
LESSON STRANDS OVERVIEWD75 Alternate Assessment Curriculum Framework 7th Grade Math Module 4: Statistic and ProbabilityPage 12
Cards
Certain
Chart
Coin
Data
Die/Dice
Graph (bar, line, picture, pie,
histogram, etc.)
Impossible
Likelihood
Likely
No (0)
Predict/Prediction
Probability
Spinner
Survey
Unlikely
Yes (1)
1. Collect and display data.
2. Determine that the probability of an event occurring as certain (yes/1) or impossible (no/0).
3. Determine the probability of an event occurring (likely/unlikely/impossible).
4. Making predictions based on data.
LEARNING PLANS AND ACTIVITIES
NOTE: Preferred Mode of Communication (PMC) should be considered for all students
in all activities across all levels.
Lesson Strand 1: Collect and display data.
LEARNING PLANS AND ACTIVITIES LEVEL D: Engage in collecting data by using PMC (i.e. picture symbols, programmatic device, etc.) to ask
the data question and/or placing objects/pictures/symbols in appropriate place on a given data
collection template (can be on Smartboard, large scale on board, etc.). Data will be collected
on:
o Daily attendance - How many students are in school today? – Students engage with
pictures/objects/etc. (i.e. using Smartboard to move students “into” school, move
students’ pictures to “in school” on a T-chart, etc.)
o Daily weather – What is the weather like today? - both temperature and condition.
o Classmates’ favorite colors – What is your favorite color?
o Classmates’ heights – What is your height? – Students can engage in measuring each
other’s height
o Number of siblings each classmate has – How many brothers/sisters do you have?
o Classmates’ favorite subject/school activity – What is your favorite subject?
o Classmates’ favorite snack and favorite hobby – What is your favorite snack? Hobby?
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o Classmates’ favorite sport and favorite team – What is your favorite sport? Team?
o Classmates’ favorite singer and favorite song – Who is your favorite singer? Song?
**For survey questions, students can be presented with an array of choice (i.e. “what is
your color” – red or blue).
Engage with materials (objects, pictures, etc.) in order to display collected data on graph/chart
(bar graph, pictograph, pie chart, etc.) – can use Smartboard, large scale graph, etc.
Engage with materials in order to label parts of a graph/chart – using pictures/symbols, etc. (i.e.
label title, number of people, etc.).
LEARNING PLANS AND ACTIVITIES LEVEL C: Participate in creating survey questions using picture symbols/sentence strips. Possible
questions can include:
o What is your favorite color?
o What is your height/weight? – Students can measure each other’s’ height if unknown
o How many brothers/sisters do you have?
o What is your favorite school subject?
o What is your favorite snack?
o What is your favorite hobby?
**Students can be presented with an array of choices to answer questions.
Participate in collecting data by asking survey questions and recording data on a given data
collection template.
In small groups, select a survey question to display/graph. Create a graph/table to represent
that data (bar graph, pictograph, pie chart, etc.). Students can be given a graph template to aid
them.
Label parts of a graph/chart – using pictures/symbols, etc. (i.e. label title, number of people,
what information was collected?, etc.).
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In small groups, collect 2 sets of data (unrelated or related – i.e. favorite sport/team, favorite
singer/song, etc.) using data collection templates and pictures/symbols/etc.
In small groups, display the 2 sets of data on a graph /chart (i.e. two-way table, scatter plot).
LEARNING PLANS AND ACTIVITIES LEVEL B: In small groups, create survey questions. Possible questions can include:
o What is your favorite color?
o What is your height/weight? – Students can measure each other’s’ height if unknown
o How many brothers/sisters do you have?
o What is your favorite school subject?
o What is your favorite snack?
o What is your favorite hobby?
Collect data by asking survey questions and recording data (students can be supplied with a
graphic organizer to help them record data).
In small groups, select a survey question to display/graph. Create a graph/table to represent
that data (bar graph, pictograph, pie chart, etc.). Students generate statements about what
they have displayed (i.e. more students like gym than math, more students like Oreos than
chocolate chip cookies) – possible guiding question(s): What do you notice? What trends do you
see? What is the data telling you?
In small groups, collect 2 sets of data (unrelated or related – i.e. favorite sport/team, favorite
singer/song, eye color/height, etc.).
In small groups, display the 2 sets of data on a graph /chart (i.e. two-way table, scatter plot).
Students generate statements about the relationship(s) between two sets of data (i.e. most
students who like football like the Giants, in our class, students with brown eyes are tallest,
most students who like Justin Bieber like his song “Baby” best, etc. ) – possible guiding
question(s): What do you notice? What trends do you see? What is the data telling you?
