Gloucester Township Public Schools



Gloucester Township Public Schools

Math Curriculum – updated Summer 2017

Grade 6

Overview

Mathematics 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.

Math – Grade Six

Unit 1: Operations and Statistical Variability

|Standards |Topics |Activities |Resources |Assessments |

|6.NS.1. Interpret and compute quotients of fractions, and solve word |Division of Fractions Using |Ch4 PSI |4-6 |-STAR Math |

|problems involving division of fractions by fractions, e.g., by using |Models and Equations |(Problem Solving |4-7 |Are You Ready? |

|visual fraction models and equations to represent the problem. | |Investigation) |4-8 |Pre-test |

| | | | |Chapter Quiz |

|For example, create a story context for (2/3) ÷ (3/4) and use a visual | | | |Vocabulary Test |

|fraction model to show the quotient; use the relationship between | |IQL 4-6 | |Chapter Test 1A & 1B* |

|multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because | |(Inquiry Lab) | |Chapter Test 2A & 2B |

|3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much | | | | |

|chocolate will each person get if 3 people share 1/2 lb of chocolate | |IQL 4-7 | | |

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

|wide is a rectangular strip of land with length 3/4 mi and area 1/2 | |Unit Projects | | |

|square mi? | |Geometer’s Sketchpad | | |

| | |Real-World Math | | |

| | | | | |

| | | | |*Resource Room |

|6.NS.2. Fluently divide multi-digit numbers using the standard algorithm.|Multi-Digit Division | |3-5 |-STAR Math |

| | | |3-6 |Are You Ready? |

| | | | |Pre-test |

| | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals|Add and Subtract Decimals |IQL 3-4 |3-1 |-STAR Math |

|using the standard algorithm for each operation. | |Ch3 PSI |3-3 |Are You Ready? |

| |Multiplying Decimals | |3-4 |Pre-test |

| | | |3-7 |Chapter Quiz |

| |Dividing Decimals | |3-8 |Vocabulary Test |

| | | |6-1 |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.NS.5. Understand that positive and negative numbers are used together |Understanding Positive and |IQL 5-1 |5-1 |-STAR Math |

|to describe quantities having opposite directions or values (e.g., |Negative Number Are Arranged in|IQL 5-2 | |Are You Ready? |

|temperature above/below zero, elevation above/below sea level, |Opposite Directions |Ch5 PSI | |Pre-test |

|credits/debits, positive/negative electric charge); use positive and | | | |Chapter Quiz |

|negative numbers to represent quantities in real-world contexts, |Meaning of Zero in a Situation | | |Vocabulary Test |

|explaining the meaning of 0 in each situation. | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | | |

| | | | |*Resource Room |

|6.SP.1. Recognize a statistical question as one that anticipates |Statistical Questions |IQL 11-1 | |-STAR Math |

|variability in the data related to the question and accounts for it in | |Ch 11 PSI | |Are You Ready? |

|the answers. For example, “How old am I?” is not a statistical question, | | | |Pre-test |

|but “How old are the students in my school?” is a statistical question | | | |Chapter Quiz |

|because one anticipates variability in students’ ages. | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.SP.2. Understand that a set of data collected to answer a statistical |Understanding and Analyzing | |12-3 |-STAR Math |

|question has a distribution which can be described by its center, spread,|Graphs | |12-4 |Are You Ready? |

|and overall shape. | | | |Pre-test |

| | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.SP.3. Recognize that a measure of center for a numerical data set |Median, Mean, Mode, Range, |IQL 11-1 |11-1 |-STAR Math |

|summarizes all of its values with a single number, while a measure of |Maximum and Minimum | |11-2 |Are You Ready? |

|variation describes how its values vary with a single number. | | |11-3 |Pre-test |

| | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.SP.5. Summarize numerical data sets in relation to their context, such |Stem-and Leaf Plots |Ch12 PSI |11-2 |-STAR Math |

|as by: |Median and Mean |IQL 12-4 |11-3 |Are You Ready? |

|a. Reporting the number of observations. |Broken-Line Graph |IQL 12-6 |11-4 |Pre-test |

| |Center | |11-5 |Chapter Quiz |

|b. Describing the nature of the attribute under investigation, including |Variability | |12-1 |Vocabulary Test |

