ps37r.altervista.orgps37r.altervista.org/nysaacc/math m5 6.docx · web viewps37r.altervista.org

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

D75 Alternate Assessment Curriculum 6 Grade Math Module 5: Mathematical Practices

materials lists

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


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


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.


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.


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.


District 75 Alternate Assessment Curriculum FrameworkGrade 6 MATH Module 5 Mathematical Practices

CONTEXTUNIT TOPIC: Mathematical Practices

Mathematics is a language for translating real-life situations into numerical models. Expressions and equations are two ways we can translate situations into the language of mathematics and in grades 6-8 students are exposed and taught this. Students are to be exposed to and taught these mathematical concepts through hands-on instruction that emphasizes concrete manipuliatives, examples, and application to real world problems.

In 6th grade students learn to use variables to represent an unknown number in a mathematical sentence or phrase, solve simple one-step addition and multiplication sentences, and be able to write inequalities based on real-world situations. In 7th grade students extend what they learned in 6th grade by using variables in inequalities, to expand their expressions based on the all of the basic operations, and solve two-step problems, including problems with the distributive property. In the 8th grade, students will primarily work with graphing and solving equations and inequalities, in addition work more with exponents.

In 6th grade students are taught and exposed to where rational numbers are placed on a number line and understand absolute value. In addition, students are expected to be able to fluently add, subtract, multiply, and divide fractions and multi-digit decimals. In the 7th grade, students will continue working on multiplying and dividing fractions in real-world problems, but they will also be expected to add and subtract various types of rational numbers. In the 8th grade, students will continue working with rational numbers and start being exposed to irrational numbers and how they relate in terms of square roots.

In the 6th grade students work on measuring and understand the concepts of area and perimeter. It is important to spend satisfactory time on each of these concepts individually and not do both right away in the same lesson. Often students are introduced to these concepts in tandem, which is why many students get confused or even mix up the two concepts. Throughout the module, students will learn about the


different properties of shapes that allow for the creation of standardized formulas. In circles the formula for find the perimeter or “circumference” is the diameter times pi ( c = dπ) and the area is pi times the radius squared (a =πr2). In triangles the perimeter is the sum of the three sides and the area is base times height divided by two. In rectangles the sum of the four sides is perimeter and the area is length times width.

Statistics and probability are introduced in Grade 6 and continued through upper grades, 7 and 8. Statistics begins with understanding what is a statistic? What do stats show and what stats are used for in everyday life? Statistical questions involve data, data collection, and differences in answers as opposed to a question with only one single answer. What are the heights of the students in class? How many siblings do your classmates have? What pets does the class have? How much time did the class spend reading? The results show data, which is summarized in a graph. The type of graph used depends on the data. In order to organize the data, we interpret it by looking at tendencies, or mean, median and mode. What are the average heights? What is the height for the most people and what is the middle height? The data can be used to interpret the likelihood of an event, the probability of an event occurring.

The sample activities outlined are designed to elicit performances of mathematical thinking and behaviors, but also provide opportunities for students to get a concrete understanding of we use mathematical language to describe situations in the real-world. Teachers should emphasize concrete examples and repeated regular practice using manipuliatives and visualizations.

The activities in this module should be reinforced with regularly vocabulary review and simple equations throughout the day. Simple rate formulas should be used regularly during this module, in order to prepare students for rates, ratios, and percent later in later modules. Also, these are real-life examples that provide functional math skills for reasoning.

ASSESSMENTFORMATIVE ASSESSMENT EVIDENCE:

Pictures of students participating in various classroom lessons and activities

Data collection

Student work samples, as appropriate

Checkpoints using various questioning techniques


STANDARDS

MATH COMMON CORE STANDARDS:6.EE.6 Use variables to represent numbers and write expressions when solving a real-

world or mathematical problem; understand that a variable can represent an unknown

number, or, depending on the purpose at hand, any number in a specified set.

6. EE.7 Solve real-world and mathematical problems by writing and solving equations of

the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational

numbers.

6. EE.8 Write an inequality of the form x > c or x < c to represent a constraint or

condition in a real-world or mathematical problem. Recognize that inequalities of the

form x > c or x < c have infinitely many solutions; represent solutions of such inequalities

on number line diagrams.

