COURSE OF STUDY UNIT PLANNING GUIDE


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1 COURSE OF STUDY UNIT PLANNING GUIDE FOR: MATHEMATICS GRADE LEVEL: FOURTH GRADE PREPARED BY: TERESA KELLY AND TRACY BUCKLEY B.O.E. ADOPTED AUGUST 20, 2015 REVISED AUGUST 2015 ALIGNED TO THE 2014 NJCCCS
2 UNIT TOPIC 1 UNIT TITLE: Numeration TOPICS COVERED: 17 (9 topics) UNIT LENGTH: 11 days Performance Indicators (Standards and Objectives) 4.NBT 2. Read and write multidigit whole numbers using base ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Essential Questions 11 What are some ways to represent numbers in the thousands? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 1Review what you know Identify and say numbers by place value in standard, expanded and word form 1 day Review and model Thousands, hundreds, tens Word form, standard form, expanded form, value, period Place value blocks, charts 4.NBT What are some ways to represent numbers in the millions? Identify and say numbers by place value 1 day Review and model charts Hundred millions to ones period Place value charts to millions 4.NBT 1. Recognize that in a multidigit whole number, a digit in one place represents 10 times what it represents in the place to the right. 4.NBT 2 13A How are the digits in a multidigit number related to each other? Reason that each place value is 10 times more 1 day Multiply by ten. Whole group guided practice, small group, partner work, Place value blocks, charts Number line 4.NBT 1 4.NBT 2 4.NBT 3. Use place value understanding to round multidigit whole numbers to any place. 13 How do you compare numbers? 14 How can you round numbers? Use place value to determine greater than less than 1 day Use strategy to round numbers to any place value. 2 days Evaluate proper place value to compare numbers; >,<,= Model rounding strategy and practice. Whole group guided practice, small group, partner work, Place value blocks, charts Supplemental resources 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of 15 How are decimals related to money? Place numbers up to hundredths on place value chart Relate dollars, dimes, pennies to place value blocks/chart 1 day Tenths, Hundredths. Model and compare amounts. Whole group guided practice, small group, partner work, Decimal place value chart
3 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 Money manipulatives Supplemental resources 4.MD How do you count money? Sort, counting up Counting by 5 s, 10 s, 20 s 25 s, 1 s; making change 1 day Addition, subtraction Multistep calculations Dollar bills, quarters, dimes, nickels, pennies. Whole group guided practice, small group, partner work, Place value decimal chart 4.MD 2 17A How can you use counting up to make change? Sort, counting up Counting by 5 s, 10 s, 20 s 25 s, 1 s, making change 1 day Addition, subtraction Multistep calculations Dollar bills, quarters, dimes, nickels, pennies. Whole group guided practice, small group, partner work, Money manipulatives (Calculator) 4.OA.3. Solve multistep word problems posed with whole numbers and having whole number answers using the four operations. 17 How can you use a list to find possible combinations? create lists, tables, bar diagrams use reasoning 1 day Organized list, combinations Model and review. Use lists, tables and diagrams to solve problems. Whole group guided practice, small group, partner work, 4.NBT.1/2,4.MD.2,4.OA.3 Topic Test. Review concepts. Assess independently. Provide support and modifications..
4 UNIT TOPIC 2 UNIT TITLE: Adding and Subtracting CHAPTERS/TOPIC COVERED: 17 UNIT LENGTH: 8 days Whole Numbers Performance Indicators (Standards and Objectives) 4.NBT.4 Fluently add and subtract multidigit whole numbers using the standard algorithm. Essential Questions 21 How can you use mental math to add and subtract? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 2 Review What You Know. Use mental math strategies to subtract numbers up to thousands. 1 day Properties of Addition: Commutative, Associative, Identity; Break apart, compensation, counting on white boards, Study Island, Bar diagram 4.NBT.3 Use place value understanding to round multidigit numbers to any place. 4.NBT How can you estimate sums and differences of whole numbers? Use rounding to estimate sums and differences to thousands. 1 day Estimate; rounding rule, place value. Whole group guided practice, small group, partner work, whiteboards, Study Island 4.OA.3 Solve multistep word problems posed with whole numbers and having wholenumber 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. 23 What information is needed to solve a problem? Solve word problems by eliminating extra information or decide you need more information. 1 day Read with precision; draw a diagram. Whole group guided practice, small group, partner work, Bar diagram, white boards, Study Island 4.NBT How do you add whole numbers? Review/use regrouping to add whole numbers to the hundred thousdands 1 day Use regrouping and estimation to check reasonableness; solve word problems using diagrams whiteboards, Study Island,
5 4.NBT.4 4.NBT How do you subtract whole numbers? 26 How do you subtract across zeroes? Use regrouping and inverse operations to subtract whole numbers to the thousands. 1 day Model and practice regrouping across place values for numbers to the thousands with one or more zeroes. 1 day Use regrouping and inverse operation (addition) to check precision; solve word problems Use estimation and regrouping to solve; solve word problems using various strategies. white boards 4.OA How can a bar diagram help you solve an addition or subtraction problem? Read and understand: what do I know; What do I need to find? Plan strategy and solve word problems 1 day Use all strategies for addition and subtraction to solve a variety of word problems. Whole group guided practice, small group, partner work, white boards, bar diagrams, problem solving worksheet 4.NBT.3/4,4.OA.3 Topic Test. Review concepts. Assess independently. Provide support and modifications..
