6th Grade Lesson Core Connections 1 MS-CCRS Taught Preparation for 6.NS.A.1 Interpret and compute division of fractions. Focus for Lesson Chapter 5 MS-CCRS Specific Problem(s) Optional Supplements and Adjustments Pre-requisite standards and skills The focus is to provide students visual models and repetitive practice of multiplying fractions. (5-1) 5-6 (6.NS.8) An adjusted lesson is provided in order to place a heavier emphasis on practice. 5.NF.B.7 Dividing unit fractions by whole numbers and visa versa. The focus is to model multiplication of fractions using multiple methods. (5-9 and 5-11) 5-15 (6.NS.7c) Focus problems from this lesson could be combined with the focus problems from lesson 5.1.2 and completed in one day. See modified lesson. 5.NF.B.7 Dividing unit fractions by whole numbers and visa versa. See suggested adjustment. (5-18) None Focus problems from this lesson could be combined with the focus problems from lesson 5.1.2 and completed in one day. See modified lesson. 5.NF.B.7 Dividing unit fractions by whole numbers and visa versa. 5.1.1 Preparation for 6.NS.A.1 Interpret and compute division of fractions. 5-16 (6.EE2a, EE.6) 5.1.2 Preparation for 6.NS.A.1 Interpret and compute division of fractions. 5.1.3 College Preparatory Mathematics Desoto County Schools 6th Grade Lesson Core Connections 1 MS-CCRS Taught Preparation for 6.NS.A.1 Interpret and compute division of fractions. Chapter 5 MS-CCRS Specific Problem(s) Optional Supplements and Adjustments Provide students with repetitive practice of working with real-world situations and multiplication of mixed numbers. (5-31* eliminate b, and 5-32) 5-36 (6.NS.6c) Modified lesson provided emphasizes common misconception and provides practice. 5.NF.B.7 Dividing unit fractions by whole numbers and visa versa. Focus of the lesson is to relate multiplication of decimals to real-world situations. Teachers may choose to refresh students understanding of the percent ruler with the below focus problems. (5-39 and 5-40) 5-48 (6.RP.3c, NS.3) Teacher may choose to teach only 5-39 and 5-40 then supplement the remainder of the lesson with a worksheet covering decimal operations. 5.NBT.B.5 Fluently multiply multi-digit whole numbers Focus for Lesson Pre-requisite standards and skills 5.1.4 5.2.1 6.RP.A.3c Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. College Preparatory Mathematics 5-50 (6.NS.3) 5-51 (6.EE.6) 5.NBT.B.6 Find whole number quotients 5.NBT.B.7 Operations with decimals. Desoto County Schools 6th Grade Lesson Core Connections 1 MS-CCRS Taught Preparation for 6.NS.A.1 Interpret and compute division of fractions. Focus for Lesson Chapter 5 MS-CCRS Specific Problem(s) This solidifies the conceptual understandings of what happens to a product when multiplying fractions. (5-56) 5-61 (6.RP.3c) The focus of the lesson is to have students understand decomposing and rearranging shapes and how it effects or doesn’t effect the area of the shape. (5-66 and 5-67) None 5.2.2 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Optional Supplements and Adjustments This lesson does not directly tie to a standard but does touch on a conceptual understanding of products when multiplied by a number less than one and greater than one. Ultimately, it may be skipped if the teacher feels the need. Pre-requisite standards and skills 5.NF.B.7 Dividing unit fractions by whole numbers and visa versa. 5.NF.B.4b Find area of a rectangle with fractional side lengths. 5.3.1 College Preparatory Mathematics Desoto County Schools 6th Grade Lesson Core Connections 1 MS-CCRS Taught 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Focus for Lesson Chapter 5 MS-CCRS Specific Problem(s) Optional Supplements and Adjustments Pre-requisite standards and skills Provides practice for students to decompose shapes and calculate the area. (5-78) 5-80 (6.G.1) 5.NF.B.4b Find area of a rectangle with fractional side lengths. The focus is to how to find the area of a triangle and how the formula relates to that of finding the area of a rectangle or parallelogram. (5-86) 5-92 (6.G.1) 5.NF.B.4b Find area of a rectangle with fractional side lengths. 5.3.2 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 5-93 (6.NS.6b, 6c,8; 6.G.3) 5-94 (6.NS.4) 5.3.3 College Preparatory Mathematics 5-95 (6.NS.6c) Desoto County Schools 6th Grade Lesson Core Connections 1 MS-CCRS Taught 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 5.3.4 College Preparatory Mathematics Focus for Lesson The focus of this lesson is to understand the formula for calculating the area of a trapezoid and determining why the formula works. (5-97 and 5-98) Chapter 5 MS-CCRS Specific Problem(s) 5-101 (6.G.1) 5-102 (6.NS.5) 5-104 (6.EE.2a, 6) Optional Supplements and Adjustments Pre-requisite standards and skills 5.NF.B.4b Find area of a rectangle with fractional side lengths. 