6. NS.1 Interpret and compute quotients of fractions, and solve word problems involving

division of fractions by fractions, e.g., by using visual fraction models and equations to

represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a

visual fraction model to show the quotient; use the relationship between multiplication

and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general,

(a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb

of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How

wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

6. NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the

standard algorithm for each operation.

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and

polygons by composing into rectangles or decomposing into triangles and other shapes;

apply these techniques in the context of solving real-world and mathematical problems.


6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by

packing it with unit cubes of the appropriate unit fraction edge lengths, and show that

the volume is the same as would be found by multiplying the edge lengths of the prism.

Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with

fractional edge lengths in the context of solving real-world and mathematical problems.

6.SP.A.1 Develop understanding of statistical variability. Recognize a statistical

question as one that anticipates variability in the data related to the question and

accounts for it in the answers. For example, "How old am I?" is not a statistical question,

but "How old are the students in my school?" is a statistical question because one

anticipates variability in students' ages.

6.SP.B.4 Summarize and describe distributions. Display numerical data in plots on a

number line, including dot plots, histograms, and box plots.

CAREER DEVELOPMENT AND OCCUPATIONAL STANDARDS

Standard 2 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 and to understand their potential application in the world of work.

Standard 3a.1: Basic skills include the ability to read, write, listen, and speak as well as

perform arithmetical and mathematical functions.

ESSENTIAL QUESTIONS

1. How do expressions and equations help us make sense of real-world problems?

2. How does knowing about the quantity and position of numbers help us

understand our world?


3. How do we learn about shapes and their attributes as well as their area,

perimeter, and volume and how we can measure it?

4. What are data, variability, and a survey? How do we organize and display our

data?

VOCABULARY addition apart balance difference division equal equivalent expression greater inequalities left less more multiplication number line numbers (one-

twenty) right solve subtraction sum together variable

categorical compare data numerical population questions range Sample statistics survey variability equation operations addition subtraction multiplication division total penny, nickel, dime,

quarter half, third, quarter,

whole repeat count decimal fraction number line balance, scale translate

circle square rectangle triangle hexagon perimeter area volume base width angle ruler height length measure fill around into on volume radius circumference diameter formula


LESSON STRANDS OVERVIEW

1. REVIEW OF MODULE 1 Identify numbers, given corresponding words

Identify mathematical symbols, given corresponding words

Identify algebraic expressions using manipulatives

Identify algebraic expressions, in a word problem

Identify two equivalent equations and identify inequalities using a number

line diagram to describe real-world mathematical problems.

2. REVIEW OF MODULE 2 Manipulate equal parts of a whole, into a whole or part of a whole by

putting together and pulling apart

Solve word problems involving fractions and mixed numbers.

Add, subtract, multiply and/or divide two-digit numbers by one-digit

numbers using

Solve repeated addition problems where the addends are the same, using

concrete manipulatives.

Add, subtract, multiply and/or divide numbers with decimals.

3. REVIEW OF MODULE 3 Label parts of a circle (radius, center, and diameter), a triangle (base and

height), and a rectangle (length and width) to measure.

Compose and decompose rectangles into triangles and/or other shapes.

Label shapes with given dimensions (numbers)

Determine the perimeter and/ or the area of a rectangle using

manipulatives to create a rectangle or draw on graph paper D75 Alternate Assessment Curriculum 6 Grade Math Module 5: Mathematical Practices

Apply the concept of identifying volume (l x w x h) in a rectangular prism

by choosing from a variety of containers.

4. REVIEW OF MODULE 4 Know the difference between questions that result in a single response

vs. a group of responses.

Display simple data using numbers, images, or objects in the appropriate

graphing format (line, chart, circle, bar, etc.)

Develop quantitative survey questions.

Collect and record quantitative survey data into the appropriate

graphing format

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: Identify numbers, given corresponding words. Identify mathematical

symbols, given corresponding words. Identify algebraic expressions using manipulatives.

Identify algebraic expressions, in a word problem.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engages with representations of numbers in word format ( large tactile word-

cards).


Attending to a teacher presenting number of objects that represent the

corresponding word.

Engages with models of operational symbols.

Identify and/or place the operation symbol between two groups of objects or

numerals.

Attend to visual, auditory, or tactile materials that represent algebraic

expressions.

