Coordinate Plane Content Module

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{{BACK TO|[[Content Modules]]}}
 
{{BACK TO|[[Content Modules]]}}
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=Skills for Transformations in the Coordinate Plane=
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==Elementary School==
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* 4.GM.1j1 Recognize a point, line and line segments, rays in two-dimensional figures
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* 4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures
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* 5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures
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* 5.GM.1a1 Recognize properties of simple plane figures
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* 5.GM.1b1 Distinguish plane figures by their properties
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* 5.GM.1c1 Locate the x and y axis on a graph
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* 5.GM.1c2 Locate points on a graph
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* 5.GM.1c3 Use order pairs to graph given points
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==Middle School==
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* 6.GM.1c4 Locate points on a graph
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* 6.GM.1c5 Use order pairs to graph given points
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* 6.GM.1c6 Find coordinate values of points in the context of a situation
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* 6.GM.1c7 Use coordinate points to draw polygons
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* 6.NO.1d5 Find given points between -10 and 10 on both axes of a coordinate plane
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* 6.NO.1d6 Label points between -10 and 10 on both axes of coordinate plane
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* 7.GM.1e1 Construct or draw plane figures using properties
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* 8.GM.1f1 Recognize a rotation, reflection, or translation of a figure
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* 8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates
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* 8.GM.1g1 Recognize congruent and similar figures
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==High School==
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* H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures
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* H.GM.1c1 Construct, draw, or recognize a figure after its rotation, reflection, or translation
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* H.GM.1d1 Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles
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* H.GM.1e1 Make formal geometric constructions with a variety of tools and methods
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=Plot the Course=
 
=Plot the Course=
 
[[File:Plotthecourse.jpg|thumb|x200px|link=http://www.worthwhilesmile.com/air-balloons-kaleidoscope/|http://www.worthwhilesmile.com/air-balloons-kaleidoscope/|alt=three hot air balloons floating in the sky]]
 
[[File:Plotthecourse.jpg|thumb|x200px|link=http://www.worthwhilesmile.com/air-balloons-kaleidoscope/|http://www.worthwhilesmile.com/air-balloons-kaleidoscope/|alt=three hot air balloons floating in the sky]]
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==The Rationale==
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Remember the old saying "a picture is worth a thousand words?" The ability to look a graph and interpret its meaning is an integral skill in both everyday life and almost any profession. For example, when you receive your electricity bill, a graph is often included so that the customer can see what months they used the most electricity at a quick glance.
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==The rationale==
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Understanding how to find points on a coordinate plane not only serve academic purposes, but also address real-life skills students may use on a daily basis like navigating using a map or an atlas. In addition to reading a map, the concept of graphing on the coordinate plane is also used in games such as Battleship or some of the simulation games in which students build amusement parks or entire cities. Other recreation leisure activities, especially in art, incorporate transformation in the coordinate plane like quilting. Mathematically, graphing in the coordinate plane is a prerequisite for many skills across grade bands such as transformations in the coordinate plane, finding missing attributes of polygons, and interpreting graphs.
  
 
==Module Goal==
 
==Module Goal==
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The goal of this module is to provide detailed instruction on the more difficult concepts of functions (i.e., linear, and quadratic) to teachers of students with disabilities at the middle and high school level. This module promotes a mathematical understanding of these concepts so that a teacher can begin to plan how to teach the concepts to students. Additionally, this module will provide instructors with potential adaptations and modifications to consider when designing materials and instruction for students with severe disabilities.
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The goal of this module is to provide detailed instructions on how to graph and create polygons in the coordinate plane as well as how to perform transformations (i.e., reflections, rotations, and translations) within the coordinate plane to teachers of students with disabilities at the elementary, middle, and high school level. This module promotes a mathematical understanding of these concepts so that a teacher can begin to plan how to teach the concepts to students. Additionally, this module will provide instructors with potential adaptations and modifications to consider when designing materials and instruction for students with severe disabilities.
  
