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Vocational and Educational Services for Individuals with Disabilities (VESID)
Special Education and Vocational Rehabilitation Services

New York State Alternate Assessment

Mathematics
RESOURCE GUIDE
to the
Learning Standards
and
Alternate Performance Indicators
for
Students with Severe Disabilities

Click here for Word or PDF Format for printing

Below you will find an annotated page of the Resource Guide. The information in each box provides a point of reference when using this guide and clarifies important terms and ideas found within this document.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 1 – Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level: Mathematical Analysis

Alternate Performance Indicator (Mandatory):

Students will relate mathematics to their immediate environment.

Sample Approaches for this Alternate Performance Indicator (API)

Students make connections with mathematics and their immediate environment during activities such as:

• Matching the time of day with an event on the daily classroom schedule (See sample instructional activity below). (E, I, S)
• Determining what time to leave the house to arrive at work on time. (S)
• Sharing equal amounts of a different snack with a classmate. (E, I)
• Calculating how much change you will receive after making a purchase. (I, S)
• Matching daily temperature from the Internet to the temperature reading on a thermometer. (E, I, S)
• Crossing off steps on a numbered checklist when completing the steps of a task or activity. (E, I, S)
• Using a microwave touch pad to heat their lunch. (I, S)

Sample Instructional Activity for matching the time of day with an event on the daily classroom schedule

• Students create drawings or are provided with symbols representing different events to the related digital times common to their daily schedule, i.e. wake up for school (6:00), when the school bus arrives (7:00), when lunchtime takes place (11:00), physical education class (1:00) etc.
• Through repeated trials, the students match pictures or audio-clips of corresponding events to times listed on their daily schedule.
• Flashcards are created with whole-hour time segments.
• When provided with a daily event occurring on their schedule, students indicate the flashcard containing the correct time.
• When listening to the sounds of a particular activity on his/her schedule, students use a voice output device to select whole-hour time of day.
• Homework: Students use pictures of different daily events (i.e., wake up, eat lunch, go to sleep) to complete a chart with three columns labeled 6:00 (morning), 11:00, and 7:00 (evening).

• A series of sequenced captioned photographs exhibit the student arranging pictures/symbols of his/her daily schedule in order on a Velcro board.
• Teacher documents the student’s identification of the whole-hour time of day on his/her daily schedule and the activity linked to it.
• Given repeated trials, the teacher collects data on the student’s ability to accurately and independently match pictures or audio-clips of corresponding events to times listed on their daily schedule.
• The teacher collects data on student’s ability to identify a morning activity from an afternoon activity.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 1 – Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level: Mathematical Analysis

Alternate Performance Indicator:

Students will use mathematics and symbolism to communicate in mathematics.

Sample Approaches for this Alternate Performance Indicator (API)

Students use mathematics to communicate by:

• Expressing verbally, through gestures, or with pictures or objects, the concept of "more" (See sample instructional activity below). (E, I, S)
• Using numbers to list the steps of a task in order. (E, I, S)
• Using language to describe "how much", i.e., she has more, I do not have any, etc. (E, I, S)
• Identifying symbols associated with different mathematical amounts (dollars, cents, inches, etc.). (E, I, S)
• Understanding and following through with a direction that involves mathematical language, i.e., give each student one piece of paper and one pencil. (E, I, S)

Sample Instructional Activity for expressing verbally the concept of "more"

• Students are provided with a laminated card with the word and sign of "more."
• The card is placed on the student’s tray.
• Students demonstrate through his/her preferred mode of communication that he/she wants "more" the teacher then verbally states, [Student’s Name] wants "more."
• At the same time, the teacher assists the student to remove the "more" card and hand it to the teacher, or otherwise connect the "more" card with the term "more" and satisfaction of a desire for an additional amount of something.
• Teacher uses a prompt hierarchy based on his/her knowledge of the student to provide the greatest possible opportunity for student independence.
• By repeated pairing or the use of the symbol comparative to satisfaction of need, the student begins to make the connection between handing or indicating the card for "more" and receiving more snack, time to play, drink, etc.