Manipulate objects used to add and subtract known and unknown quantities

Manipulate objects used to represent variables in given expressions based on

word problems.

Move materials either together or apart from each other based on given word

problem to represent the operation from the expressions being done

LEARNING PLANS AND ACTIVITIES LEVEL C: Manipulate objects to represent a requested number by forming separate piles.

Match a numeral to a given amount of objects providing the word form with the

set of objects.

Label’s the operation when given a picture of a mathematical symbol.

Identify operation symbols when given flashcards.

Sorting algebraic expressions based on mathematical symbols (addition (+);

multiplication (x); subtraction (-) division (÷, /)).

Sorting algebraic expressions based on similar numerical values. (ie: equations

that =10 are placed together, expressions that contain the number 2 are placed

together)

Identifying known quantities used in a word problem using PMC

When given two choices, students will select correct operation after listening

to/reading a simple word problem.


LEARNING PLANS AND ACTIVITIES LEVEL B: Use flashcards with numbers in word format, student will identify the

corresponding numeral.

Construct flashcards when given a set amount of numbers by providing the

numerical symbol, number and the set amount of objects.

Indicate the correct operational symbols to complete simple mathematical

equations (2 _ 1= 3).

Solves equations using the same numbers but different operational symbols

4+2=, 4-2=, 4÷2=, 4×2=

When given an algebraic expression, students will place correct sets of objects to

represent each numeral.

When expression is read aloud, student will identify the operational symbols and

numerals named

Students will translate verbal expressions into numerical expressions after

listening to expression (teacher states, “six plus two”).

Students will translate written expressions into numerical expressions after

reading an expression (reads; six plus two).

Lesson Strand 2: Review of: manipulate equal parts of a whole, into a whole or

part of a whole by putting together and pulling apart. Solve word problems involving

fractions and mixed numbers. Add, subtract, multiply and/or divide two-digit numbers

by one-digit numbers using. Solve repeated addition problems where the addends are

the same, using concrete manipulatives. Add, subtract, multiply and/or divide numbers

with decimals.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage with teacher/peers matching a whole to its parts.


Engage with teacher/peers breaking a whole into equal-size parts and then

reassembling into a whole.

Interact with (touch, feel, hold) part and/or whole objects as presented.

Attend as teacher cuts fruits in half to follow a recipe (cutting fruit into equal

parts to make a fruit salad).

Attend to/engage with teacher grouping two sets of objects to demonstrate

addition, using objects totaling ten or more.

Adds by pushing two groups of objects together to create a given set.

Engage with teacher/peers solving repeated addition problems using hands-on activities, manipulatives, and technology.

Engage with teacher using money during purchasing activities

LEARNING PLANS AND ACTIVITIES LEVEL C: Identify half and quarter fractions as represented by manipulatives and real-

world objects

Match a whole to its parts, using objects and/or pictorial representations.

Put a stamp/sticker on a whole shape and then match the parts that make up

the whole.

Participate in cutting fruits into halves and quarters to follow a recipe (E.g cutting

fruit into equal parts to make a fruit salad).

Demonstrate addition/subtraction strategies of “one more ” or “one less”, using

two-digit and one-digit numbers. (Use SmartBoard, manipulatives, etc.)

Record responses of addition and subtraction problems (using charts, notebooks,

templates, technology, etc.).

Utilize visual templates to repeat count coins and other manipulatives.

Students use dollar bills and coins to participate in activities for adding decimals

LEARNING PLANS AND ACTIVITIES LEVEL B:D75 Alternate Assessment Curriculum 6 Grade Math Module 5: Mathematical Practices

Represent a given fraction (½, ¼, 1/3) using manipulatives or real-world objects.

Cut or shade a given whole into the requested fractional parts

Follow directions in a recipe to cut fruits into various fractions to make a fruit

salad.

Identify and label a whole and the corresponding equal-size parts, with or

without objects.

Create addition/subtraction/multiplication/division equations with two-digit and

one-digit numbers using a model.

Translate verbal and/or written addition/subtraction/multiplication/division

equations. (E.g. “Twelve apples plus two apples” translates to 12 + 2 = ?)