 
==Module Objectives==
 
==Module Objectives==
 
After viewing the content module, teachers will:
 
After viewing the content module, teachers will:
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# Identify independent and dependent variables
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# Apply strategies for finding ordered pairs and graphing in the coordinate plane
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# Identify a linear function
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# Identify attributes of polygons
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# Identify a quadratic function
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# Perform transformations in the coordinate plane
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# Discriminate between functions and non-functions when provided graphs
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# Apply transformations in the coordinate plane to real-world applications and activities
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=Time for Take Off=
 
=Time for Take Off=
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[[File:Timefortakeoff.jpg|thumb|A flame used to lift hot air balloon]]
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[[File:Timefortakeoff.jpg|thumb|alt=flame used to lift hot air balloon]]
  
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Understanding the vocabulary used within functions is important for both teachers and students in planning and implementing math lessons. As a teacher, knowing and using the mathematical terms not only ensures your instruction stays true to the math content, but will also help with collaborating with other math teachers or content experts. When choosing which vocabulary to teach, it is most important that the teacher selects the most salient, important, or most frequently used vocabulary for each lesson.  
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Understanding the vocabulary used within the coordinate plane is important for both teachers and students in planning and implementing math lessons. As a teacher, knowing and using the mathematical terms not only ensures your instruction stays true to the math content, but also will help with collaborating with other math teachers or content experts. When choosing which vocabulary to teach, it is most important that the teacher selects the most salient, important, or most frequently used vocabulary for each lesson.  
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Below you will find a list of vocabulary included within this module. It may or may not be necessary to provide instruction for all terms as students may have learned them previously. Functions are mostly covered in middle school so vocabulary for this content module has been combined. If you are a high school teacher and are not confident your students know some of these vocabulary terms, you may want to review and teach some unknown terms in the focus and review part of your lesson plan. While providing vocabulary instruction, you may consider including pictures or objects to make the instruction more concrete for students with disabilities (See Ideas to support vocabulary learning below).  
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Below you will find a list of vocabulary included within this module. It may or may not be necessary to provide instruction for all terms as students may have learned them previously. If you are a secondary teacher and are not confident your students have been taught the elementary vocabulary terms, you may want to add those unknown terms to the focus and review of your lesson plan.
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While providing vocabulary instruction, you may consider including pictures or objects to make the instruction more concrete for students with disabilities (See Ideas to support vocabulary learning below).  
  
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==Vocabulary==
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==Elementary School==
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* Variable – a term that includes a letter that represents a value (e.g., in the equation ''y = 2x + 4'', 2x is the variable).
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* Point- an exact location
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* Constant – a fixed value (e.g., in the equation ''y = 2x + 4'', 4 is the constant)
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* Line- a straight path that extends forever
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* Independent variable – what is being manipulated in the situation. For example, when measuring a child's height as they get older, the aging process is the independent variable (age is what is being changed).
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* Line segment- part of a line with two endpoints
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* Dependent variable – what is changed as a result of manipulating the independent variable. For example, when measuring a child's height as they get older, their height is the dependent variable (it changes as a result of the independent variable).
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* Ray- part of a line that starts at one endpoint and extends forever in one direction
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* Function – mathematical operations demonstrating the relationship between the input and output of an expression.
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* Perpendicular- lines that intersect at a 90º angle
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* Linear function – represented by an equation in the form of ''y = mx + b''; when graphed the coordinates provided will form a straight line.
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* Parallel- lines that never intersect
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* Quadratic function – represented by the an equation in the form of ''y = mx<sup>2</sup> + bx + c; when graphed the coordinates provided will form a U-shape.''
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* Coordinate Plane- formed by two axes that intersect at a right angle
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* Exponential function – represented by an equation in the form of ''y = mx'', where a is a positive number not 1; a common exponential function is the growth of some organism (including humans).
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* Right angle- an angle that measures 90º formed by two perpendicular lines
  
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==Ideas to Support Vocabulary Learning==
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==Middle and High School==
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* Teach students to discriminate between linear, quadratic, and exponential functions based on the appearance of graphs.
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* Polygon- closed plane figure made by three or more line segments
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* Rotation- when you turn a figure at one point
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* Reflection- a mirror image of an object when the original is flipped
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* Translation- when you slide a figure along a line without turning it
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* Congruent figures- figures that have the same size and shape. If two polygons have the same corresponding sides and angles, they are congruent.
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* Similar figures- figures with the same shape but not the same size
  
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[[File:LinFunction.JPG|250px| A line on a graph starting at (0,0) and rising with a slope of 1]]  [[File:QuadFunction.JPG|250px| A line on a graph starting at (0,0) rising exponentially across the y axis]]
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==Idea to support vocabulary learning==
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* Have student match term with the correct picture
  
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[[File:ExpFunction.JPG|250px| A line on a graph starting at (0,-2) rising exponentially as the x increases]]
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[[File:Coordinate Plane1.jpg|alt=a point, a line, a ray, a line segment, parallel lines, perpendicular lines, right angle, coordinate plane, a three sided polygon, a four sided polygon, and a non polygon]]
  