• Teacher documents the number of times the student uses the "more" card to express his/her desire for an additional amount of something (snack, drink etc…).
• Teacher records the level and frequency of cues or prompts required in order for the student to successfully exchange the card when he/she desires "more."
• A series of sequenced captioned photographs indicate the student utilizing the more card to indicate his/her desire for an additional amount of something.
• Over a course of two weeks, the teacher charts the student’s progress in matching the "more" card to his/her desire for an additional amount of something. Denominator equals opportunity to express a desire for more, numerator equals number of times "more" card was used to indicate desire for an additional amount of something.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 1 – Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level: Mathematical Analysis

Alternate Performance Indicator:

Students will demonstrate knowledge of mathematical relationships.

Sample Approaches for this Alternate Performance Indicator (API)

Students show their knowledge of mathematical relationships when:

• Matching room numbers to a clipboard when delivering mail for a school job (See sample instructional activity below). (I)
• Demonstrating through drawings and pictures a similar amount of different items (i.e., 5 apples and 5 oranges). (E, I, S)
• Setting a table for 4 by counting out sets of 4 dishes, spoons, forks, knives, etc. (I, S)
• Following a recipe to measure the correct quantities of ingredients. (E, I, S)
• Recognizing that the larger size of the same product costs more and contains more. (I, S)

Sample Instructional Activity for matching room numbers to a clipboard when delivering mail for a school job

• Students are provided with a clipboard, with 5 different classrooms identified as 1-5 through Velcro-ed number cards.
• Each classroom indicated on the student’s clipboard has been pre-labeled with a corresponding number 1-5 on its door.
• Based on the numbers on the clipboard, the student picks up classroom mail for each classroom on his/her list from the office.
• The mail for each classroom has been placed in a manila envelope with the corresponding classroom number 1-5.
• Student travels to each of five classrooms using his/her clipboard to deliver classroom mail.
• Student attempts to correctly and independently deliver each envelope of mail to the correct appropriate classroom.

• Step 1: Based on the numbers on the clipboard, the student’s level of accuracy and independence selecting the correct envelopes from the school office corresponding to the classrooms on his/her delivery route is documented.
• Step 2: The student’s level of accuracy and independence for matching numbers on his/her clipboard to the numbers on each classroom door on the delivery route is documented.
• Step 3: The student’s level of accuracy and independence for matching the numbers on each envelope with the number on each corresponding door is documented.
• Teacher transcribes the documentation of Steps 1-3 onto a data collection sheet.
• A series of sequenced captioned photographs exhibit the student accuracy and level of independence in Steps 1-3 on the student’s ability to match the numbers on his/her clipboard and each mail envelope to the number on each classroom door.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 1 – Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level: Mathematical Analysis

Alternate Performance Indicator:

Students will compare and describe quantities.

Sample Approaches for this Alternate Performance Indicator (API)

Students compare and describe quantities through activities such as:

• Matching quantities of items through 1:1 correspondence (See sample instructional activity below). (E, I, S)
• Performing the measurements necessary to follow a simple recipe. (I, S)
• Demonstrating the concept of trading/sharing equal amounts. (E, I, S)
• Describing quantities of items by using language, such as more, less, equal, and/or the same. (E, I, S)
• Grouping and comparing similar quantities, such as coins. (E, I, S)
• Using the symbols >, < and = to create simple numerical sentences to compare sets. (I, S)
• Using manipulatives to solve problems to determine a quantity. (E, I, S)

Sample Instructional Activity for matching quantities of items through 1:1 correspondence

• Students will identify the whole-dollar amount for a given item through referencing store flyers, catalogs, cafeteria menu, price tags on items, etc.
• Students match the whole dollar amount (e.g., 9 in $9.00) to the correct number on a vertical number line, using numbered flash cards, etc.
• Students match the number of dollars needed to purchase the item using a template of dollar bills corresponding to the number identified (template use does not count as a cue since the task is matching rather than counting).
• Once the correct dollar amount is identified, students place the correct dollar amount into an envelope labeled with a picture, word, or image of the item to be purchased.
• Later, students locate the item to be purchased and match the correct envelope to make a single purchase in the cafeteria, school store, or in the community, etc.

