Grade 7… · Web viewGloucester Township Public Schools. Math Curriculum – updated Summer...

Gloucester Township Public SchoolsMath Curriculum – updated Summer 2017

Grade 7

OverviewMathematics is a universal language enmeshed in both the everyday experiences of human society and the natural world

around us. The Gloucester Township Public School District recognizes that mathematics is a fluid and intricately connected web of conceptual understandings, as opposed to segmented isolated skills and arbitrary units of study.

A nation that trains and prepares students to become mathematically literate problem solvers is an entity that sends citizens into the workforce ready to compete in a global economy laden with technology and problem solving opportunities. A school district that intends to have an accomplished field of mathematicians, engineers, medical professionals, scientists, and innovative entrepreneurs must plan and prepare standards-based curriculum that adheres to the Common Core Standards, includes 21st Century technology skills, and explores the variety of careers steeped in mathematics.

In consideration of the rigor and depth of mastery needed by students in our Nation's public school system, we have constructed the following curriculum guide and supporting documentation for Gloucester Township Public Schools through adoption of the New Jersey Department of Education Model Curriculum for Mathematics. Every student in our schools shall have the opportunity to become engaged in an enriching, real world approach to mathematics instruction that is based on solid educational research and data-driven instruction.

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Benchmark and Cross Curricular Key

__Red: ELA

__ Blue: Math

__ Green: Science

__ Orange: Social Studies

__ Purple: Related Arts

__ Yellow: Benchmark Assessment

Math – Grade SevenUnit 1- The Number System

Standards Topics Activities Resources Assessments7.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.

a. Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

- Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

- Compare and order rational numbers both positive and negative

- Add integers using a number line

- Add integers using a model

- Subtract integers using a number line

- Subtract integers using a model

Absolute Value

Inquiry Lab 3-2Inquiry Lab 3-3Inquiry Lab 4-3STEM ProjectsUnit Projects

Geometer’s SketchpadReal-World Math

3-23-34-34-44-5

-STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational


Inquiry Lab 3-4 (two in this section)

3-43-54-14-24-64-7

-STAR MathAre You Ready?Pre-testChapter QuizVocabulary Test

2

numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

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

d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

- Multiply integers

- Divide integers

4-8 Chapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)


- Adding, subtracting, multiplying, and dividing rational numbers using real world word problems.

Inquiry Lab 3-2Inquiry Lab 3-3

Ch3 PSI (Problem Solving Invest)


Ch4 PSICh5 PSI

1-23-23-33-43-54-34-44-54-64-74-8


*Resource Room

Math – Grade SevenUnit 2- Expressions and Equations

Standards Topics Activities Resources Assessments

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7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

- Use properties of operations to generate equivalent expressions.

- Evaluate a numerical expression, with parentheses and exponents, using order of operations.

Inquiry Lab 5-8STEM ProjectsUnit Projects


5-35-45-55-65-75-8


*Resource Room

7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

- Use properties of operations to generate equivalent expressions.

- Writing Equations

2-65-35-45-55-65-75-8


*Resource Room7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

- Solve real‐life and mathematical problems using numerical and algebraic expressions and equations.

- Multi-step problem solving using real world scenarios.

- Ex.) Whole number, fractions, and decimals


Ch2 PSIInquiry Lab 2-5

Ch3 PSICh4 PSICh6 Psi

2-12-22-42-52-62-72-83-23-44-14-24-34-44-54-64-8


*Resource Room

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.

- Solve real‐life and mathematical problems using numerical and algebraic expressions and

Inquiry Lab 6-1Inquiry Lab 6-2Inquiry Lab 6-3Inquiry Lab 6-4

6-16-26-36-4

-STAR MathAre You Ready?Pre-test

4

a. 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?

b. 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.

equations.

- Use the distributive property to simplify an algebraic expression.

- Solve a 2-step linear inequality in one variable.

- Determine the graph of the solutions to a 2-step linear inequality in one variable.