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==Congruent Shapes==
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[[File:Coordinate Plane2.jpg|alt=Two congruent squares, two congruent parallelograms]]
  
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=Floating on Air=
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==Similar Shapes==
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[[File:Floatingonair.jpg|thumb|A close up of one hot air balloon with a second floating in the distance]]
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Before you can begin teaching functions, you need a deep understanding of these mathematical concepts. Some of these concepts may be familiar to you. Below is a list of skills that should be covered at each grade level. For concepts that you need more information about, please view the accompanying PowerPoint presentations that will walk you through an example as well as make some suggestions for instruction.
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==Middle and High School==
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[[File:Coordinate Plane3.jpg|bottom|alt=Two similar squares, two similar parallelograms]]
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In middle and high school skills include:
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* 6.PRF.2a4 Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation
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* 8.PRF.2c1 Given two graphs, describe the function as linear and not linear
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* 8.PRF.2e1 Distinguish between functions and non-functions, using equations, graphs or tables
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* H.PRF.2c1 Make predictions based on a given model (for example, a weather model, data for athletes over years)
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C%21389&app=PowerPoint&wdo=1| Linear Functions PowerPoint]
 
  
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C%21388&app=PowerPoint&wdo=1| Exponential Functions PowerPoint]
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Idea for systematic instruction: demonstrate the concepts of congruent and similar shapes using examples and non-examples. For example:  "This is ________, This is __________, This is NOT __________, This is NOT __________, This is ____________. Show me __________"
  
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C%21390&app=PowerPoint&wdo=1| Quadratic Functions PowerPoint]
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'''Rotation'''
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[[File:Coordinate Plane4.jpg|alt=Triangle rotated one hundred eighty degrees]]
  
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Great! Now that you have viewed the PowerPoint presentation most useful to you, the next section will provide some ideas to consider when planning for Universal Design for Learning.
 
  
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  NOTE: All PowerPoint presentations begin with the same “What is a function” slides for review.
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'''Reflection'''
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[[File:Coordinate Plane5.jpg|alt=Triangle reflected across y axis of coordinate plane]]
  
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'''Translation'''
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=Sharing the Sky=
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[[File:Coordinate Plane6.jpg|alt=Triangle translated diagonally across coordinate plane]]
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[[File:Sharethesky2.jpg|thumb|bottom|Two hot air balloons in the distance]]
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<font size=3>'''UNIVERSAL DESIGN FOR LEARNING'''</font>
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{|border=1
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=Floating on Air =
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| colspan=5 style="background-color:#FFFFFF;"|'''Some examples of options for teaching functions to students who may present instructional challenges due to:'''
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[[File:Floatingonair.jpg|thumb|alt=close up of one hot air balloon with a second floating in the distance]]
  
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Before you can begin teaching students to use reflections, rotations, and translations of figures in the coordinate plane, you must have a deep understanding of these mathematical concepts. Some of these concepts may be familiar to you. Below is a list of skills that should be covered at each grade level in the mathematical strand of measurement. For more complicated concepts, please view the accompanying PowerPoint that will walk you through an example as well as make some suggestions for instruction.
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==Elementary School==
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In elementary school skills include:
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* 4.GM.1j1 Recognize a point, line and line segments, rays in two-dimensional figures
 +
* 4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures
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* 5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures
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* 5.GM.1a1 Recognize properties of simple plane figures
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C!229&app=PowerPoint&wdo=1| Properties of Plane Figures PowerPoint]
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* 5.GM.1b1 Distinguish plane figures by their properties
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* 5.GM.1c1 Locate the x and y axis on a graph
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* 5.GM.1c2 Locate points on a graph
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* 5.GM.1c3 Use order pairs to graph given points
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==Middle and High School==
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In middle school skills include:
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* 6.GM.1c4 Locate points on a graph
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* 6.GM.1c5 Use order pairs to graph given points
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* 6.GM.1c6 Find coordinate values of points in the context of a situation
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C!230&app=PowerPoint&wdo=1| Graphing in the Coordinate Plane PowerPoint]
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* 6.GM.1c7 Use coordinate points to draw polygons
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* 7.GM.1e Construct or draw plane figures using properties
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* 8.GM.1f1 Recognize a rotation, reflection, or translation of a figure
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* 8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C!216&app=PowerPoint&wdo=1| Rotations in the Coordinate Plane PowerPoint]
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C!214&app=PowerPoint&wdo=1| Reflections in the Coordinate Plane PowerPoint]
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[https://onedrive.live.com/view.aspx?cid=8CCFD53B6E28BB4C&resid=8CCFD53B6E28BB4C!215&app=PowerPoint&wdo=1| Translations in the Coordinate Plane PowerPoint]
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* 8.GM.1g Recognize congruent and similar figures
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Insert congruent vs. similar figures PowerPoint here
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* H.GM.1b Use definitions to demonstrate congruency and similarity in figures
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* H.GM.1c Construct, draw, or recognize a figure after its rotation, reflection, or translation
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(See rotations, reflections, and translations PowerPoints)
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* H.GM.1d Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles
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(See rotations, reflections, and translations PowerPoints)
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* H.GM.1e Make formal geometric constructions with a variety of tools and methods
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{|style = "border-style:dotted; color:blue; border-radius:5px;"
 