6 UNIT TOPIC 3 UNIT TITLE: Multiplication Meanings CHAPTERS/TOPIC COVERED: 17 UNIT LENGTH: 6 days and Facts Performance Indicators (Standards and Objectives) 4.NBT.5. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit whole 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. Essential Questions 31 How can we use arrays to understand multiplication? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 3: Review What You Know. Use groups to multiply factors to find the product. 1 day Grouping factors. Whole group guided practice, small group, partner work, Mixed problem solving, manipulatives 5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. 32 What patterns can help you remember multiplication facts for 2 s and 5 s and 9 s? Identify and count by multiples 1/2 day Counting by multiples, determining products, solving word problems. Whole group guided practice, small group, partner work, Study Island 4.NBT What happens when you multiply two numbers and switch the order of the factors? What happens when you multiply by 0? If you multiply by 1? Use Commutative Property of Multiplication to solve. ½ day small group, partner work 4.OA.4. Find all factor pairs for whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range of is a multiple of a given onedigit number. Determine whether a given whole number in the range is prime or composite. 34 How can the Distributive Property and knowledge of basic multiplication facts be used to find other products? Practice using distributive property with factors of 3 and 4 ½ day Break apart. Modeling, whole group guided practice, small group, partner work whiteboards
7 4.OA How do you use multiplication facts and the Distributive Property to find the products for other multiplication facts? Practice using distributive property with factors of 6,7 and 8 ½ day Break apart. Modeling, whole group guided practice, small group, partner work, whiteboards 4.NBT How can you use patterns for multiplying by 10 to multiply by 11 and 12? Practice patterns for multiples and break apart to solve. 1 day Break apart. Modeling, whole group guided practice, small group, partner work, white 4.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 comparison. 37 How can a bar diagram help you solve a problem? Read and understand: what do I know; What do I need to find? Plan strategy and solve word problems by drawing a picture and writing an equation. 1 day Solve word problems involving factors using various strategies. Study Island, bar diagrams, problem solving worksheet 4.NBT.5, 4.OA.2/4 Topic Test. Review concepts. Assess independently. Provide support and modifications..
8 UNIT TOPIC 4 UNIT TITLE: Division Meanings CHAPTERS/TOPIC COVERED: 15 UNIT LENGTH: 5 days and Facts Performance Indicators (Standards and Objectives) 4.NBT.6. Find whole number quotients and remainders with up to four digit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationships between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Essential Questions 41 How can you use counters to show that division can be thought of as repeated subtraction or sharing equally? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 4:Topic Opener/Review what you know. Interactive Learning. Problem solving. 1 day Divide by sharing equally or repeated subtraction to find the number of groups. Divisor, quotient, dividend. Whole group guided practice, small group, partner work, counters, bar diagrams 4.NBT.6 4.NBT.6 4.NBT.5. Multiply a whole number by up to four digits by a onedigit whole number, and multiply two twodigit 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. 4.NBT How are multiplication and division related? 43 How can you divide using 1 and 0? 44 How can the inverse relationship between multiplication and division be used to find division facts? Use fact families and inverse operations solve. 1/2 day Determine rules for multiplying and dividing by 1 and 0. 1/2 day Use multiplication facts to help find quotients. 1 day Multiply, divide, problem solving. Whole group guided practice, small group, partner work, Divide and compare quotients. small group, partner work Solving for factors and quotients. Whole group guided practice, small group, partner work Study Island whiteboards, Study Island, Math facts practice, flashcards 4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g. by using drawings and equations 45 How can a bar diagram help you solve a division problem? Read and understand: what do I know; What do I need to find? Plan strategy and solve word problems by drawing a picture Solve word problems involving division using various strategies. Check answers using inverse operation (multiplication).