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Lesson Strand 2: Determine that the probability of an event occurring as certain (yes/1) or
impossible (no/0).
LEARNING PLANS AND ACTIVITIES LEVEL D: Attends to probability song – “Tell the Future” – http://www.flocabulary.com/probability/
Students are given paddle with “yes(1)” on one side and “no(0)” on other – students engage
with paddle to rate whether the following situations are certain or impossible:
o Sunday to come after Monday
o Having lunch
o Going to bed at night
o Snow in summer
o Getting a blue ball from a bag of all blue balls
o Getting a red marble from a bag of all yellow marbles
**Teacher can add more to this list.
Engage with materials in “mystery bag” containing all one-color objects (i.e. red balls, blue
marbles, yellow fish, etc.).
Engage with turn taking to pick items from “mystery bag” - teacher records the number of each
color on chart.
Engage with a voice output/programmatic device to answer probability questions based on
“mystery bag” (i.e. in a bag of all blue marbles, Can you pick a yellow marble? – “no”, Can you
pick a blue marble? – “yes”, etc.).
LEARNING PLANS AND ACTIVITIES LEVEL C: Attends to teacher’s introduction of probability – “We have been learning to collect and display
data – now we will learn to make choices and predictions based on data”
Listens to probability song – “Tell the Future” – http://www.flocabulary.com/probability/
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Participate in completing word search containing probability related vocabulary:
http://www.learninggamesforkids.com/math_games/4th-grade-math/data-statistics-4th/data-
statistics-word-search-4th.html
Practice probability vocabulary and definitions at
http://www.learninggamesforkids.com/math_games/4th-grade-math/data-statistics-4th/data-
statistics-word-o-rama-4th.html
Using a rating sheet, students participate in rating the following as impossible [no(0)] or certain
[yes(1)]:
o Sunday to come after Monday
o Snow in summer
o Getting a blue ball from a bag of all blue balls
o Getting a red marble from a bag of all yellow marbles
o When rolling one die – getting a 7
o When rolling one die – getting a 6
**Teacher can add more to this list.
LEARNING PLANS AND ACTIVITIES LEVEL B: Attends to teacher’s introduction of probability – “We have been learning to collect, display,
and analyze data – now we will learn to make choices and predictions based on data”
Listens to probability song – “Tell the Future” – http://www.flocabulary.com/probability/ – and
reads lyrics.
Complete word search containing probability related vocabulary:
http://www.learninggamesforkids.com/math_games/4th-grade-math/data-statistics-4th/data-
statistics-word-search-4th.html
Practice probability vocabulary and definitions at
http://www.learninggamesforkids.com/math_games/4th-grade-math/data-statistics-4th/data-
statistics-word-o-rama-4th.html
D75 Alternate Assessment Curriculum Framework 7th Grade Math Module 4: Statistic and ProbabilityPage 17
In small groups, students create a list of events that are certain [yes(1)] and impossible [no(0)] –
students can use a graphic organizer. Examples can include: Sunday to come after Monday,
snow in summer, getting a blue ball from a bag of all blue balls, getting a red marble from a bag
of all yellow marbles, when rolling one die – getting a 7, when rolling one die – getting a 6,
getting 5 kings from a standard deck of cards, getting 4 queens from a deck of cards, etc.
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Lesson Strand 3: Determine the probability of an event occurring (likely/unlikely/impossible).
LEARNING PLANS AND ACTIVITIES LEVEL D: Engage with flipping a coin – either with a coin, a large scale coin, or using technology (see
resources).
Activate switch to roll die at http://nces.ed.gov/NCESKIDS/chances/index.asp
Active programmatic device to define probability as chance event will occur using voice output
device.
Engage with die or dice if rolling dice
Active switch/button to turn spinner with 2 or 4 choices
Engage with materials (paddle, etc.) in order to state what happened in the following
probability situations:
O When rolling a die, use paddle with numbers/number cards to sate the number on die
O When flipping a coin, use head and tail symbols on a paddle to say if the coin landed on
heads or tails
Given a bag of red and black objects (i.e. red balls and black balls) choose red or black using two
choices symbols to say which color was pulled picked by teacher
Engage with materials in “mystery bag” – as students pick different colored objects, teacher
records the number of each color on chart.
Engage with going “fishing”. Given a “pond” (can just be a large bowl or a small blow-up pool)
with various colors of “fish” (can be made out of paper/plastic/etc.), engage with materials (i.e.
fishing pole) to “fish” for the different colors of fish in the pond. Teacher records class results
on chart.
