Topic+Thirteen

= Topic Thirteen: Extending Fraction Concepts = 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.4a: 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// // ´ (//**// 1 //**// / //**// 4 //**//), recording the conclusion by the equation// **// 5 //**// / //**// 4 //** //= 5// // ´ (//**// 1 //**// / //**// 4 //**//).//
 * 4.NF.4b : Under stand 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 //// ´ //// ( //** // 2 // **// / //** // 5 // **// ) //// as 6 //// ´ //// ( //** // 1 // **// / //** // 5 // **// ), recognizing this product as //** // 6 // **// / //** // 5 // **// . // (In general, // n // ´ ( ** // a // ** / ** // b // ** ) = ( // n // ´ // a // ) / // b // .)
 * 4.NF.4c: 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?//
 * 4.NF.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.[[file:///C:/Users/csantosuosso/Downloads/0311%20(16).doc#_ftn1|[1]]] //For example, express// **// 3 //**// / //**// 10 //** //as// **// 30 //**// / //**// 100 //**//, and add// **// 3 //**// / //**// 10 //** //+// **// 4 //**// / //**// 100 //** //=// **// 34 //**// / //**// 100 //**//.//
 * 4.NF.6: Use decimal notation for fractions with denominators 10 or 100. //For example, rewrite 0.62 as// **// 62 //**/**// 100 //**//; describe a length as 0.62 meters; locate 0.62 on a number line diagram.//
 * 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.
 * 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.

__ 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 // **.
 * 3.NF.3.a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
 * 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.
 * 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. //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 //**//.//
 * c. 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.

__"I Can" Statements:__
 * I can multiply a fraction by a whole number.
 * I can solve word problems involving multiplication of a fraction by a whole number.
 * I can show a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 in order to add the two fractions.
 * I can use decimals to show fractions with denominators of 10 and 100.
 * I can compare two decimals to hundredths by reasoning about their size.
 * I can use the four operations (+, -, x, ) to solve word problems involving measurement; including simple fractions and decimals. ||
 * __Big Ideas:__
 * __Comparison and Relationships:__ Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways.
 * __Numbers and the Number Line__: The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line.
 * __ Equivalence __ : Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
 * __The Base-Ten Numeration System:__ The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.
 * __Practices, Processes, and Proficiencies:__ Mathematics content and practices can be applied to solve problems. || __Essential Questions:__
 * How is decimal numeration related to whole number numeration?
 * How can decimals be composed and ordered?
 * How are fractions and decimals related? ||
 * __Students will know...__
 * Physical representations and symbols can be used to develop the understanding that a/b=a x 1/b.
 * Models can be used to find the product of a whole number and a fraction.
 * To multiply a fraction by a whole number, one must multiply the whole number by the numerator of the fraction and then divide the product by the denominator of the fraction.
 * A decimal is another name for a fraction.
 * Each fraction, mixed number, and decimal can be associated with a unique point on the number line.
 * Every fraction can be represented by an infinite number of equivalent fractions, but each fraction is represented by the same decimal or an equivalent form.
 * Decimal numeration is just an extension of whole number numeration.
 * Place value can be used to compare and order numbers.
 * Relationships among dollars, dimes, and pennies are a good model for decimal numeration.
 * Information in a problem can often be shown with a picture or diagram and used to understand and solve the problem.

__Vocabulary:__ unit fraction, decimal point, hundredth, tenth || __Students will be skilled at...__ 13-1:Physical representations and symbols can be used to develop the understanding that a/b=a x 1/b. 13-2:Models can be used to find the product of a whole number and a fraction. 13-3:To multiply a fraction by a whole number, one must multiply the whole number by the numerator of the fraction and then divide the product by the denominator of the fraction. 13-4:A decimal is another name for a fraction. 13-5: Each fraction, mixed number, and decimal can be associated with a unique point on the number line. 13-6:Every fraction can be represented by an infinite number of equivalent fractions, but each fraction is represented by the same decimal or an equivalent form 13-7:Decimal numeration is just an extension of whole number numeration. 13-8:Place value can be used to compare and order numbers. 13-9 Relationships among dollars, dimes, and pennies are a good model for decimal numeration. 13-10: Information in a problem can often be shown with a picture or diagram and used to understand and solve the problem. ||
 * Using unit fractions and multiplication, describe fractions that are multiples of the unit fractions.
 * Multiplying a fraction by a whole number using models.
 * Multiplying a whole number and a fraction to solve problems.
 * Write fractions as decimals and decimals as fractions.
 * Locating and naming fractions and decimals on a number line.
 * Using equivalent fractions, writing fractions as decimals.
 * Using models and place value charts, representing decimals to hundredths.
 * Reading and writing decimals in expanded, standard, and word form.
 * Using models and place value charts, comparing decimals to hundredths.
 * Using greater than and less than symbols, order decimal numbers.
 * Using place value charts, reading, writing, and comparing decimals in tenths and hundredths using money.
 * Solving problems using the strategy Draw a Picture. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__ || __Other Evidence:__ ||
 * ~ = Learning Plan = ||
 * __Learning Activities:__
 * __Resources:__

__Problem of the Month:__ [|Party Time]

__Centers:__ __[|Models for Fraction Multiplication]__ __[|Multiplying a Fraction by a Number]__ __[|Whole Number Times Fraction Word Problems]__ __[|Sums of 1]__ __[|Equivalent Fractions with a Denominator of 100 Problems]__ __[|Decimals in Money]__ __[|Representing Decimals with Base Ten Blocks]__ __[|Decimal Riddles]__ __[|Metric Relationships]__ __[|Comparing Decimals]__ __[|Decimal Sort]__

__Literature Connection:__ __[|Full House: A Connection to Fractions]__

__Additional Units:__ [|Chocolate Bar Fractions] ||