9 with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. and writing an equation. 1 day Study Island, bar diagrams, problem solving worksheet, Digital tools/counters 4.NBT.5/6,4.OA.2 Topic Test. Review concepts. Assess independently. Provide support and modifications..
10 UNIT TOPIC 5 UNIT TITLE: Multiplying by CHAPTERS/TOPIC COVERED: 18 (10 lessons) UNIT LENGTH: 9 days 1 digit numbers Performance Indicators (Standards and Objectives) 4.NBT.5. Multiply a whole number by up to four digits by a onedigit whole number, and multiply two twodigit 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. Essential Questions 51 What place value patterns can be seen when you multiply 1digit numbers by multiples of 10 and 100? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 4:Topic Opener/Review what you know. Determine patterns when multiplying by 10 and day 4.NBT What are some ways to multiply mentally? Use mental math strategies to solve multiplication problems. 1 day Practice break apart and compatible numbers to solve. Study Island 4.NBT.5 4.NBT.3. Use place value understanding to round multidigit whole numbers to any place. 53 How can you use rounding to estimate when you multiply? Use rounding and mental math to estimate products. 1/2 day Estimation. Whole group guided practice, small group, partner work 4.NBT.3 4.OA.3. Solve multistep word problems posed with whole numbers and having wholenumber 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 54 How do you know if your answer is reasonable? Estimate sand solve word problems and decide if answers are reasonable. ½ day Use problem solving strategies. Estimate and explain reasonableness. Whole group guided practice, small group, partner work whiteboards, Study Island,
11 estimation strategies including rounding. 4.NBT How can you record multiplication? Use arrays and expanded algorithm to find products. 1 day Model partial products strategy and drawing arrays to record multiplication. Interactive learning activity. Whole group guided practice, small group, partner work, place value blocks, Teaching tool 20 4.NBT A What is a common way to record multiplication? Use expanded algorithm to multiply. 1 day Partial products. Problem based interactive learning activity. whiteboards, Study Island, 4.NBT How do you multiply a 2 digit number by a 1digit number? Use expanded algorithm to multiply. ½ day Partial products. Whole group guided practice, small group, partner work, whiteboards, Study Island, 4.NBT.5 4.NBT.5 4.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 comparison. 57 How do you multiply larger numbers? ½ day 58A How do you multiply larger numbers? 58 How can you draw a picture and write an equation to solve a problem? Use regrouping to multiply and solve problems. ½ day Use strategies to multiply larger numbers. 1 day Read and understand: what do I know; What do I need to find? Plan strategy and solve word problems by drawing a picture and writing an equation. 1 day Regrouping. Model strategy. Practice strategies. small group, partner work, Interpret bar diagrams and graphs to solve a variety of word problems. Whole group guided practice, small group, partner work, whiteboards, Study Island, whiteboards, Study Island, Digital calculator 4.NBT.5, 4.NBT.3, 4.AO.2 Topic Test. Review concepts. Assess independently. Provide support and modifications.
12 UNIT TOPIC 6 UNIT TITLE: Variables and CHAPTERS/TOPIC COVERED: 14 (4 lessons) UNIT LENGTH: 5 days Expressions Performance Indicators (Standards and Objectives) 4.OA.3. Solve multistep word problems posed with whole numbers and having wholenumber 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. 4.NBT.5. Multiply a whole number by up to four digits by a onedigit whole number, and multiply two twodigit 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. Essential Questions 61 How can you use expressions with variables? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 4:Topic Opener/Review what you know. Write and solve algebraic expressions. 1 day, problem based interactive learning 4.NBT.4. Fluently add and subtract multidigit whole numbers using the standard algorithm. 62 How can you find a rule and write an addition and subtraction expression? Make/use a table to find sums and differences. 1 day Use problem solving strategies., problem based interactive learning model. Study Island 4.OA.3 4.NBT How can you find a rule and write a multiplication and division expression? Make/use table to find factors and divisors 1 day Use problem solving strategies., problem Study Island
13 4.OA.3 4.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 comparison. 64 How can you use objects and reasoning to solve a problem? Read and understand: what do I know; What do I need to find? Plan strategy and solve word problems 1 day based interactive learning model. Use problem solving strategies. small group, partner work whiteboards, Study Island, 4.OA.2/3; 4.NBT.4/5 Topic Test/Performance based assessment. 1 day Review concepts. Assess independently. Provide support and modifications.