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LEARNING PLANS AND ACTIVITIES LEVEL C: Participate in completing probability sheet found at
http://flocabulary.s3.amazonaws.com/pdfs/probability-exercises.pdf
Participate in Classroom Suite activities “Color Bug Race Game,” “Coin Toss” Classroom Suite
activity, “Flip the Coin” http://aex.intellitools.com/searchdetails.php?act_key=flipthecoin
Define probability as “chance event will occur”
Distinguish heads and tails, colors (or variables) on Spinner, numbers on die
Count dots on die
Write number after counting dots
In small groups, use a graphic organizer to record results from flipping a coin, rolling a die,
choosing a card (red or black), using a spinner.
In small groups, decide how many times to roll a die. Roll the die and for each time record
results on a graphic organizer. Go to website (http://nces.ed.gov/NCESKIDS/chances/index.asp)
and answer following questions as a group: What number did you roll most? What number did
the website roll most?
In small groups, given a bag of various colored marbles, take turns picking marbles. Record
results on a graphic organizer.
Use picture symbols/word cards with likely/unlikely to identify possibility of event occurring
(i.e. probability of rolling a 3, getting tails, getting a red card, given a red marble and a red
marble what is probability or choosing a red marble, etc.).
In small groups, use a graphic organizer (i.e. T-chart with Likely/Unlikely written on top) to rate
the following real-life events as likely or unlikely (teacher can add more):
O Given a bag containing 5 Oreo cookies, 3 oatmeal cookies and 1 chocolate chip cookie -
likelihood of pulling out an Oreo cookie/chocolate chip cookie/Oatmeal cookie
O Given a sunny day – likelihood of it raining
O Likelihood of play video games all night
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LEARNING PLANS AND ACTIVITIES LEVEL B: Complete probability sheet found at http://flocabulary.s3.amazonaws.com/pdfs/probability-
exercises.pdf
Define probability as “chance event will occur”.
Write probability formula Probability = number of desired outcomes/total outcomes possible
In small groups, discuss the probability of flipping a coin and getting heads (then tails). Decide
how many times to flip a coin – begin flipping coin and take data on a graphic organizer. Answer
questions as a group (How many times did you flip the coin? What were your results? What is
the probability of flipping a coin and getting tails? Head?) and report results to class.
Classroom Suite activities “Color Bug Race Game,” “Coin Toss” Classroom Suite activity, “Flip
the Coin” http://aex.intellitools.com/searchdetails.php?act_key=flipthecoin
In pairs, decide how many times to roll a die. Roll the die and for each time record results on a
graphic organizer. Go to website and compare group’s results to the website’s results
(http://nces.ed.gov/NCESKIDS/chances/index.asp). Record findings on a graphic organizer and
report to class.
In pairs, take turns spinning a spinner/top with four sides – each side containing different
symbols/colors (can also use Dreidel). Record results and answer the following questions:
o What is the probability of getting red? blue? yellow? green?
o If you spin the spinner 9 times, what is the probability of getting a red or a blue?
o If you only roll the spinner 2 times, what are all the possible combinations?
**Teacher can add more questions.
In pairs, after being given a bag containing 5 Oreo cookies, 3 oatmeal cookies and 1 chocolate
chip cookie, decide the probability of getting:
o An Oreo cookie (5/9)
o A chocolate chip cookie (1/9)
o An oatmeal cookie (3/9=1/3)
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o An Oreo cookie or an oatmeal cookie (8/9)
o An oatmeal cookie and a chocolate chip cookie (4/9)
**Challenge**In pairs, after being given a drawer of unmatched socks contains 19 blue socks
and 11 green socks and 9 white socks, without looking, decide the probability of getting:
o A blue sock (19/39)
o A green sock (11/39)
o A white sock (9/39)
o A blue or white sock (28/39)
o A green or white sock (20/39)
o A blue or green sock (30/39)
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Lesson Strand 4: Making predictions based on data.
LEARNING PLANS AND ACTIVITIES LEVEL D: Teacher puts items into “mystery bag” – showing each item to students (paired with picture
symbols). Teacher begins to pull items out of bag one at a time. Students engage with a
programmatic device to predict the next item the teacher will pull out.
In small groups, students engage with large die by rolling it (can use AAC device to ask para to
roll, physically roll, etc.). Before each roll, students engage with number card to predict next
roll.
Given a large spinner (i.e. All-Turn-It spinner) with 4 sections – each section a different color,
students engage with spinning spinner. Before each spin, students engage with color cards
and/or programmatic device to predict next spin.
