Unit Overview - Tewksbury Township Schools



|Unit Overview |

|Content Area: Math |

|Unit Title: Ratios and Rates Unit: 3 |

|Target Course/Grade Level: Sixth Grade Timeline: 3 weeks |

|Unit Summary: Students learn to recognize ratios, rates, and unit rates. They gain the understanding that a ratio is a comparison of two |

|quantities by division. They find equivalent ratios by multiplying or dividing both terms of the ratio by the same number and find unit rates |

|by dividing the numerator by the denominator of a given rate. Bar diagrams and ratio tables enable students to see how multiplication and |

|division are used to solve ratio and rate problems. Students apply their knowledge of ratios and rates to solve real-world problems. Learning|

|to reason about the relationships between quantities help students become efficient problem solvers. |

|Primary interdisciplinary connections: Language Arts and Technology |

|9.1 21st-Centuries Life & Career Skills |

|Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function |

|successfully as both global citizens and workers in diverse ethnic and organizational cultures. |

|Strand: A. Critical Thinking and Problem Solving |

|B. Creativity and Innovation |

|C. Collaboration, Teamwork and Leadership |

|Content Statement: |

|9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem |

|solving skills to solve the problem is a lifelong skill that develops over time. |

|9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources, |

|including global perspective, fosters creativity and innovative thinking. |

|9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals |

|with greater efficiency. |

|Leadership abilities develop over time through participation in group and or teams that |

|that are engaged in challenging or competitive activities. |

|21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and |

|Leadership, Creativity and Innovation |

|Mathematical Practices: |

|6.MP.1 Make sense of problems and persevere in solving them. |

|6.MP.2 Reason abstractly and quantitatively. |

|6.MP.4 Model with mathematics. |

|6.MP.5 Use appropriate tools strategically. |

|6.MP.6 Attend to precision. |

|6.MP.7 Look for and make use of structure. |

|Learning Targets |

|Domain: Ratios and Proportional Relationships |

|Cluster: Understand ratio concepts and use ratio reasoning to solve problems |

|Standard # | Standards |

|6.RP.1 |Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. |

|6.RP.2 |Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a |

| |ration relationship. |

|6.RP.3 |Use ratio and rate reasoning to solve real-world and mathematical problems. |

|6.RP.3a |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. |

|6.RP3b |Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow|

| |4 lawns, than at t6hat rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed. |

|9.1.8.A.1 |Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and |

| |problem-solving skills. |

|9.1.8.A.2 |Implement problem-solving strategies to solve a problem in school or the community. |

|9.1.8.B.2 |Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, |

| |generational, etc.) and determine how the data can best be used to design the multiple solutions. |

|9.1.8.C.1 |Determine an individual’s responsibility for personal actions and contributions to group activities. |

|9.1.8.C.2 |Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, |

| |assignments and projects. |

|9.1.8.C.3 |Model leadership skills during classroom and extracurricular activities. |

|Unit Essential Questions |Unit Enduring Understandings |

|How are ratios, rates, and equivalent ratios used in the real world? |A ratio is a comparison of two quantities by division (fraction). |

|How are fractions, ratios, and rates related? |Equivalent ratios express the same relationship between two quantities. |

|How are ratio tables like other tables? How are they different? | |

|Describe a real-world situation when it would be helpful to find an | |

|equivalent rate. | |

|Unit Learning Targets |

|Students will ... |

|Express ratios and rates in fraction form. |

|Determine unit rates. |

|Use ratio tables to represent and solve problems involving equivalent ratios |

|Solve problems by looking for a pattern. |

|Determine if two ratios are equivalent. |

|Solve real-world problems using ratios and rates. |

|Evidence of Learning |

|Summative Assessment |

|Use multiplication and division to find equivalent ratios and rates. |

|Interpret and compare pairs of ratios or rates. |

|Use ratio tables, bar diagrams, and reasoning to solve ratio and rate problems |

|Equipment needed: Smart Board, white boards, calculators, Elmo |

|Teacher Instructional Resources: TBD |

|Study Island |

|Khan Academy Videos |

|Formative Assessments |

|Skill sheets |Homework |

|Quizzes/Tests |Math games |

|Student workbook |Study Island |

| |

|Integration of Technology: |

|Smart Board to play online games, utilize online resources, generate models with Smart Software. |

|Kahn Academy Videos |

|Elmo – for demonstration |

|Study Island |

|Technology Resources: |

| |

| |

| – Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice |

|modules for additional practice/remediation. |

| |

| - Web-based instruction, practice, assessment and reporting built from NJ standards. |

| |

| - IXL 6th grade online interactive activities for the students to complete |

| |

| - AAA math 6th grade – online interactive activities and problems for the student to complete. |

| |

| – Grade level material for practice, lessons, games, etc. |

| |

| |

|Opportunities for Differentiation: |

|Decelerate: Have students look for patterns, including numerical or geometric and develop their own. Have students match equivalent grids by |

|finding the ratio of shaded squares to total squares. |

| |

|Accelerated: Applying ratio and rates by solving intricate word problems. Research Golden Ratio. |

|Teacher Notes: |

|Ratios are part of a whole. |

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