Solve repeated addition problems using hands-on activities with real money

Introduce decimals using all coins

Lesson Strand 3: Review of: label parts of a circle, a triangle, and a rectangle to

measure. Compose and decompose rectangles into triangles and/or other shapes. Label

shapes with given dimensions. Determine the perimeter and/ or the area of a rectangle

using manipulatives to create a rectangle or draw on graph paper. Apply the concept of

identifying volume (l x w x h) in a rectangular prism by choosing from a variety of

containers.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engages with real world objects in their environment such as cups, plates, balls,

markers and (other classroom object)s to explore items that are representative

of shapes

Engage with shapes by touching triangles and squares

Attend to and explore triangles and squares with different modalities


Engage with the representations of a given base and height of various shapes

Engages with and attend to real world objects in classroom environment to

explore perimeter and area of rectangles.

Engages with manipulatives (rice, cubes, water, beans) to explore volume of

rectangular prisms.

LEARNING PLANS AND ACTIVITIES LEVEL C: Student participates in matching and sorting circles, squares, and triangles into

different containers.

Students participate in tracing circles, squares, and triangles using dashed lines

or concrete manipulatives.

Student participates in using physical manipulatives, such as straws or popsicle

sticks, to show shapes within shapes.

Student participates in identifying shapes within other shapes

Student participates in labeling the missing measurements in rectangles and

squares.

Student participates in determining the area of rectangles and squares using

foam squares, Wheat Things, Cheez-Its, rice Chex, etc.

Student participates in determining the volume of rectangular prisms in the

classroom using the volume formula and a calculator.

LEARNING PLANS AND ACTIVITIES LEVEL B: Student participates in a presentation on rectangles and squares in the real-

world as well as parts of squares and rectangles: four sides, parallel sides, 90°

angles.

Student participates in creating a “shape poster” on squares and rectangles with

a diagram of the parts and squares and rectangles.


Student draws lines to decompose shapes on white/chalk/SMARTboard

Student composes shapes out of other shapes using concrete manipulatives.

Student labels the parts of real-world shapes in the classroom.

Student determines the area of rectangles and squares using standard

measurements and multiplication.

Student determines the volume of rectangular prisms in the classroom using the

volume formula and a calculator.

Lesson Strand 4: Review of: Know the difference between questions that result in

a single response vs. a group of responses. Display simple data using numbers, images,

or objects in the appropriate graphing format. Develop quantitative survey questions.

Collect and record quantitative survey data into the appropriate graphing format

LEARNING PLANS AND ACTIVITIES LEVEL D: Attend to http://www.brainpop.com/science/scientificinquiry/statistics/

Attend to question what are the favorite colors of 6th graders?

Attend to examples of different types of graphs to display data

Attend to image/example of bar graph

Attend to survey questions, Example: What is your favorite snack?

Attend to picture symbols that represent answer choices to survey questions

Engage in identifying highest number in given set

Engage in identifying lowest number in a given set

LEARNING PLANS AND ACTIVITIES LEVEL C: Predict number of items in a jar as statistical question

Collect responses by writing or using color block cards

Answer questions using graph

Recognize, by pointing, where to find data on graph


Identify possible responses questions used to make data

Make tallies to record answers for questions posed

Identify highest number in given set

Identify lowest number in a given set

LEARNING PLANS AND ACTIVITIES LEVEL B: Determine data that is being asked needed to answer statistical question

Determine whether data is categorical or numerical data

Show evidence from book to support interpretations of data

Organize data into a table

Construct survey questions

Record results from survey questions

Order data from highest to lowest

Identify subtraction as math concept used to find range

Use math concepts involving multi-digit numbers to determine range or calculator


MATERIALS/ RESOURCES

Smart Board

Computers

Projectors

AAC Device (when necessary)

Pre-Programmed Switches (when necessary)

Hand-on worksheets using real money (See Attainment Math, Equals, Touch

Math, etc.)

Hundreds Board for skip counting multiples

Money

Visual templates/charts

Manipulatives (E.g. Attribute blocks, fraction pieces, base ten blocks, etc.)