Attend to the poem Closet Full of Shoes. In small groups, given a bag full of shoes, engage with
shoes by removing them one at a time from bag. Before each turn, students engage with
pictures/symbols/programmatic device/etc. to predict what color shoe will be picked next.
LEARNING PLANS AND ACTIVITIES LEVEL C: In small groups, take turns rolling a die and collect data (record results of each experiment on
graphic organizer). Before each roll, predict what number will be next (can use number cards).
In small groups, take turns flipoing a coin and collect data (record results of each experiment on
graphic organizer). Before each flip, predict what will be next (can use picture symbols).
In small groups, take turns picking a card form a standard deck and collect data (record results
of each experiment on graphic organizer). Before each pick, predict what will be next (can use
picture symbols).
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Listen to the poem Closet Full of Shoes. In small groups, given a bag full of shoes, take turns
picking a shoe out of the bag. Before each pick, predict what will be next (can use picture
symbols).
Listen to the book Do You Wanna Bet? by Jean Cushman (teacher can pick a section to read, if
you start from the beginning of the book, read the section, "One Out of Two: Heads or Tails").
Extension – Participate in predicting results from flipping a coin, rolling a die, choosing color of
card suit using “What are My Chances” worksheet
http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/
WhatAreMyChances-AS.pdf
LEARNING PLANS AND ACTIVITIES LEVEL B: In pairs, collect data (record results of each experiment on graphic organizer) and make a
prediction:
o Roll a die 10 times. What is the probability of rolling a 3 on your next roll?
o Test predictions by rolling die again. Record results.
o What is the probability of rolling 2 sixes in a row with a single die?
o Test predictions by rolling die again. Record results.
o Roll 2 dice 10 times. What is the probability of rolling an even number? Odd number?
o Test predictions by rolling dice again. Record results. Share results with class.
In pairs, collect data (record results of each experiment on graphic organizer) and make a
prediction:
o Flip a coin 15 times. What is the probability of getting tails when you flip a coin on your
next flip? Heads?
o Test predictions by flipping coin again. Record results.
o What is the probability of getting tails 4 times in a row while flipping a coin?
o Test predictions by flipping coin. Record results. Share results with class.
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In pairs, collect data (record results of each experiment on graphic organizer) and make a
prediction:
o Pull 10 cards from a standard deck, one at a time. What is the probability of pulling a
jack, queen or king on your next chance?
o Test predictions by picking another card. Record results.
o What is the probability of getting a 2 on your next chance?
o Test predictions by picking another card. Record results. Share results with class.
Read the poem Closet Full of Shoes. In small groups, given a bag full of shoes, return one
orange shoe and one green shoe to the bag. Answer following questions and record response:
o What is the probability
o Put two orange flip-flops and 2 green in the bag. What is the probability of someone
drawing an orange flip-flop out of the bag now? Green? Do I have a better probability of
picking orange now?
o Add 3 blue, 2 black and 1 yellow flip flop to the bag. How many black flip flops would
need to be added to the bag so that the probability of drawing a black flip flop is ½?
Given the book Do You Wanna Bet? by Jean Cushman, in pairs, pick a section of the book to
read. (If you start from the beginning of the book, read the section, "One Out of Two: Heads or
Tails".)
Extension – Predict results from flipping a coin, rolling a die, choosing color of card suit using
“What are My Chances” worksheet
http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/
WhatAreMyChances-AS.pdf
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MATERIALS Classroom Suite activities “Color Bug Race Game,” “Coin Toss” Classroom Suite activity, “Flip
the Coin” http://aex.intellitools.com/searchdetails.php?act_key=flipthecoin HTTP://
ILLUMINATIONS.NCTM.ORG/ACTIVITY.ASPX?ID=3537
http://flocabulary.s3.amazonaws.com/pdfs/probability-exercises.pdf ~~ Probability Worksheet
http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/
WhatAreMyChances-AS.pdf
HTTP://JMATHPAGE.COM/JIMSPROBABILITYPAGE.HTML
http://mathandreadinghelp.org/teaching_probability_to_kids.html
http://mrnussbaum.com/coolgraphing - more graphs
HTTP://MRNUSSBAUM.COM/GRAPHMASTER-IPAD.HTML - Creates various graphs based on
data entered
http://nces.ed.gov/NCESKIDS/chances/index.asp
http://nces.ed.gov/NCESKIDS/chances/index.asp
HTTP://NCES.ED.GOV/NCESKIDS/CREATEAGRAPH/DEFAULT.ASPX
HTTP://NLVM.USU.EDU/EN/NAV/FRAMES_ASID_186_G_2_T_5.HTML?OPEN=ACTIVITIES
HTTP://RESOURCES.WOODLANDS-JUNIOR.KENT.SCH.UK/MATHS/HIGHER-LOWER/
HTTP://WWW.EDUCATION.COM/ACTIVITY/PROBABILITY-STATISTICS/
http://www.learninggamesforkids.com/math_games/4th-grade-math/data-statistics-4th/data-
statistics-word-search-4th.html
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http://www.livingmath.net/ReaderLists/ProbabilityStatGraphsDataFactorials/tabid/390/
language/en-US/Default.aspx
http://www.mathsisfun.com/data/survey-conducting.html ~~Steps on How To Do a Survey with
students.