6-56-66-76-8

Chapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

Math – Grade SevenUnit 3 – Ratios and Proportions

Standards Topics Activities Resources Assessments7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

- Analyze proportional relationships and use them to solve real‐world and mathematical problems.

Inquiry Lab 1-1STEM ProjectsUnit Projects

1-2 -STAR MathAre You Ready?

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For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour.

- Determine a unit rate.

- Use a unit rate to solve a problem.

- Solve using like and different unit rates.

Geometer’s Sketchpad

Real-World Math

Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room7.RP.2. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.


- Solve a proportion using tables, graphs, and equations.

- Writing proportional relationships and equations.

- Determine a graph that can represent a situation involving a varying rate of change.

Inquiry Lab 1-1Ch1 PSI


1-11-31-41-51-61-71-81-92-4


*Resource Room

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7.RP.3. Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.


- Solving proportional problems with real world financial problems.


Ch2 PSIInquiry Lab 2-5Inquiry Lab 2-8

1-31-62-12-22-32-42-52-62-72-84-7


*Resource Room

7.G.1. Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

- Draw, construct, and describe geometrical figures and describe the relationships between them.

Ch7 PSI

Inquiry Lab 7-4(two in this

section)

7-4 -STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

7.G.2. Draw (with technology, with ruler and protractor as well as freehand) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.


Inquiry Lab 7-3(two in this

section)

7-3 -STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*

7

Chapter Test 2A & 2B

*Resource Room

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Math – Grade SevenUnit 4 – Statistics and Probability

Standards Topics Activities Resources Assessments7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.


STEM ProjectsUnit ProjectsGeometer’s Sketchpad

Real-World Math


*Resource Room7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

- Use random sampling to draw inferences about a population.

Ch10 PSI 10-110-2


*Resource Room7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

- Use random sampling to draw inferences about a population.

- Estimate and predict based on random samples for a population.

Inquiry Lab 10-2 10-110-2


*Resource Room7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the

- Draw informal comparative inferences about two populations.

Inquiry Lab 10-4(two in this section)

-STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*

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soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Chapter Test 2A & 2B

*Resource Room

7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

- Draw informal comparative inferences about two populations.

- Use measures of center to draw informal inferences about two populations

Inquiry Lab 10-4 10-4 -STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

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. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

- Investigate chance processes and develop, use, and evaluate probability models. - Understanding chance events between 0-1.

9-19-5


*Resource Room

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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

- Investigate chance processes and develop, use, and evaluate probability models.

- Evaluate chance events to predict outcomes.

Inquiry Lab 9-2 -STAR MathAre You Ready?Pre-testChapter QuizVocabulary TestChapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

7.SP.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.


- Develop a probability model from

Inquiry Lab 9-2(two in this section)

9-19-2

-STAR MathAre You Ready?Pre-testChapter QuizVocabulary Test

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a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

experimental and theoretical probability

Chapter Test 1A & 1B*Chapter Test 2A & 2B

*Resource Room

7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?


- Evaluate compound events using organized lists, tables, tree diagrams, and experiments.

- Calculate probability of independent events or dependent events.

- Use permutations and combinations.

Inquiry Lab 9-4Ch9 PSI

Inquiry Lab 9-7

9-39-49-59-69-7


*Resource Room

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Math – Grade SevenUnit 5 - Geometry

Standards Topics Activities Resources Assessments7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.


- Multi-step problem solving using real world scenarios.

Ex.) Whole number, fractions, and decimals


Ch2 PSIInquiry Lab 2-5

Ch3 PSICh4 PSICh6 PSI

STEM ProjectsUnit Projects


2-12-22-42-52-62-72-83-23-44-14-24-34-44-54-64-8


*Resource Room

12

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.

a. 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?

b. 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.


- Use the distributive property to simplify an algebraic expression.

- Solve a 2-step linear inequality in one variable.

- Determine the graph of the solutions to a 2-step linear inequality in one variable.

