ALEX Lesson Plan

     

Geometry City

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  This lesson provided by:  
Author:Aimee Smith
System: Cullman City
School: Cullman Middle School
The event this resource created for:GEMS
  General Lesson Information  
Lesson Plan ID: 24037

Title:

Geometry City

Overview/Annotation:

In this lesson, students will review coordinate plane concepts, practice map skills, review shapes, transform geometric figures, and calculate the area and perimeter of figures.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
25. Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

a. Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

b. Use coordinates to find the length of a side between points having the same x-coordinate or the same y-coordinate.

c. Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same x-coordinate or the same y-coordinate).
Unpacked Content
Evidence Of Student Attainment:
Students:
Given real-world and mathematical problems involving the mapping of polygons onto a coordinate system,
  • Determine the length of a side joining points with the same first coordinate or the same second coordinate.
  • Determine missing vertices of a rectangle.
  • Graph polygons in coordinate plane given vertices and solve real-world problems.
Teacher Vocabulary:
  • Polygon
  • Coordinate plane
  • Vertices
  • X-coordinate
  • Y-coordinate
Knowledge:
Students know:
  • Terminology associated with coordinate systems.
  • Correct construction of coordinate systems.
Skills:
Students are able to:
  • Graph points corresponding to ordered pairs.
  • Represent real-world and mathematical problems on a coordinate plane.
  • Interpret coordinate values of points in the context of real-world and mathematical situations.
  • Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate or the same second coordinate.
Understanding:
Students understand that:
  • A variety of representations such as diagrams, number lines, charts, and graphs can be used to illustrate mathematical situations and relationships.
  • These representations help in conceptualizing ideas and in solving problems.
  • Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.25.1: Define vertices.
M.6.25.2: Apply absolute value to find the length of a side joining points with the same first coordinate or the same second coordinate.
M.6.25.3: Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
M.6.25.4: Identify ordered pairs.
M.6.25.5: Recognize polygons.
M.6.25.6: Define perimeter and area.
M.6.25.7: Identify the length between vertices on a coordinate plane.
M.6.25.8: Calculate the perimeter and area using the distance between the vertices.

Prior Knowledge Skills:
  • Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.
  • Identify triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons based on the number of sides, angles, and vertices.
  • Understand 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 attributes of shapes.
  • Recall the vocabulary of shapes (labels, sides, faces, vertices, etc.). Sort shapes into categories.
  • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points. Label the horizontal axis (x).
  • Label the vertical axis (y).
  • Identify the x- and y- values in ordered pairs.
  • Model writing ordered pairs.
  • Define vertex/vertices and angle.
  • 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.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.25 Graph squares, rectangles, and triangles in the first quadrant of the coordinate plane.


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: 8
23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Describe the changes occurring to the x-and y-coordinates of a figure after a transformation.
Teacher Vocabulary:
  • Coordinates
  • Congruent
  • Rotation
  • Reflection
  • Translation
  • Dilation
  • Scale factor
Knowledge:
Students know:
  • What it means to translate, reflect, rotate, and dilate a figure.
  • How to perform a translation, reflection, rotation, and dilation of a figure.
  • How to apply (x, y) notation to describe the effects of a transformation.
Skills:
Students are able to:
  • Select and apply the proper coordinate notation/rule when given a specific transformation for a figure.
  • Graph a pre-image/image for a figure on a coordinate plane when given a specific transformation or sequence of transformations.
Understanding:
Students understand that:
  • the use of coordinates is also helpful in proving the congruence/proportionality between figures.
  • The relationships between coordinates of a preimage and its image for dilations represent scale factors learned in previous grade levels.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.23.1: Define dilation.
M.8.23.2: Recall how to find scale factor.
M.8.23.3: Give examples of scale drawings.
M.8.23.4: Recognize translations.
M.8.23.5: Recognize reflections.
M.8.23.6: Recognize rotations.

Prior Knowledge Skills:
  • Define scale, scale drawings, length, area, and geometric figures.
  • Locate/use scale on a map.
  • Identify proportional relationships.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.23 Recognize the reflection (across the x or y axis) and translation (across quadrants) of a two dimensional figure on a coordinate plane (limited to non-equilateral rectangles and triangles).


Mathematics
MA2019 (2019)
Grade: 8
24. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Explain how transformations can be used to prove that two figures are similar.
  • Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.
Teacher Vocabulary:
  • Translation
  • Reflection
  • Rotation
  • Dilation
  • Scale factor
Knowledge:
Students know:
  • How to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
  • What makes figures similar and congruent.
Skills:
Students are able to:
  • Use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
  • Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.
Understanding:
Students understand that:
  • There is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
  • The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.24.1: Define similar.
M.8.24.2: Recognize dilations.
M.8.24.3: Recognize translations.
M.8.24.4: Recognize rotations.
M.8.24.5: Recognize reflections.
M.8.24.6: Identify similar figures.
M.8.24.7: Analyze an image and its dilation to determine if the two figures are similar.

Prior Knowledge Skills:
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Define reflections.
  • Calculate the distances between points having the same first or second coordinate using absolute value.

Local/National Standards:

NCTM: NM-GEO.6-8.4 • Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Primary Learning Objective(s):

The primary learning objective is to transform figures on a coordinate plane, mimicking real world planning skills.

Additional Learning Objective(s):

Students will also practice important map skills, review different shapes, and calculate area and perimeter.

 Preparation Information 

Total Duration:

61 to 90 Minutes

Materials and Resources:

  • Worksheet copies
  • Technology Resources Needed:

  • 1 computer with Internet access
  • LCD projector
  • Background/Preparation:

    Students should have prior knowledge of coordinate planes, how to plot points, and how to calculate area and perimeter.

      Procedures/Activities: 
    1.)Show United Streaming Transformations Video [Discovering Math: Geometry; Introduction (2:22), Example 1: Translations (1:22), Example 2: Rotations (1:28)] Please note that ALL Alabama educators have free access to United Streaming through Alabama Public Television. If you do not have a login or need assistance, you can contact Alabama Public Television for assistance.

    2.)Discuss transformations, working examples on the board as a group. If an LCD projector is available, use the following website to assist with group practice.
    (MathsNet.)

    3.)If students have access to computers, allow them to manipulate the website in step 2. If students do not have computer access, explore step 2 as a class.

    4.)Distribute the Geometry City worksheet. (see attachment)

    5.)Allow students to work on the worksheet as you move through the class to provide guidance. Please note that due to the fact that multiple answers may be correct, no answer key is provided.

    6.)Collect worksheets prior to students leaving class so that they may be redistributed to other students during the next class session for checking.

    7.)At the next class meeting, have students check another student's work based upon their own understanding of the content (no answer key provided). If a student marks an answer wrong they must be able to justify their decision. Allow approximately 25 minutes for this task.


    Attachments:
    **Some files will display in a new window. Others will prompt you to download.
      Assessment  

    Assessment Strategies

    Informal assessment will be used as the class is viewing the activity on the Internet. As students are working, the teacher should move through the classroom asking students about their work. Students will turn in the worksheet which will be graded for accuracy. In addition, the student's attempt at grading another students work will be taken into account with the worksheet grade.

    Acceleration:

    Students needing additional material can spend time on the MathsNet website, working problems of increasing difficulty, or students may explore tessellations on the following webquest: Tesselations

    Intervention:

    Allow students in need of remediation to use foam shapes and a gridded whiteboard to assist in completing the activity. Proximity may also be used for these students, for reassurance purposes.


    View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.