HTTP://WWW.MATHSISFUN.COM/PROBABILITY_LINE.HTML
HTTP://WWW.MATHWIRE.COM/DATA/DICETOSS1.HTML
http://www.nctm.org/ ~~ NCTM. National Council of Teachers of Mathematics
HTTP://WWW.PEARSONSCHOOL.COM/LIVE/IMAGES/CUSTOM/ENVISIONMATH_CA/GAMES/
POND.HTML
HTTP://WWW.SHODOR.ORG/INTERACTIVATE/ACTIVITIES/RACINGGAMEWITHONEDIE/
HTTP://WWW.TEACHERLED.COM/RESOURCES/DICE/DICELOAD.HTML - virtual dice
www.BrainPop.com/educators ~~ mapped to the common core, this website provides
interactive learning.
http://www.kidsmathgamesonline.com/numbers/probability.html
MANIPULATIVES Balls
Coins
Data collection sheets
Deck of cards
Dice
Fish cutouts
Graphic organizers
Graphing paper
Marbles
Number lines
Pictures/items as required by each lesson
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Rulers
Spinner (object or website)
Surveys
Various coins
Weather symbols
BOOKS (including but not limited to)
**The following books are meant to give ideas for concepts to create adapted books, which would
be more age-appropriate for the students at the high school level.
Tally O'Malley by Stuart Murphy and Cynthia Jabar
Lemonade for Sale by Stuart Murphy and Tricia Tusa
The Great Graph Contest by Loreen Leedy
Graphs: All Aboard Math Reader by Bonnie Bader and Mernie Cole
Less Than Zero by Stuart Murphy and Frank Remkiewicz
Who's Got Spots by Linda Aber and Gioia Fiammenghi
Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Cindy Bickel
Harriet’s Halloween Candy by Nancy Carlson
A Closet Full of Shoes and Picture Puzzle Piece by Shel Silverstein
Probably Pistachio by Stuart J. Murphy
Do You Wanna Bet? by Jean Cushman
Teacher Resource Books:
The Complete Book of Graphing by Douglas C. McBroom
Great Graphs and Sensational Statistics: Games and Activities that Make Math Easy and Fun
by Lynette Long
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VIDEO Bill Nye Video about Probability (advanced)~~ https://www.youtube.com/watch?
v=Sqq4k50dxbI
Drawing Graphs ~~ www.youtube.com/watch?v=sSG8C2vKIg8
Probability Song ~~ https://www.youtube.com/watch?v=0xm1SDlnvh4
Probability Video (advanced) ~~ https://www.youtube.com/watch?v=usY1oY0bWQ8
Probability Video ~~ https://www.youtube.com/watch?v=QpfMwA0z_1Y
Song and video~~ http://www.flocabulary.com/probability/
Various math concepts ~~ pbskids.org/cyberchase/videos
**The following videos may be inappropriate for students’ cognitive levels, and are meant as a
resource for teachers:
Another Probability Lesson ~~ https://www.youtube.com/watch?v=rlUZXrJGuf8
How to Teach Probability Using M&Ms ~~ https://www.youtube.com/watch?v=ijbuU75wiVo
Monty Hall Problem ~~ https://www.youtube.com/watch?v=mhlc7peGlGg
Probability 101 ~~ https://www.youtube.com/watch?v=YpvE0Co66nU
Probability for Kids ~~ https://www.youtube.com/watch?v=lN6dkVRzsZA
Probability Lesson ~~ https://www.youtube.com/watch?v=ihH7ZXemEdI
Statistics: Decisions Through Data: Unit 1 What is Statistics? ~~
www.neok12.com/php/watch.php?v=zX0761455c61787e6542705d&t=Statistics
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Essential Thinking Skills and Behaviors: Definitions and Explanatory Notes
EngagementEngagement is a behavior involving the focusing of the mental process upon someone or something. It is commonly demonstrated by a voluntary and sustained or repeated attention to stimuli. Engagement may be expressed through a wide variety of sensory, motor and/or speech, communication and language forms. Student’s physical, emotional, cognitive, social and cultural development impact significantly on the nature of the attention they are able, or choose, to demonstrate. Therefore, individual modes of student engagement need to be identified, taught, developed, refined, and/or expanded upon. These modes may include, but not limited to: exploration through touching, listening, looking, smelling, and/or tasting; and increase/decrease or initiation/cessation of body movement; and vocalizations/verbalizations. Without engagement, additional information processing cannot take place.
