<p> MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Unit Description Unit: 1 Title: Ratios Suggested Length: 3 weeks</p><p>Big Idea(s) Enduring Understanding What enduring Connect the fluency and understanding of multiplication and division with ratios to understandings are essential solve problems. for application to new situations within or beyond this content? Enduring Skills Rubric measures competency of the following skills: Equivalence • Every fraction/ratio can be represented by an infinite set of different but equivalent fractions/ratios. Comparison • A comparison of a part to the whole can be represented using a fraction. • A ratio is a multiplicative comparison of quantities; there are different types of comparisons that can be represented as ratios. • Ratios give the relative sizes of the quantities being compared, not necessarily the actual sizes. Proportionality • A ratio is a multiplicative comparison of quantities. • Ratios give the relative sizes of the quantities being compared, not necessarily the actual sizes.</p><p>Essential Question(s) What questions will provoke • Why would it be useful to know the greatest common factor of a set of and sustain student numbers? engagement while focusing • Why would it be useful to know the least common multiple of a set of learning? numbers? • How can the distributive property help me with computation?  What kinds of problems can I solve by using ratios? • How can I tell if a relationship is multiplicative? • What is the difference between a multiplicative and an additive relationship? • What are equivalent ratios? </p><p>Standards Standards for Mathematical Practice </p><p>1. Make sense of problems and persevere in solving them. Students understand the problem context in order to translate them into ratios. 2. Reason abstractly and quantitatively. Students understand the relationship between two quantities in order to express them mathematically. They use ratio notation as well as visual models and contexts to demonstrate reasoning. Curriculum and Instruction 2015-2016 Page 1 of 6 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding appropriateness of representations given ratio contexts. For example, does a tape diagram adequately represent a given ratio scenario. 4. Model with mathematics. Students can model problem situations symbolically (tables), visually (graphs or diagrams) and contextually to form real-world connections. Students use number lines and tape diagrams to find least common multiple and greatest common factor 5. Use appropriate tools strategically. Students choose appropriate models for a given situation, including tables, expressions or equations, tape diagrams, number line models, etc. 6. Attend to precision. Students use and interpret mathematical language to make sense of ratios and rates. 7. Look for and make use of structure. The structure of a ratio is unique and can be used across a wide variety of problem-solving situations. For instance, students recognize patterns that exist in ratio tables, including both the additive and multiplicative properties. In addition, students use their knowledge of the structures of word problems to make sense of real-world problems 8. Look for and express regularity in repeated reasoning. Students utilize repeated reasoning by applying their knowledge of ratio problem solving structures to new contexts. Students can generalize the relationship between representations, understanding that all formats represent the same ratio.</p><p>Standards for Mathematical Content 6.NS.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. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).</p><p>6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”</p><p>6.RP.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.</p><p> 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.</p><p>Supporting Standard(s) Which related standards will After looking at the 5th grade standards, ratios have not been addressed (unless it Curriculum and Instruction 2015-2016 Page 2 of 6 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 be incorporated to support was prior to 5th grade) but fractions were taught as follows; and enhance the enduring standards? 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. </p><p>5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. </p><p>5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. </p><p>5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.</p><p>Instructional I am learning to…. Outcomes What must students learn  Find the factors of two whole numbers less than or equal to 100. and be able to do by the end Determine the GCF of 2 numbers less than or equal to 100 (listing method, of the unit?  prime factorization and Venn diagram).  Identify the multiples of two whole numbers less than or equal to 12.  Determine the LCM of 2 numbers less than or equal to 12 (listing method, prime factorization and Venn diagram).  Use the distributive property to express the sum of two whole numbers 1-100 with a common factor (ex. Express 36 + 8 as 4(9 + 2).  Write a ratio using all 3 notations--__:__, __ to __, __/__  Know order matters when writing a ratio  Know ratios can be simplified  Know ratios compare two quantities; the quantities do not have to be the same unit of measure  Recognize that ratios appear in a variety of different contexts; part-to-whole, part-to-part, and rates  Generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship  Analyze your context to determine which kind of ratio is represented  Make a table of equivalent ratios using whole numbers.  Find the missing values in a table of equivalent ratios.  Use tables to compare proportional quantities</p><p>Vocabulary Essential Vocabulary What vocabulary must Bar Model students know to understand Common Factor and communicate effectively Common Multiple Curriculum and Instruction 2015-2016 Page 3 of 6 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 about this content? Distributive Property Equivalent Equivalent Ratios Factor Greatest Common Factor (GCF) Least Common Multiple (LCM) Multiple Number Line Prime Factorization Ratio Simplest Form Simplify Table Tape Diagram Supporting Vocabulary Common denominator Denominator Divisible Equivalent Fractions Fraction Fraction Bar Numerator Prime Number</p><p>Resources/Activities Resources/Activities What resources could we use to best teach this unit? https://www.georgiastandards.org/Common-Core/Common%20Core %20Frameworks/CCGPS_Math_6_6thGrade_Unit2.pdf</p><p>The following website is a website with lessons to address CCSS: https://www.engageny.org/resource/grade-6-mathematics</p><p>Khan Academy -- www.khanacademy.org</p><p>IXL – www.ixl.com</p><p> http://www.insidemathematics.org/common-core-resources/mathematical-content- standards/standards-by-grade/6th-grade</p><p> http://www.mathchimp.com/6th-grade-math-resources</p><p>Remember there are other sources in your school that may not be listed on this resources list due to variation in each individual school. If you have a good resource that you would be willing to share, please let Mendy Mills know so that she can share with other math teachers. Please include the unit for the</p><p>Curriculum and Instruction 2015-2016 Page 4 of 6 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 resource. [email protected] </p><p>Curriculum and Instruction 2015-2016 Page 5 of 6</p><p>Curriculum and Instruction 2015-2016 Page 6 of 6</p>