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Grade 6 Mathematics Module 5, Topic D: Nets and Surface Area

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 5, Topic D: Nets and Surface Area

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Module 5 concludes with deconstructing the faces of solid figures to determine surface area. Students note the difference between finding the volume of right rectangular prisms and finding the surface area of such prisms. In Lesson 15, students build solid figures using nets. They note which nets compose specific solid figures and also understand when nets cannot compose a solid figure. From this knowledge, students deconstruct solid figures into nets to identify the measurement of the solids’ face edges. With this knowledge from Lesson 16, students are prepared to use nets to determine the surface area of solid figures in Lesson 17. They find that adding the areas of each face of the solid will result in a combined surface area. In Lesson 18, students find that each right rectangular prism has a front, a back, a top, a bottom, and two sides. They determine that surface area is obtained by adding the areas of all the faces. They understand that the front and back of the prism have the same surface area, the top and bottom have the same surface area, and the sides have the same surface area.  Thus, students develop the formula SA = 2lw + 2lh + 2wh (6.G.A.4). To wrap up the module, students apply the surface area formula to real-life contexts and distinguish between the need to find the surface area or volume within contextual situations. 

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
27. Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given real-world and mathematical problems involving surface area,
  • Use models of the relating net of the 3-D figure to explain and justify solutions and solution paths.
Teacher Vocabulary:
  • Nets
  • Surface area
  • Rectangular prism
  • Triangular prism
  • Square pyramid
  • Rectangular pyramid
  • Triangular pyramid
Knowledge:
Students know:
  • Measurable attributes of objects, specifically area and surface area.
  • Strategies for representing the surface area of a 3-D shape as a 2-D net.
Skills:
Students are able to:
  • Communicate the relationships between rectangular models of area and multiplication problems.
  • Model the surface area of 3-D shapes using 2-D nets.
  • Accurately measure and compute area of triangles and rectangles.
  • Strategically and fluently choose and apply strategies for finding surface areas of 3-D figures.
Understanding:
Students understand that:
  • Area is additive.
  • Surface area of a 3-D shape is represented by the sum of the areas of the faces of the object.
  • Models represent measurable attributes of objects and help to solve problems.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.27.1: Define three-dimensional figures, surface area, and nets.
M.6.27.2: Identify three-dimensional figures.
M.6.27.3: Draw nets to find the surface area of a given three-dimensional figure.
M.6.27.4: Recall how to calculate the area of a rectangle.
M.6.27.5: Select and create a three-dimensional figure using manipulatives.

Prior Knowledge Skills:
  • Describe attributes of three-dimensional figures.
  • Describe attributes of two-dimensional figures.
  • Identify solid figures.
  • Recall the formula for area (L × W).
  • Recognize that unit squares are equal.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.27 Calculate problems involving perimeter of squares, triangles, rectangles, and other polygons with sides up to 10 units and calculate problems involving the area of rectangles and squares with sides up to 10 units (whole numbers only).

Mathematics
MA2019 (2019)
Grade: 6
28. Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

a. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a right rectangular prism with fractional edge lengths within a real-world or mathematical problem context,
  • Find and justify the volume of the prism as part or all of the problem's solution by relating a cube filled model to the corresponding multiplication problem(s).
Given cubes with appropriate unit fraction edge lengths,
  • Create and explain rectangular prism models to show that the volume of a right rectangular prism with fractional edge lengths l, w, and h is represented by the formulas V = l w h and V = b h.
Teacher Vocabulary:
  • Right rectangular prism
  • V = b h (Volume of a right rectangular prism = the area of the base x the height)
Knowledge:
Students know:
  • Measurable attributes of objects, specifically volume.
  • Units of measurement, specifically unit cubes.
  • Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.
  • Strategies for determining volume.
  • Strategies for finding products of fractions.
Skills:
Students are able to:
  • Communicate the relationships between rectangular models of volume and multiplication problems.
  • Model the volume of rectangles using manipulatives.
  • Accurately measure volume using cubes with unit fraction edge lengths.
  • Strategically and fluently choose and apply strategies for finding products of fractions.
  • Accurately compute products of fractions.
Understanding:
Students understand that:
  • The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.
  • Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.28.1: Define volume, rectangular prism, edge, and formula.
M.6.28.2: Recall how to multiply fractional numbers.
M.6.28.3: Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
M.6.28.4: Use models and volume formulas (V=lwh and V=Bh) to find volumes in the context of solving real-world and mathematical problems.
M.6.28.5: Calculate the volume of a rectangular prism using fractional lengths.
M.6.28.6: Test the formula V= lwh and V=Bh with the experimental findings.
M.6.28.7: Experiment with finding the volume using a variety of sizes of rectangular prisms manipulatives.

Prior Knowledge Skills:
  • Define volume.
  • Recognize the formula for volume.
  • Recall the attributes of three-dimensional solids.
  • Compare the unit size of volume/capacity in the metric system including milliliters and liters.
  • Measure and estimate liquid volumes.
  • Describe attributes of three-dimensional figures.
  • Describe attributes of two-dimensional figures.
  • Define volume including the formulas V = L × W × h, and V = B × h.
  • Define solid figures.
  • Define unit cube.
  • Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
  • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
  • Describe attributes of three-dimensional figures.
  • Describe attributes of two-dimensional figures.
  • Compare the unit size of volume/capacity in the metric system including milliliters and liters.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.28 Solve real-world and mathematical problems involving the volume of cubes and rectangular prisms.
Tags: edge, figures, formula, length, nets, realworld, rectangles, right Rectangular prism, surface area, threedimensional, triangles, unit cubes, volume
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Comments

There are eight lessons on this topic.

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Author: Hannah Bradley
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