• Student points to the appropriate number on a number line when looking at items priced at different whole-dollar amounts.
• Student identifies 3 items that he/she would like to purchase from the Internet, then creates a collage of the items and pastes the correct flashcard number with the dollar amount indicated in each item.
• Student matches the dollar amount in the price of an item to the number on a work sample.
• Student uses a flyer to find 10 items priced at whole-dollar amounts ranging from $1-$10.
• A series of sequenced captioned photographs exhibit the student matching the correct envelope to the item to be purchased in a given setting.
• Teacher collects data on the student’s ability to accurately and independently match numbers ranging from 1-10.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Number and Numeration

Alternate Performance Indicator:

Students will use single digit whole numbers to identify locations, quantify groups of objects, and measure distances.

Sample Approaches for this Alternate Performance Indicator (API)

Students use whole numbers to identify locations, group objects and measure distances when:

• Using a pre-programmed phone to match/dial the numbers 1-10 (See sample instructional activity below). (I, S)
• Identifying and match the street number in their address. (I, S)
• Finding the location of a friend’s house by matching the street number in an invitation to the door number.
• Identifying and dialing personal phone number. (E, I, S)
• Matching pairs of socks when doing laundry. (E, I, S)
• Grouping objects or manipulatives by 2’s, 3’s, 4’s. (E, I, S)

Sample Instructional Activity for using a pre-programmed phone to match/dial the numbers 1-10

• With the teacher, students identify 10 family members, friends, important numbers (i.e., 911), and services (i.e., movie theater).
• Each person, important number, or service is paired with a number and picture/photograph.
• Students create a visual book pairing the specific phone number with the specific photo/picture (i.e., Mom and Dad are paired with the number 1).
• Students pair the phone number to be dialed based on the specific photo with the number on the pre-programmed phone.
• Before the students make phone calls they identifiy the number they will call and match the desired number to the correct number on the pre-programmed telephone.

• Using a template, the student matches pictures paired with each phone number to the correct number from one to ten.
• Student matches numbers with photographs/pictures on a worksheet.
• A series of sequenced captioned photographs exhibit the student dialing/selecting a correct phone number.
• Teacher collects data on the student’s ability to identify and dial the correct phone number when requested to do so.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Number and Numeration

Alternate Performance Indicator:

Students will use concrete materials to model numbers and number relationships for whole numbers and simple fractions.

Sample Approaches for this Alternate Performance Indicator (API)

Students model whole numbers and simple fractions with concrete materials by:

• Creating fraction sets, i.e. halves, thirds, fourths (See sample instructional activity below). (E, I)
• Sharing 12 cookies equally with three friends. (E, I, S)
• Dividing a sandwich in half or a pizza in eighths. (E, I, S)
• Using manipulatives to solve simple word problems involving whole numbers and fractions. (E, I, S)
• Using fraction cards to create whole amounts, i.e., one half and two fourths equals one whole. (E, I)

Sample Instructional Activity for creating fraction sets

• Students count out three paper plates and three different colored crayons as materials to create fraction sets.
• Students color code the plates by shading each one with a different colored crayon.
• Students keep one plate intact and label it 1 whole.
• Students, with supervision or guidance, cut the remaining two plates into different fraction sets, including halves and fourths.
• Students use his/her knowledge of fractions to share a pizza with three peers.
• Teacher holds up different pieces of each fraction set and asks the student to identify the indicated fraction.
• The pieces in each fraction set are matched to the appropriate fraction number or word.

• On a video clip, student points to or indicates the indicated fraction.
• Teacher collects data on the student’s ability to identify whole, half, and fourth of an object.
• Student matches pieces in each fraction set to the appropriate fraction number or word.
• Student creates his/her own fraction set using different materials, i.e., sentence strips, an apple, etc.
• A series of sequenced captioned photographs exhibits the student arranging/identifying different fraction amounts with his/her fraction set.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Number and Numeration

Alternate Performance Indicator:

Students will relate counting and grouping using manipulatives.