14 UNIT TOPIC 7 UNIT TITLE: Multiplying by CHAPTERS/TOPIC COVERED: 17 (8 lessons) UNIT LENGTH: 8 days 2 digit numbers Performance Indicators (Standards and Objectives) 4.NBT.1 Recognize that in a multidigit whole number, a digit in the one place represents ten times what it represents in the place to its right. (700 divided by 70 = 10; 70 x 10 = 700) 4.OA.3. Solve multistep word problems posed with whole numbers and having wholenumber 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. Essential Questions 71 How can you multiply 1 digit numbers by multiples of 10 and 100? 72 What are some ways to estimate products? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 7:Topic Opener/Review what you know. Use mental math when multiplying by 10 and day Use rounding and compatible numbers strategies to estimate multiplication problems. 1 day Practice rounding and compatible numbers to solve., problem based interactive learning model. center games Study Island, whiteboards 4.NBT.5. Multiply a whole number by up to four digits by a onedigit whole number, and multiply two twodigit 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. 74A How can you record multiplication? 1 day (see also 73) Use arrays and expanded algorithm to find products. 1 day Use grid paper or tables to solve 2 digit by 2 digit multiplication problems. Whole group guided practice, small group, partner work,. white boards, Study Island 4.NBT.5 How can you use rounding to estimate when you multiply? Estimate sand solve word problems and decide if answers are reasonable. ½ day Use problem solving strategies. Estimate and explain reasonableness. Whole group guided practice, small group, partner work whiteboards, Study Island,
15 4.NBT.5 4.NBT.3. Use place value understanding to round multidigit whole numbers to any place. 4.NBT How can you find the product of 2 numbers? 75 How can you multiply 2 digit by 2 digit numbers? Use regrouping and break apart to multiply and solve problems involving multiples of day Use regrouping and partial products strategies to multiply larger numbers. 1 day Interactive learning activity. Problem based interactive learning activity. Whole group guided practice, small group, partner work, whiteboards, Study Island, 4.NBT How do you multiply greater numbers? Use mental math strategies to multiply with zeroes. ½ day whiteboards, 4.OA How do you use the answer from one question to answer a second question? Read and understand: what do I know; solve one problem and use your answer to solve another. ½ day Model strategy for 2 step problems. Problem based interactive learning, whole group guided practice, whiteboards, Study Island, 4.NBT.1/3/5, 4.AO.3 Topic Test. Review concepts. Assess independently. Provide support and modifications.
16 UNIT TOPIC 8 UNIT TITLE: Dividing by 1 digit CHAPTERS/TOPIC COVERED: 110 (14 lessons) UNIT LENGTH: 13 days Divisors Performance Indicators (Standards and Objectives) 4.NBT.6. Find whole number quotients and remainders with up to four digit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationships between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. Essential Questions 81 How can you use place value and patterns to help you divide mentally? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 8:Topic Opener/Review what you know. Interactive Learning. Problem solving. 1 day Use patterns/mental math to find quotients. Whole group guided practice, small group, partner work, bar diagrams 4.NBT When and how do you estimate quotients to solve problems? Use estimation and compatible numbers to solve. 1/2 day ReModel compatible number strategy/mental math. Problem based interactive learning, whole group guided practice, small group, partner work, white boards 4.NBT What does it mean when you divide and some are left over? Use counters/diagrams to show division with remainders. Check your answer with inverse operation. 1 day Model. Whole group guided practice, small group, partner work 4.NBT.6 4.OA.3. Solve multistep word problems posed with whole numbers and having wholenumber 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. 83A How do you estimate quotients using place value? Use place value to estimate quotients for 2, 3 and 4 digit dividends. 1 day Place value/estimation. Problem based interactive learning, whole group guided practice, small group, partner work Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, whiteboards
17 4.NBT.4 Fluently add and subtract multidigit whole numbers using the standard algorithm. 4.NBT.6 83B How can subtraction help you divide? Show how subtraction and division are related. ½ day Use counters to show division as repeated subtraction strategy. Problem based interactive learning, whole group guided practice, small group, partner work,. Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, whiteboards 4.NBT.4 4.NBT.6 83C How can you record division using repeated subtraction? Solve division problems using algorithm for repeated subtraction. ½ day Use counters to show division as repeated subtraction strategy. Problem based interactive learning, whole group guided practice, small group, partner work,. Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, whiteboards 4.NBT How can place value help you divide? Solve division problems with remainders using models and diagrams. 1 day Use place value blocks/diagrams to solve division problems, whole group guided practice,. Study Island, bar diagrams, 4.NBT What is a common way to record division? Solve division problems with remainders using. Check answers by multiplying. 