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Gloucester Township Public SchoolsMath Curriculum – updated Summer 2017 Grade 4OverviewMathematics 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.Benchmark and Cross Curricular Key__Red: ELA__ Blue: Math__ Green: Science__ Orange: Social Studies__ Purple: Related Arts__ Yellow: Benchmark AssessmentIn 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 FourUnit 1 - Use the four operations with whole numbers to solve problems.StandardsTopicsActivitiesResourcesAssessments4.NBT.1 - Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.1-1, 4-1, 6-1-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice--Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NBT.2 - Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.1-2, 1-3, 1-4, 1-6-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NBT.3 - Use place value understanding to round multi-digit whole numbers to any place.1-5, 1-6, 2-4, 4-2, 4-10, 5-2, 6-2-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice--Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.OA.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.3-3-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice--Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.OA.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison3-3, 3-4, 3-8-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource RoomsMath – Grade FourUnit 2 - Compute with multi-digit whole numbers. Generate equivalent fractions.StandardsTopicsActivitiesResourcesAssessments4.OA.4 - Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.3-7, 4-1, 6-1, 8-1, 8-2-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms 4.NBT.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 2-9, 5-5-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NBT.5 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.3-1, 3-5, 3-6, 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 4-8, 4-9, 4-10, 4-11, 5-1, 5-2, 5-3, 5-4, 5-5, 5-6-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NBT.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.3-1, 3-2, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NF.1 - Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.8-3, 8-4, 8-5-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.OA.3 - Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.2-5, 2-6, 2-9, 4-8, 5-5, 6-11, 7-7, 7-9-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource RoomsMath – Grade FourUnit 3 - Properties of operations with multi-digit arithmetic and addition/subtraction with fractions.StandardsTopicsActivitiesResourcesAssessments4.OA.5 - Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.2-2, 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-8, 7-9-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NF.2 - Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 8-6, 8-7, 8-8-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NF.3 - Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 8-9, 8-10, 9-1, 9-2, 9-3, 9-4, 9-5, 9-6, 9-7-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.1 - Know relative sizes of measurement units within one system of units including km, m, cm, mm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...11-1, 11-2, 11-3, 11-4, 11-5, 11-6, 11-7, 12-1, 12-2, 12-3, 12-5, 12-6-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.OA.3 - Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.2-5, 2-6, 2-9, 4-8, 5-5, 6-11, 7-7, 7-9-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NBT.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 2-9, 5-5-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource RoomsMath – Grade FourUnit 4 - Extend understanding of fractions and solve word problems. Introduction to decimals.StandardsTopicsActivitiesResourcesAssessments4.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?9-8, 9-9-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.2 - Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 11-1, 11-2, 11-3, 11-4, 11-5, 11-6, 11-7, 11-9, 11-10, 12-4, 12-5, 12-6-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NF.5 - Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.8-4, 10-4, 10-5, 10-6, 10-8-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.NF.6 - Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7, 10-8-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.3 - Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.13-1, 13-2, 13-3, 13-4, 13-5-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.4 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.11-8-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.OA.3 - Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.2-5, 2-6, 2-9, 4-8, 5-5, 6-11, 7-7, 7-9-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource RoomsMath – Grade FourUnit 5 - Compare decimals and measure/classify geometric figuresStandardsTopicsActivitiesResourcesAssessments4.NF.7 - Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.10-1, 10-7-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.5 - Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.14-3, 14-4, 14-5-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.G.1 - Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14-7, 14-8, 14-9, 14-11-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.G.2 - Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.14-8, 14-9, 14-11-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.6 - Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.14-5, 14-6-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.MD.7 - Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.14-7-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource Rooms4.G.3 - Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.14-10-Lesson Presentations from ConnectEd-Problem of the Day-Common Core Quick Check-Investigate the Math-My Homework-Reteach & Enrich Worksheets-Guided Practice-Independent Practice-Virtual Manipulatives -Am I Ready?