Ratcheting Up the Three R s All SubjectsInstructional Unit Plan

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Carmella Fields
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Subject: Mathematics Ratcheting Up the Three R s All SubjectsInstructional Unit Plan Estimated Length of Unit: 25 Beginning Date: April 24 Module: 6 Area, Surface, and Volume Problems Grade: 6

1 Subject: Mathematics Ratcheting Up the Three R s All SubjectsInstructional Unit Plan Estimated Length of Unit: 25 Beginning Date: April 24 Module: 6 Area, Surface, and Volume Problems Grade: 6 Projected Ending Date: May 24 Unit Theme, Big Idea, or Essential Question: Students move from building arrays to using arrays to find area and move to decomposing three-dimensional shapes into layers that are arrays of cubes. Students use their previous experiences in shape composition and decomposition in order to understand and develop forums for area, volume, and surface area. UBD Stage One-Desired Results A. Students will 1. use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons; students determine that area is additive. 2. discover through composition that the area of a parallelogram is the same as a rectangle. 3. compose rectangles using two copies of a right triangle. 4. extend previous knowledge about the area formula for rectangles to evaluate the area of the rectangle using A = bh and discover through manipulation that the area of a right triangle is exactly half that of its corresponding rectangle. 5. discover that any triangle may be decomposed into right triangles. B. Students will know 1. that two formulas can be used to find the volume of a right rectangular prism. 2. that volume is additive and find the volume of composite solid figures. 3. to apply volume formulas and use their previous experience with solving equations to find missing volumes and missing dimensions. C. Students will be skilled at 1. deconstructing the faces of solid figures to determine surface area. 2. determining the difference between finding the volume of right rectangular prisms and finding the surface area of such prisms. 3. determining the surface area of solid figures. 4. distinguishing between the need to find surface area of volume within contextual situations. Frameworks and Common CoreState Standards Textbook Resources CCSS Math Eureka Math A Story of Ratios Module 5 Glencoe (McGraw Hill): This Unit Corresponds with Chapters 9 and 10 of the Glencoe Math textbook 6.G.A.1- Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving

2 real-world and mathematical problems. Note: Trapezoids will be defined to be a quadrilateral with at least one pair of opposite sides parallel, therefore all parallelograms are trapezoids. 6.G.A.2- Find the volume of a right rectangular prism including whole number and 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 = l w h and V = B h to find volumes of right rectangular prisms including fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.A.3- Apply the following techniques in the context of solving real-world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 6.G.A.4- Apply the following techniques in the context of solving real-world and mathematical problems. Represent three-dimensional figures using nets made up of rectangles and triangles Use the nets to find the surface area of these figures.

3 Review Skills 6.EE.A.2- Write, read, and evaluate expressions in which letters (variables) stand for numbers. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5 or y less than 5" as 5 - y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 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 particular order (Order of Operations). For example, use the formulas involved in measurement such as V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. 6.EE.B.5- Understand solving an equation or inequality as a process of answering a question: Using substitution, which values from a specified set, if any, make the equation or inequality true? 6.EE.B.6- Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or any number in a specified set.

4 6.EE.B.7- Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Unit Specific Vocabulary: Altitude and Base of a Triangle Cube Hexagon Line Perpendicular to a Plane Net Parallel Planes Pentagon Right Rectangular Prism Surface of a Prism Triangular Region Angle Area Length of a Segmet Parallel Parallelogram Perimeter Perpendicular Rectangle Segment Square Trapezoid Triangle Volume Pre Assessment Attach Copy at the End of the Unit UBD Stage Two-Evidence Traditional Assessment Each unit of study should have a traditional assessment with at least 1/3 of the points possible coming from constructed response questions. Proposed Date for Traditional Assessment Attach a copy to the end of this unit. B. Project-Based Assessment Choose four options for this Unit of Instruction that students can choose from for their project-based Assessment. Create a handout that lists the four options and includes instructions and a rubric for each choice. Proposed Date for Project-Based Assessment Presentations Attach a copy of the handout explaining the choices for the project and how to

5 obtain the rubric to the end of this unit. Introducing the Unit Anchoring Activity This activity should engage the students and establish the relevance of the entire unit of study. Anchoring Activity Description of Anchoring Activity Now that you have established what the students need to know and be able to do at the end of this unit of study, now plan the day-to-day learning experiences. Lesson # Date/Day UBD Stage Three-Learning Plan Teaching/ Delivery Method (What I will say or do) Check for Understanding (What will the students say or do)

Mathematics Curriculum

6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...