Area - Picasso

CCGPS Math 6 Unit 5 – Lesson 1
Unit Outline Title: Area and Volume
Name of Lesson: Area
Standards: Solve real-world and mathematical problems involving area, surface area, and
MCC6.G.1 Find 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.
Essential Question(s):
Unit: What is the relationship among area, volume, and surface area?
 How can we find the area of figures?
 How can we cut and rearrange irregular polygons in order to find their area?
 How can we use one figure to determine the area of another?
 Is there a common way to calculate area? How do you know?
 How can shapes be combined to create new shapes?
 How can a shape be broken down into smaller shapes?
 How do we figure the area of a shape without a formula for that shape?
 How are the areas of geometric figures related to each other?
 How can the formulae for the area of plane figures be used to solve problems?
 How can we find the area of regular and irregular polygons when you don’t have a specific
Assessment Description/Performance Task:
Constructed response:
 Decomposing Polygons to Find Area
 Base and Height
 Same Base and Height Variation 1
 Same Base and Height Variation 2
Informal assessment: Various Interactive Online Activities
Formative assessment: Area of Composite Figures
Performance Tasks: The following performance task are from the GA DOE
 Who Put the Tang in Tangram?,
 What's My Area?,
 King Arthur's New Table
 Rectangle Wraparound
 Finding Areas of Polygons
Selected response: Area of Triangle Quiz - Form A, Area of Triangle Quiz - Form B
CCSD Version Date: 2/9/2016
Instructional Methods
 It is expected that students will have prior knowledge/experience related to using
parentheses, brackets, or braces in numerical expressions and evaluate expressions with
these symbols, generating two numerical patterns using two given rules, interpreting a
fraction as division, and operations with whole numbers, fractions, and decimals. It may
be necessary to pre-assess in order to determine if time needs to be spent on conceptual
activities that help students develop a deeper understanding of these concepts.
 The Conceptual Framework may be used to build teacher understanding of representing
inequalities in context and on a number line.
By the conclusion of this lesson, students should be able to demonstrate the following
 Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals
 Find areas of composite figures and polygons by composing into rectangles and
decomposing into triangles and other shapes
 Solve real-world and mathematical problems involving area
 Know the properties of various regular and irregular polygons
 Compose and decompose regular and irregular polygons using various shapes
 Apply formulas to find areas of regular and irregular polygons
 Solve real-world and mathematical problems involving area
 The area of irregular and regular polygons can be found by decomposing the polygon into
rectangles, triangles, and other shapes.
 Word Splash – Write the words area, parallelogram, triangle, rectangle, square, etc.
in the middle of the board or chart paper. You may choose other vocabulary terms related
to the lesson. Students make predictions and generate statements about the topic. After
the lesson, students will spend time correcting their statements. Encourage students to
make corrections to their statements during the lesson.
 To review finding area of a rectangle, you may use Holt Mathematics Course 1, 10-1
Hands-on Lab, page 1 “Estimating and Finding Area.”
 Study Jams – Area of a Parallelogram, Area of a Triangle
 Create a Fortune Teller Foldable for Formulas. See page two of the document for a visual
on how to create the foldable
Work Session
 Holt Mathematics Course 1, 10-1 Hands-on Lab, page 2 “Estimating and Finding
Area” allows students to derive area formulas.
 Special quadrilaterals include rectangles, squares, parallelograms, trapezoids,
rhombi, and kites. Students can use tools such as the Isometric Drawing Tool on NCTM’s
Illuminations site to shift, rotate, color, decompose and view figures in 2D or 3D. Students
will use the Area Tool and Geoboard Recording Paper during the task.
 GeoGebra – Interactive Online Activities
o Finding Triangle Areas
o Finding Area of a Parallelogram (one parallelogram)
o Finding Area of a Parallelogram (two polygons – rectangle and parallelogram)
 In collaborative pairs, students may complete Decomposing Polygons to Find Area.
 Performance Task: Who Put the Tang in Tangram? This task will help students
determine the area of tangram pieces without using formulae. Then students will use their
knowledge to help them develop and use formulae to determine the area of squares,
rectangles, triangles, and parallelograms.
 Performance Task: What's My Area?
 Performance Task: King Arthur's New Table
 Performance Task: Rectangle Wraparound
 Performance Task: Finding Areas of Polygons
CCSD Version Date: 2/9/2016
 Mini-Quiz on Area of Triangles (Form A and Form B)
 In the Know Surface Area Formula Summarizer
o Create the chart below on the board, Smart Board, Chart Paper, etc. for the entire
class to view.
o Give students post-it notes.
o Students will draw the three dimensional figures and write the surface area formula
for each on the post-it.
o Students will place their three dimensional figures and formulas in one of the
columns. (As students progress throughout the lesson and unit, they can move
their post-it. The teacher will monitor student understanding using the results on
the chart.)
? – Students will place the formula in this column if the formula is unknown
to them
, - Students understand the formula, but they cannot use it correctly.
! – Students understand the formula and can use it to correctly to solve a
Arizona Department of Education
Granite School District, Salt Lake City, Utah
Georgia Department of Education
Differentiation: (to be created)
Tiered Assignments
 Differentiation Strategies for Mathematics: Tiered Assignments Grades 6-8,
Rectangular Prims, Cylinders, and Cones (modify to exclude cylinders and cones) (Focus on
the Surface Area Portion)
Leveled Questions
Multiple Intelligences
Using Realia/CRA
Choices Board
Open-Ended Tasks
Problem-Based Learning
Learning Contracts
Tiered Graphic Organizers
CCSD Version Date: 2/9/2016
Textbook/Online Resources:
 McGraw-Hill Georgia Math Grade 6: Chapter 8, Lessons 1-5
 Mathematics Course 1 Textbook Connection: Chapter 10, Lessons 1-4
 Mathematics Course 2 Textbook Connection:
 Hands-on Standards: Grades 5-6: (Measurement section) Area of Trapezoids; Constant
Perimeter and Changing Area
 Hands-on Standards: Grades 7-8: (Measurement section) Perimeter and Area; Area of a
Parallelogram; Area of a Triangle
 Graphing Calculator Strategies-Middle School Math: Lesson 18 (Computing Area and
 Math in Context: Reallotment: Geometry and Measurement: Section B-Area Patterns,
Section C-Measuring Area, Section D-Perimeter and Area
 Connected Math (Grade 6): Covering and Surrounding: Two-Dimensional Measurement
 Isometric Drawing Tool
 Online Dot Paper
 2-Dimensional
 area
 compose
 decompose
 dimension
 equilateral triangle
 formula
 isosceles triangle
 kite
 parallelogram
CCSD Version Date: 2/9/2016
right triangle
scalene triangle