Inquiry Lab 6-1Inquiry Lab 6-2Inquiry Lab 6-3Inquiry Lab 6-4Inquiry Lab 6-5Inquiry Lab 6-6

6-16-26-36-46-56-66-76-8


*Resource Room

7.G.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.


- Describe 2D shapes when sliced from 3D shapes.

- Comparing prisms and pyramids.


*Resource Room

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7.G.4. Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

- Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume.

- Problems for circumference and area of circles.


Ch8 PSI

8-18-28-3


*Resource Room7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.


- Analyze angle relationships to write and use equations to solve for missing information.

7-17-2


*Resource Room

7.G.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.

- Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume.

- Solve for area, volume, and surface area of the following shapes; triangles, quadrilaterals, polygons, cubes, and right prisms.

Ch8 PSIInquiry Lab 8-5Inquiry Lab 8-6Inquiry Lab 8-8

8-38-48-58-68-78-8


*Resource Room

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Appendix A Adaptations for Special Education Students, English Language Learners, and Gifted and Talented Students

Making Instructional Adaptations

Instructional Adaptations include both accommodations and modifications.

An accommodation is a change that helps a student overcome or work around a disability or removes a barrier to learning for any student.

Usually a modification means a change in what is being taught to or expected from a student.

-Adapted from the National Dissemination Center for Children with Disabilities

ACCOMMODATIONS MODIFICATIONSRequired when on an IEP or 504 plan, but can be implemented for any student to support their learning.

Only when written in an IEP.

Special Education Instructional Accommodations

Teachers will use Approaching Level Tier 2: Strategic Intervention in RtI Differentiated Instruction section of Glencoe lessons.

Teachers will use the Targeted Strategic Intervention from the Glencoe Online Support. Teachers shall implement any instructional adaptations written in student IEPs. Teachers will implement strategies for all Learning Styles (Appendix B) Teacher will implement appropriate UDL instructional adaptations (Appendix C )

Gifted and Talented Instructional Accommodations

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Teachers will use Beyond Level in RtI Differentiated Instruction section of Glencoe lessons Teachers will use the Enrichment Masters from the Glencoe Online Support Teacher will implement Adaptations for Learning Styles (Appendix B) Teacher will implement appropriate UDL instructional adaptations (Appendix C)

English Language Learner Instructional Accommodations

Teachers will use the ELL Differentiated English Language Learner Support section of Glencoe lessons. Teachers will use the Differentiated ELL Support from the Glencoe Online Support. Teachers will implement the appropriate Teachers will implement the appropriate instructional adaptions for English Language Leaners (Appendix E)

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APPENDIX BLearning Styles

Aadapted from The Learning Combination Inventories (Johnson, 1997)and VAK (Fleming, 1987)

Accommodating Different Learning Styles in the Classroom:All learners have a unique blend of sequential, precise, technical, and confluent learning styles. Additionally, all learners

have a preferred mode of processing information- visual, audio, or kinesthetic.It is important to consider these differences when lesson planning, providing instruction, and when differentiating

learning activities. The following recommendations are accommodations for learning styles that can be utilized for all students in your class.

Since all learning styles may be represented in your class, it is effective to use multiple means of presenting information, allow students to interact with information in multiple ways, and allow multiple ways for students to show what they have learned when applicable.

Visual Utilize Charts, graphs, concept maps/webs, pictures, and cartoons

Watch videos to learn information and concepts

Encourage students to visualize events as they read math word problems

Use flash cards to practice basic math facts

Model by demonstrating tasks or showing a finished product

Have written directions available for student

Use power point presentations

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Color code and highlight operation symbols (+, -, x, ÷)

Color code and highlight key words in math word problems

Audio Allow students to give oral presentations or explain concepts verbally

Present information and directions verbally or encourage students to read directions aloud to themselves.