1 day Use algorithm to solve division problems with remainders, whole group guided practice,. Study Island, bar diagrams, 4. NBT How can you divide numbers in the hundreds? Estimate and divide. Check if the quotient is reasonable. 1 day Use estimation and standard algorithm to solve division problems with remainders. Check for reasonableness.. Study Island 4.NBT.6 4.OA.4. Find all factor pairs for whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range of is a multiple of a given onedigit number. Determine whether a given whole number in the range is prime or composite. 87 What do you do when there are not enough hundreds to divide? Decide where to start dividing and check your answer. 1 day Model examples of numbers with insufficient hundreds to divide. Use division strategies and place value. whole group guided practice, small group, partner work,. Study Island
18 4.NBT.6 88A How can you estimate larger quotients? Estimate and solve for larger dividends. 1 day Use division strategies and place value and estimation to check. Problem based interactive learning, whole group guided practice, small group, partner work,. Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, whiteboards 4.OA How can you use multiplication to find all the factors of a number? Use multiplication facts to find factors of a number. 1 day Use counters/diagrams and factor pairs to find products. whole group guided practice,. Study Island 4.OA.4 4.OA How can you sort numbers by their factors? 810 What hidden questions lie within a multiple step problem? Define and identify prime and composite numbers. 1 day Read and understand: what do I know; What do I need to find? What is the hidden question? Plan strategy and solve word problems 1 day Model concept of prime and composite numbers and sort. whole group guided practice,. Model strategy for multistep problems. Problem based interactive learning, whole group guided practice, Study Island Study Island 4.NBT.6, 4.OA.3/4 Topic Test. Review concepts. Assess independently. Provide support and modifications..
19 UNIT TOPIC 9 UNIT TITLE: Lines, Angles and CHAPTERS/TOPIC COVERED: 17 (9 lessons) UNIT LENGTH: 10 days Shapes Performance Indicators (Standards and Objectives) 4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two dimensional figures. Essential Questions 91 What are some important geometric terms for lines? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 4:Topic Opener/Review what you know. Define and identify lines in geometric terms. ½ day Parallel, intersecting, perpendicular, point, line, plane. Whiteboards 4.G.2. Classify twodimensional 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. 4.G.1, 4.G.2 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. 92 What geometric terms describe types of angles? Identify parts of lines and angles. ½ day Right, acute, obtuse and straight angles. Whole group guided practice, small group, partner work, Study Island 4.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 a onedegree angle, and can be used to measure angles. b. An angle that turns through n 93 How can you draw an angle? Identify, measure and draw angles using a protractor. 1 day Protractor, degrees. Problem based interactive learning, Smartboard, (protractor on line) textbook, Reteach, Practice, Enrichment pages Study Island whiteboards, Study Island,
20 onedegree angles is said to have an angle measure of n degrees. 4.MD.6. Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 4.MD.6 93A What is the unit used to measure angles? Relate angle measurement to 360 degrees in a circle. 1 day Problem based interactive learning model, whole group guided practice, small group, partner work, Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, whiteboards 4.MD.6 4.MD.5 93B How are angles measured using objects? Use pattern block angles to measure angles. 1 day Problem based interactive learning model, whole group guided practice, small group, partner work, Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, pattern blocks 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into nonoverlapping 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. 4.MD.5 94A How can you add and subtract to find unknown angle measures? Use knowledge of right angles (90 degrees) to deconstruct/construct angle measurement. 1 day Problem based interactive learning model, whole group guided practice, small group, partner work, Transition to the Common Core workbook, Reteach, Practice, Enrichment pages, 4.G How do you identify polygons? Identify polygons based on number of sides and angles. ½ day Review polygons triangle, quadrilateral, pentagon, hexagon, octagon. Whole group guided practice, small group, partner work, whiteboards, Study Island, Pattern blocks 4.G How do you classify triangles? Identify triangles based on their sides and angles. ½ day Equilateral, isosceles, scalene, right, acute, obtuse triangles. whiteboards, Study Island,
21 4.G How can you classify quadrilaterals? Define and identify quadrilaterals. ½ day Parallelogram, rectangle, square, trapezoid, rhombus. Whole group guided practice, small group, partner work, whiteboards, Study Island, 4.G How can you test generalizations? Make and test generalizations about shapes. Plan and solve. 1 day Model strategy for making and testing generalizations. Problem based interactive learning, whole group guided practice, 4.G.1/2, 4.MD.5/6/7 Topic Test (includes use of protractor) Review concepts. Assess independently. Provide support and modifications.