Explanatory Notes: When providing students with opportunities for engagement it is critical that the same
opportunities be presented daily over time. Variation in the means of story presentation, along with increased familiarity with expectations, should serve to sustain student motivation and interest. In addition, the presentation of materials should be supplemented with ongoing, direct instruction to facilitate targeted skills and behaviors specific to the content area.
Emphasis should be placed on relating meaningful activities/materials to student’s prior knowledge and experience.
Extensive efforts should be placed on involving, to the greatest extent possible, a student’s family in providing opportunities for student engagement. Such efforts might include: planning instructional materials; inviting family members to read stories in class; planning family related fairs; encourage family members to learn about and visit public and other community resources; and responding to educational needs as expressed by a student’s family.
Each student should possess a public library card, and be a member of other community organizations when appropriate and feasible.
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Environmental Differentiation
Environmental Differentiation is the recognition of differences in the attributes of things/places with which, and individuals with whom, one comes in contact and includes recognition of self as a distinct entity. It is usually demonstrated by distinct patterns of exploration or reaction to different stimuli and may be evidenced through various modes of student response. Environmental Differentiation may, but does not necessarily, include knowledge of the names/functions of the materials/places/individuals involved.
Explanatory Notes: The purpose for having students learn to differentiate is to help them develop a basis from which
they will be able to use materials functionally, make informed choices and develop concepts related to materials. However, instruction related to Environmental Differentiation should not preclude instruction toward other essential skills or behaviors (e.g. Functional Use of Objects; Self Regulation).
When various content area materials are being functionally used by a student, the student is already demonstrating environmental differentiation.
For a student with a limited response repertoire (i.e. a student with additional significant physical/sensory impairments), differentiation may be evidenced through the engagement with different stimuli. For example, a student might demonstrate differentiation simply by focusing on or maintaining hand contact with one stimulus for a significantly longer period of time than another stimulus.
For a student who is not environmentally differentiating, an implication for instruction is that the student may need to be provided with increased opportunities for sensory exploration of/interaction with the materials and for using the materials functionally. In providing these increased opportunities, it is essential to insure that a student’s safety and dignity are maintained, especially with regard to social context and age appropriateness.
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Conceptualization
Conceptualization is the formation of mental representations or ideas for categorizing information or mental connections to prior experiences. As children develop, new concepts about objects, people, places and the relationship between them are continually being learned. Conceptualization may be demonstrated through a range of initiated utterances/actions or responses to questions, comments, or directions. Individual communication modes may vary, and need to be identified, taught, developed, refined and/or expanded upon.
Explanatory Notes: In identifying a concept that a student is expected to learn, it is important to make known to
instructors and students the intended definition of that concept.
It is important that incidental displays of knowledge of identified concepts/meanings are noted/documented as they occur throughout the day.
In order for a student to demonstrate the knowledge of a concept/meaning, it is necessary for the student to exhibit a behavior that is intentional. For instance, a student who might typically sit without movement would not be considered to demonstrate knowledge of “wait” by remaining in a motionless position. Rather, the student would need to initiate a movement at the proper turn-taking time in order to have displayed knowledge of what “waiting” means.
Learning environments should be picture cue/object cue/print rich, so as to facilitate the learning of the concepts.
In expecting demonstration of knowledge of specific concepts, it is important that the other concepts/meanings used contextually by the instructor are known by the student or made clear (e.g. through demonstration) to the student. This is especially important with regards to concepts/meanings that define an expected mode of performance (e.g. touch, press, look).
Beyond the concepts/meanings that are found in this curriculum frameworks, which is based on the ELA and Math Common Core Learning Standards and Science and Social Studies NYS/NYC Scope and Sequence for grade level instructional content, there are other NYS standards based concepts that may be important to explicitly address in relation to each content area. For example, in Career Development and Occupational Studies, these may include: work; start/begin; end/finish; put away/put back; more/enough; and no. In Health, these may include; privacy, danger, emergency, clean, stranger, helper, friend, “feeling uncomfortable”, sick/hurt, exercise, medicine, and choice. These other concepts can identified by referring to New York State’s Learning Standards for Family and Consumer Sciences, Health, Phys. Ed., Career Development and Occupational Studies, The Arts, as well as, the NYSAA Alternate Grade Level
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Indicators for Science and Social Studies, and the grade level Extensions for English Language Arts and Math.
