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2 | Mathematics Grade 5 | |||||||||||||||||||||||

3 | Planning Grid (Gantt Chart) | |||||||||||||||||||||||

4 | Links to Materials | Sequence instruction by academic year quarter. | ||||||||||||||||||||||

5 | Click colored cells to download: Worksheet Series / Activities / Related Videos/ Links | Indicate when you are introducing a skill by flagging the appropriate quarter green. | ||||||||||||||||||||||

6 | Worksheet #1 | 📽 Related Video | Worksheet #2 | Related Link | Worksheet #3 | Worksheet #4 | Flag the skill red when students will practice the skill on independent assignments (homework). | |||||||||||||||||

7 | Same background color indicates that these resources are related. Precursor skills are different colors. | |||||||||||||||||||||||

8 | Blue flag: priority skill- to be assessed on Progress Monitoring Tests | MCAS Grade 5 Math Reference Sheet | Instructional level of skill: flag green | Independent level of skill: flag red. | ||||||||||||||||||||

9 | Q1 | Q2 | Q3 | Q4 | ||||||||||||||||||||

10 | CC # | Operations and Algebraic Thinking | Sept-Oct | Nov-Jan | Feb-Mar | Apr -Jun | ||||||||||||||||||

11 | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, e.g.,(6 x 30) + (6 x 1 ∕ 2). | ||||||||||||||||||||||

12 | Write expressions to match semantic cues and document steps with symbolic self-prompts | Semantic-based Distributive property | ||||||||||||||||||||||

13 | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them: For example, write "add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. | ||||||||||||||||||||||

14 | 5.OA.3 | Graph and compare two related functions. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | ||||||||||||||||||||||

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16 | Q1 | Q2 | Q3 | Q4 | ||||||||||||||||||||

17 | Number and Operations in Base Ten | Sept-Oct | Nov-Jan | Feb-Mar | Apr -Jun | |||||||||||||||||||

18 | 5.NBT.1 | Recognize that in a multi-digit number, including decimals, a digit in any place represents 10 times as much as it represents in the place to its right and 1 ∕ 10 of what it represents in the place to its left. | ||||||||||||||||||||||

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20 | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | ||||||||||||||||||||||

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22 | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | ||||||||||||||||||||||

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24 | 5.NBT.3a | Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). | ||||||||||||||||||||||

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26 | 5.NBT.3b | Read, write, and compare decimals to thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | ||||||||||||||||||||||

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28 | 5.NBT.4 | Use place value understanding to round decimals to any place. | ||||||||||||||||||||||

29 | Round decimals to 1s 10ths or 100ths | |||||||||||||||||||||||

30 | Precursor | Add and subtract multidigit numbers with regrouping. | ||||||||||||||||||||||

31 | Add and subtract review and generate 2x using diagrams, 2 x md | |||||||||||||||||||||||

32 | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | ||||||||||||||||||||||

33 | Add decimal numbers using a graphic organizer "Box dollar shade penny" | Fish Bucks Thematic Unit and Game | Solve Various Word Problems Using Graphic Organizer Templates | |||||||||||||||||||||

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37 | Q1 | Q2 | Q3 | Q4 | ||||||||||||||||||||

38 | Multiplication and Division | Sept-Oct | Nov-Jan | Feb-Mar | Apr -Jun | |||||||||||||||||||

39 | 4.NBT.MA.5a | Know multiplication facts and related division facts through 12 x 12. | ||||||||||||||||||||||

40 | Multiplication and Division Facts for the Whole-to-Part Visual Learner Fluency Program | |||||||||||||||||||||||

41 | Click for book link. | Diagram Facts Dry Erase | 📽 Woodin Ladder Chart Instructional Video | Color Coded Ladder Chart with Divisibility Rule References | ||||||||||||||||||||

42 | 4.NBT.5* | Multiply two two-digit numbers by using equations, rectangular arrays, and/or area models. | ||||||||||||||||||||||

43 | Ballistic VMI Multidigit Multiplication Drill Template | 2d x 2d Model Pipe Plans | 2d x 2d Base 10 Block Area - w color | 2-digit x 2-digit Fading Templates | Templates for 2-Digit X | 2d x 2d highlight template | ||||||||||||||||||

44 | 📽 Ballistic VMI Multidigit Multiplication Drill Instructional Movie | 2d x 2d Base 10 Block Area - book version b/w | MDX with Estimate 2-Digit x 2-Digit | 📽 2d x 2d highlight movie | ||||||||||||||||||||

45 | 20 x 2d Magnitudes of 10 | 50 x 2d Magnitudes of 10 | ||||||||||||||||||||||

46 | 5.NBT.5 | Fluently multiply multi-digit whole numbers. (Include two-digit x four-digit numbers and, three-digit x three-digit numbers) using the standard algorithm. | ||||||||||||||||||||||

