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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

D 75 Alternate Assessment Curriculum Grade 7 Math Module 5: Mathematical Practices

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

D 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

who are cognitively young and require mastery of those skills related to engagement before any further content knowledge acquisition could be expected.


Revision ProtocolThe 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 Framework Grade 7 MATH Module 1

Expressions and Equations

CONTEXT

UNIT 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 7th 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 7th 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 7th grades students work on understanding and creating geometric shapes working towards the concepts surface area and volume. Students will start with constructing geometric shapes based on specific instructions and measurements from the teacher. Working with 2D shapes will prepare the student to work with the concepts of perimeter and area, which they will work with by doing actual measurements with


rulers, yard sticks, or non-standard measurements. After constructing and measuring shapes, students will be asked to recreate shapes at different sizes. This will introduce the students to the concepts of scale and similar shapes. One example of create similar shapes is to have a student create a square out of 4 popsicle sticks and then a second square out of 8 popsicle sticks. Both shapes are squares but they are different sizes, which makes them similar shapes.

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 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.


ASSESSMENT

FORMATIVE ASSESSMENT EVIDENCE: Pictures of students participating in various classroom lessons and activities

Data collection

Student work samples, as appropriate

STANDARDS

MATH STANDARDS

7. EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand

linear expressions with rational coefficients.

7. EE.4 Use variables to represent quantities in a real-world or mathematical problem,

and construct simple equations and inequalities to solve problems by reasoning about

the quantities.

7. EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r,

where p, q, and r are specific rational numbers. Solve equations of these forms fluently.

Compare an algebraic solution to an arithmetic solution, identifying the sequence of the

operations used in each approach. For example, the perimeter of a rectangle is 54 cm.

Its length is 6 cm. What is its width?

7. EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r,

where p, q, and r are specific rational numbers. Graph the solution set of the inequality

and interpret it in the context of the problem. For example: As a salesperson, you are

paid $50 per week plus $3 per sale. This week you want your pay to be at least $100.

Write an inequality for the number of sales you need to make, and describe the

solutions.

7.NS.1 Apply and extend previous understandings of addition and subtraction to add

and subtract rational numbers; represent addition and subtraction on a horizontal or

vertical number line diagram. Apply properties of operations as strategies to add and

subtract rational numbers.


7. NS.2 Apply and extend previous understandings of multiplication and division and of

fractions to multiply and divide rational numbers. Apply properties of operations as

strategies to multiply and divide rational numbers.

7. NS.3 Solve real-world and mathematical problems involving the four operations with

rational numbers.

7.G.A.1 Solve problems involving scale drawings of geometric figures, including

computing actual lengths and areas from a scale drawing and reproducing a scale

drawing at a different scale.

7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface

area of two- and three-dimensional objects composed of triangles, quadrilaterals,

polygons, cubes, and right prisms

7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional

figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

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.

CAREER DEVELOPMENT AND OCCUPATIONAL STANDARDS

3a.1: Universal Foundation Skills Basic skills include the ability to read, write, listen, and

speak as well as perform arithmetical and mathematical functions.

3a.2: Thinking skills lead to problem solving, experimenting, and focused observation

and allow the application of knowledge to new and unfamiliar situations.

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 D 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

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.

ESSENTIAL QUESTIONS

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

2. How do we use addition, subtraction, multiplication and division in our day-to-

day life?

3. How do we measure geometric shapes, properties, surface area?

4. How can we use data to make decisions and/or represent patterns and trends in

real world situations?

VOCABULARY

Addition Altogether Decrease (less) Division Factor Greater than Increase (more) Known Less than Mathematical expression Multiplication Subtraction Term Unknown Variable Cards Certain Chart Coin Data Die/Dice Predict/Prediction

angle side measure length width height area perimeter volume surface area sphere cone ruler compass protractor geometric nets obtuse angle acute angle right angle Probability Spinner

LESSON STRANDS OVERVIEW


REVIEW OF LESSON STRAND 1:

Apply properties of operations as strategies to add and/or subtraction and/or factor.

A variable refers to a letter or symbol representing an unknown quantity. Generate expressions and/or equations with a variable. [e.g., 3+x = 5] Use numerals, variables and operational symbols to translate a word problem

into a simple equation. [e.g., Henry read 2 books yesterday. Today Henry may read x amount of books- (2+x)] and/or an inequality [4> 2; 5<7].

