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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