-My Vocabulary Cards-My Foldable-Manipulative Masters & Manipulative Kit-Real World Problem Solving Readers-My Learning Stations-STAR Math-Am I Ready Assessments-Pretest-Check My Progress Quiz-Vocabulary Test-Chapter Test 1A & 1B*-Chapter Test 2A & 2B*Resource RoomsAppendix A Adaptations for Special Education Students, English Language Learners, and Gifted and Talented StudentsMaking Instructional AdaptationsInstructional 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 ACCOMMODATIONSMODIFICATIONSRequired 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 My Math lessons.Teachers will use the Targeted Strategic Intervention from the My Math 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 AccommodationsTeachers will use Beyond Level in RtI Differentiated Instruction section of My Math lessonsTeachers will use the Enrichment Masters from the My Math Online SupportTeacher will implement Adaptations for Learning Styles (Appendix B) Teacher will implement appropriate UDL instructional adaptations (Appendix C)English Language Learner Instructional AccommodationsTeachers will use the ELL Differentiated English Language Learner Support section of My Math lessons.Teachers will use the Differentiated ELL Support from the My Math Online Support. Teachers will implement the appropriate Teachers will implement the appropriate instructional adaptions for English Language Leaners (Appendix E) APPENDIX BLearning StylesAadapted 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.VisualUtilize Charts, graphs, concept maps/webs, pictures, and cartoonsWatch videos to learn information and conceptsEncourage students to visualize events as they read math word problemsUse flash cards to practice basic math factsModel by demonstrating tasks or showing a finished productHave 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 problemsAudioAllow students to give oral presentations or explain concepts verballyPresent information and directions verbally or encourage students to read directions aloud to themselves.Allow students to work in pairs Utilize songs and rhymesAsk for choral responses in instruction, example have the entire class chant in unison multiples, evens/odds, or skip counting by 2s, 5,s or 10sRepeat, clarify, or reword directionsVerbally guide students through task stepsKinestheticAct out concepts and dramatize eventsUse flash cardsUse manipulativesAllow students to deepen knowledge through hands on projectsSequential: 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 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 conceptsTechnical: 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 lecturesConfluent: 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 detailAPPENDIX CUniversal Design for Learning AdaptationsAdapted from Universal Design For LearningTeachers will utilize the examples below as a menu of adaptation ideas. Provide Multiple Means of RepresentationStrategy #1: Options for perceptionGoal/PurposeExamplesTo 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 blocksDifferentiate operation symbols by color coding Draw pictures when possible Use interactive websites and appsUse modeling to help students solve problemsProvide examples of a correctly solved problem at the beginning of each lessonHave students work each step in a different colorUse songs and rhymes to help remember informationUse mnemonics like “Please Excuse My Dear Aunt Sally” (order of operations) to remember sequenced steps Simplify and rephrase vocabulary in word problemsStrategy #2: Options for language, mathematical expressions and symbolsGoal/PurposeExamplesTo make words, symbols, pictures, and mathematical notation clear for all students.Use larger font size and/or magnifiersHighlight important parts of problems, example: key words or operation signsUse 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 alignedPut boxes around each problem to visually separate themSimplify and rephrase vocabulary in word problemTurn lined paper vertically so the student has ready made columnsColor code and highlight keywords in math word problemsStrategy #3: Options for ComprehensionPurposeExamplesTo provide scaffolding so students can access and understand information needed to construct useable knowledge.Use diagrams.Use semantic maps and diagramsChunk pieces of information together, example: learn facts in sets of 3Review previous lessonsUse a buddy system to clarifyUse 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 problemsUse graph paper to keep numbers alignedUse modeling to help students solve problemsIntroduce concepts using real life examples whenever possibleTeach fact families and build fluency with games and understandingWhen teaching number lines use tape or draw a number line on the floor for students to walk on Provide Multiple Means of Action and ExpressionStrategy #4: Options for physical actionPurposeExamplesTo provide materials that all learners can physically utilize Use of computers when availablePreferential or alternate seatingProvide assistance with organizationProvide graph paper to organize place valueProvide appropriate manipulatives Use flash cards Provide highlighters for students when solving problemsAllow students to use desk top copies of fact sheets, multiplication/division tables etc.Use individual dry-erase boardsStrategy #5: Options for expression and communicationPurposeExamplesTo allow the learner to express their knowledge in different waysAllow oral responses or presentationsStudents show their knowledge with charts and graphsGive students extra time to respond to oral questionsHave students verbally or visually explain how to solve a math problemStrategy #6: Options for executive functionPurposeExamplesTo scaffold student ability to set goals, plan, and monitor progressProvide clear learning goals, scales, and rubricsModel skills Utilize checklistsGive examples of desired finished productChunk longer assignments into manageable partsTeach and practice organizational skillsUse a problem solving strategy checklist so that students can monitor their progressTeach students to use self-questioning techniquesReduce the number of practice or test problems on a pageProvide Multiple Means of EngagementStrategy #7: Options for recruiting interestPurposeExamplesTo make learning relevant, authentic, interesting, and engaging to the student.Provide choice and autonomy on assignmentsUse colorful and interesting designs, layouts, and graphics Use games, challenges, or other motivating activitiesProvide positive reinforcement for effortUse manipulativesProvide learning aids such as calculators and/or operation tables (addition/subtraction and multiplication/division tables)Introduce concepts using real life examples whenever possibleUse individual dry-erase boardsUse magnetic manipulatives examples: numbers, operation signs, ten frames, base ten blocks, etc.Strategy #8: Options for sustaining effort and persistencePurposeExamplesTo create extrinsic motivation for learners to stay focused and work hard on tasks.Show real world applications of the lessonUtilize collaborative learningAssign a peer tutorIncorporate student interests into lessonPraise growth and effort Recognition