|how it was measured and its units of measurement | | |12-2 |Chapter Test 1A & 1B* |

| | | |12-3 |Chapter Test 2A & 2B |

|c. Giving quantitative measures of center (median and/or mean) and | | |12-4 | |

|variability (interquartile range and/or mean absolute deviation), as well| | | | |

|as describing any overall pattern and any striking deviations from the | | | | |

|overall pattern with reference to the context in which the data were | | | | |

|gathered. | | | | |

| | | | | |

|d. Relating the choice of measures of center and variability to the shape| | | | |

|of the data distribution and the context in which the data were gathered.| | | | |

| | | | | |

| | | | | |

| | | | |*Resource Room |

Math – Grade Six

Unit 2: Expressions

|Standards |Topics |Activities |Resources |Assessments |

|6.EE.1. Write and evaluate numerical expressions involving |Exponents |STEM Projects | |-STAR Math |

|whole-number exponents. | |Unit Projects |6-1 |Are You Ready? |

| | |Geometer’s Sketchpad |6-2 |Pre-test |

| | |Real-World Math | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.EE.2. Write, read, and evaluate expressions in which letters |Evaluating Expressions |IQL 6-1 |6-3 |-STAR Math |

|stand for numbers. | |IQL 6-4 |6-4 |Are You Ready? |

|Write expressions that record operations with numbers and with |Writing Expressions with Variables |Ch6 PSI |6-7 |Pre-test |

|letters standing for numbers. For example, express the calculation | | |8-1 |Chapter Quiz |

|“Subtract y from 5” as 5 – y. |Identifying the Parts of an | |8-2 |Vocabulary Test |

|Identify parts of an expression using mathematical terms (sum, |Expression | | |Chapter Test 1A & 1B* |

|term, product, factor, quotient, coefficient); view one or more | | | |Chapter Test 2A & 2B |

|parts of an expression as a single entity. For example, describe |Evaluate Expression with Specific | | | |

|the expression 2(8+7) as a product of two factors; view (8+7) as |Values | | | |

|both a single entity and a sum of two terms | | | | |

|Evaluate expressions at specific values of their variables. Include|Simplifying Expressions | | | |

|expressions that arise from formulas used in real-world problems. | | | |*Resource Room |

|Perform arithmetic operations, including those involving | | | | |

|whole-number exponents, in the conventional order when there are no| | | | |

|parentheses to specify a particular order (Order of Operations). | | | | |

|For example, use the formulas V=s3 and A=6 s2 to find the volume | | | | |

|and surface area of a cube with sides of length s=1/2. | | | | |

|6.EE.3. Apply the properties of operations to generate equivalent |Associative Property |IQL 6-6 |6-5 |-STAR Math |

|expressions. For example, apply the distributive property to the | | |6-6 |Are You Ready? |

|expression 3 (2 + x) to produce the equivalent expression 6 + 3x; |Commutative Property | |6-7 |Pre-test |

|apply the distributive property to the expression 24x + 18y to | | | |Chapter Quiz |

|produce the equivalent expression 6 (4x + 3y); apply properties of |Distributive Property | | |Vocabulary Test |

|operations to y + y + y to produce the equivalent expression 3y. | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | | |

| | | | |*Resource Room |

|6.EE.4. Identify when two expressions are equivalent (i.e., when |Identifying Equivalent Expressions |IQL 6-7 |6-7 |-STAR Math |

|the two expressions name the same number regardless of which value | | | |Are You Ready? |

|is substituted into them). For example, the expressions y + y + y | | | |Pre-test |

|and 3y are equivalent because they name the same number regardless | | | |Chapter Quiz |

|of which number y stands for. | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.NS.4. Find the greatest common factor of two whole numbers less |Greatest Common Factor | |1-1 |-STAR Math |

|than or equal to 100 and the least common multiple of two whole | | |6-6 |Are You Ready? |

|numbers less than or equal to 12. Use the distributive property to |Least Common Multiple | | |Pre-test |

|express a sum of two whole numbers 1–100 with a common factor as a | | | |Chapter Quiz |

|multiple of a sum of two whole numbers with no common factor. For |Use Distributive Property to Rename | | |Vocabulary Test |

|example, express 36 + 8 as 4(9+2). |Sums of Whole Numbers | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