REVIEW OF LESSON STRAND 2:

Demonstrate the properties of addition with rational numbers using a number line. Demonstrate the properties of subtraction with rational numbers, using a number

line. Additive Inverse (Opposite numbers: when added together equal 0 Ex. -1+1=0) Use the properties of multiplication of rational numbers to interpret products in the

real world. Use the properties of division of rational numbers to interpret quotients in the

real world. Convert fractions to decimals.

REVIEW OF LESSON STRAND 3: Draw, using ruler, protractor, or Technology shapes when given the measurements Solve problems involving drawings of geometric figures, such as actual lengths and

areas. Reproducing a drawing of a geometric figure at a different size. Surface area and geometric nets Application of the principle of volume (LxWxH) by using containers and

manipulatives to determine the actual volume of the containers.

REVIEW OF LESSON STRAND 4: Collect and display data. Determine that the probability of an event occurring as certain (yes/1) or

impossible (no/0). Determine the probability of an event occurring (likely/unlikely/impossible). 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: Review of: Apply properties of operations as strategies to add

and/or subtraction and/or factor. A variable refers to a letter or symbol representing an

unknown quantity. Generate expressions and/or equations with a variable. Use

numerals, variables and operational symbols to translate a word problem into a simple

equation. [e.g., Henry read 2 books yesterday. Today Henry may read x amount of

books- (2+x)] and/or an inequality [4> 2; 5<7].

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage with peers counting a set of objects.

Engages with counting by using an Augmentative Communication Device.

Engage with peers who are exploring the differences between the words

“known” and “unknown” using mystery items. Select the mystery item from a

box or brown bag.

Engage with peers performing various actions related to using a deck of cards

containing the numbers 2 through 10 in order to make number sentences.

Engage with peers answering simple expressions and/or equations. Level D

students use an augmentative device to “agree” and/or “disagree” with the

answer.

Engage with peers performing various actions related to adding and subtracting

dominos to solve for an unknown number.

Engage with a person (teacher or peer) completing word problems. Activate a

pre-programmed switch with the correct answer.

With or without assistance, push objects together or apart to represent

mathematical operation (addition or subtraction) for word problems.

LEARNING PLANS AND ACTIVITIES LEVEL C:


Conduct a sensory box search in which students dig inside to find objects and

place the correct number of objects into a numbered container.

Participate in a activity in which students match corresponding numbers to

themselves and/or objects

Substitute simple, single digit numbers with objects that would make number

sentences true.

Using a calculator, find an unknown number in a number sentence that would

make it true.

Participate/Identify with substitution of objects with the correct number that

would make the number sentences true

Using a calculator, base-10 blocks or linking cubes to find an unknown number in

a number sentence that would make it true

Use a white board and dry erase marker to draw the operational symbol

(addition or subtraction) needed to complete word problems.

Match appropriate operational symbols to word problems in order to select the

correct answer.

LEARNING PLANS AND ACTIVITIES LEVEL B: Complete addition and/or subtraction word problems using student names. If

necessary, provide students with base-10 blocks, number lines and calculators.

Students complete activities in Math Journals (i.e., gluing and pasting, paper and

pencil, etc.) using picture cue strips to create math sentences.

Listen to and/or read a word problem. Represent the word problem by creating a

number sentence.

Substitute simple single digit numbers in numbers sentences with letters (A, B,

C).

Listen to and/or read teacher presentation of word problems, represent the

word problem using numbers and/or symbols and, if possible, solve.

Use a whiteboard and dry eraser marker to create equations for peers to solve.D 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

Teacher will present two numbers. Students will use an oven mitt as an alligator

to eat the larger number to reinforce the concept of inequalities (greater than or

less than)

Using laminated numbers and a number line, students will compare numbers by

verbalizing the given inequality ( 5 is greater than _3 )

Lesson Strand 2: Review of: Demonstrate the properties of addition with rational

numbers using a number line. Demonstrate the properties of subtraction with rational

numbers, using a number line. Additive Inverse Use the properties of multiplication of

rational numbers to interpret products in the real world. Use the properties of division of

rational numbers to interpret quotients in the real world. Convert fractions to decimals.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage in with a number line divided into fractions.