Calculator

WEBSITES AND TECHNOLOGY: http://www.teachertube.com

http://tarheelreader.org

http://www.brainpopjr.com

http://nlvm.usu.edu/en/nav/category_g_3_t_2.html (virtual manipulatives)

http://exchange.smarttech.com/details.html?id=95389bb2-3ffa-4889-9922-

d552d9ec2be8

http://exchange.smarttech.com/details.html?id=183d99d1-cfd0-4c61-a6e1-

f371ade2fbf9

http://schools.nyc.gov/Offices/District75/Departments/Mathematics/

Resources/default.htm

http://www.algebra4children.com/grade_game_algebraic%20expressions.html

http://www.learner.org/interactives/geometry/area_surface.html

http://lessonplanspage.com/MathVolumeDefinitionsAndFormulas8.htm/


http://lessonplanspage.com/MathVolumeDefinitionsAndFormulas8.htm/

http://www.learner.org/interactives/geometry/area_surface.html

http://www.algebra4children.com/grade_game_algebraic%20expressions.html

http://schools.nyc.gov/Offices/District75/Departments/Mathematics/Resources/default.htm

http://schools.nyc.gov/Offices/District75/Departments/Mathematics/Resources/default.htm

http://exchange.smarttech.com/details.html?id=183d99d1-cfd0-4c61-a6e1-f371ade2fbf9

http://exchange.smarttech.com/details.html?id=183d99d1-cfd0-4c61-a6e1-f371ade2fbf9

http://exchange.smarttech.com/details.html?id=95389bb2-3ffa-4889-9922-d552d9ec2be8

http://exchange.smarttech.com/details.html?id=95389bb2-3ffa-4889-9922-d552d9ec2be8

http://nlvm.usu.edu/en/nav/category_g_3_t_2.html

http://www.brainpopjr.com/

http://tarheelreader.org/

http://www.teachertube.com/

Survey lesson found at

http://www.educationworld.com/a_tsl/archives/05-1/lesson033.shtml

Fractionshttp://www.coolmath4kids.com/fractions

http://www.funbrain.com/fract/

Decimalshttp://www.coolmath.com/prealgebra/02-decimals/

http://www.brainpop.com/math/numbersandoperations/decimals/

MANIPULATIVES Blocks

snap cubes

coins

magnetic numbers

flash cards

,number lines

shape templates

photographs of real-world objects model shapes

graph paper

masking tape

color pencils

ruler or tape measure

BOOKS (including but not limited to) http://tarheelreader.org/2011/01/07/numbers-1-to-5/3/

Mystery Math: A First Book of Algebra, David A. Adler


http://tarheelreader.org/2011/01/07/numbers-1-to-5/3/

http://www.brainpop.com/math/numbersandoperations/decimals/

http://www.coolmath.com/prealgebra/02-decimals/

http://www.funbrain.com/fract/

http://www.coolmath4kids.com/fractions

http://www.educationworld.com/a_tsl/archives/05-1/lesson033.shtml

12 Ways to Get to 11, Eve Merriam

Apple Fractions by Jerry Pallotta and Rob Bolster

The Hershey's Milk Chocolate Bar Fractions Book by Jerry Pallotta and Robert C.

Bolster

Fraction Fun by David A. Adler and Nancy Tobin

Funny & Fabulous Fraction Stories: 30 Reproducible Math Tales and Problems to

Reinforce Important Fraction Skills... by Dan Greenberg

Do You Know Dewey?: Exploring the Dewey Decimal System (Millbrook Picture

Books) by Brian P. Cleary and Joanne Lew-Vriethoff

Piece = Part = Portion by Scott Gifford and Shmuel Thaler

The Greedy Triangle by Marilyn Burns

Spaghetti and Meatballs by Marilyn Burns

The Great Turkey Walk by Kathleen Kerr

Lemonade for Sale by Stuart J. Murphy

VIDEOS http://www.brainpopjr.com/math/multiplicationanddivision/

makingequalgroups/preview.weml

http://www.teachertube.com/viewVideo.php?video_id=77826 (number line

video)

http://www.teachertube.com/viewVideo.php?video_id=90315 (greater than, less

than, equal to)


http://www.teachertube.com/viewVideo.php?video_id=90315

http://www.teachertube.com/viewVideo.php?video_id=77826

http://www.brainpopjr.com/math/multiplicationanddivision/makingequalgroups/preview.weml

http://www.brainpopjr.com/math/multiplicationanddivision/makingequalgroups/preview.weml

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.


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.


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 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).


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.


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.


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.

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.


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.

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.


ps37r.altervista.orgps37r.altervista.org/nysaacc/math m5 6.docx · web viewps37r.altervista.org

Documents