Allow students to work in pairs

Utilize songs and rhymes

Ask for choral responses in instruction, example have the entire class chant in unison multiples, evens/odds, or skip counting by 2s, 5,s or 10s

Repeat, clarify, or reword directions

Verbally guide students through task steps

Kinesthetic Act out concepts and dramatize events

Use flash cards

Use manipulatives

Allow students to deepen knowledge through hands on projects

Sequential: following a plan. The learner seeks to follow step-by-step directions, organize and plan work carefully, and complete the assignment from beginning to end without interruptions.Accommodations: Repeat/rephrase directionsProvide a checklist or step by step written directionsBreak assignments in to chunksProvide samples of desired productsHelp the sequential students overcome these challenges: over planning and not finishing a task, difficulty reassessing and improving a plan, spending too much time on directions and neatness and overlooking concepts

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Precise: seeking and processing detailed information carefully and accurately. The learner takes detailed notes, asks questions to find out more information, seeks and responds with exact answers, and reads and writes in a highly specific manner.Accommodations: Provide detailed directions for assignmentsProvide checklistsProvide frequent feedback and encouragementHelp precise students overcome these challenges: overanalyzing information, asking too many questions, focusing on details only and not concepts

Technical: working autonomously, "hands-on," unencumbered by paper-and-pencil requirements. The learner uses technical reasoning to figure out how to do things, works alone without interference, displays knowledge by physically demonstrating skills, and learns from real-world experiencesAccommodations: Allow to work independently or as a leader of a groupGive opportunities to solve problems and not memorize informationPlan hands-on tasksExplain relevance and real world application of the learningWill be likely to respond to intrinsic motivators, and may not be motivated by gradesHelp technical students overcome these challenges: may not like reading or writing, difficulty remaining focused while seated, does not see the relevance of many assignments, difficulty paying attention to lengthy directions or lectures

Confluent: avoiding conventional approaches; seeking unique ways to complete any learning task. The learner often starts before all directions are given; takes a risk, fails, and starts again; uses imaginative ideas and unusual approaches; and improvises.Accommodations: Allow choice in assignmentsEncourage creative solutions to problemsAllow students to experiment or use trial and error approachWill likely be motivated by autonomy within a task and creative assignmentsHelp confluent students overcome these challenges: may not finish tasks, trouble proofreading or paying attention to detail

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APPENDIX CUniversal Design for Learning Adaptations

Adapted from Universal Design For Learning

Teachers will utilize the examples below as a menu of adaptation ideas.

Provide Multiple Means of Representation

Strategy #1: Options for perception

Goal/Purpose ExamplesTo present information through different modalities such as vision, hearing, or touch.

Use visual demonstrations, illustrations, and models

Present a power point presentation.

Use appropriate manipulatives, such as base 10 block, counters, or pattern blocks

Differentiate operation symbols by color coding

Draw pictures when possible

Use interactive websites and apps

Use modeling to help students solve problems

Provide examples of a correctly solved problem at the

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beginning of each lesson

Have students work each step in a different color

Use songs and rhymes to help remember information

Use mnemonics like “Please Excuse My Dear Aunt Sally” (order of operations) to remember sequenced steps

Simplify and rephrase vocabulary in word problems

Strategy #2: Options for language, mathematical expressions and symbols

Goal/Purpose ExamplesTo make words, symbols, pictures, and mathematical notation clear for all students.

Use larger font size and/or magnifiers

Highlight important parts of problems, example: key words or operation signs

Use place value charts, number grids, and operation tables (addition/subtraction and multiplication/division tables)

Allow students to trace important visual patterns

Use graph paper to keep numbers aligned

Put boxes around each problem to visually separate them

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Simplify and rephrase vocabulary in word problem

Turn lined paper vertically so the student has ready made columns

Color code and highlight keywords in math word problems

Strategy #3: Options for Comprehension

Purpose ExamplesTo provide scaffolding so students can access and understand information needed to construct useable knowledge.

Use diagrams.