Activate an AAC device indicating that addition means “put together” or “plus.”

Engage in skip counting by interacting with a 100s board or touch board that has

been modified to prompt students to select numbers by 2s, 5s or 10s.

Engage with division problems by grouping manipulatives and/or materials with

support, while a classmate or teacher models solving the problem.

Engage with coins by attending to a teacher or classmate while they model

converting fractions to decimals during a money lesson in class and/or real

world.

LEARNING PLANS AND ACTIVITIES LEVEL C: Demonstrate one-to-one correspondence on a number line.

Utilize a number line to solve real world addition problems.


Solve simple real world problems demonstrating the additive inverse

Use a calculator to solve real-world multiplication problems.

Participate in real world division problems by independently distributing

materials to classmates using JARS routines and scripts with mathematical

language.

Solve real world money problems involving adding up to $1.00 or making change

from $1.00.

LEARNING PLANS AND ACTIVITIES LEVEL B: Utilize a number line or other tools strategically, to solve real world subtraction

problems involving rational numbers in any form

Utilize a number line or other tools strategically, to solve real world multi-step

addition problems involving rational numbers in any form

Demonstrate additive inverse in equations and on number lines, with all types of

rational numbers

Use tools and strategies (multiplication chart, skip counting, and calculator) to

independently solve multiplication problems.

Use tools and strategies (multiplication chart, skip counting, and calculator) to

independently solve division problems.

Compare the value of fractions and decimals using manipulatives and/or visual

representations in class and in the real world.

Lesson Strand 3: Review of: Draw, using ruler, protractor, or Technology shapes

when given the measurements. Solve problems involving drawings of geometric figures,

such as actual lengths and areas. Reproducing a drawing of a geometric figure at a different

size. Surface area and application of the principle of volume (LxWxH) by using containers

and manipulatives to determine the actual volume of the containers.


LEARNING PLANS AND ACTIVITIES LEVEL D: Student engages with using a ruler to draw a straight line to create a triangle and

connect three dots to make a triangle.

Student engages with protractor to create an acute, right, and obtuse angle and

to determine if an angle is acute, obtuse, or right.

Engages with ink stamper to identify the number of vertexes in a geometric

shape.

Engages with measuring the perimeter of square, triangle, rectangle, etc.

Engages with a presentation of reproduced geometric shapes in different sizes.

Engages with the sensory stimuli presented with attribute blocks of different

sizes of the same shape.

Student Engages with repeated and sustained attention to a presentation on

geometric nets and decomposing 3D shapes.

Explore containers filled with various media to discover volume.

LEARNING PLANS AND ACTIVITIES LEVEL C: Student participates with using a ruler to draw a straight line to create a triangle

and to connect three dots to make a triangle.

Student participates with protractor to create an acute, right, and obtuse and to

identify if an angle is obtuse, acute, or right.

Student counts the square units out of various geometric shapes drawn on graph

paper.

Student builds area models of multiplication using foam squares to show

rectangular area formula.

Student participates in a presentation about reproducing geometric shapes of

different sizes.

Student participates in sorting attribute blocks based on size and geometric

shape.


Student participates describing the attributes of the shape: number of sides,

what 2D shapes make up the 3D shapes, the number of vertex’s or “corners,”

etc.

Student participates in comparing different types of rectangular prisms to

determine which prism has the greater volume and the least volume.

LEARNING PLANS AND ACTIVITIES LEVEL B: Student will utilize a ruler to draw straight lines to create a triangle and connect

dots to make triangles.

Student will utilize a protractor to create an acute, right, and obtuse triangle and

to draw and identify all three types of triangles.

Student with prompts and supports measures the perimeter of a rectangular

desk or table.

Student measures circumference of circles from the classroom with a string and

then uses a tape measurer or ruler to find the length.

Student decomposes 3D shapes into 2D shapes.

Student compares and contrasts different types of rectangular prisms to

determine which prism has the greater volume or the least volume.

Lesson Strand 4: Review of: Collect and display data, Determine that the

probability of an event occurring as certain (yes/1) or impossible (no/0), Determine the

probability of an event occurring (likely/unlikely/impossible), and Making predictions

based on data.