|-
 
|-
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| style="background-color:#FFFFFF;"|  
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||<span style="color:black;">'''Note:''' In high school transformations in the coordinate plane are presented within word problems and students must determine which transformations (e.g., rotations) need to be performed. Also in middle and high school, students are expected to perform combinations of transformations in the coordinate plane.</span>
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|}
  
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|align="center" style="background-color:#FFFFFF;"|'''Visual Impairment or Deaf/Blind'''
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Great! Now that you have viewed the PowerPoints most useful to you, the next section will provide some ideas to consider when planning for universal design for learning
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<div>[[File:Sharethesky.jpg|thumb|bottom]]</div>
  
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|align="center" style="background-color:#FFFFFF;"|'''Physical Impairment: Little/No Hand Use'''
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=Sharing the Sky=
  
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|align="center" style="background-color:#FFFFFF;"|'''Lacks Basic Numeracy Concepts'''
 
  
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|align="center" style="background-color:#FFFFFF;"|'''Motivational/Attention Issues'''
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==UNIVERSAL DESIGN FOR LEARNING==
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{|border=1
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|width = "20%" style="background-color:#FFFFFF;"|
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|width = "20%" style="background-color:#FFFFFF;"|'''Visual Impairment or Deaf/Blind'''
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|width = "20%" style="background-color:#FFFFFF;"|'''Physical Impairment: '''
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'''Little/ No Hand Use'''
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|width = "20%" style="background-color:#FFFFFF;"|'''Lacks Basic Numeracy Concepts'''
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|width = "20%" style="background-color:#FFFFFF;"|'''Motivational/ Attention Issues'''
  
 
|-
 
|-
 
| style="background-color:#FFFFFF;"|'''Representation'''
 
| style="background-color:#FFFFFF;"|'''Representation'''
  
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| style="background-color:#FFFFFF;"|Add texture to graphs and axis so students can feel the shape of the function's input and output.
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| style="background-color:#FFFFFF;"|Use graphs and coordinate planes with raised lines and textures
  
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| style="background-color:#FFFFFF;"|Manipulate graphing software using assistive technology (switches, laser pointer).
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| style="background-color:#FFFFFF;"|Use computer representation of figures that can be manipulated with switch; create a grid (coordinate plane) on a large surface on the floor that the student can walk over or ride over in wheelchair to find ordered pairs
  
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| style="background-color:#FFFFFF;"|Always pair equation with its graphic representation.
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| style="background-color:#FFFFFF;"|Color code equations and corresponding parts of a graphing calculator to support students correctly entering equations
  
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| style="background-color:#FFFFFF;"|Enter ordered pairs into graphing software instead of drawing by hand.
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| style="background-color:#FFFFFF;"|Incorporate technology including computer representations, videos, animations, and talking calculators
  
 
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| style="background-color:#FFFFFF;"|'''Expression'''
 
| style="background-color:#FFFFFF;"|'''Expression'''
  
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| style="background-color:#FFFFFF;"|Students scan textured graphs to discriminate between linear, exponential, and quadratic functions; Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer.
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| style="background-color:#FFFFFF;"|Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer
  
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| style="background-color:#FFFFFF;"|Focus on students ability to discriminate between functions based on the graph versus computation; use a switch to indicate correct answers; use an eye gaze board to select answer; phrase questions so that they require a "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc.
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| style="background-color:#FFFFFF;"|Student scans and selects points on a graph that represent ordered pairs; use a switch to indicate correct answers; use an eye gaze board to select answer; phrase questions so that they require a "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc.
  
