ALEX Classroom Resource

  

Measurement: Square Feet

  Classroom Resource Information  

Title:

 Measurement: Square Feet

URL:

 https://aptv.pbslearningmedia.org/resource/ketae.geo.meas.sqft/measurement-square-feet/

Content Source:

 PBS
Type: Informational Material

Overview:

To find area, you must figure out how many square units will fit inside the shape. Patricia Wilkins, a landscape designer, explains how she calculated square feet for a project in her yard.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a variety of triangles and quadrilaterals:
  • Find their area.
  • Justify their solutions and solution paths by composing shapes into rectangles and decomposing into triangles or other shapes.
Given real-world and mathematical problems involving area of triangles and other polygons,
  • Compose and decompose shapes to find solutions.
  • Interpret solutions.
Teacher Vocabulary:
  • Right triangles
  • Special quadrilaterals
  • Polygons
  • Area
  • Decompose
  • Compose
Knowledge:
Students know:
  • Appropriate units for measuring area: square inches, square units, square feet, etc..
  • Strategies for composing and decomposing shapes to find area.
Skills:
Students are able to:
  • Communicate the relationship between models of area and the associated real-world mathematical problems.
  • Use logical reasoning to choose and apply strategies for finding area by composing and decomposing shapes.
  • Accurately compute area of rectangles using multiplication and the formula.
Understanding:
Students understand that:
  • The area of a figure is measured by the number of same-size unit squares that exactly cover the interior space of the figure.
  • Shapes can be composed and decomposed into shapes with related properties,
  • Area is additive.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.26.1: Define area, special quadrilaterals, right triangles, and polygons.
M.6.26.2: Analyze the area of other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
M.6.26.3: Apply area formulas to solve real-world mathematical problems.
M.6.26.4: Demonstrate how the area of a rectangle is equal to the sum of the area of two equal right triangles.
M.6.26.5: Explain how to find the area for rectangles.
M.6.26.6: Select manipulatives to demonstrate how to compose and decompose triangles and other shapes.
M.6.26.7: Recognize and demonstrate that two right triangles make a rectangle.

Prior Knowledge Skills:
  • Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
  • Recall the formula for area (L × W).
  • Recognize that unit squares are equal.
  • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
  • Recall basic addition and multiplication facts.
  • Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
  • Partition a shape into 4 parts with equal area, and describe the area of each part as 1 of the area of the shape.
  • Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths.
  • Recognize that equal shares of identical wholes need not have the same shape.
  • Demonstrate equivalent fractions using concrete objects or pictorial representations.
  • Define right angle.
  • 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.
  • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
  • Identify triangles.
Mathematics
MA2019 (2019)
Grade: 7
22. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
  • Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
  • Use the formula for volume to find missing measurements of a prism.
Teacher Vocabulary:
  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubes
  • Right rectangular prisms
Knowledge:
Students know:
  • that volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.
Skills:
Students are able to:
  • find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
Understanding:
Students understand that:
  • two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • the volume of a pyramid is 1/3 the volume of a prism with the same base.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.22.1: Define volume, surface area, triangles, quadrilaterals, polygons, cubes, and right prisms.
M.7.22.2: Discuss strategies for solving real-world mathematical problems.
M.7.22.3: Recall formulas for calculating volume and surface area.
M.7.22.4: Identify the attributes of triangles, quadrilaterals, polygons, cubes, and right prisms.

Prior Knowledge Skills:
  • Recognize the formula for volume.
  • Define volume, rectangular prism, edge, and formula.
  • Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
  • Set up V=lwh and V=Bh to find volumes in the context of solving real-world and mathematical problems.
  • Discover the volume of a rectangular prism using manipulatives.
  • Define three-dimensional figures, surface area, and nets.
  • Evaluate how to apply using surface area of a three-dimensional figure to solving real-world and mathematical problems.
  • Draw nets to find the surface area of a given three-dimensional figure.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.22 Determine the area regular, two-dimensional figures. Determine the volume of rectangular prisms, limited to whole numbers.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
39. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. [Grade 7, 22]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
  • Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
  • Use the formula for volume to find missing measurements of a prism.
Teacher Vocabulary:
  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubs
  • Right rectangular prisms
Knowledge:
Students know:
  • That volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.
Skills:
Students are able to:
  • Find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
Understanding:
Students understand that:
  • Two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • The area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • The volume of a pyramid is 1/3 the volume of a prism with the same base.
Diverse Learning Needs:
Tags: area, reallife modeling, square feet
License Type: Attribution Non-Commercial Share Alike
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
Accessibility
Comments

This resource contains a background essay and discussion questions.

  This resource provided by:  
Author: Kristy Lacks
This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Copyright © 2017, Alabama Learning Exchange
Alabama State Department of Education
Alabama State Department of Education