Use semantic maps and diagrams

Chunk pieces of information together, example: learn facts in sets of 3

Review previous lessons

Use a buddy system to clarify

Use mnemonic aids to signal steps, example “Does McDonalds Sell Cheese Burgers” (long division: divide, multiply, subtract, check, bring down)

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Provide students with a strategy to use for solving word problems

Use graph paper to keep numbers aligned

Use modeling to help students solve problems

Introduce concepts using real life examples whenever possible

Teach fact families and build fluency with games and understanding

When teaching number lines use tape or draw a number line on the floor for students to walk on

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Provide Multiple Means of Action and Expression

Strategy #4: Options for physical action

Purpose ExamplesTo provide materials that all learners can physically utilize

Use of computers when available

Preferential or alternate seating

Provide assistance with organization

Provide graph paper to organize place value

Provide appropriate manipulatives

Use flash cards

Provide highlighters for students when solving problems

Allow students to use desk top copies of fact sheets, multiplication/division tables etc.

Use individual dry-erase boards

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Strategy #5: Options for expression and communication

Purpose ExamplesTo allow the learner to express their knowledge in different ways

Allow oral responses or presentations

Students show their knowledge with charts and graphs

Give students extra time to respond to oral questions

Have students verbally or visually explain how to solve a math problem

Strategy #6: Options for executive function

Purpose ExamplesTo scaffold student ability to set goals, plan, and monitor progress

Provide clear learning goals, scales, and rubrics

Model skills

Utilize checklists

Give examples of desired finished product

Chunk longer assignments into manageable parts

Teach and practice organizational skills

Use a problem solving strategy checklist so that students can monitor their progress

Teach students to use self-questioning techniques

Reduce the number of practice or test problems on a 25

page

Provide Multiple Means of Engagement

Strategy #7: Options for recruiting interest

Purpose ExamplesTo make learning relevant, authentic, interesting, and engaging to the student.

Provide choice and autonomy on assignments

Use colorful and interesting designs, layouts, and graphics

Use games, challenges, or other motivating activities

Provide positive reinforcement for effort

Use manipulatives

Provide learning aids such as calculators and/or operation tables (addition/subtraction and multiplication/division tables)

Introduce concepts using real life examples whenever possible

Use individual dry-erase boardsUse magnetic manipulatives examples: numbers, operation signs, ten frames, base ten blocks, etc.

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Strategy #8: Options for sustaining effort and persistence

Purpose ExamplesTo create extrinsic motivation for learners to stay focused and work hard on tasks.

Show real world applications of the lesson

Utilize collaborative learning

Assign a peer tutor

Incorporate student interests into lesson

Praise growth and effort

Recognition systems

Behavior plans

Repeat directions as needed

Provide immediate feedback

Strategy #9: Options for self-regulation

Purpose ExamplesTo develop intrinsic motivation to control behaviors and to develop self-control.

Give prompts or reminders about self-control

Self-monitored behavior plans using logs, records, journals, or checklists

Ask students to reflect on behavior and effort

Post class rules using pictures and words

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Post daily schedule using pictures and words

Circulate around the room

Develop a signal for when a break is needed

Provide consistent praise to elevate self-esteem

Model and role play problem solving

Desensitize students to anxiety causing events

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Appendix D Gifted and Talented Instructional Accommodations

How do the State of NJ regulations define gifted and talented students?

Those students who possess or demonstrate high levels of ability, in one or more content areas, when compared to their chronological peers in the local district and who require modification of their educational program if they are to achieve in accordance with their capabilities.

What types of instructional accommodations must be made for students identified as gifted and talented?

The State of NJ Department of Education regulations require that district boards of education provide appropriate K-12 services for gifted and talented students. This includes appropriate curricular and instructional modifications for gifted and talented students indicating content, process, products, and learning environment. District boards of education must also take into consideration the PreK-Grade 12 National Gifted Program Standards of the National Association for Gifted Children in developing programs..

What is differentiation?

