Topic+Eleven

= Topic Eleven: Fraction Equivalence and Ordering = 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.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.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ** 1 ** / ** 2 ** . Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
 * 4.OA.4: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

__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: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 * a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
 * b. Recognize and generate simple equivalent fractions, e.g., ** 1 ** / ** 2 ** = ** 2 ** / ** 4 **, ** 4 ** / ** 6 ** = ** 2 ** / ** 3 ** . Explain why the fractions are equivalent, e.g., by using a visual fraction model.
 * c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. // Examples: Express 3 in the form 3 = //** // 3 // **// / //** // 1 // **// ; recognize that //** // 6 // **// / //** // 1 // **// = 6; locate //** // 4 // **// / //** // 4 // **// and 1 at the same point of a number line diagram. //
 * d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

__"I Can" Statements:__
 * "I can find all factor pairs for a number from 1 to 100."
 * "I can determine whether a given whole number up to 100 is a prime or composite number."
 * "I can explain (and show models for) why multiplying a numerator and a denominator by the same number does not change the value of a fraction."
 * "I can compare two fractions with different numerators and different denominators by creating common denominators or numerators or by comparing them to a benchmark fraction like one-half."
 * "I can recognize that comparisons of fractions are valid only when the two fractions refer to the same whole."
 * "I can compare fractions using symbols and justify the comparison by using models." ||
 * __Big Ideas:__
 * Number Uses, Classifications, and Representation: Numbers can be used for different purposes, and numbers can be classified and represented in different ways.
 * Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
 * Comparison and Relationships: Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways.
 * Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems. || __Essential Questions:__
 * How can the same fractional amount be named using symbols in different ways?
 * How can fractions be compared and ordered? ||
 * __Students will know...__
 * Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.
 * Some counting numbers have exactly two factors; others have more than two.
 * The product of any nonzero number and any other nonzero number is divisible by each number and is called a multiple of each number.
 * The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.
 * If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction. If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.
 * Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to the other numbers.
 * Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand.

__Vocabulary:__ fraction, denominator, numerator, benchmark fraction, equivalent fraction, prime number, composite number || __Students will be skilled at...__
 * Learning how to factor whole numbers,\.
 * Learning to identify prime and composite numbers.
 * Finding the multiples of a number.
 * Using models and computation to show equivalent fractions.
 * Using a number line to identify and write equivalent fractions.
 * Using benchmark fractions to compare fractions with unlike denominators.
 * Using common denominators and equivalent fractions to order fractions with unlike denominators.
 * Writing to explain whether an answer is correct or not. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__

__[|4.NF.1: Picking Fractions]__ || __Other Evidence:__ ||
 * ~ = Learning Plan = ||
 * __Learning Activities:__

11-1: Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers. 11-2: Some counting numbers have exactly two factors; others have more than two 11-3: The product of any nonzero number and any other nonzero number is divisible by each number and is called a multiple of each number. 11-4: The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number. 11-5: The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number. 11-6: If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction. If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction. 11-7: Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to the other numbers. 11-8: Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand. ||
 * __Resources:__

__Problem of the Month:__

__[|4.NF.1: Fractured Numbers]__ __[|4.NF.2: Got Your Number]__

__Centers:__ __[|Creating Equivalent Fractions]__ __[|Fraction Wall Game]__ __[|Birthday Fractions]__ __[|Pattern Block Fractions]__ __[|Who Ate More?]__ __[|Fraction Compare]__ __[|Fraction Cards]__ __[|Which is Larger?]__ __[|Snack Time]__

__Additional Units:__ [|Fractions: Size Matters] ||