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| style="background-color:#FFFFFF;"|Enter equations into graphing calculators; use graphing functions to find x and y intercepts or specific ordered pairs; Focus on students ability to discriminate between functions based on the graph versus computation.
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| style="background-color:#FFFFFF;"|Student selects graphs versus drawing them; selection of correct answer is done after a model; student answers "yes/no" questions regarding slope, quadrants, etc.  
  
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| style="background-color:#FFFFFF;"|Utilize all the technological possibilities when studying functions (e.g., graphing calculators, talking calculators, free online computer software).
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| style="background-color:#FFFFFF;" rowspan=2|Have students create graphs using high interest manipulative (e.g. stickers for ordered pair coordinates)
  
 
|-
 
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| style="background-color:#FFFFFF;"|'''Engagement'''
 
| style="background-color:#FFFFFF;"|'''Engagement'''
  
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| style="background-color:#FFFFFF;"|Create personally-relevant stories to accompany the graph (e.g., for an exponential function develop a story about their own growth from birth to school age).
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| style="background-color:#FFFFFF;"|Teach students to use their hands to scan the raised graph or parts of the coordinate plane
  
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| style="background-color:#FFFFFF;"|Use bright colors to call attention to salient feature of the graph (e.g., the shape, where it cross an axis); pair student with another student without a physical impairment and have them work together to create fraction and decimal representations.
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| style="background-color:#FFFFFF;"|Use a computer with AT where the student can click to answer; use figures that are large enough to accommodate the movements that the student is able to make; pair student with another student without a physical impairment and have them work together  
  
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| style="background-color:#FFFFFF;"|Use a graphing calculator or free online graphing software that allows student to enter an equation as it appear and creates the graph for the student.
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| style="background-color:#FFFFFF;"|Student uses talking calculator and graphing calculator
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| style="background-color:#FFFFFF;"|Utilize graphing software on computer or tablet PCs; pair with another student to complete problems in pairs.
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|-
 
|}
 
|}
  
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=Prepare for Landing =
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=Prepare for Landing=
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[[File:Prepareforlanding.jpg|thumb|alt=a h ot air balloon in the distance preparing to land]]
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[[File:Prepareforlanding.jpg|thumb|A hot air balloon in the distance preparing to land]]
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Below you will find ideas for linking graphing and transformations in the coordinate plane to real-world applications, the college and career readiness skills addressed by teaching these concepts, module assessments for elementary, middle school, and high school teachers, sample general education lesson plans incorporating Universal Design for Learning framework, blog for teachers to share their ideas, and a place to upload and share lesson plans from teachers who completed this module.  
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Teaching a variety of strategies for using the coordinate plane may seem like a lot of work and developing creative, yet concrete demonstrations can be difficult. One way to help assist in a special educator's development within this curricular area is through collaboration with other teachers in your building. Often these skills are practiced outside of a math classroom in other curricular areas like art. Some activities with real world connection include:  
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Below you will find ideas for linking functions to real-world applications, the college and career readiness skills addressed by teaching these concepts, module assessments for teachers, sample general education lesson plans incorporating universal design for learning framework, blog for teachers to share their ideas, and a place to upload and share lesson plans from teachers who completed this module.  
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# Make a snowflake reflection.
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One way to help assist in a special educator's development within this curricular area is through collaboration with other teachers in your building. Some activities with real world connection include:  
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# When creating patterns, slides and flips are used by the Kuba people of the Congo (Zaire) region of Africa. Look at some samples of Kuba cloth.  
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* Anything that grows (e.g., bacteria, plants, students)
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# Take students outside and allow them to trace reflections of themselves using sidewalk chalk.
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* Focus on using the mathematic tools (e.g., graphing calculators), these skills can be possibly generalized into data entry or operating a cash register
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# Using construction and tissue paper, make a mock quilt using reflections, rotations, and transformation of different shapes (have different quilts for different polygons).
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# Use amalgamations to make an art project.
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# Cut a picture of a preferable object in half. Use the second half to demonstrate a reflection (putting the two sides together) and a rotation (put the pictures together with one side upside down).
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# Use examples which incorporate home décor. For example, a student might have to use a reflection to show where the next picture should be hung on the wall to complete a grouping of pictures. Or, students may use the vocabulary terms like "rotate" to describe where to put furniture in a home decorating layout.
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# Use a photo program and have students orient the pictures correctly.
  