Curriculum Differentiation is a process teachers use to increase achievement by improving the match between the learner’s unique characteristics:

Prior knowledge Cognitive LevelLearning Rate Learning StyleMotivation Strength or Interest

And various curriculum components:Nature of the Objective Teaching ActivitiesLearning Activities ResourcesProducts

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Differentiation involves changes in the depth or breadth of student learning. Differentiation is enhanced with the use of appropriate classroom management, retesting, flexible small groups, access to support personal, and the availability of appropriate resources, and necessary for gifted learners and students who exhibit gifted behaviors (NRC/GT, University of Connecticut).

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Gifted & Talented Accommodations Chart

Adapted from Association for Supervision and Curriculum Development

Teachers will utilize the examples below as a menu of adaptation ideas.

Strategy Description Suggestions for AccommodationHigh Level Questions

Discussions and tests, ensure the highly able learner is presented with questions that draw on advanced level of information, deeper understanding, and challenging thinking.

Require students to defend answers Use open ended questions Use divergent thinking questions Ask student to extrapolate answers when given

incomplete informationTiered assignments

In a heterogeneous class, teacher uses varied levels of activities to build on prior knowledge and prompt continued growth. Students use varied approaches to exploration of essential ideas.

Use advanced materials Complex activities Transform ideas, not merely reproduce them Open ended activity

Flexible Skills Grouping

Students are matched to skills work by virtue of readiness, not with assumption that all need same spelling task, computation drill, writing assignment, etc. Movement among groups is common, based on readiness on a given skill and growth in that skill.

Exempt gifted learners from basic skills work in areas in which they demonstrate a high level of performance

Gifted learners develop advanced knowledge and skills in areas of talent

Independent Projects

Student and teacher identify problems or topics of interest to student. Both plan method of investigating topic/problem and identifying type of product student will develop. This product should address the problem and demonstrate the student’s ability to apply skills and knowledge to the problem or topic

Primary Interest Inventory Allow student maximum freedom to plan, based

on student readiness for freedom Use preset timelines to zap procrastination Use process logs to document the process

involved throughout the study

Learning Centers

Centers are “Stations” or collections of materials students can use to explore, extend, or practice skills and content. For gifted students, centers should move beyond basic exploration of topics and practice of basic skills.

Develop above level centers as part of classroom instruction

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Instead it should provide greater breadth and depth on interesting and important topics.

Interest Centers or Interest Groups

Interest Centers provide enrichment for students who can demonstrate mastery/competence with required work/content. Interest Centers can be used to provide students with meaningful learning when basic assignments are completed.

Plan interest based centers for use after students have mastered content

Contracts and Management Plans

Contracts are an agreement between the student and teacher where the teacher grants specific freedoms and choices about how a student will complete tasks. The student agrees to use the freedoms appropriately in designing and completing work according to specifications.

Allow gifted students to work independently using a contract for goal setting and accountability

Compacting A 3-step process that (1) assesses what a student knows about material “to be” studied and what the student still needs to master, (2) plans for learning what is not known and excuses student from what is known, and (3) plans for freed-up time to be spent in enriched or accelerated study.

Use pretesting and formative assessments Allow students who complete work or have

mastered skills to complete enrichment activities

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Appendix E English Language Learner Instructional Accommodations

Adapted from World-class Instructional Design and Assessment guidelines (2014), Teachers to English Speakers of Other Languages guidelines, State of NJ Department of Education Bilingual

Math

Instruction: Provide bilingual dictionaries. Simplify language, clarify or explain directions. Build background (discuss, allow for questions, and use visuals if applicable) prior to giving assessment make the text meaningful. Pre-teach difficult vocabulary. Highlight key word or phrases. Allow ELL students to hear word problems twice and have a second opportunity to check their answers. Allow ELL students extended time for word problems. Provide specific seating arrangement (close proximity for direct instruction, teacher assistance, and buddy).

Response: Allow for oral explanations Allow the use of word walls and vocabulary banks.

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Grade 7… · Web viewGloucester Township Public Schools. Math Curriculum – updated Summer...

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