Topic+Twelve

= Topic Twelve: Adding and Subtracting Fractions and Mixed Numbers with Like Denominators = Pacing (Duration of Unit):
 * ~ = 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:__


 * 4.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.
 * 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.

__Pre-Requisite Standards:__
 * 3.NF.1: Understand a fraction ** 1 ** / **// b //** as the quantity formed by 1 part when a whole is partitioned into //b// equal parts; understand a fraction **// a //** / **// b //** as the quantity formed by //a// parts of size ** 1 **/**// b //**.
 * 4.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 numbers and sizes of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

__"I Can" Statements:__ I can understand that improper fractions have a greater numerator than denominator. I can understand addition and subtraction of fractions as joining and separating parts referring to the same whole. I can decompose a fraction into a sum of fractions with the same denominator. I can add and subtract mixed numbers with like denominators. I can solve word problems involving addition and subtraction of fractions with like denominators. ||
 * __Big Ideas:__
 * __Basic Facts and Algorithms__: There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
 * __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.
 * __Equivalence:__ Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same whole.
 * __Practices, Processes, and Proficiencies__: Mathematics content and practices can be applied to solve problems. || __Essential Questions:__


 * What does it mean to add and subtract fractions with mixed numbers with like denominators?
 * What is a standard procedure for adding and subtracting fractions and mixed numbers with like denominators?
 * How can fractions and mixed numbers be added and subtracted on a number line? ||
 * __Students will know...__
 * A model can be used to add two or more fractions.
 * When adding fractions with like denominators, you are adding portions of the same size. So, you can add the numerators without changing the denominator.
 * A model can be used to subtract two or more fractions.
 * When subtracting fractions with like denominators, you are subtracting portions of the same size. So, you can subtract the numerators without changing the denominators.
 * Positive fractions can be added or subtracted by locating a fraction on the number line and then moving to the right to add or to the left to subtract.
 * Fractional amounts greater than 1 can be represented using a whole number and a fraction. Whole numb er amounts can be represented as fractions. When the numerators and denominators are equal, the fraction equals 1.
 * Models can be used to show different ways of adding and subtracting mixed numbers.
 * One way to add mixed numbers is to add the fractional parts and then add the whole number parts. Sometimes whole numbers or fractions need to be renamed.
 * One way to subtract mixed numbers is to subtract the fractional parts and then subtract eh whole number parts. Sometimes whole numbers or fractions need to be renamed.
 * A fractional amount can be decomposed into a sum of fractions in more than one way.

__Vocabulary:__ mixed number, improper fraction || __Students will be skilled at...__
 * Using models to add fractions with like denominators
 * Using computational procedures to add fractions with like denominators and solve problems.
 * Using models to subtract fractions with like denominators.
 * Using computational procedures to subtract fractions with like denominators and solve problems.
 * Using the number line to add and subtract fractions with like denominators.
 * Identifying and writing mixed numbers as improper fractions and improper fractions as mixed numbers.
 * Using models to add ans subtract mixed numbers.
 * Using models and computational procedures to add mixed numbers.
 * Using models and computational procedures to subtract mixed numbers.
 * Decomposing fractions and representing them as compositions of fractions in a variety of ways. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__

__[|MARS Task-4.NF.3-Leapfrog Fractions]__ || __Other Evidence:__ ||
 * ~ = Learning Plan = ||
 * __Learning Activities:__

12-1: A model can be used to add two or more fractions. 12-2: When adding fractions with like denominators, you are adding portions of the same size. So, you can add the numerators without changing the denominator. 12-3: A model can be used to subtract two or more fractions. 12-4: When subtracting fractions with like denominators, you are subtracting portions of the same size. So, you can subtract the numerators without changing the denominators. 12:5:Positive fractions can be added or subtracted by locating a fraction on the number line and then moving to the right to add or to the left to subtract. 12-6:Fractional amounts greater than 1 can be represented using a whole number and a fraction. Whole numb er amounts can be represented as fractions. When the numerators and denominators are equal, the fraction equals 1. 12-7: Models can be used to show different ways of adding and subtracting mixed numbers. 12-8:One way to add mixed numbers is to add the fractional parts and then add the whole number parts. Sometimes whole numbers or fractions need to be renamed. 12-9: One way to subtract mixed numbers is to subtract the fractional parts and then subtract eh whole number parts. Sometimes whole numbers or fractions need to be renamed. 12-10: A fractional amount can be decomposed into a sum of fractions in more than one way. ||
 * __Resources:__

__Centers:__ __[|Adding and Subtracting Fractions]__ __[|Adding Fractions Using Pattern Blocks]__ || [|Sense or Nonsense-1[[http://www.k-5mathteachingresources.com/support-files/sense-or-nonsense-2.pdf|Sense or Nonsense-2]]] [|Decomposing Fractions] [|Pizza Share] [|Adding Mixed Numbers] [|Subtracting Mixed Numbers] [|Fraction Word Problems] [|Addition Word Problems with Fractions] [|Subtraction Word Problems with Fractions]
 * [|The Chocolate Bar Problem]

__Additional Units:__ __[|Building Fractions from Unit Fractions]__ ||  ||