Sample Approaches for this Alternate Performance Indicator (API)

Students use manipulatives to count and group when:

• Using manipulatives to create sets and count (See sample instructional activity below). (E, I)
• Using objects to solve simple word problems. (E, I, S)
• Counting pictures/name cards removed from a monthly calendar to determine how many days each student was absent/present. (I, S)
• Counting out 5 pennies for a nickel. (E, I, S)
• Using a number line to keep track of the inning number /number of outs in a baseball game. (E, I, S)

Sample Instructional Activity for using manipulatives to create sets and count

• Student takes various types of milk from refrigerator, places them on a cart, and then wheels the cart to the serving cooler.
• Student sorts various types of milk using carton color and lines them up in serving cooler.
• Student creates sets of ten within each category of milk.
• Student counts each group of ten to determine total number of whole, chocolate, strawberry, skim and 2% milk and records totals on tracking chart with teacher support.

• A series of sequenced captioned photographs exhibit the student sorting the milk cartons by type color and placing milk cartons in cooler in sets of ten.
• As evident in a video clip, the student counts each pile out loud to determine the total number in each pile.
• The teacher collects data on the student’s ability to sort milk into sets of ten.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Number and Numeration

Alternate Performance Indicator:

Students will recognize the order of whole numbers up to 12 and commonly used simple fractions.

Sample Approaches for this Alternate Performance Indicator (API)

Students order whole numbers and use simple fractions when:

• Following a numbered list in order from first to last (See sample instructional activity below). (E, I, S)
• Using manipulatives to demonstrate piles of numbers 1-12. (E, I)
• Placing flashcards of the numbers 1-12 in order. (E, I, S)
• Arranging fractions in order using manipulatives. (E, I, S)
• Recognizing that an eighth of a pizza is smaller than a fourth. (E, I, S)
• Comparing two whole numbers or fractions and identify which number is smaller, larger, and/or whether they are the same number. (E, I, S)
• Finding the correct page in a book, using knowledge of order of numbers. (I, S)

Sample Instructional Activity for following a numbered list in order from first to last

• Teacher has paired each numbered step of the task with a picture of the task to be completed.
• Students are presented with five steps of a simple task, i.e., feeding the classroom pet.
• Students follow and complete the steps of the task in order from numbers 1 to 5.
• Students identify the first step as number 1 and the last step as number 5.
• Students use pictures to place each step of a simple task in order.
• Students identify another school task and sequence the task into five individual steps from beginning to end.

• A series of sequenced captioned photographs exhibit the student participating in a task by sequencing each step of the task in order.
• Student creates a poster with pictures and drawings to demonstrate five individual steps of a simple task from beginning to end.
• Teacher collects data on the student’s ability to put the numbers one to five in order.
• Teacher graphs the student’s accuracy and independence when sequencing a numbered task in the correct order.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Number and Numeration

Alternate Performance Indicator:

Students will recognize coins and dollars and their value.

Sample Approaches for this Alternate Performance Indicator (API)

Students recognize the value of coins and dollars during situations such as:

• Identifying the coins and/or bills necessary to purchase a food item in the school cafeteria (See sample instructional activity below). (E, I, S)
• Recognizing that coins are less valuable than paper money. (I, S)
• Placing coin and dollar values in order. (E, I, S)
• Matching the price of an item in the store to an amount in a sale advertisement. (I, S)
• Identifying the whole dollar amount when making a purchase. (I, S)
• Using different coin sets to identify the same amount. (I, S)
• Matching coin amounts to values on store coupons. (I, S)

Sample Instructional Activity for identifying the coins and/or bills necessary to purchase a food item in the school cafeteria

• Teacher prepares flash cards for food items commonly purchased in the cafeteria.
• Each flash card contains a photograph of the food item paired with the coins and/or bills necessary for purchasing the item. For instance, a card with a picture of milk and one quarter, one dime and one nickel glued on the card.
• Students choose the card corresponding with the food item that he/she will purchase in the cafeteria.
• Students take the card to the cafeteria with a wallet containing paper money and coins.
• Students take out coins and match each coin/bill necessary to purchase the particular item.
• Students give the correct amount to the cashier.
• Students create new flashcards of items on the school lunch menu paired with the appropriate monetary value.