 
In addition to the real-world applications of these concepts, skills taught within this content module also promote the following college and career readiness skills.
 
In addition to the real-world applications of these concepts, skills taught within this content module also promote the following college and career readiness skills.
  
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<u>Communicative competence:</u>
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<u>Communicative competence: </u>
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Students will increase their vocabulary to include concepts related to "growth", "output", "relation" or "input" In addition, they will be learning concepts such as "exponent".
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Students will increase their vocabulary to include concepts related to "coordinate plane, rotations, reflections, and translations" In addition, they will be learning concepts such as: "up", "down", "left", "right", "positive", and "negative".
  
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<u>Fluency in reading, writing, and math</u>
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<u>Fluency in reading, writing, and math:</u>
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Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to "functions" such as number recognition, counting, and interpreting a graph.
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Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to the "coordinate plane" such as number recognition, counting, and one-to-one correspondence.
  
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<u>Age appropriate social skills</u>
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<u>Age appropriate social skills:</u>
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Students will engage in peer groups to solve problems related to "functions" that will provide practice on increasing reciprocal communication and age appropriate social interactions.
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Students will engage in peer groups to solve problems related to the coordinate plane that will provide practice on increasing reciprocal communication and age appropriate social interactions. For example, students might work together with their peers to find ordered pairs to graph the translation of a quadrilateral.
  
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<u>Independent work behaviors</u>
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<u>Independent work behaviors:</u>
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By working with real life problems related to "functions" students will improve work behaviors that could lead to employment such as marketing or any job that has to analyze sales rates, stock clerks, order fillers, retail cashier, and laboratory assistant based professions. When providing opportunities for real life problems leave some materials out and prompt/teach the students to determine who they should ask and what they should ask for to be able to solve the problem.
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By solving real life problems related to the coordinate plane, students will improve work behaviors that could lead to employment such as locating items on a map.
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<u>Skills in accessing support systems</u>
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At times, students will need to ask for assistance to complete activities related to "functions" which will give them practice in accessing supports. Students will gain practice asking for tools such as graphing calculators or other manipulatives. They can ask a peer to complete the physical movements of the tasks they are not about to do themselves. Be sure to teach students to ask versus having items or supports automatically given to them.
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In addition to collaborating with other educational professionals in your building, the following list of resources may also help provide special educators with ideas for activities or support a more thorough understanding of the mathematical concepts presented in this content module.
+
  
 +
In addition to collaborating with other educational professionals in your building, the following list of resources may also help provide special educators with ideas for activities or support a more thorough understanding of the mathematical concepts presented in this content module
  
 
==Additional Resources==
 
==Additional Resources==
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* [http://itools.subhashbose.com/grapher/ http://itools.subhashbose.com/grapher/] - This website allows you to simply input x and y-coordinates and it will graph the function for you
+
* [http://www.ncpublicschools.org/acre/standards/common-core-tools/#unpacking- http://www.ncpublicschools.org/acre/standards/common-core-tools/#unpacking] - this website provides an "unpacking document" for the Mathematics Common Core Standards that helps teachers identify what is most important and the essential skills for each standard
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* [http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] - This website provides an "unpacking document" for the Mathematics Common Core Standards that helps teachers identify what is most important and the essential skills for each standard.
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* [http://www.teachertube.com/ www.teachertube.com] - Youtube for teachers! Simply search for your content area and this website provides a variety of videos including videos of math experts working through math problems step by step (''''''free registration required)''''''
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* [http://www.shodor.org/interactivate/lessons/ http://www.shodor.org/interactivate/lessons/] - Website include fully developed and interactive general education lesson plans for a variety of math topics including functions.
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* [http://www.k8accesscenter.org/training_resources/math.asp http://www.k8accesscenter.org/training_resources/math.asp\#webinar] - this website not only provides some ideas and activities to use in your classroom, but also includes presentations and webinars from the North Carolina Department of Public Instruction about research-based strategies that have proven effective in teaching math for students with varying level of disability.
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* [http://www.mathforum.com/ http://www.mathforum.com/] - Website specifically for teachers which provides a variety of ideas and activities to use in your classroom.
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* [http://exchange.smarttech.com/search.html?subject=Mathematics- http://exchange.smarttech.com/search.html?subject=Mathematics] - this SMART board exchange has developed lessons by classroom teachers differentiated by grade level. You can also search by skill and/or state standards.
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* [http://www.teachertube.com/ www.teachertube.com] - Youtube for teachers! Simply search for your content area and this websites provides a variety of videos including videos of math experts working through math problems step by step ('''free registration required).'''
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*[http://www.google.com/url?q=http://www.ksde.org/LinkClick.aspx%3Ffileticket%3DVq9AjrFFWzE%253D%26tabid%3D3763%26mid%3D11170&sa=U&ei=8lB3Try4CJOltwfmq5DfDA&ved=0CBIQFjAA&usg=AFQjCNE_DzuxI_rhYkU0H1qpjuqmM9sjng-- ksde.org] - this website provides a webinar about how to adapt materials for students who have visual impairments
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* [http://www.ksde.org/ www.ksde.org] - This website provides a webinar about how to adapt materials for students who have visual impairments.
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* [http://www.teachforever.com/2008/11/coordinate-plane-battleship-game-2008.html- http://www.teachforever.com/2008/11/coordinate-plane-battleship-game-2008.html] - website with a lesson plan for using battleship to practice finding ordered pairs in the coordinate plane
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* [http://funbasedlearning.com/- http://funbasedlearning.com/] - website provides tutorials for graphing that range from easy to hard
 +
* [http://commoncoretools.wordpress.com/ http://commoncoretools.wordpress.com/] - website provides explanation of common core connectors
  