Math – Grade Six

Unit 3: Equations and Inequalities

|Standards |Topics |Activities |Resources |Assessments |

|6.EE.5. Understand solving an equation or inequality as a process of |Using Specific Values to Solve |IQL 7-2 |7-1 |-STAR Math |

|answering a question: which values from a specified set, if any, make the |Equations or Inequalities |IQL 7-3 |7-2 |Are You Ready? |

|equation or inequality true? Use substitution to determine whether a given | |IQL 7-4 |7-3 |Pre-test |

|number in a specified set makes an equation or inequality true. | |IQL 7-5 |7-4 |Chapter Quiz |

| | |IQL 8-5 |7-5 |Vocabulary Test |

| | |IQL 8-7 |8-5 |Chapter Test 1A & 1B* |

| | |STEM Projects |8-7 |Chapter Test 2A & 2B |

| | |Unit Projects | | |

| | |Geometer’s Sketchpad | |*Resource Room |

| | |Real-World Math | | |

|6.EE.6. Use variables to represent numbers and write expressions when |Use Variables to Write | |6-3 |-STAR Math |

|solving a real-world or mathematical problem; understand that a variable can|Expressions for Real-World | |6-4 |Are You Ready? |

|represent an unknown number, or, depending on the purpose at hand, any |Problems | |8-2 |Pre-test |

|number in a specified set. | | |8-6 |Chapter Quiz |

| |Variables Represent Unknown | |8-7 |Vocabulary Test |

| |Amounts | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | | |

| | | | |*Resource Room |

|6.EE.7. Solve real-world and mathematical problems by writing and solving |Write and Solve Real-World |IQL 7-2 |7-2 |-STAR Math |

|equations of the form x + p = q and px = q for cases in which p, q and x are|Equations |IQL 7-3 |7-3 |Are You Ready? |

|all nonnegative rational numbers | |Ch7 PSI |7-4 |Pre-test |

| | |IQL 7-4 |7-5 |Chapter Quiz |

| | |IQL 7-5 | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.EE.8. Write an inequality of the form x > c or x < c to represent a |Write and Solve Real-World |IQL 8-5 |8-5 |-STAR Math |

|constraint or condition in a real-world or mathematical problem. Recognize |Inequalities |IQL 8-7 |8-6 |Are You Ready? |

|that inequalities of the form x > c or x < c have infinitely many solutions;| | |8-7 |Pre-test |

|represent solutions of such inequalities on number line diagrams. |Recognize Inequalities may have | | |Chapter Quiz |

| |multiple solutions | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | |*Resource Room |

|6.G.1. Find the area of right triangles, other triangles, special |Deriving Formulas for Area |IQL 9-1 |9-1 |-STAR Math |

|quadrilaterals, and polygons by composing into rectangles or decomposing | |IQL 9-2 |9-2 |Are You Ready? |

|into triangles and other shapes; apply these techniques in the context of | |IQL 9-3 |9-3 |Pre-test |

|solving real-world and mathematical problems. | |Ch9 PSI |9-4 |Chapter Quiz |

| | |IQL 9-6 |9-5 |Vocabulary Test |

| | | |9-6 |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.G.2. Find the volume of a right rectangular prism with fractional edge |Find Volume Using Unit Cubes |IQL 10-1 |10-1 |-STAR Math |

|lengths by packing it with unit cubes of the appropriate unit fraction edge | |Ch10 PSI | |Are You Ready? |

|lengths, and show that the volume is the same as would be found by |Apply Volume Formulas to | | |Pre-test |

|multiplying the edge lengths of the prism. Apply the formulas V = l w h and |Real-World Problems | | |Chapter Quiz |

|V = B h to find volumes of right rectangular prisms with fractional edge | | | |Vocabulary Test |

|lengths in the context of solving real-world and mathematical problems. | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | | |

| | | | |*Resource Room |

|6.G.4. Represent three-dimensional figures using nets made up of rectangles |Use Nets to Find Surface Area |Ch10 PSI |10-3 |-STAR Math |

|and triangles, and use the nets to find the surface area of these figures. | |IQL 10-3 |10-4 |Are You Ready? |