• A series of sequenced captioned photographs exhibits the student matching coins and bills through 1:1 correspondence.
• Teacher collects data on the student’s ability to identify and match coins and bills.
• Teacher collects data on the student’s accuracy and independence to make a purchase correctly.
• A video clip exhibits the student successfully completing a purchase for the exact amount with his/her flashcard(s). The video confirms the documented level of independence and accuracy.
• Student creates a visual of common coins/bills and corresponding value (work sample).

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Operations

Alternate Performance Indicator:

Students will add and subtract whole numbers under 12 using manipulatives or a calculator.

Sample Approaches for this Alternate Performance Indicator (API)

Students add and subtract whole numbers when:

• Identifying key words referring to addition and subtraction to solve word problems correctly (See sample instructional activity below). ( I, S)
• Using blocks to add two plus two. (E, I)
• Using a calculator to subtract one from ten. (I, S)
• Renting three movies from the video store. Then, returning two that were viewed and then communicating that one movie has not been returned/watched. (I, S)
• Counting out four markers for three different students. (I, S)
• Using a calculator to add purchases made at a store. (I, S)

Sample Instructional Activity for identifying key words referring to addition and subtraction to solve word problems correctly.

• Students are guided to create a chart of words that represent adding (all together, in all, total) or subtracting (remain, left, how many more).
• Teacher creates simple word problems involving addition and subtraction, such as:
• Mary has 5 markers. John has 3 markers. How many markers do Mary and John have all together?
• Sandy bought 6 bottles of water. She drank 4 bottles of water. How many bottles of water are left?
• Jessie has 6 dollars. Bobby has 8 dollars. How many more dollars does Bobby have?
• Students identify the word that indicates which operation to perform in each word problem.
• Students use manipulatives and/or a calculator to solve the problem using the correct operation.

• Student underlines the word that reminds him/her to add or subtract on a worksheet, then writes the symbol for the correct operation over the identified word.
• A series of sequenced captioned photographs demonstrate the student’s ability to solve a simple word problem correctly using manipulatives.
• Student creates his/her own addition or subtraction problem and draws a picture to represent the solution.
• Teacher collects data on the student’s accuracy and independence when adding or subtracting whole numbers under 12.
• Teacher graphs the student’s accuracy and independence at solving simple addition and subtraction problems over time.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Measurement

Alternate Performance Indicator:

Students will use appropriate standard and nonstandard measurement tools in measurement activities.

Sample Approaches for this Alternate Performance Indicator (API)

Students use measurement tools when:

• Identifying the measurement with the corresponding tool (See sample instructional activity below). (E, I, S)
• Measuring ingredients for a recipe using measuring cups (1 cup, ½ cup) and measuring spoons (tablespoon, teaspoon). (E, I, S)
• Measuring the length of an object using paper clips, finger width, or blocks. (E, I)
• Using a ruler to measure the growth of a plant in class. (E)
• Using pictures on a daily schedule to keep track of time throughout the school day. (E, I, S)

Sample Instructional Activity for identifying the measurement with the corresponding tool

• Teacher reviews different types of measurement with the student such as length, height, weight, temperature, time, etc.
• Students use the computer to find pictures/clip-art that will represent different things to be measured.
• Teacher pairs each tool with the student’s pictures.
• Students identify the measurement each tool will be used to determine.
• Teacher presents different scenarios/problems related to measurement.
• Students identify the tool that will need to be used in each scenario/problem.

• The teacher collects data as the student correctly pairs the measurement tool with the appropriate situation.
• The student matches pictures of each measurement tool to the appropriate measurement (work sample).
• The student creates a measurement book with each page identifying a different tool, what it measures, a drawing of the tool, and a situation when the tool can be used.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of numbers (i.e.: systems, geometry, algebra, data analysis, probability, and trigonometry).

Alternate Level: Measurement

Alternate Performance Indicator:

Students will understand the simple attributes of length, weight, volume, time, and temperature.