22 UNIT TOPIC 10 UNIT TITLE: Understanding Fractions TOPICS COVERED: 1,39 (8 lessons) UNIT LENGTH: 9 days Performance Indicators (Standards and Objectives) 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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. Essential Questions 101 How can you name and show parts of a region? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 10Topic Opener/Review what you know Identify and create regions and sets1 day Review and model Regions and sets Vocabulary: fractions, numerators, denominators Fraction Models 4.NF How can you estimate parts? Review and model benchmark fractions, show examples of benchmark fractions 1 day Benchmark fractions, use of a number line to estimate fractions Benchmark Fractions images 4.NF How can you find two fractions that name the same part of a whole? Fraction strips to create and show equivalent fractions 1 day Equivalent fractions, fraction strips as manipulatives Fraction strips 4.NF How do you write a fraction in simplest form? Write fractions in simplest form, use division rules to simplify 1 day Fraction strips to model simplest form Vocabulary: Simplest Form Fraction strips 4.NF.1 4.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 ½. Recognize that comparisons are 105A How can you find equivalent fractions on a number line? Use a number line to create pairs of equivalent fractions 1 day Number lines to create equivalent fractions, fraction strips Supplemental resources, Number lines, fraction strips
23 valid only when the two fractions refer to the same whole. Record the result of comparisons with symbols l >, =, or <, and justify the conclusions, e.g. by using a visual fraction model. 4.NF.3 a/c Understand fraction a/b with a>1 as a sum of fraction 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. c. Add and subtract mmixed numbers with like denominators. E.g. by replacing the mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction How can you name whole regions and parts of a region in two different ways? Use improper fractions and mixed numbers to show parts of a region or whole regions 1 day Model mixed numbers and improper fractions using fraction strips Vocabulary: Improper fractions, mixed numbers Fraction strips 4.NF How can you use benchmark fractions to compare fractions? Compare fractions using greater than or less than signs 1 day Review and model greater than, less than, comparing fractions Fraction strips 4.NF How can you use equivalent fractions to compare and order fractions? Compare and order fractions using fraction strips 1 day Compare and order fractions Vocabulary: Common denominators Fraction strips 4.NF.3 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 How do you write a good math explanation? Write to explain whether an answer is correct or not 1 day Whole Group/Small Group Open ended math writing responses 4.NF.13 Topic Test Review concepts. Assess independently. Provide support and modifications.
24 UNIT TOPIC 11 UNIT TITLE: Adding & Subtracting Fractions TOPICS COVERED: 1,45F (9 lessons) UNIT LENGTH: 10 days Performance Indicators (Standards and Objectives) 4. NF.3 a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Essential Questions 111 How can you add and subtract fractions with like denominators? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 11Review what you know activity Add and subtract fractions with like denominators1 day Review fractions, add and subtraction fractions Vocabulary: numerator, denominator Fraction strips 4.NF.3.b Understand fraction a/b with a>1 as a sum of fraction 1/b 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 111A How can you use addition to represent a fraction in a variety of ways? Compose and decompose fractions using addition sentences 1 day Problem based interactive learning, Whole group guided practice, small group, partner work, Addition of fractions, number sentences Fraction strips, Supplemental Resources 5. NF.1 Enrich/5 th grade. Add and subtract fractions with unlike denominators (including mixed numbers) by placing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 5. NF.1 Enrich/5 th grade How can you add fractions with unlike denominators? (save for end of year) 113 How can you subtract fractions with unlike denominators? (save for end of year) Find common denominators to add fractions Find common denominators to subtract fractions Unlike denominators, find common denominators Unlike denominators, find common denominators Fraction strips, Supplemental Resources 4.NF.3 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 What operation is needed to solve a problem with fractions? Model drawing pictures and writing equations to solve problems with fractions 1 day Draw pictures and write equations to solve problems dealing with fractions Fraction strips, Supplemental Resources 4.NF.3.c Understand a fraction a/b with a>1 as a sum of fractions 1/b: c. Add and subtract mixed numbers 115A How can you model addition of mixed numbers? Use models to show addition of mixed numbers 1 day
