6G-Solve+real-world+and+mathematical+problems+involving+area,+surface+area,+and+volume

6.G.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 real-world and mathematical problems. 6.G.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 = l w h// and //V = b h// to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.3. 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. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.4. Represent three-dimensional figures using nets made up of rectangles and 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. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard**===
 * Make sense of problems and persevere in solving them.
 * Reason abstractly and quantitiatively.
 * Construct viable arguments and critique the reasoning of others.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Attend to precision.
 * Look for and make use of stucture.
 * Look for and express regularity in repeated reasoning. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking: Remembering, Understanding, Analyzing, Evaluating, Creating**=== ||

Students continue to understand that area is the number of squares needed to cover a plane figure. Students should know the formulas for rectangles and triangles. “Knowing the formula” does not mean memorization of the formula. To “know” means to have an understanding of why the formula works and how the formula relates to the measure (area) and the figure. This understanding should be for all students.

Finding the area of triangles is introduced in relationship to the area of rectangles – a rectangle can be decomposed into two congruent triangles. Therefore, the area of the triangle is ½ the area of the rectangle. The area of a rectangle can be found by multiplying base x height; therefore, the area of the triangle is ½ bh or (b x h)/2.

Students decompose shapes into rectangles and triangles to determine the area

In 6th grade the unit cube will have fractional edge lengths. (ie. ½ • ½ • ½ ) Students find the volume of the right rectangular prism with these unit cubes

In addition to filling boxes, students can draw diagrams to represent fractional side lengths, connecting with multiplication of fractions. This process is similar to composing and decomposing two-dimensional shapes.

Students are given the coordinates of polygons to draw in the coordinate plane. If both x-coordinates are the same (2, -1) and (2, 4), then students recognize that a vertical line has been created and the distance between these coordinates is the distance between -1 and 4, or 5. If both the y-coordinates are the same (-5, 4) and (2, 4), then students recognize that a horizontal line has been created and the distance between these coordinates is the distance between -5 and 2, or 7. Using this understanding, student solve real-world and mathematical problems, including finding the area and perimeter of geometric figures drawn on a coordinate plane.

Students represent three dimensional figures whose nets are composed of rectangles and triangles. Students recognize that parallel lines on a net are congruent. Using the dimensions of the individual faces, students calculate the area of each rectangle and/or triangle and add these sums together to find the surface area of the figure.

Students construct models and nets of three-dimensional figures, describing them by the number of edges, vertices, and faces. Solids include rectangular and triangular prisms. Students are expected to use the net to calculate the surface area

Students can create nets of 3D figures with specified dimensions using the Dynamic Paper Tool on NCTM’s

Students also describe the types of faces needed to create a three-dimensional figure. Students make and test conjectures by determining what is needed to create a specific three-dimensional figure.

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**Solve real-world and mathematical problems involving area, surface area, and volume. ===


 * I can find the area of polygons.
 * I can find the volume of a right rectangular prism.
 * I can draw polygons using the coordinate plane.
 * I can use coordinates to find the length of a side of a polygon.
 * I can represent 3-D figures using nets made up of rectangles and triangles.
 * I can calculate the surface area of a 3-D figure by combining the area of each side of a net.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
area, surface area, volume, decomposing, edges, dimensions, net, vertices, face, base, height, trapezoid, isosceles, right triangle, quadrilateral, rectangles, squares, parallelograms, trapezoids, rhombi, kites, right rectangular prism

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**

 * Daily Spiral Review**
 * Signaling**
 * Questioning**
 * Teacher Observation**
 * Thinkgate**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Teaching the Common Core Math Standards with Hands-On Activities: It's Half (page 54) Teaching the Common Core Math Standards with Hands-On Activities: It's Awe Sum (page 55) Teaching the Common Core Math Standards with Hands-On Activities: It's Voluminous (page 57) Teaching the Common Core Math Standards with Hands-On Activities: Initials (page 60) Teaching the Common Core Math Standards with Hands-On Activities: Finding the Surface Area of Nets (page 63)

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**

 * Quantiles 1**
 * Quantiles 2**

Plotting Land Activity p. 87 __Navigating Through Algebra__

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (pages 91, 98, and 106) Carnegie Learning: Chapter 13, Chapter 14 Unit Notes [|Points and Distances] Surface Area and Nets Foldable (Teacher Copy) Surface Area and Nets Foldable (Student Copy) Area of Irregular Figures Worksheet Notes/Examples Practice 1 Practice 2

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===