Sample Approaches for this Alternate Performance Indicator (API)

Students demonstrate understanding of simple attributes involving measurement by:

• Using an adapted thermometer to determine the appropriate clothing to wear based on a given temperature (See sample instructional activity below). (E, I, S)
• Using a digital or analog clock to tell time to the hour and half-hour. (E, I, S)
• Using an environmental cue (school bell) to follow the school schedule. (E, I, S)
• Using a calendar to mark days completed. (E, I, S)
• Recording special events and holidays on a calendar using picture symbols. (E, I, S)
• Using a scale to weigh oneself. (I, S)
• Filling a beaker to the correct measurement line to determine volume. (I, S)

Sample Instructional Activity for using an adapted thermometer to determine the appropriate clothing to wear based on a given temperature

• Teacher creates an adapted thermometer, separating the numerical values into four qualitative values: hot, warm cool, and cold.
• Students use a variety of sources to determine the daily temperature (television, newspaper, Internet).
• Students match the temperature to the adapted thermometer and identifies whether it will be hot, warm, cool or cold.
• Students match the weather type to appropriate clothing to wear on that day (i.e., cold à scarf).

• Teacher collects data when the student matches the daily temperature to the adapted thermometer and determines the weather type.
• Student creates his/her own adapted thermometer using the teacher’s thermometer as a model (work sample).
• Student creates a poster divided into four cells, containing each weather type and pictures of clothing appropriate for the particular weather.
• Given a set of degrees, a series of sequenced captioned photographs or video documents the student’s level of independence and accuracy in using his/her thermometer to find temperature values (hot, warm, cool, cold) listed on a worksheet.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Measurement

Alternate Performance Indicator:

Students will measure the length or volume of an object.

Sample Approaches for this Alternate Performance Indicator (API)

Students measure the length or volume of an object when:

• Counting and measuring the sides of different shapes (See sample instructional activity below). (E, I, S)
• Performing basic measurements, such as length, width and height. (I, S)
• Filling a liquid measuring cup to a particular volume when watering classroom plants. (E, I, S)
• Using a growth chart to measure height. (E, I)
• Comparing two objects and describing similarities/differences in length or volume (longer, shorter, more, less). (E, I, S)

Sample Instructional Activity for counting and measuring the sides of different shapes

• Students are given four pieces of wood of equal length.
• Students are guided to make a square picture frame with the four pieces of wood.
• Students are then given 6 pieces of wood, four of which have the same length.
• Students select four pieces of the same size from the 6 pieces and form a square picture frame.

• Teacher collects data on the student’s ability to select pieces of wood of equal size.
• Teacher collects data on the student’s selection of four pieces of wood to form a square picture frame.
• A series of sequenced captioned photographs or a video clip indicate the students’ level of accuracy and independence in selecting wood of equal length and forming a square picture frame.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Measurement

Alternate Performance Indicator:

Students will collect and display simple data.

Sample Approaches for this Alternate Performance Indicator (API)

Students collect and display simple data in activities that include:

• Keeping a ledger of the number of dollars earned from a given job (See sample instructional activity below). (S)
• Charting and taking photographs to describe the growth of a plant over time. (E, I)
• Graphing one’s change in height and weight over time. (I, S)
• Recording the number of sit-ups and push-ups completed during each gym class. (E, I, S)
• Identifying the number of school days which have passed and that remain in a school year. (E)

Sample Instructional Activity for keeping a ledger of the amount of money earned from given job

• Teacher sets up a ledger on which the student will record the amount of money earned each week he/she works.
• When students receive his/her pay, he/she records the amount of money earned in the correct location of the ledger.
• Students use a calculator to add the amount earned to the total amount of previous earnings.

• Students make adjustments in his/her ledger when he/she makes a purchase.

• Teacher collects data on the student’s level of independence and accuracy recording his/her weekly earnings and determining his/her total amount earned, identifying the balance.
• Student creates a graph on the computer, with teacher assistance, to demonstrate his/her increase in total earnings over time.
• Student uses a graphic organizer to record his weekly earnings each week.
• In a video clip, the student refers to his/her ledger to answer questions about his/her weekly earnings and ledger balance.
• A series of sequenced captioned photographs or video demonstrates the student completing his ledger for a given week. The evidence must verify the documented level of independence or accuracy.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Patterns/Functions

Alternate Performance Indicator:

Students will recognize and duplicate simple patterns.

