Topic+Ten

= Topic Ten: Fraction Comparison and Equivalence = Pacing (Duration of Unit): 3. Construct viable arguments and critique the reasoning of others. 4**. Model with mathematics.** 6. Attend to precision. 8. Look for and express regularity in repeated reasoning. ||
 * ~ = Desired Results = ||
 * **Transfer:**
 * Standards for Mathematical Practices**
 * 1. Make sense of problems and persevere in solving them.**
 * 2. Reason abstractly and quantitatively.**
 * 5. Use appropriate tools strategically.**
 * 7. Look for and make use of structure.**
 * **Established Goals:**


 * 3.NF.2** Understand a fraction as a number on the number line; represent fractions on a number line diagram.


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


 * 3.NF.3.c** Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.


 * 3.NF.3.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.


 * Prerequisite Standards:**
 * 2.MD.6** Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0,1,2..., and represent the whole-number sums and differences within 100 and on a number line diagram.


 * 3.NF.1** Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. ||
 * **Big Ideas:**

Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways.
 * Comparison and Relationships**

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.
 * Numbers and the Number Line**

Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
 * Equivalence**

Mathematics content and practices can be applied to solve problems. || **Essential Questions:**
 * Practice, Processes, and Proficiencies**
 * What are different ways to compare fractions? ||
 * **Students will know...**
 * 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.
 * Fractions can be compared to each other by comparing them to the benchmark numbers such as 0, 1/2, and 1.
 * Number lines can be used to compare fractions with like denominators or like numerators.
 * A fraction is relative to the size of the whole. Models can be used to compare fractional amounts.
 * Number lines can be used to compare fractions with like denominators and numerators.
 * Equivalent fractions name the same point on a number line.
 * If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction.
 * The same fractional amount can be represented by an infinite set of different but equivalent fractions.
 * Equivalent fractions name the same point on a number line.
 * If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction.

|| **Students will be skilled at...** || Other Evidence: ||
 * Vocabulary:**
 * equivalent fractions
 * simplest form
 * comparing fractions with the same denominator using models and quantitative reasoning.
 * comparing fractions with the same numerator using models and quantitative reasoning.
 * comparing fractions with the same numerator or the same denominator using benchmark numbers.
 * comparing fractions with like denominators or like numerators using number lines.
 * computing equivalent fractions using models.
 * computing equivalent fractions using number lines.
 * naming whole numbers as fractions using fraction strips and number lines.
 * comparing and ordering fractions to solve problems.
 * drawing a picture to solve problems. ||
 * ~ = Assessment Evidence = ||
 * **Performance Assessment:**
 * ~ = Learning Plan = ||
 * **Learning Activities:**

**10-1** If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.

**10-2** If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.

**10-3** Fractions can be compared to each other by comparing them to the benchmark numbers such as 0, 1/2, and 1.

**10-4** Number lines can be used to compare fractions with like denominators or like numerators.

**10-5** The same fractional amount can be represented by an infinite set of different but equivalent fractions.

**10-6** Equivalent fractions name the same point on a number line.

**10-7** If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction.


 * 10-8** A fraction is relative to the size of the whole. Models can be used to compare fractional amounts.


 * 10-9** If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction. ||
 * **Resources:**

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 * Home School Connection:**