 
==Module Assessments==
 
==Module Assessments==
 +
Below are links to assessments for the purpose of self-checking your understanding of the content in this module. After answering the assessment questions, you may want to review the key to check your work.
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[[Media:Coordinate Plane Elementary School Assessment.pdf|Elementary Assessment]]
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[[Media:Coordinate Plane Elementary School Assessment Key.pdf|Elementary Assessment Key]]
  
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[[Media:Functions Content Module assessment.pdf| Functions Content Module Assessment]]
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[[Media:Coordinate Plane Middle and High School Assessment.pdf|Middle and High School Assessment]]
  
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[[Media:Functions Content Module assessment key.pdf| Functions Content Module Assessment Key pdf]]
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[[Media:Coordinate Plane Middle and High School Assessment Key.pdf|Middle and High School Assessment Key]]
  
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==Sample General Education lesson plans==
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==Sample General Education Lesson Plans==
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Insert developed lesson plans here
  
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<!--
 
 
==Have an idea: Upload the lesson plans you've created here==
 
==Have an idea: Upload the lesson plans you've created here==
 
Insert link for teachers to upload lesson plans
 
Insert link for teachers to upload lesson plans
  
 
==Teacher's Corner: Blog with other teachers==
 
==Teacher's Corner: Blog with other teachers==
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Insert forum or blog for teachers to share ideas
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-->
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[[File:Upforachallenge.JPG|500px|center|Up for a Challenge]]
 
[[File:Upforachallenge.JPG|500px|center|Up for a Challenge]]
  
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Adapt the following general education lesson plan; adapt, and upload. These lesson plans may be shared with higher education professionals developing strategies to provide meaningful academic instruction in mathematics to students with severe disabilities.
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Insert forum or blog for teachers to share ideas
  
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[[Media:Determining Functions Using Regression.pdf| Determining Functions Using Regression Lesson One pdf]]
 
  
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[[Media:Determining Functions Using Regression Lesson Two.pdf| Determining Functions Using Regression Lesson Two pdf]]
 
  
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Adapt the following general education lesson plan; adapt, and upload. These lesson plans may be shared with higher education professionals developing strategies to provide meaningful academic instruction in mathematics to students with severe disabilities. 
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Insert blank lesson plan form with UDL chart here
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Insert link for teachers to upload lesson plans
  
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=Printable Materials=
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[[Category:Links for later]]
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[[Media:Functions Content Module complete.pdf| Functions Content Module pdf]]
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[[Category: Math]]
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[[Category:Content Modules]]
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[[Category: Content Modules]]
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[[Category:Math]]

Revision as of 08:42, 4 August 2014

BACK TO Content Modules

Contents

Skills for Transformations in the Coordinate Plane

Elementary School

  • 4.GM.1j1 Recognize a point, line and line segments, rays in two-dimensional figures
  • 4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures
  • 5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures
  • 5.GM.1a1 Recognize properties of simple plane figures
  • 5.GM.1b1 Distinguish plane figures by their properties
  • 5.GM.1c1 Locate the x and y axis on a graph
  • 5.GM.1c2 Locate points on a graph
  • 5.GM.1c3 Use order pairs to graph given points