Sample Approaches for this Alternate Performance Indicator (API)

Students recognize and duplicate simple patterns when:

• Using manipulatives to explain, copy, create, and extend a simple pattern (See sample instructional activity below). (E, I, S)
• Identifying recurring patterns in daily schedule or a common routine. (E, I, S)
• Using a template to organize a set of materials for a work-related activity. (I, S)
• Following a routine task in the same way on different occasions. (I, S)

Sample Instructional Activity for using manipulatives to explain, copy, create, and extend a simple pattern

• Teacher uses manipulatives to demonstrate a simple pattern, such as red, blue; red, blue; red, blue.
• Students create the pattern using similar manipulatives.
• Students extend the pattern beyond what was demonstrated.
• Students use different colored blocks to create his/her own pattern, such as yellow, green; yellow, green.
• Teacher presents different sets of patterns.
• Given the various patterns, students extend each set.

• Teacher collects data on the student’s ability to explain, copy, and extend a given pattern.
• A series of sequenced captioned photographs or video demonstrates the student’s level of independence and accuracy copying a pattern from a template and extending the pattern with manipulatives.
• In a video clip, student communicates the pattern demonstrated (i.e., activating colors on a communication box overlay).
• Student creates a drawing of a simple pattern (work sample).

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Patterns/Functions

Alternate Performance Indicator:

Students will use a variety of manipulative materials and technologies to explore patterns.

Sample Approaches for this Alternate Performance Indicator (API)

Students can explore patterns with various manipulatives or technologies by:

• Identifying and describing patterns that exist in a particular sport or game (See sample instructional activity below). (I, S)
• Reviewing a pattern and discussing the likeliness or probability that a pattern will continue to occur. (I, S)
• Creating a pattern using a variety of art materials. (I, S)
• Finding patterns of numbers on a 100’s chart. (I, S)
• Drawing a picture representing a creative pattern. (I, S)
• Using a drawing software program to create a simple pattern. (I, S)

Sample Instructional Activity for identifying and describing patterns that exist in a particular sport or game

• Teacher explains the patterns evident in a baseball game.
• Teacher demonstrates each pattern using laminated number and word cards (top/bottom, 3 strikes = 1 out, 3 outs = half an inning).
• Students watch an inning of a taped baseball game and identify the patterns discussed by the teacher.
• Students participate in a game of baseball in gym class and follow the patterns (rules) of the game.
• Students watch a baseball game after school and describe the patterns he/she observes to a peer.

• Student creates a visual to represent different patterns in a baseball game (i.e., balls, strikes, three outs, player runs to first base before other bases).
• A series of sequenced captioned photographs or video demonstrates the student’s level of independence and accuracy in arranging cards on a Velcro board to keep track of the patterns during each inning.
• Teacher graphs the student’s ability to identify, explain, and follow the pattern in a sport or game (balls, strikes, outs).

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 3 – Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Alternate Level: Patterns/Functions

Alternate Performance Indicator:

Students will recognize simple patterns in nature, art, music, and literature.

Sample Approaches for this Alternate Performance Indicator (API)

Students recognize simple patterns across their curriculum when:

• Identifying recurring patterns in nature, such as day and night, the four seasons, or the patterns in a butterfly’s wing or caterpillar’s back (See sample instructional activity below). (E, I, S)
• Recognizing patterns in art, such as paint by numbers. (I, S)
• Listening to a story and predicting or repeating the pattern in the story. (E)
• Writing a poem representing a particular pattern. (E, I, S)
• Recognizing the pattern of repeating the chorus in a popular song. (E, I, S)
• Sequencing a group of pictures or events to demonstrate the pattern in a given piece of literature. (E, I, S)

Sample Instructional Activity for identifying recurring patterns in nature, such as patterns in a butterfly’s wing or a caterpillar’s back

• Teacher describes that a pattern occurs when something repeats, or happens over and over again.
• Teacher shows pictures of insects to demonstrate repeating patterns such as patterns on a butterfly’s wings or patterns on a caterpillar’s back.
• Teacher sends away for butterfly cocoons and students hatch butterflies, study patterns and release the butterflies.
• Students are provided a drawing of a butterfly or caterpillar with a pattern shown/started. The student repeats/draws the pattern.