LEARNING PLANS AND ACTIVITIES LEVEL D: Engage in collecting data by using PMC


Engage with materials in order to label parts of a graph/chart – using

pictures/symbols, etc. (i.e. label title, number of people, 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”

Engage with materials (paddle, etc.) in order to state what happened in different

probability situations.

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.

LEARNING PLANS AND ACTIVITIES LEVEL C: Participate in creating survey questions using picture symbols/sentence strips

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.

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”

Count dots on die and writes/ identifies the 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, 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).


LEARNING PLANS AND ACTIVITIES LEVEL B: 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?

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.

In pairs, decide how many times to roll a die. Roll the die and for each time

record results on a graphic organizer. Record findings on a graphic organizer and

report to class.

In pairs, collect data (record results of each experiment on graphic organizer)

and make a prediction.

MATERIALS/ MANIIPULATIVES Smartboard

iPad App- Algebra Touch

Multiple sizes and colors of 2D Shapes (squares, rectangles, triangles, trapezoids,

circles, hexagons, etc.)

Multiple sizes and colors of 3D shape (cubes, prisms, pyramids, spheres, etc.)D 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

Geo-Board

Foam/Plastic square counters

Ruler and/or tape measure

String

Shape templates

Fraction Sticks

Fraction Pies

Unifix cubes, Base-10 Blocks

Multiplication Chart

100s Chart

Number Lines

Quarters, Dimes, Nickels, Pennies, Dollar bills

Balls

Coins

Data collection sheets

Deck of cards

Dice

Surveys

Various coins

BOOKS (including but not limited to)

The Doorbell Rang

The Hershey’s Fraction Book

The Pizza Counting Book

Eating Fractions

Tally O'Malley by Stuart Murphy and Cynthia Jabar

Lemonade for Sale by Stuart Murphy and Tricia TusaD 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

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

Websites: www.Flocabulary.com “Math Term Party”

www.Harveyshomepage.com

www.shodor.org/interactivate/activities/FunctionsMachine/

www.shodor.org/interactivate/activities/Factorize/

http://exchange.smarttech.com/search.html?

q=equations&subject=Mathematics&grade=All+grades&region=en_US -

Equations

http://more2.starfall.com/m/math/addResulttennis/load.htm?f&d=demo&filter=first

Word Problems: Addition

http://more2.starfall.com/m/math/subChange-umbrellas/load.htm?f&d=demo&filter=first

Word Problems: Subtraction-

www.jc-schools.net/tutorials/interact-math.htm (gives numerous interactive

www.mathisfun.com

www.pinterest.com

http://www.coolmath-games.com/

http://www.mathplayground.com/games.html


http://www.mathplayground.com/games.html

http://www.coolmath-games.com/

http://www.pinterest.com/

http://www.mathisfun.com/

http://www.jc-schools.net/tutorials/interact-math.htm

http://more2.starfall.com/m/math/subChangeumbrellas/load.htm?f&d=demo&filter=first

http://more2.starfall.com/m/math/addResulttennis/load.htm?f&d=demo&filter=first

http://exchange.smarttech.com/search.html?q=equations&subject=Mathematics&grade=All+grades&region=en_US

http://exchange.smarttech.com/search.html?q=equations&subject=Mathematics&grade=All+grades&region=en_US

http://www.shodor.org/interactivate/activities/Factorize/

http://www.shodor.org/interactivate/activities/FunctionsMachine/

http://www.Harveyshomepage.com/

http://www.Flocabulary.com/

http://www.brainpopjr.com/math/geometry/planeshapes/

http://www.brainpopjr.com/math/geometry/solidshapes/

http://www.brainpopjr.com/math/measurement/area/

http://www.brainpop.com/math/geometryandmeasurement/geometry/

http://www.flocabulary.com/probability/


http://www.flocabulary.com/probability/

http://www.brainpop.com/math/geometryandmeasurement/geometry/

http://www.brainpopjr.com/math/measurement/area/

http://www.brainpopjr.com/math/geometry/solidshapes/

http://www.brainpopjr.com/math/geometry/planeshapes/

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 ObjectsD 75 Alternate Assessment Curriculum Grade 7 Math Module 1: Expressions and Equations

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 Solving


Problem 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.


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