|Apply these techniques in the context of solving real-world and mathematical| |IQL 10-4 |10-5 |Pre-test |

|problems. | |IQL 10-5 | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

Math – Grade Six

Unit 4: Rational Numbers

|Standards |Topics |Activities |Resources |Assessments |

|6.NS.6. Understand a rational number as a point on the number line. Extend number line |Opposite Numbers |IQL 5-1 |5-1 |-STAR Math |

|diagrams and coordinate axes familiar from previous grades to represent points on the | |IQL 5-4 |5-2 |Are You Ready? |

|line and in the plane with negative number coordinates. |Understand Changes in Signs of |STEM Projects |5-5 |Pre-test |

|Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the|Ordered Pairs Depending on Quadrant |Unit Projects |5-6 |Chapter Quiz |

|number line; recognize that the opposite of the opposite of a number is the number | |Geometer’s Sketchpad |5-7 |Vocabulary Test |

|itself, e.g., -(-3) = 3, and that 0 is its own opposite. |Position Rational Numbers on Number |Real-World Math | |Chapter Test 1A & 1B* |

|Understand signs of numbers in ordered pairs as indicating locations in quadrants of the |Line | | |Chapter Test 2A & 2B |

|coordinate plane; recognize that when two ordered pairs differ only by signs, the | | | | |

|locations of the points are related by reflections across one or both axes. | | | | |

|Find and position integers and other rational numbers on a horizontal or vertical number | | | |*Resource Room |

|line diagram; find and position pairs of integers and other rational numbers on a | | | | |

|coordinate plane. | | | | |

|6.NS.7. Understand ordering and absolute value of rational numbers. |Comparing Rational Numbers |IQL 5-2 |5-2 |-STAR Math |

|a. Interpret statements of inequality as statements about the relative position of two | |IQL 5-4 |5-3 |Are You Ready? |

|numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 |Absolute Value | |5-5 |Pre-test |

|is located to the right of –7 on a number line oriented from left to right. | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.NS.8. Solve real-world and mathematical problems by graphing points in all four |Graphing Ordered Pairs in Four |IQL 5-7 |5-7 |-STAR Math |

|quadrants of the coordinate plane. Include use of coordinates and absolute value to find |Quadrants | |9-5 |Are You Ready? |

|distances between points with the same first coordinate or the same second coordinate. | | | |Pre-test |

| |Use Absolute Value to Find Distances| | |Chapter Quiz |

| |Between Two Points | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

| | | | | |

| | | | | |

|6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use |Draw Polygons Using Coordinate | |9-5 |-STAR Math |

|coordinates to find the length of a side joining points with the same first coordinate or|Points | | |Are You Ready? |

|the same second coordinate. Apply these techniques in the context of solving real-world | | | |Pre-test |

|and mathematical problems. | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.SP.4. Display numerical data in plots on a number line, including dot plots, |Data with large numbers |Ch12 PSI |12-1 |-STAR Math |

|histograms, and box plots. | |IQL 12-4 |12-2 |Are You Ready? |

| | | |12-3 |Pre-test |

| | | | |Chapter Quiz |

| | | | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.SP.5. Summarize numerical data sets in relation to their context, such as by: |Stem-and Leaf Plots |Ch12 PSI |11-2 |-STAR Math |

|a. Reporting the number of observations. |Median and Mean |IQL 12-4 |11-3 |Are You Ready? |

|b. Describing the nature of the attribute under investigation, including how it was |Broken-Line Graph |IQL 12-6 |11-4 |Pre-test |

|measured and its units of measurement |Center | |11-5 |Chapter Quiz |

|c. Giving quantitative measures of center (median and/or mean) and variability |Variability | |12-1 |Vocabulary Test |

|(interquartile range and/or mean absolute deviation), as well as describing any overall | | |12-2 |Chapter Test 1A & 1B* |

|pattern and any striking deviations from the overall pattern with reference to the | | |12-3 |Chapter Test 2A & 2B |

|context in which the data were gathered. | | |12-4 | |

|d. Relating the choice of measures of center and variability to the shape of the data | | | | |

|distribution and the context in which the data were gathered. | | | |*Resource Room |