5-105 (6.NS.2, 3) Desoto County Schools 6th Grade Core Connections 1 Chapter 5 Assessment Understanding According to PARCC (Section Quiz and Chapter Assessment) MS-CCRS EOY or PBA Math Practice Preparation for 6.NS.A.1-2 Solve word problems involving division of fractions by fractions. For example, “How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?” Clarifications EOY 4 6.NS.B.3-1 Fluently add multi-digit decimals using the standard algorithm for each operation. EOY - College Preparatory Mathematics Only the answer is required; explanations and representations are not assessed here. Note that the italicized examples correspond to three meanings/uses of division: (1) equal sharing; (2) measurement; (3) unknown factor. These meanings/uses of division should be sampled equally. Tasks may involve fractions and mixed numbers but not decimals. Tasks do not have a context. Only the sum is required. Prompts do not include visual models. The answer sought is a number, not a picture. The given addends are such to require an efficient standard algorithm (e.g., 72.63+4.875). Addends in the task do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 16.999+3.501). Each addend is greater than or equal to 0.001 and less than or equal to 99.999. Calculator or No Calculator Chapter Mastery Now Multiplication of fractions. No calculator Coming Up Sections 6.1 and 7.2 are on division of fractions. Now Can be fully assessed. No calculator Coming Up No additional lessons. Desoto County Schools 6th Grade Core Connections 1 MS-CCRS EOY or PBA Math Practice Clarifications 6.NS.B.3-2 Fluently subtract multi-digit decimals using the standard algorithm for each operation. EOY 6.NS.B.3-3 Fluently multiply multi-digit decimals using the standard algorithm for each operation. EOY College Preparatory Mathematics Tasks do not have a context. Only the difference is required. Prompts do not include visual models. The answer sought is a number, not a picture. The given subtrahend and minuend are such to require an efficient standard algorithm (e.g., 177.3-72.635). The subtrahend and minuend do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 20.5-3.501). The subtrahend and minuend are each greater than or equal to 0.001 and less than or equal to 99.999. Positive differences only. (Every included subtraction problem is an unknown-addend problem included in 6.NS.31.) Tasks do not have a context. Only the product is required. Prompts do not include visual models. The answer sought is a number, not a picture. The given factors are such to require an efficient standard algorithm (e.g., 72.3 x 4.87). Factors in the task do not suggest any obvious ad hoc or mental strategy. Problems are effectively 3-digit by 3-digit or 2-digit by 5-digit. (For example, 7.68 x 15.3 or 0.35 x 18.241.) Chapter 5 Calculator or No Calculator Chapter Mastery Now Can be fully assessed. No calculator Coming Up No additional lessons. Now Can be fully assessed. No calculator Coming Up No additional lessons. Desoto County Schools 6th Grade Core Connections 1 MS-CCRS EOY or PBA Math Practice Clarifications 6.NS.B.3-4 Fluently divide multi-digit decimals using the standard algorithm for each operation. EOY - 6.RP.A.3c - 1 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity). College Preparatory Mathematics EOY 2, 5, 7, and 8 Tasks do not have a context. Only the quotient is required. Prompts do not include visual models. The answer sought is a number, not a picture. The given dividend and divisor are such to require an efficient standard algorithm (e.g., 177.3÷0.36). The dividend and divisor do not suggest any obvious ad hoc or mental strategy. Problems are effectively 4-digit divided by 2digit or 3-digit divided by 3-digit. (For example, 14.28÷0.68 or 2.394÷0.684.) Every quotient is a whole number or a decimal terminating at the tenths,, hundredths, or thousandths place. Every included division problem is an unknown-factor problem included in 6.NS.3-3. The testing interface can provide students with a calculation aid of the specified kind for these tasks. Pool should contain tasks with and without contexts. Expectations for ratios in this grade are limited to ratios of non-complex fraction. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. Chapter 5 Calculator or No Calculator Chapter Mastery Now Can be fully assessed. No calculator Coming Up Lesson 7.2.3 connects fraction division to decimal division. Now Multiplication of fractions. Calculator Coming Up Section 9.2 is dedicated to percentages. Desoto County Schools 6th Grade Core Connections 1 MS-CCRS EOY or PBA Math Practice 6.RP.A.3c - 2 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c) Solve problems involving finding the whole, given a part and the percent. EOY 2, 5, 7, and 8 College Preparatory Mathematics 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Clarifications EOY 1, 2, 5, and 7 The testing interface can provide students with a calculation aid of the specified kind for these tasks. Expectations for ratios in this grade are limited to ratios of non-complex fraction. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. The testing interface can provide students with a calculation aid of the specified kind for these tasks. A trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.” Chapter 5 Calculator or No Calculator Chapter Mastery Now Multiplication of fractions. Calculator Coming Up Section 9.2 is dedicated to percentages. Now Can be fully assessed. Calculator Coming Up No additional lessons. Desoto County Schools