25 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. Use of models, addition of mixed number examples Mixed Number images, supplemental resources 4.NF.3.c 115B How can you add mixed numbers? Model and practice addition of mixed numbers 1 day Practice adding mixed numbers, Vocabulary: mixed number, number sentences supplemental resources 4.NF.3.c 115C How can you subtract mixed numbers? Model and practice subtraction of mixed numbers 1 day Practice subtracting mixed numbers Vocabulary: mixed number, number sentences Supplemental resources 4.NF.4.a 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 x (1/4) recording the conclusion by the equation 5/4 = 5 x 1/4 115D How can you describe a fraction using a unit fraction? Discuss a unit fraction and how it relates to describing fractional amounts 1 day Relate how unit fractions make up fractions supplemental resources 4.NF.4.b. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.: 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (in general, n x (a/b) = (n x a)/b). 115E How can you find the product of a fraction multiplied by a whole number? Model and practice multiplication of a fraction and a whole number 1 day Multiply fractions and whole numbers supplemental resources
26 4.NF.4.c Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 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? 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (in general, n x (a/b) = (n x a)/b). 115F How can you use the product of a fraction and a whole number to solve a problem? Relate multiplication of a fraction and a whole number to solve word problems 1 day Use multiplication of a fraction and whole number knowledge to answer word problems supplemental resources 4.NF.3 and 4.NF.4 Topic Test Review concepts. Assess independently. Provide support and modifications.
27 UNIT TOPIC 12 UNIT TITLE: Understanding Decimals TOPICS COVERED: 16 (7 lessons) UNIT LENGTH: 8 days Performance Indicators (Standards and Objectives) 4.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. Essential Questions 121 What are some ways to represent decimals? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 12Review what you know activity Use standard, expanded, and word form to represent decimals 1 day Introduce decimals/tenths and hundredths place, read/write/speak decimals Vocabulary: tenths, hundredths Place value blocks 4.NF.7 4. NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.7 4.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 How do you compare decimals? 123 How can you write a fraction as a decimal? 124 How can you locate points for decimals on a number line? 125 How can you locate mixed numbers and decimals on a number line? \ Use place value charts to compare and order decimals 1 day Model and practice writing fractions as decimals and decimals as fractions 1 day Model and practice using number lines to locate specific decimal points 1 day Model and practice using number lines to locate mixed numbers and decimals 1 day Use place value charts and greater than and less than symbols to compare decimals Place value charts and blocks to show relationship between fractions and decimals Locate and name fractions and decimals on number lines Locate and name mixed numbers and decimals on number lines Place value charts place value charts, place value blocks number lines number lines
28 4.NF. 5 Express a fraction with a denominator 10 as an equivalent fraction with a denominator of 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/ NF A How can you use equivalent fractions to change a fraction to a decimal? Model using equivalent fractions to change fractions to decimals 1 day, problem based interactive learning Use equivalent fractions to change fractions to decimals and decimals to fractions supplemental resources 4.NF How can you draw a picture to solve a problem? Model and practice using pictures to solve problems dealing with decimals 1 day Solve word problems using the strategy of drawing a picture Inch rulers 4.NF.5,6,7 and 4.MD.2 Topic Test Review concepts. Assess independently. Provide support and modifications.