Math – Grade Six

Unit 5: Ratio and Proportion

|Standards |Topics |Activities |Resources |Assessments |

|6.RP.1. Understand the concept of a ratio and use ratio language to |Ratios and Ratio Language |IQL 1-2 |1-2 |-STAR Math |

|describe a ratio relationship between two quantities. For example, “The | |STEM Projects | |Are You Ready? |

|ratio of wings to beaks in the bird house at the zoo was 2:1, because for | |Unit Projects | |Pre-test |

|every 2 wings there was 1 beak.” “For every vote candidate A received, | |Geometer’s Sketchpad | |Chapter Quiz |

|candidate C received nearly three votes.” | |Real-World Math | |Vocabulary Test |

| | | | |Chapter Test 1A & 1B* |

| | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | |*Resource Room |

|6.RP.2. Understand the concept of a unit rate a/b associated with a ratio |Unit Rates and Vocabulary |IQL 1-3 |1-3 |-STAR Math |

|a:b with b ≠ 0, and use rate language in the context of a ratio | | | |Are You Ready? |

|relationship. For example, “This recipe has a ratio of 3 cups of flour to 4| | | |Pre-test |

|cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We | | | |Chapter Quiz |

|paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” | | | |Vocabulary Test |

|(Expectations for unit rates in this grade are limited to non-complex | | | |Chapter Test 1A & 1B* |

|fractions.) | | | |Chapter Test 2A & 2B |

| | | | | |

| | | | | |

| | | | |*Resource Room |

|6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical |Decimal / Percent Conversions |IQL 1-2 |1-2 |-STAR Math |

|problems, e.g., by reasoning about tables of equivalent ratios, tape |Percent of a Number |IQL 1-3 |1-3 |Are You Ready? |

|diagrams, double number line diagrams, or equations. | |Ch1 PSI |1-4 |Pre-test |

|Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity | |IQL 1-7 |1-5 |Chapter Quiz |

|means 30/100 times the quantity); solve problems involving finding the | |Ch2 PSI |1-6 |Vocabulary Test |

|whole, given a part and the percent. | |IQL 2-7 |1-7 |Chapter Test 1A & 1B* |

| | | |2-6 |Chapter Test 2A & 2B |

| | | |2-7 | |

| | | |2-8 | |

| | | |4-5 | |

| | | |7-4 |*Resource Room |

|6.EE.9. Use variables to represent two quantities in a real-world problem |Write Equations Using Two |Ch8 PSI |8-1 |-STAR Math |

|that change in relationship to one another; write an equation to express |Variables | |8-2 |Are You Ready? |

|one quantity, thought of as the dependent variable, in terms of the other | | |8-3 |Pre-test |

|quantity, thought of as the independent variable. Analyze the relationship |Dependent and Independent | |8-4 |Chapter Quiz |

|between the dependent and independent variables using graphs and tables, |Variables | | |Vocabulary Test |

|and relate these to the equation. | | | |Chapter Test 1A & 1B* |

| |Understand the Relationship | | |Chapter Test 2A & 2B |

|For example, in a problem involving motion at constant speed, list and |Between Two Variables | | | |

|graph ordered pairs of distances and times, and write the equation d = 65t | | | | |

|to represent the relationship between distance and time. | | | | |

| | | | | |

| | | | | |

| | | | |*Resource Room |

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 |MODIFICATIONS |

|Required when on an IEP or 504 plan, but can be implemented for any student to support|Only when written in an IEP. |

|their learning. | |

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

➢ 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)

APPENDIX B

Learning 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 |

| | |

| |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 directions |

|Provide a checklist or step by step written directions |

|Break assignments in to chunks |

|Provide samples of desired products |

|Help 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 |

|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 assignments |

|Provide checklists |

|Provide frequent feedback and encouragement |

|Help 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 experiences |

|Accommodations: |

|Allow to work independently or as a leader of a group |

|Give opportunities to solve problems and not memorize information |

|Plan hands-on tasks |

|Explain relevance and real world application of the learning |

|Will be likely to respond to intrinsic motivators, and may not be motivated by grades |

|Help 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 assignments |

|Encourage creative solutions to problems |

|Allow students to experiment or use trial and error approach |

|Will likely be motivated by autonomy within a task and creative assignments |

|Help confluent students overcome these challenges: may not finish tasks, trouble proofreading or paying attention to detail |