In addition to basic key concepts related to a content area, it is critical that students learn concepts needed for them to use their individual system of communication during assessment and instructional situations (e.g. point, touch, look, press, pick-up, give, tell, me/say).
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Functional Use of Objects
Functional Use of Objects is the appropriate utilization of materials in alignment with the purpose(s) for which they exist in a given culture. It may be applied to the use of an object that has undergone modifications. Students unable to utilize materials functionally due to a physical impairment may achieve this standard by communicating the purpose of the materials.
Explanatory Notes: Emphasis should be placed on involving family members in encouraging a student to use content
related materials during functional daily activities. For example, in the area of English Language Arts/Native Language Arts, some activities might include: giving a greeting card to a relative or friend; bringing a shopping list, with accompanying tangible symbols, to the supermarket; marking important dates on a calendar; labeling household items; and engaging with books and magazines.
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Problem SolvingProblem solving is the directing of one’s actions towards achieving a goal that presents uncertainty or difficulty. It presupposes an awareness of the existence of a problem. It generally involves taking into account factors related to a problem, and trying or considering more than one way to solve a problem. Resolution of a problem may be unattainable even though problem solving behaviors have been applied. Explanatory Notes:
When considering problem solving, an emphasis should be placed on a student’s involvement in the process of solving a problem rather than on a student’s resolution of a problem.
A student’s performance of Problem Solving may take the form of a variety of actions/response modes.
An implication for instruction is a recognition of the need to provide students with adequate time and opportunities “to try” or consider more than one way of solving a problem before intervening in the process.
Problem Solving may be accomplished through the completion of tasks formulated with the intent of providing opportunities for students to demonstrate specific problem solving behaviors. It may be accomplished, however, within a broader framework of general content area assignments, which naturally include a variety of problem solving situations.
A distinction involves the student’s completion of the task that the student has previously demonstrated an ability to do readily, while problem solving involves an element of uncertainly or difficulty for the student.
When a student secures needed help, instructors should not simply complete an action for the student. Rather, the student should be guided through the problem solving process, with help provided only to the extent actually needed by the student. In this way, a student hopefully will begin to approach future problem solving situations by trying another way before securing help.
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Self-Regulation
Self-regulation is an ongoing monitoring of ones’ own sensory/physical/social/cognitive conditions, and an adjusting of these conditions to maintain a desired and comfortable internal state. Self-regulation involves knowing and applying a repertoire of behaviors to diverse settings, making informed choices, and acting upon or indicating a desire or need for change.Explanatory Notes: (Self-Regulation, General) The following conditions may necessitate self-regulation
o Sensory, including sensitivities to light, sound texture taste, smell and surrounding physical space.
o Physical, including pain, pleasure, hunger, thirst, discomfort, fatigue, hyperactivity, illness, and a need to use the bathroom.
o Emotional, including distress, loneliness, need for solitude, anger, aggressiveness, withdrawal, sadness, frustration, disappointment, elation, fear, anxiety, and stress.
o Social, including segregation, lack of privacy, and numbers/appearance/behaviors of individuals in the environment
o Cognitive, including level of subject content (either too high or too low), nature of subject matter presentation, and lack of appropriate means for accessing/expressing information.
Students may exhibit behaviors that are self-regulatory in nature but fail to meet the standard for self-regulation (as they are not desired behaviors). These include:
o Behaviors which are unsafe (e.g. abuse to self or others; object destruction)o Behaviors which interfere with one’s own learning or the learning of others (e.g. replacing
attention to task with stereotypic response; continuous noise production)o Behaviors which interfere with positive social interactions (e.g. grabbing belongings of
others; public disrobing).
Recognition should be given to the fact that most individuals engage in some common mannerisms or behaviors (e.g. finger-tapping; shaking of a glass with ice cubes; nail biting) through which they express their internal state. These behaviors, for the most part, are accepted by other individuals and do not seem to interfere in the development and maintenance of social relationships. Although the behavior of a student may differ in nature from these more common expressions, there is an expectation that such student behaviors, if exhibited in a safe and healthy manner, should be understood and accepted by others as an inherent part of “who” the student is. In fact, it may be precisely through such a particular behavior that a student is self-regulating.
In order to maintain internal control for self-regulating, students may need to be provided with positive behavioral support systems, including attention to communication and/or sensory needs and abilities.
