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 * Grade: 4 Unit: 4 Week: 7** **Content: Math – Fractions (Wk 1) Dates: February 19-22**


 * Theme Essential Question **** : How can I use fractions to solve real world problems? **


 * Essential Questions: **
 * ** How can I use models to show equivalent fractions? **
 * ** How can I write a pair of fractions as fractions with a common denominator? **
 * ** How can I represent addition and subtraction as joining and separating parts referring to the same whole? **
 * ** How can I decompose a fraction into a sum of fractions with the same denominator in more than 1 way? **
 * ** How can I record decomposition of fractions using an equation or a visual fraction model? **


 * Standards **
 * ** 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size 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.3a Understand a fraction a/b with a>1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. **
 * ** 4.NF.3b Understand a fraction a/b with a>1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same demominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 2/8 + 1/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8+ 1/8. **

Objectives
 * I can write fractions equivalent to a group of fractions.
 * I can use equivalent fractions to solve real world problems.
 * I can use equivalent fractions to represent a pair of fractions as fractions with a common denominator.
 * I can model a fraction as part of a whole that is divided into equal parts.
 * I can use multiplication to find equivalent fractions.
 * I can join and separate fractional parts of the same whole.
 * I can decompose fractions with the same denominator in more than 1 way.

Students can identify a given fraction (such as 2/3) on a 4 X 6 grid and explain how they know it is two-thirds (or the given fraction).
 * Assessment **
 * Product
 * Key Questions (match Standard)
 * Can the student explain why a given fraction (such as 1/2) is equivalent to another fraction (2 x 1)/2 x 2) by using visual models?
 * Can the student join and separate parts of a given whole to create a given fraction?
 * Can the student decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each by an equation?


 * Observable Student Behaviors (Performance)
 * The student will be able to partition an area (a grid) into given fractional parts.
 * The student will be able to find a given fraction of a grid with numerator of 1 (1/3) and with numerators greater than 1 (2/3).
 * The student will be able to explain how they know the partition equals a given fraction.
 * The student will be able to use correct fraction notation for the parts they identify.


 * **Mathematical Practices **
 * Make sense of problems and persevere in solving them.
 * Reason abstractly and quantitatively.
 * 3. Construct viable arguments and critique the reasoning of others.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Attend to precision.
 * Look for and make use of structure.
 * 8. Look for and express regularity in repeated reasoning. ||

Equivalent fractions Numerator Denominator Factor Multiple Common factor Simplest form Common multiple Common denominator ||
 * Vocabulary **
 * ** Math ** ||
 * Fractions

These lessons focus on finding fractional parts of a rectangular area; interpreting the meaning of the numerator and denominator of a f raction; writing, reading, and applying fraction notation; identifying relationships between unit fractions when one denominator is a multiple of the other (e.g., halves and fourths, thirds and sixths); and identifying equivalent fractions.
 * Suggested Activities **
 * Math Investigations ** : Unit 6-__Fraction Cards and Decimal Squares (__Sessions 1.1 and 1.2)


 * On-Core: ** Lesson 47 (pp. 93-94) and Lesson 56 (pp. 111-112)


 * __ Hands-on Standards __**** (grades 3-4) Equivalent Fraction pgs. 48, 49; Adding and Subtracting Fractions pgs.54, 55; **


 * Homework **


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  ||
 * ** Multicultural Concepts **

************************************************************************************************************
 * Resources **
 * __ Professional Texts __**
 * ** Teaching Student-Centered Mathematics, Grades 3-5 (Van de Walle and Lovin): ** Equivalent Fraction Concepts (pp. 151-157)-Activity 5.14 “Different Fillers”, Activity 5.15 “Dot Paper Equivalencies”, Activity 5.19 “Slicing Squares”
 * ** Extending Children’s Mathematics: Fractions and Decimals (Empson and Levi). **

**Literary Texts**

**Informational Texts**
 * **List**

**Art, Music, and Media**
 * **List**


 * Manipulatives **
 * Library of Virtual Manipulatives @http://nlvm.usu.edu/
 * Fractions Bars
 * Two-color Counters
 * Fraction Tower Equivalency Cubes
 * Fraction Circles


 * Games **
 * List

**Videos**
 * **List**

**Sight Words**
 * **List**

**Smartboard Lessons****, Promethean Lessons ** Add and Subtract Fractions with Like Denominators Develop fluency with addition and subtraction of non-- ‐ negative rational numbers with like denominators.
 * AEGOM Lesson G3M014 **

Add and Subtract Fractions Develop fluency with addition and subtraction of non—negative rational numbers with unlike denominators.
 * AEGOM Lesson G4M014 **

Add and Subtract Fractions (with like and unlike denominators) Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelnhs; finhs, tenths, hundredths, thousandths; mixed numbers)
 * AEGOM Lesson G5M008 **

Equivalent Fractions Use models, points of reference and equivalent forms to judge the size of fractions. Round fractions to the nearest half.
 * AEGOM Lesson G5M007 **

@http://exchange.smarttech.com/details.html?id=e56d2346-d250-47f2-8a74-fa5251329351

@http://exchange.smarttech.com/details.html?id=e53e7dc2-ac9e-43a5-8dce-83f0653da32e


 * Other Activities, etc. **
 * List


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