6.G.1 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 AGL Geometry

6.G.1

About the Math

Full Standard

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.

 

Learning Targets (I can)

  • Explain the area of a triangle as it relates to a rectangle using representations.
  • Explain the area of a special quadrilateral as it relates to a rectangle using representations.
  • Find the area of a polygon by decomposing it into triangles and rectangles.
  • Solve real-world problems by finding the area of a polygon.

 

About the Math

Students learning Grade 6 mathematics standards build on their work with area in the previous grades by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 mathematics by drawing polygons in the coordinate plane. Essential vocabulary for this standard includes: area, compose, decompose, polygon, quadrilateral, rectangle, right angle, right triangle, trapezoid, and triangle. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

Common Misconceptions

  • Students often forget or confuse the formulas for area, surface area and volume. Exposing students to these concepts in a manner in which they understand the meaning behind the terms as the standards suggest will be important in fostering their conceptual development.
  • Care should be given to ensuring students understand the units that each of these terms require:
    • perimeter-linear units (cm, m, in, yd)
    • area and surface area- square units(sq. cm, sq. m, sq. in, sq. yd)
    • volume- cubic units (cm3)
  • Common errors when plotting points in the coordinate plane include transposing the x and y-coordinates, mistaking a vertical or horizontal line on the plane by miscounting or struggling visually with the difference between the lines, and confusing the positive and negative parts of the perpendicular number lines when plotting points.

 

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 
  • Explain the area of a triangle as it relates to a rectangle using representations.
  • Explain the area of a special quadrilateral as it relates to a rectangle using representations.
  • Find the area of a polygon by decomposing it into triangles and rectangles.
  • Solve real-world problems by finding the area of a polygon.

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5 Grade 7
  • Multiply a whole number and/or a  fraction by a fraction ( 5.NF.4 )
  • Solve problems involving scale drawings of geometric figures (7.G.1)
  • Solve problems with area and circumference of a circle (7.G.4)
  • Solve problems involving area, volume, and surface area of two dimensional and three dimensional objects (7.G.6)
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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • A parallelogram has an area of 200 square inches. What could its length and height be? Give two different answers.
  • Sketch a triangle with an area of 12.5 square inches. Label its base and height? Can you sketch and label a second triangle?
  • A roll of wallpaper is 1 yard by 10 yards. How many rolls of wallpaper would we need to cover all the walls of our classroom?
  • Draw a sample patio design that can be subdivided into triangle(s) and quadrilaterals. Label the dimensions and ask a friend to calculate the area.
  • A parking lot is in the shape of a trapezoid and the area is 20,625 square feet. What could the dimensions of the lot be?
  • Describe two situations in which you would want to know the area of something.
  • What happens to the area of a square when its dimensions are doubled? Tripled? Is the same pattern true for a rectangle? A triangle?

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 12 • Area and Volume

Area of Triangles:

Area of Quadrilaterals and Irregular Figures:

 

Additional Tasks 

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.] 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 6-8 Area of a Parallelogram, Activity 14.12, Page 313
Area of a Triangle, Activity 14.13, Page 314

Hands-On Standards Common Core

 

 6 106-117 (Lessons 1-4)

Groundworks: Measurement

4

 

 

5

88-95 (Unknown Areas 1)

104-111 (Rectangle Stretch)


88-95 (Inside Triangles)

Groundworks: Geometry

 6 80-87 (Separating Shapes)

Problem-Driven Math

5

 

 

6

32 (Rectangular Roses)
33 (All Cooped Up)
34 (Carpet Costs)


3 (Carpet Feet)
35 (Rectangle Wranglers)

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

 

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Assessment

Learning Targets

rubric

  • Explain the area of a triangle as it relates to a rectangle using representations.
  • Explain the area of a special quadrilateral as it relates to a rectangle using representations.
  • Find the area of a polygon by decomposing it into triangles and rectangles.
  • Solve real-world problems by finding the area of a polygon.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.