29 UNIT TOPIC 13 UNIT TITLE: Understanding Decimals TOPICS COVERED: Lesson 7 only UNIT LENGTH: 1 days **Lessons 16 are not in the 4 th grade Common Core Standards/ Complete at end of year Performance Indicators (Standards and Objectives) 5.NBT.7 (Enrichment/prepares for 5 th grade) 5.NBT.7 (Enrichment/prepares for 5 th grade) Essential Questions 131 How do you round a decimal number? 132 How can you estimate sums and differences of decimals? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 13Review what you know activity Round decimals using rounding rules Use rounding rules to estimate sums and differences of decimals Whole Group/Small Group Practice rounding decimals Whole Group/Small Group Practice using estimating to solve adding and subtraction problems with decimals 5.NBT.7 (Enrichment/prepares for 5 th grade) 5.NBT.7 (Enrichment/prepares for 5 th grade) 133 How do you use a grid model to add and subtract decimals? 134 How can you subtract decimal numbers? Model and practice using grids to add and subtract decimals Model and practice lining up decimals to add and subtract Whole Group/Small Group Use grids to add and subtract Whole Group/Paired Work Adding and subtracting decimals Place value grids 5.NBT.7 (Enrichment/prepares for 5 th grade) 135 How can you multiply a decimal by a whole number? Model and practice multiplying a decimal by a whole number Whole Group/ Paired Work Multiplying a decimal and a whole number 5.NBT.7 (Enrichment/prepares for 5 th grade) 136 How do you divide a decimal by a whole number? Model and practice dividing a decimal by a whole number Whole Group/ Paired Work Dividing a decimal by a whole number 5.NBT.7/4.OA.3. Solve multistep word problems posed with whole numbers and having wholenumber 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 How can you solve a problem by trying, checking, and revising your work? Model and practice the strategy of trying, checking, and revising 1 day independent practice, problem solving. Try a solution, check the solution, and, if not correct, revise the solution, following the same method until the correct solution is determined by checking
30 UNIT TOPIC 14 UNIT TITLE: Area and Perimeter TOPICS COVERED: 13, 69 (8 lessons) UNIT LENGTH: 9 days **Lessons 45 are not in the 4 th grade Common Core Standards/ Complete at end of year Performance Indicators (Standards and Objectives) 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Essential Questions 141 How can you estimate the area of objects and figures? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Topic 14Review what you know activity Estimate area by using figures on grids 1 day Measure area by counting the number of square units that cover a region grid paper 4.MD How do you measure the amount of space a figure covers? Use the formula length times width to find the area of squares and rectangles 1 day Practice using length times width formula for area 4.MD How can you find the area of an irregular figure? Model and practice finding the area of irregular shapes 1day, problem based interactive learning Use grids to find area grid paper Enrich/prepares for 6 th grade. Enrich/prepares for 6 th grade 144 How can you find the area of a parallelogram? 145 How can you use a parallelogram to find the area of a triangle? Model and practice finding the area of a parallelogram Model and practice finding the area of a triangle Use the base times height formula to find the area of a parallelogram Whole Group/ Paired Work Use the formula to find the area of a triangle 4.MD How can you find the distance around an object? Model and practice finding the perimeter of an object 1 day Find the perimeter of a polygon by adding the lengths of the sides or by using a formula
31 Enrich/Extends 4.MD How can rectangles with the same perimeter have different areas? Model and practice using rectangles that have the same perimeter but different areas 1 day Use grid paper to create rectangles with the same perimeter but different areas grid paper 4.MD A How can you use perimeter and area to solve problems? Model and practice solving word problems involving perimeter 1 day Solve word problems involving perimeter grid paper Enrich/Extends 4.MD How can rectangles with the same area have different perimeters? Use grid paper to show that rectangles can have the same area but different perimeters 1 day Use of grid paper to show same area/different perimeter grid paper 4.MD How can you solve a simpler problem and make a table? Model and practice using tables and solving simpler problems to find the solution to a word problem 1 day Break problems into smaller more manageable pieces and find a pattern to fit (use a table) 4.MD.3 Topic Test Review concepts. Assess independently. Provide support and modifications.
32 UNIT TOPIC 15 UNIT TITLE: Area and Perimeter TOPICS COVERED: Lesson 5 (1 lesson) UNIT LENGTH: 1 days **Lessons 14 are not in the 4 th grade Common Core Standards/ Complete at end of year Performance Indicators (Standards and Objectives) 6.G.4 Enrich/prepares for 6 th grade 6.G.4 Enrich/prepares for 6 th grade Essential Questions 151 How can you describe and classify solids? 152 How can you use a twodimensional shape to represent a threedimensional solid? Activities (Approximate Time Frame) Strategies/Methods/Vocabulary Resources (Including Digital Tools Describe and classify solids Use a twodimensional shape to represent a threedimensional object (Nets) Whole Group/Small Group Classifying solids Whole Group/Small Group Practice using nets to show threedimensional objects Nets 6.G.4 Enrich/prepares for 6 th grade 153 How can you get information about a solid from different perspectives? Interpret views of solids as seen from different perspectives Whole Group/Small Group Use blocks and nets to determine objects Nets 5.MD.4 Enrich/prepares for 5 th grade 154 How can you measure volume? Measure volume by counting cubic units or by using a formula Whole Group/Paired Work Count cubic units and use a formula to find the volume cubes 4.AO.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 How can a pattern help you solve a problem? Model and practice recognizing patters and be able to continue the pattern 1 day, problem based interactive learning Use patterns to help solve problems continue patterns as needed
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