Madison County Public Schools

MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 7 Unit Description Unit 8 Applications of Geometry Suggested Length: 3 weeks

Big Idea(s) Enduring Understandings What enduring Understanding and application of geometric properties of 2-D and 3-D figures understandings are essential (link enduring skills rubric here) for application to new Rubric measures competency of the following enduring skills: situations within or beyond  Use geometric figures this content?  Slicing geometric figures  Solving problems involving geometric figures  Use angle relationships Essential Question(s)  How do you find and use the circumference of a circle? What questions will provoke  How are the diameter and circumference of a circle related? and sustain student  What is pi? How does it relate to the circumference and diameter of a engagement while focusing circle? learning?  How do you find and use the area of a circle?  Why is the area of a circle measured in “square units” when a circle isn’t square?  How is the formula for the area of a circle related to the formula for the area of a square? parallelogram?  How do you find the area of a composite figure?  How are the perimeter and area of a shape related?  How are the areas of geometric figures related to each other?  How can the formulas for the area of plane figures be used to solve problems?  What strategies can be used to find area of regular and irregular polygons without having a specific formula?  How do you find the surface area of a figure made up of cubes and prisms?  How do you find the volume of a figure made up of cubes and prisms?

 How can the concepts of surface area and volume be used to solve problems? Standards: Standards for Mathematical Practice Which standards provide 1 – Make sense of problems and persevere in solving them. endurance beyond the 4 – Model with mathematics. course, leverage across 5 – Use appropriate tools strategically. multiple disciplines, and 7 – Look for and make use of structure. readiness for the next level?

Standards for Mathematical Content 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 circumference and area of a circle.

Curriculum and Instruction 2015-2016 Page 1 of 5 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 7 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.

Supporting Standard(s): 7.G.1 Solve problems involving scale drawings of geometric figures, including Which related standards will computing actual lengths and areas from a scale drawing and reproducing a be incorporated to support scale drawing at a different scale. and enhance the enduring standards? 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3 Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Instructional Outcomes I am learning to… What must students learn  Identify the parts of a circle including radius, diameter, area, and be able to do by the end circumference, center, and chord (not a test item) of the unit to demonstrate  Identify pi (π) (not a test item) mastery?  Find the area of a circle, given its circumference. (7.G.4)  Find the circumference of a circle, given its area (7.G.4)  Apply the formulas for circumference and area of a circle to solve mathematical and real-world problems. (7.G.4)  Justify that pi can be derived from the circumference and diameter of a circle. (7.G.4)  Justify the formulas for area and circumference of a circle and how they relate to pi. (7.G.4)  Informally derive the relationship between circumference and area of a circle. (7.G.4)  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. (7.G.6) Vocabulary Essential Vocabulary What vocabulary must students know to understand Circumference, diameter, Pi, radius, adjacent, area, circumference, and communicate effectively complementary, diameter, plane section, polygon, prism, pyramid, about this content? quadrilateral, supplementary, surface area, triangle, vertical, volume

Supporting Vocabulary adjacent angles, complimentary angles, supplementary angles, transversal, vertical angles

Curriculum and Instruction 2015-2016 Page 2 of 5 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 7 Resources/Activities Resources/Activities What resources could we  From https://www.georgiastandards.org/Pages/default.aspx Use use to best teach this unit? the following unit to access tasks and instructional strategies specific to percent proportions. (insert link to Georgia standards frameworks unit 3)  Dan Meyer – Holes http://mrmeyer.com/threeacts/holes/  Making Math Magic Resources - http://www.makingmathmagic.net/kcm.html  Ann Shannon Formative Assessment Lessons (search by standard) http://map.mathshell.org/lessons.php?gradeid=22  Shodor Activities by Content Strand - http://www.shodor.org/interactivate/standards/organization/354/  EngageNY Lessons by Strand - https://www.engageny.org/resource/grade-7-mathematics  NCTM Illuminations – search for games, lessons and interactives by grade level and content http://illuminations.nctm.org

Remember there are other sources in your school that may not be listed on this common resources list due to variation in each individual school. Examples of other great resources your school may have access to include: GoMath, Connected Math, IXL, Compass, MobyMax, Laying the Foundation, Carnegie, etc. The Kentucky Numeracy Project is also a great resource that can be searched by CCSS and grade level K-4 for RTI and gap closure purposes. Find this resource at http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky teachers can use it for free. Just put in your school email address and the username “mathfun”, and password is “859”. Common Misconceptions  Students can have trouble deciding which quantity should be the numerator versus the denominator.  A common error is to reverse the position of the variables when writing equations.  Students need to look for patterns between the x and y as opposed to looking at the quantities as separate entities.  Students need to look for the relationship of the quantities in relation to the problem as opposed to just giving the numerical values.  Students tend to have difficulty grasping percents that are greater than 100. You may need to model problems and discuss situations when they may occur.  Students may need visual reinforcement of the concept that 100 percent is the “whole” and the “whole” can be of varying quantities.

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