2014-2015 Curriculum Blueprint Grade: 6 Course: MJ1 Approximate Time: 10 Days Unit #11: Problem Solving With Volume and Surface Area Learning Goal Students will understand and be able to solve real-world and mathematical problems involving area, surface area, and volume. Link to Learning Scale Surface Area and Volume   Essential Question(s) When you want to find the volume of a rectangular prism that has sides with fractional lengths, what are some methods you can use? Why is a net helpful when calculating the surface area of pyramids and prisms? Focus Standards Bullets are the deconstructed standards These should be used to develop concise learning statements/daily objectives/scales. 6th Grade Math Test Item Specifications Unit Overview In this unit, students learn how to find volume of rectangular prisms with fractional side lengths. Students also model 3--‐D figures with nets and use the nets to find surface area. Students apply their ability to evaluate expressions as they calculate area, surface area, and volume using appropriate formulas. As students investigate volume of surface area of 3-D figures, they select and use appropriate tools—such as formulas, nets, and unit cubes— strategically (MP.5). Understanding how net models of 3-D figures relate to their surface areas requires that students look for and make use of structure (MP.7). Applying formulas to find volumes with fractional edge lengths requires that students attend to the degree of precision appropriate for a given situation (MP.6). Vertical Progression: http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine remediation needs or enrichment opportunities) 5th Grade Students find the area and volume of an object. MAFS.6.G.1.2 (DOK 2): Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Know how to calculate the volume of a right rectangular prism.  Model the volume of a right rectangular prism, with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths. 7th Grade Students draw and determine the actual area based on a scale drawing. Unit Sequence Be selective in choosing problems aligned to the standards within each lesson MAFS.6.G.1.4 (DOK 2): Represent three-dimensional figures using nets made up of rectangles and Volume of Rectangular Prism with Fractional Lengths triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  EngageNY Module 5: Lesson 11 – (page 150)  Know that 3-D figures can be represented by nets.  NC Lessons for Learning Task: “Block Party” – Performance Task for determining volume  Apply knowledge of calculating the area of rectangles and triangles to a net, and combine the with fractional edge lengths (page 24) areas for each shape into one answer representing the surface area of a three-dimensional figure. Understanding & Application of the formula V=Bh  Solve real-world and mathematical problems involving surface area using nets.  EngageNY Module 5: Lesson 12/13 – (page 170) Collaborative Centers Task is MAFS.6.EE.1.2 (DOK): Write, read, and evaluate expressions in which letters stand for included numbers.  Holt 9-6 c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real- world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a Representing & Using Nets of 3-D figures particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the  EngageNY Module 5: Lesson 15/16 – (page 213) volume and surface area of a cube with sides of length s = 1/2.  Substitute specific values for variables  Translate written phrases into algebraic expressions.            Essential Vocabulary Volume Surface Area Dimensions Right Rectangular Prisms Pyramids Cube Fractional Edge Lengths Nets Higher Order Questions/Stems Do we need to know the length and the width to find the volume of the rectangular prism? Why or Why Not? How does the formula relate to the measure and the figure? How can you use a net to calculate surface area? 2014-2015 Curriculum Blueprint Grade: 6 Course: MJ1 Approximate Time: 10 Days Unit #11: Problem Solving With Volume and Surface Area Mathematical Practice Standards Link to Mathematical Practice Standards Rubric Surface Area of 3-D Figures  EngageNY Module 5: Lesson 17/18 (page 262)  Holt 9-8 (excluding cylinders) MAFS.K12.MP.5.1: Use appropriate tools strategically. MAFS.K12.MP.6.1: Attend to precision MAFS.K12.MP.7.1: Look for and make use of structure. Surface Area and Volume - Real World Applications  EngageNY Module 5: Lesson 19 - (page 288)  Translate algebraic expressions into written phrases. Supplemental Resources 6th Grade Flip Book – A user-friendly resource regarding specifications of the Common Core State Standards.   Writing Connections When you want to find the volume of a rectangular prism that has sides with fractional lengths, what are some methods you can use? Explain the processes. How is the formula 𝑉=𝑙∙𝑤∙ℎ related to the formula 𝑉= B∙h? Writing Template Tasks These template tasks are designed from the Mathematical Practice Standards. When filled in, these templates become teaching tasks that create opportunities for teaching literacy skills in mathematics. EngageNY Grade 6 Module 5 – Word documents Link to Problem Solving Rubric can be found using this link Link to Webb’s DOK Guide o Teacher Materials - The teacher materials consist of scripted lessons, instructional strategies, and structured plans. o Student Materials - The student materials consist of the student pages for each lesson in this Module. o Copy Ready Materials - A collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials. Georgia Unit 5: Geometry Tasks aligned to standards 6.G.1.2 and 6.G1.4: o Finding Surface Area – page 69 o How Many Ways? – page 73 o Banana Bread – page 79 o Volume and Cubes – page 82 o Packaging Our Goods – page 91 o Painting Barns – page 97 o Boxing Bracelets – page 107 o The File Cabinet – page 114 o STEM Fish Tank Foam Packaging Design – page 119 MARS Task: “Packing It In” – A formative assessment lesson intended to help students reason precisely, defend their conclusions, and use mathematics to model a scenario concerning volume. PowerPoint to support is found under the Resources heading at bottom of page 2014-2015 Curriculum Blueprint Grade: 6 Course: MJ1 Unit #11: Problem Solving With Volume and Surface Area MARS Task: “Candle Box” – Performance task for creating a Hexagonal net. MARS Task: "Smoothie Box" – Performance task for creating a box to hold 12 bottles (net). Illustrative Mathematics – 6th grade tasks developed under the direction of writers of the CCSS at the University of Arizona. Following is a series of 4 Tasks Aligned to 6.G.1.2 that gradually build in complexity: o Volume#1 o Volume #2 o Volume #3 o Volume #4 Engage NY Module 5 – Short task to scaffold for understanding of a cube with fractional edge length (page 161) RTTT Item Specifications – page 27 Teaching Channel Video 2 min video with focus on Improving Participation with Talk Moves (Personalized Learning Opportunity). Approximate Time: 10 Days