APPENDIX C

Universal 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 |Examples |

|To present information through different modalities such as vision, hearing, or |Use visual demonstrations, illustrations, and models |

|touch. |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 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 |Examples |

|To make words, symbols, pictures, and mathematical notation clear for all |Use larger font size and/or magnifiers |

|students. | |

| |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 |

| | |

| |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 |Examples |

|To provide scaffolding so students can access and understand information needed to|Use diagrams. |

|construct useable knowledge. | |

| |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) |

| | |

| |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 |

Provide Multiple Means of Action and Expression

Strategy #4: Options for physical action

|Purpose |Examples |

|To 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 |

Strategy #5: Options for expression and communication

|Purpose |Examples |

|To 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 |Examples |

|To 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 page |

Provide Multiple Means of Engagement

Strategy #7: Options for recruiting interest

|Purpose |Examples |

|To 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 boards |

| |Use magnetic manipulatives examples: numbers, operation signs, ten frames, base|

| |ten blocks, etc. |

Strategy #8: Options for sustaining effort and persistence

|Purpose |Examples |

|To create extrinsic motivation for learners to stay focused and work hard on |Show real world applications of the lesson |

|tasks. | |

| |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 |Examples |

|To 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 |

| | |

| |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 |

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 Level

Learning Rate Learning Style

Motivation Strength or Interest

And various curriculum components:

Nature of the Objective Teaching Activities

Learning Activities Resources

Products

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).

[pic]

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 Accommodation |

|High Level Questions |Discussions and tests, ensure the highly able |Require students to defend answers |

| |learner is presented with questions that draw on |Use open ended questions |

| |advanced level of information, deeper |Use divergent thinking questions |

| |understanding, and challenging thinking. |Ask student to extrapolate answers when given incomplete information |

|Tiered assignments |In a heterogeneous class, teacher uses varied |Use advanced materials |

| |levels of activities to build on prior knowledge |Complex activities |

| |and prompt continued growth. Students use varied |Transform ideas, not merely reproduce them |

| |approaches to exploration of essential ideas. |Open ended activity |

|Flexible Skills |Students are matched to skills work by virtue of |Exempt gifted learners from basic skills work in areas in which they |

|Grouping |readiness, not with assumption that all need same |demonstrate a high level of performance |

| |spelling task, computation drill, writing |Gifted learners develop advanced knowledge and skills in areas of |

| |assignment, etc. Movement among groups is common, |talent |

| |based on readiness on a given skill and growth in | |

| |that skill. | |

|Independent Projects |Student and teacher identify problems or topics of|Primary Interest Inventory |

| |interest to student. Both plan method of |Allow student maximum freedom to plan, based on student readiness for|

| |investigating topic/problem and identifying type |freedom |

| |of product student will develop. This product |Use preset timelines to zap procrastination |

| |should address the problem and demonstrate the |Use process logs to document the process involved throughout the |

| |student’s ability to apply skills and knowledge to|study |

| |the problem or topic | |

|Learning Centers |Centers are “Stations” or collections of materials|Develop above level centers as part of classroom instruction |

| |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. Instead it should | |

| |provide greater breadth and depth on interesting | |

| |and important topics. | |

|Interest Centers or |Interest Centers provide enrichment for students |Plan interest based centers for use after students have mastered |

|Interest Groups |who can demonstrate mastery/competence with |content |

| |required work/content. Interest Centers can be | |

| |used to provide students with meaningful learning | |

| |when basic assignments are completed. | |

|Contracts and |Contracts are an agreement between the student and| |

|Management Plans |teacher where the teacher grants specific freedoms|Allow gifted students to work independently using a contract for goal|

| |and choices about how a student will complete |setting and accountability |

| |tasks. The student agrees to use the freedoms | |

| |appropriately in designing and completing work | |

| |according to specifications. | |

| | | |

|Compacting |A 3-step process that (1) assesses what a student |Use pretesting and formative assessments |

| |knows about material “to be” studied and what the |Allow students who complete work or have mastered skills to complete |

| |student still needs to master, (2) plans for |enrichment activities |

| |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.| |

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.

-----------------------

Benchmark and Cross Curricular Key

__Red: ELA

__ Blue: Math

__ Green: Science

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