Unit Overview - Tewksbury Township Schools
|Unit Overview |
|Content Area: Math |
|Unit Title: Volume and Surface Area Unit: 8 |
|Target Course/Grade Level: Seventh Grade Timeline: 3 weeks |
|Unit Summary: Students explore the concepts of surface area and volume of three-dimensional shapes including prisms, cylinders, pyramids, and |
|cones. They will discover relationships between the volumes of prisms and pyramids and cylinders and cones to justify and apply surface area |
|and volume formulas. Students will also use the formulas to find volume and surface areas of three-dimensional composite shapes. Students will |
|build on these concepts as they work with similar solids. |
|Primary interdisciplinary connections: Language Arts, Science, 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 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: |
|7.MP.1 Make sense of problems and persevere in solving them. |
|7.MP.2 Reason abstractly and quantitatively. |
|7.MP.3 Construct viable arguments and critique the reasoning of others. |
|7.MP.4 Model with mathematics. |
|7.MP.5 Use appropriate tools strategically. |
|7.MP.6 Attend to precision. |
|7.MP.7 Look for and make use of structure. |
|7.MP.8 Look for and express regularity in repeated reasoning. |
| |
|Domain: Geometry |
|Cluster: Solve real-world and mathematical problems involving angle measure, area, surface area, and volume. |
|Standard # | Standards |
|7.G.4 |Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation |
| |of the relationship between the circumference and area of a circle. |
|7.G.6 |Solve real-world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects |
| |composed of triangles, quadrilaterals, polygons, cubes, and right prisms. |
|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 volume and surface used in the real world? |Volume is the measure of space occupied by a three-dimensional region. |
|How are two-dimensional representations of three-dimensional figures |It is measured in cubic units. |
|useful? |Surface area is the sum of the areas of all the surfaces, or faces of a |
|How is finding the volume of a composite figure different than finding|three-dimensional figure. It is measured in square units. |
|the surface area of a composite figure? How is it similar? |A composite figure is made up of two or more three-dimensional figures. |
|Unit Learning Targets |
|Students will ... |
|Justify formulas for the volume of prisms |
|Find the volumes of rectangular and triangular prisms |
|Find the volumes of cylinders. |
|Justify formulas for the volume of pyramids and cones. |
|Find the volume of pyramids. |
|Find the volume of cones. |
|Find the surface area of prisms and cylinders using models and nets. |
|Find the surface area of prisms. |
|Find the surface area of a cylinder. |
|Compare surface area and volume of rectangular prisms and cylinders. |
|Find the surface area of pyramids. |
|Justify the formula for the surface area of a cone by using a net |
|Solve problems by solving a simpler problem. |
|Explore volume and surface area of composite figures. |
|Find the volume and surface area of composite figures. |
|Evidence of Learning |
|Summative Assessment |
|Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. |
|Use formulas to find surface areas and volumes of three-dimensional composite shapes. |
|Equipment needed: |
|Teacher Instructional Resources: Textbook - 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 7th grade online interactive activities for the students to complete |
| |
| - AAA math 7th grade – online interactive activities and problems for the student to complete. |
| |
| – Grade level material for practice, lessons, games, etc. |
| |
| |
|Opportunities for Differentiation: |
|Decelerate: Use base-ten unit cubes to assist in determining volume. |
|Have students use empty boxes to create a net to assist in finding surface area. |
|Create composite figures by using cereal boxes and card stock to create a model. |
| |
|Accelerated: Have students write a formula for a volume of a trapezoidal prism. |
|Students use base-ten blocks to find integer dimensions rectangular prisms with a given |
|volume. |
|Students will write real-world problems that can be solved by finding volume of a |
|composite figure and one solved by finding surface area. Include a drawing for each. |
|Teacher Notes: |
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