47 | 📽Multiply 2d x 3d Circle the tens digit video | General 2d x 2d and 2d x 3d | ||||||||||||||||||||||

48 | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. | ||||||||||||||||||||||

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50 | Semantic Division | Division Icon Steps and Poster | Divide by 2 With Fractional Remainder Scaffolded Facts | Divide by 5 With Fractional Remainder Scaffolded Facts | Divide by 9 With Fractional Remainder Scaffolded Facts | Single-Digit Divisor Multi-Step Division Slides Template | ||||||||||||||||||

51 | 📽 Use shoes as manipulatives to learn division by 2 with a fractional remainder | Division Icon Steps and Poster | 5x Clock-Based division with a remainder | Scaffolded 2-step Long Division Problems | Mixed Multiplication and Division Computation With Diminishing Structure | |||||||||||||||||||

52 | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-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. | ||||||||||||||||||||||

53 | 📽 Woodin Ladder Chart Instructional Video | Color Coded Ladder Chart with Divisibility Rule References | Division Template | 📽 Woodin Ladder Chart Instructional Video | Color Coded Ladder Chart with Divisibility Rule References | |||||||||||||||||||

54 | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. | ||||||||||||||||||||||

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57 | 5 | |||||||||||||||||||||||

58 | Fractions | Instructional Article: | Durable Images Teach Fractions | Sept-Oct | Nov-Jan | Feb-Mar | Apr -Jun | |||||||||||||||||

59 | Capstone | Perform fraction operations and convert fractions to decimals using appropriate graphic organizers | ||||||||||||||||||||||

60 | 4 Operation Fraction Classification and Dictation | Fraction Frame Template | ||||||||||||||||||||||

61 | precursor | Encode fractions (fraction dictation) | ||||||||||||||||||||||

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63 | precursor | Simplify fractions using divisibility rules | ||||||||||||||||||||||

64 | Expand and Simplify Fractions While Practicing Fact Families and the Multiplication Table Area Model | SIMPLIFY FRACTIONS WITH 2,5,10,9,3,6 DIVISIBILITY RULES | ||||||||||||||||||||||

65 | 4.NF.2 | Compare two fractions with different numerators and different denominators, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. | ||||||||||||||||||||||

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67 | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc)/bd.) | ||||||||||||||||||||||

68 | Fraction Graphic Organizer Cards and Templates to Rename and add | Common Multiple Type 1,2,3 | Add and Subtract Fractions Type 1 Students Encode, then Set-up Problems | Add and subtract Type 2 with scaffolded Semantic Diagrams | ||||||||||||||||||||

69 | Type 1 2 3 fraction addition flow chart | 📽 Type 1 2 3 Flow chart video | Type 1,2,3 fraction Addition and Sorting Activity A | Type 123 mixed Sort ActivityB | Add and subtract type 1,2,3 fractions and mixed numbers | Find LCM or LCD using pendulums | ||||||||||||||||||

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71 | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole (the whole can be a set of objects), including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2 . | ||||||||||||||||||||||

72 | Solve Various Word Problems Using Graphic Organizer Templates | |||||||||||||||||||||||

73 | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100: e.g., rewrite 0.62 as 62/100. | ||||||||||||||||||||||

74 | Encode Decimal Fractions | Baseball Fraction and % Notebook Program File | ||||||||||||||||||||||

75 | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator ( a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | ||||||||||||||||||||||

76 | 📽 Convert improper fractions to mixed numbers with Fraction Universe model | Improper to mixed number worksheet series. | ||||||||||||||||||||||

77 | 5.NF.4.a | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model and/or area model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15 . (In general, (a/b) × (c/d) = ac/bd .) | ||||||||||||||||||||||

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79 | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator ( a/b = a ÷ b). e.g., interpret 3/4 as the result of dividing 3 by 4, and that 3/4 x 4 =1. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | ||||||||||||||||||||||

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81 | 5.NF.4.b | Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. | ||||||||||||||||||||||

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83 | 5.NF.5.a | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, without multiplying tell which number is greater: 225 or ¾ x 225; 11∕50 or 3 ∕2 x 11∕50? | ||||||||||||||||||||||

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85 | 5.NF.5.b | Interpret multiplication as scaling (resizing), by explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction< 1 results in a product < the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. | ||||||||||||||||||||||

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87 | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | ||||||||||||||||||||||

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89 | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | ||||||||||||||||||||||

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91 | 5.NF.7a | Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and solve the problem | ||||||||||||||||||||||

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93 | 5.NF.7b | Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. | ||||||||||||||||||||||

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95 | 5.NF.7c | Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. For example, how much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? | ||||||||||||||||||||||

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99 | Measurement and Data | Sept-Oct | Nov-Jan | Feb-Mar | Apr -Jun | |||||||||||||||||||

100 | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. |

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