systemsBehavior plansRepeat directions as neededProvide immediate feedbackStrategy #9: Options for self-regulationPurposeExamplesTo develop intrinsic motivation to control behaviors and to develop self-control.Give prompts or reminders about self-controlSelf-monitored behavior plans using logs, records, journals, or checklistsAsk students to reflect on behavior and effortPost class rules using pictures and wordsPost daily schedule using pictures and wordsCirculate around the roomDevelop a signal for when a break is neededProvide consistent praise to elevate self-esteemModel and role play problem solvingDesensitize students to anxiety causing events Appendix D Gifted and Talented Instructional AccommodationsHow 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 InterestAnd various curriculum components:Nature of the Objective Teaching ActivitiesLearning Activities ResourcesProductsDifferentiation 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).Gifted & Talented Accommodations ChartAdapted from Association for Supervision and Curriculum DevelopmentTeachers will utilize the examples below as a menu of adaptation ideas.StrategyDescriptionSuggestions for AccommodationHigh Level QuestionsDiscussions 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 answersUse open ended questionsUse divergent thinking questionsAsk student to extrapolate answers when given incomplete informationTiered assignmentsIn 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 materialsComplex activitiesTransform ideas, not merely reproduce themOpen ended activityFlexible Skills GroupingStudents 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 performanceGifted learners develop advanced knowledge and skills in areas of talentIndependent 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 topicPrimary Interest Inventory Allow student maximum freedom to plan, based on student readiness for freedomUse preset timelines to zap procrastinationUse process logs to document the process involved throughout the studyLearning CentersCenters 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. Instead it should provide greater breadth and depth on interesting and important topics. Develop above level centers as part of classroom instructionInterest Centers or Interest GroupsInterest 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 contentContracts and Management PlansContracts 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 accountabilityCompactingA 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 assessmentsAllow students who complete work or have mastered skills to complete enrichment activitiesAppendix E English Language Learner Instructional AccommodationsAdapted from World-class Instructional Design and Assessment guidelines (2014), Teachers to English Speakers of Other Languages guidelines, State of NJ Department of Education Bilingual Education and Haynes and Zacarian (2010).K-2Beginning Level: Preproduction (Newcomers) Use visuals, manipulative, and real objectsAllow responses through physical movement or manipulation of objectsAllow student to listen and observe (don’t force speaking)Group student with more advanced ELLs or cooperative peersProvide simplified text and numerous picturesSight word cardsAlphabet FolderColoring PacketPhonicsVowel booksWord book to drawPictionary Ask questions that require yes or no, or 1-3 word answersGrade the progressEarly Production (ELLs who have been in the United States between 1-2 years)Use simplified, abbreviated text materialProvide continued listening activities and visuals Use photo albumsAllow role playingSupply create ideas workbookUse simple word to ask questionsAt this stage assessment can be in the form of physical responses, manipulation of objects or simplified responseAllow extra time to complete testsModify number and length of the assignmentsUse of word bank all the time to help them Oral presentationsProjects instead of reports based on learning style of studentK-2Intermediate Level: Allow extra time to complete tests Use short written or verbal measures frequentlyPrepare short answer questionsUse checklist observing academic behaviors based on unitAssess participation indicating student mastery of contentMeasure progress on class project in teacher narrative Writing assignments scored holisticallyGrades 3-5Beginning Level: Preproduction (Newcomer)Use visuals, manipulative, and real objectsAllow responses through physical movement or manipulation of objectsAllow student to listen and observe (don’t force speaking)Group student with more advanced ELLs or cooperative peersProvide simplified text and numerous picturesSight word cardsAlphabet FolderColoring PacketPhonicsVowel booksWord book to drawPictionaryUse short written or verbal measures frequentlyIncrease amount of time for testPrepare short answer questionsUse checklist observing academic behaviors based on unitAssess participation indicating student mastery of contentMeasure progress on class project in teacher narrative Grades 3-5Early Production (ELLs who have been in the U.S.A. between 1-2 years)Use simplified, abbreviated text materialProvide continued listening activities and visuals Allow role playingSupply create ideas workbookAsk questions that require yes or no, or 1-3 word answersUse simple word to ask questionsAt this stage assessment can be in the form of physical responses, manipulation of objects or simplified responseAllow extra time to complete testsModify number and length of the assignmentsUse of word bank all the time to help them Oral presentationsProjects instead of reports based on learning style of studentRemind students to use other parts of test to help with answersDefine cue words: compare, contrast, list, etc.Break content down into smaller partsCheck background knowledgeModify tests when necessary. If some sections require language skills far above an Ells’ level, eliminate those questionsIn the content areas, do not deduct points for grammar or spelling when possibleGrades 3-5Intermediate Level: (ELLs who have been in the U.S.A. more than two years)If they can: Allow students to use bilingual dictionary during class and testsAllow extra time to complete testsWriting assignments scored holisticallyCheck background knowledgeModify tests when necessary. If some sections require language skills far above an ELL’s level, eliminate those questionsIn the content areas, do not deduct points for grammar or spelling when possibleAllow to retake the testsGrade progress ................
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