Unit+Two+Chapter+Two+Math+2013

__Number Systems__ Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
 * **Unit of Study: Unit 2 Chapter 2 Ratios and Proportions ** ||
 * **Grade: Sixth ** |||| **Topic: Fractions, Decimals, and Percents ** || **Length of Unit: 2-3 weeks ** ||
 * **Focus of Learning ** ||
 * **__Common Core Standards: __**

1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

//Compute fluently with multi-digit numbers and find common factors and multiples.//

4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

6. Understand a rational number as a point on the number line. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram;

__Ratios and Proportions__ 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. |||| **__Standards for Mathematical Practice: __** 1. Make 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. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">Use appropriate tools strategically. <span style="font-family: Calibri,sans-serif; font-size: 8pt;">6. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">Attend to precision. <span style="font-family: Calibri,sans-serif; font-size: 8pt;">7. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">Look for and make use of structure. <span style="font-family: Calibri,sans-serif; font-size: 8pt;">8. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">Look for and express regularity in repeated reasoning. ||
 * **__<span style="font-family: Calibri,sans-serif;">Enduring Understanding(s): __**//<span style="font-family: Calibri,sans-serif; font-size: 9pt;">Students will understand that… // ||
 * **__<span style="font-family: Calibri,sans-serif;">Guiding Questions: __**//<span style="font-family: Calibri,sans-serif; font-size: 9pt;">These questions will guide student inquiry. // ||
 * **<span style="font-family: Calibri,sans-serif;">Student Performance ** ||
 * **__<span style="font-family: Calibri,sans-serif;">Knowledge: __**//<span style="font-family: Calibri,sans-serif; font-size: 10pt;">Students will understand/know ////<span style="font-family: Calibri,sans-serif; font-size: 9pt;">… // |||| **__<span style="font-family: Calibri,sans-serif;">Application: __** //<span style="font-family: Calibri,sans-serif; font-size: 10pt;">Students will be able to… // ||
 * **<span style="font-family: Calibri,sans-serif;">Assessments ** <span style="display: block; font-family: Calibri,sans-serif; font-size: 9pt; text-align: center;">(Attached) ||
 * **__<span style="font-family: Calibri,sans-serif;">Assessments: __**<span style="font-family: Calibri,sans-serif; font-size: 9pt;"> //pre-assessment, formative, and post-assessment/culminating task//

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Pre-Assessment: __

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Formative Assessments: __

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Post-Assessment (Culminating Task) __ ||

Revisit the idea of consecutive odd addends making perfect squares ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Percents are a decimal form of ratios //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Write percents as decimals and decimals as percents ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Fractions are another way to express rational numbers, and represent an incomplete division problem //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Write fractions as terminating or repeating decimals and write decimals as fractions ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Fractions are another way to express ratios //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Write fractions as percents and percents as fractions ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Fractions are rational numbers, like decimals/percents, and can be compared and ordered //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Compare and order fractions, decimals, and percents ||  || Pattern blocks representation of fractions ||  ||
 * **<span style="font-family: Calibri,sans-serif;">Learning Experiences ** <span style="display: block; font-family: Calibri,sans-serif; font-size: 9pt; text-align: center;">(Lesson Plans Attached) ||
 * **__<span style="font-family: Calibri,sans-serif;">Days __** |||| **__<span style="font-family: Calibri,sans-serif;">Lesson Sequence __** || **__<span style="font-family: Calibri,sans-serif;">Materials __** ||
 * |||| **Lesson 1:** Math Workshop
 * |||| **Lesson 2:** 4-7 Percents and Decimals (pp. 206–210)
 * |||| **Lesson 3:** 4-5 Fractions and Decimals (pp. 196–200)
 * |||| **Lesson 4:** 4-6 Fractions and Percents (pp. 202–205)
 * |||| **Lesson 5:** 4-9 Comparing and Ordering Rational Numbers (pp. 215–220)
 * |||| **Lesson 6:** Math Workshop
 * **<span style="font-family: Calibri,sans-serif;">Resources ** ||
 * **<span style="font-family: Calibri,sans-serif;">Online ** |||| **<span style="font-family: Calibri,sans-serif;">Text ** ||