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Explanatory Notes: (Self-Regulation, Informed Choice-Making) An informed choice refers to a student’s selection (within a single activity) of one of two (or
possibly more) objects, activities, or environments for which opportunities for exploration/acquisition of knowledge have been provided. The informed nature of the choice may be demonstrated through a consistent response to an initial presentation (e.g. verbal; tangible; pictorial) and then to a second presentation with order/position altered**. If any doubt about a student’s selection still exists, a final presentation in either order/position can be made. Informed choice may be demonstrated in a different manner by a student who clearly has a demonstrated knowledge of the concept “yes” or “no”. Such a student needs only to reaffirm his/her choice by responding “yes” or “no” when asked if this choice is what he/she wants. Informed choice may also be demonstrated through independent indication of a choice different from the objects, activities, or environments offered.
An informed choice also assumes that a student possesses an equal opportunity to choose either of the sections available. This is especially important to consider when the student has limited motor and/or sensory abilities.
Given the concept of informed choice, various implications for instruction are evident, and include consideration of the placement of materials, the communicative means utilized by students to make choices, and steps taken to familiarize students with materials/activities/ environments available as choices.
Instructional efforts to increase a student’s opportunities to make informed choices will increase the probability of a student’s demonstration of general self-regulatory behavior, decision-making and awareness of the consequences of one’s decisions. Therefore, instructional provision for facilitating informed choice-making should be ongoing throughout a students’ day.
**It is recognized that repeatedly presenting choices in a different order/position may result in frustration on the part of students. Therefore, this type of procedure for insuring informed choice is designed primarily for the purpose of occasional assessment rather than for the purpose of ongoing instruction.
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Social Interaction
Social Interaction is reciprocal in nature and involves the use of communication for a variety of purposes. These may include having one’s desires or needs realized, or becoming involved in personal relationships. Such relationships may vary and may include being a one-time partner on a project, a member of a frequently meeting group, a helper, or a friend. Social interaction presupposes self-recognition, that is, the perception of self as a separate being, distinct form people/objects in the surrounding world. Explanatory Notes:
In general, communication refers to a process through which individuals receive from, transmit to, or exchange with others information, feelings or thoughts.
In order to help a student to learn how to socially interact, it is imperative that a student be assessed in a comprehensive and ongoing manner to determine which modes of communication are most appropriate for that student. Individual communication modes may vary and need to be identified, taught, refined, and /or expanded upon. Some students may even need to have meaning assigned to some of their naturally occurring behaviors (e.g. movements; facial expressions; vocalizations) so that they might begin intentionally to use these behaviors to communicate. Such a process should result in a student having ongoing access to and use of an effective system of communication.
In interactions with a student, it is critical to be aware of and respond immediately and consistently to any form of communication exhibited by the student, especially one of a subtle nature. In so doing, one is helping the student understand and come to expect that a communication causes others to act or respond. If such student communications are not attended to, the student most likely will discontinue communication since his/her communicative intent is not being realized.
It is beneficial to use a variety of communicative means (e.g. pictures, speech, gestures) when the student is engaged in receptive communication, even if some of these means appear to be of a nature that is beyond a student’s present cognitive level. However, a student should be taught and then have access to a means of communicating expressively that is consistent with that student’s present cognitive level.
It is critical that a student’s requests/directives and rejections/protests be addressed. Even if it is determined that the student’s attempt to control the environment cannot be accommodated, the attempt should at least be acknowledged.
To maximize a student’s social interactions, emphasis needs to be placed on providing a student with an opportunity to communicate in the context of authentic situations and environments.
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A student’s alternative/augmentative communication system (e.g. a device, board, and/or set of tangible symbols) needs to be accessible to the student throughout the day - at home, at school, and in community settings.
Significant emphasis should be placed on encouraging a student’s communication partners to accept and respond to alternate/augmentative forms of communication.
In order to interpret a student’s utterance or other communication as a request, it is subsequently necessary for the student to accept/interact with the referred to object/action/person. Otherwise, it may be that the student is merely recognizing the existence of an object/action/person.
To the greatest extent possible, and certainly to the degree mandated by a student’s IEP and by applicable educational regulations, a student should be learning to socially interact with students receiving general education services.
Certainly there is value in social interactions that occur between students and adults. Adults are able to provide appropriate models of communication and to respond readily to student initiations of communications. However, a significant emphasis also needs to be placed on providing opportunities for students to interact with peers (those receiving general and special education services).
When teaching a student to use a communication system expressively, it is critical that an instructor consistently model the use of the system in communications with the student.
The District 75 Office of Technology Solutions provides resources to students, staff, administrators, and parents in the areas of instructional, informational, and assistive technologies.
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