Topic+Ten

= Topic Ten: Adding and Subtracting Mixed Numbers =
 * ~ = Desired Results = ||
 * __Transfer:__

1. Makes sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. __//Model with mathematics//__. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * __Established Goals:__
 * 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 **// .) //
 * // 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, 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 ** . //

__Prerequisite Standards:__
 * 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 //**.)
 * 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, 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 //** //
 * I can add and subtract ffractions with unlike denominators and mixed numbers.
 * I can solve word problems that involve fractions. ||
 * __Big Ideas:__
 * __Equivalence__: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
 * __Operation Meanings and Relationships__: There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
 * __Estimation__: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Some measurements can be approximated using known referents as the unit in the measurement process.
 * __Numbers and the Number Line:__ The set of real numbers is infinite and ordered. Whole numbers, fractions, and mixed numbers are real numbers. Each real number can be associated with a unique point on the number line.
 * __Practices, Processes, and Proficiencies:__ Mathematics content and practices can be applied to solve problems. || __Essential Questions:__
 * What does it mean to add and subtract mixed numbers?
 * What is a standard procedure for adding and subtracting mixed numbers? ||
 * __Students will know...__
 * Fractional amounts greater than 1 can be represented in different ways. Whole number amounts can be represented as fractions . When the numerator and denominator are equal, the fraction is equal to 1.
 * Sums and differences of mixed numbers can be estimated by rounding each mixed number to the nearest whole number.
 * Models can be used to show different ways of adding and subtracting mixed numbers.
 * One way to add mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed.
 * One way to subtract mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed.
 * There is more than one way to add or subtract mixed numbers.
 * Information in a problem can often be shown with a picture or diagram, which can be used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation.

__Vocabulary:__improper fraction, mixed number, proper fraction || __Students will be skilled at...__
 * Writing improper fractions as mixed numbers and mixed numbers as fractions, and placing them on a number line.
 * Estimating sums and differences of fractions and mixed numbers by rounding to the nearest whole number.
 * Using models to add and subtract mixed numbers.
 * Using models and computational procedures to add mixed numbers.
 * Using models and computational procedures to subtract mixed numbers.
 * Solving more complex problems involving the addition and subtraction of mixed numbers.
 * Drawing a picture and writing and equation in order to accurately solve a problem. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__

__[|MARS Task-Fractions]__ __[|MARS Task-Cindy's Cats]__ || __Other Evidence:__ || 10-1:Fractional amounts greater than 1 can be represented in different ways. Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction is equal to 1. 10-2:Sums and differences of mixed numbers can be estimated by rounding each mixed number to the nearest whole number. 10-3:Models can be used to show different ways of adding and subtracting mixed numbers. 10-4:One way to add mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed. 10-5:One way to subtract mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed. 10-6:There is more than one way to add or subtract mixed numbers. 10-7:Information in a problem can often be shown with a picture or diagram, which can be used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation. || [|Got Your Number] [|Part and Whole] [|Diminishing Return] [|Fractured Numbers]
 * ~ = Learning Plan = ||
 * __Learning Activities:__
 * __Resources:__ ||
 * Problem of the Month:

Centers: [|Creating Equivalent Fractions to Add Unlike Fractions] [|Creating Equivalent Fractions to Subtract Unlike Fractions] [|Fraction Word Problems] [|Adding Mixed Numbers] [|Subtracting Mixed Numbers] [|Magic Squares with Fractions] [|Closest to 25] [|Mixed Number Sums] [|Mixed Number Differences] [|Addition Word Problems with Fractions] [|Subtraction Word Problems with Fractions]

Additional Units: [|Stuffed with Pizza] [|Adding and Subtracting Fractions] ||  ||