• Teacher records data on the student’s level of independence and accuracy repeating the pattern of a butterfly’s wing or a caterpillar’s back using a drawing.
• Student selects pictures of insects from nature magazines where patterns are shown.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 6 – Interconnectedness: Common Themes

Students will understand the relationships and common themes that connect mathematics, science and technology and apply the themes to these and other areas of learning.

Alternate Level: Magnitude and Scale

Alternate Performance Indicator:

Students provide examples of natural and manufactured things that belong to the same category yet have very different sizes, weights, ages, speeds, and other measurements.

Sample Approaches for this Alternate Performance Indicator (API)

Students provide examples of things that belong to the same category but have different attributes when:

• Placing modes of transportation (i.e., bike, car, bus) on a continuum from small to big (See sample instructional activity below). (E, I, S)
• Comparing the weight of small and large animals (mouse vs. rabbit). (E, I, S)
• Comparing the average age of students in high school and college. (I, S)
• Selecting the appropriate size clothing for oneself when shopping. (I, S)
• Compare fruit-bearing trees to hardwood trees (oak, maple, etc.). (E, I, S)

Sample Instructional Activity for placing modes of transportation (i.e., bike, car, bus) on a continuum from small to big

• Using a videotape of each mode of transportation, the teacher describes the size difference between a bike, car, and bus.
• Students create a brainstorm list of variables to compare size of each vehicle with teacher.
• Teacher further demonstrates size difference by comparing each mode of transportation for each variable, such as number of wheels, number of possible passengers, weight of each vehicle, etc.
• Students place the modes of transportation in order from small to big.

• Student creates graphs comparing each mode of transportation for number of wheels, number of possible passengers, weight of each vehicle, etc.
• Student creates poster, which demonstrates the continuum of modes of transportation from small to big.
• On a video clip, the student uses his/her mode of communication to describe size difference based on a given variable.
• Teacher collects data on the student’s level of independence and accuracy for distinguishing size attributes for different items in the same category.

MATHEMATICS, SCIENCE AND TECHNOLOGY
Standard 6 – Interconnectedness: Common Themes

Students will understand the relationships and common themes that connect mathematics, science and technology and apply the themes to these and other areas of learning.

Alternate Level: Magnitude and Scale

Alternate Performance Indicator:

Students identify the biggest and the smallest of values of a system when given information about its characteristics and behavior.

Sample Approaches for this Alternate Performance Indicator (API)

Students identify the biggest and the smallest of values of a system when:

• Collecting and comparing data related to the age of students in their class/grade/school, identifying oldest and youngest (See sample instructional activity below). (E, I)
• Comparing two sizes of the same item to be purchased for price and value. (S)
• Determining the area of three similar shapes of different size and ordering the shapes from biggest to smallest. (S)
• Recording the price of different models of the same item (i.e., CD players) from a catalog and sorting from least expensive to most expensive. (S)

Sample Instructional Activity for collecting and comparing data related to the age of students in their class, identifying oldest and youngest

• Teacher provides the student with a piece of graph paper with 1-inch cells.
• Teacher places the numbers 1-20 on the vertical side of the graph.
• Teacher places a picture of each student on the horizontal side of the graph.
• Students use bingo stamps to graph the age of each student on the graph.
• When the graph is complete, students identify the tallest bar as the oldest student, and the shortest bar as the youngest student.

• In a video clip, the student uses his/her communication system to ask each student his/her age and then documents the information on his/her chart.
• The student develops a graph with oldest/youngest or tallest/shortest (work sample).
• A series of sequenced captioned photographs or video exhibits the student’s level of independence and accuracy when graphing the age of a student on his/her graph.
• The teacher collects data on the student’s ability to graph information such as oldest/youngest, tallest/shortest.