Middle School

  • 6.GM.1c4 Locate points on a graph
  • 6.GM.1c5 Use order pairs to graph given points
  • 6.GM.1c6 Find coordinate values of points in the context of a situation
  • 6.GM.1c7 Use coordinate points to draw polygons
  • 6.NO.1d5 Find given points between -10 and 10 on both axes of a coordinate plane
  • 6.NO.1d6 Label points between -10 and 10 on both axes of coordinate plane
  • 7.GM.1e1 Construct or draw plane figures using properties
  • 8.GM.1f1 Recognize a rotation, reflection, or translation of a figure
  • 8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates
  • 8.GM.1g1 Recognize congruent and similar figures


High School

  • H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures
  • H.GM.1c1 Construct, draw, or recognize a figure after its rotation, reflection, or translation
  • H.GM.1d1 Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles
  • H.GM.1e1 Make formal geometric constructions with a variety of tools and methods


Plot the Course

three hot air balloons floating in the sky
http://www.worthwhilesmile.com/air-balloons-kaleidoscope/


The rationale

Understanding how to find points on a coordinate plane not only serve academic purposes, but also address real-life skills students may use on a daily basis like navigating using a map or an atlas. In addition to reading a map, the concept of graphing on the coordinate plane is also used in games such as Battleship or some of the simulation games in which students build amusement parks or entire cities. Other recreation leisure activities, especially in art, incorporate transformation in the coordinate plane like quilting. Mathematically, graphing in the coordinate plane is a prerequisite for many skills across grade bands such as transformations in the coordinate plane, finding missing attributes of polygons, and interpreting graphs.

Module Goal

The goal of this module is to provide detailed instructions on how to graph and create polygons in the coordinate plane as well as how to perform transformations (i.e., reflections, rotations, and translations) within the coordinate plane to teachers of students with disabilities at the elementary, middle, and high school level. This module promotes a mathematical understanding of these concepts so that a teacher can begin to plan how to teach the concepts to students. Additionally, this module will provide instructors with potential adaptations and modifications to consider when designing materials and instruction for students with severe disabilities.

Module Objectives

After viewing the content module, teachers will:

  1. Apply strategies for finding ordered pairs and graphing in the coordinate plane
  2. Identify attributes of polygons
  3. Perform transformations in the coordinate plane
  4. Apply transformations in the coordinate plane to real-world applications and activities

Time for Take Off

flame used to lift hot air balloon

Understanding the vocabulary used within the coordinate plane is important for both teachers and students in planning and implementing math lessons. As a teacher, knowing and using the mathematical terms not only ensures your instruction stays true to the math content, but also will help with collaborating with other math teachers or content experts. When choosing which vocabulary to teach, it is most important that the teacher selects the most salient, important, or most frequently used vocabulary for each lesson. Below you will find a list of vocabulary included within this module. It may or may not be necessary to provide instruction for all terms as students may have learned them previously. If you are a secondary teacher and are not confident your students have been taught the elementary vocabulary terms, you may want to add those unknown terms to the focus and review of your lesson plan. While providing vocabulary instruction, you may consider including pictures or objects to make the instruction more concrete for students with disabilities (See Ideas to support vocabulary learning below).

Elementary School

  • Point- an exact location
  • Line- a straight path that extends forever
  • Line segment- part of a line with two endpoints
  • Ray- part of a line that starts at one endpoint and extends forever in one direction
  • Perpendicular- lines that intersect at a 90º angle
  • Parallel- lines that never intersect
  • Coordinate Plane- formed by two axes that intersect at a right angle
  • Right angle- an angle that measures 90º formed by two perpendicular lines

Middle and High School

  • Polygon- closed plane figure made by three or more line segments
  • Rotation- when you turn a figure at one point
  • Reflection- a mirror image of an object when the original is flipped
  • Translation- when you slide a figure along a line without turning it
  • Congruent figures- figures that have the same size and shape. If two polygons have the same corresponding sides and angles, they are congruent.
  • Similar figures- figures with the same shape but not the same size

Idea to support vocabulary learning

  • Have student match term with the correct picture

a point, a line, a ray, a line segment, parallel lines, perpendicular lines, right angle, coordinate plane, a three sided polygon, a four sided polygon, and a non polygon

Congruent Shapes

Two congruent squares, two congruent parallelograms

Similar Shapes

Two similar squares, two similar parallelograms


Idea for systematic instruction: demonstrate the concepts of congruent and similar shapes using examples and non-examples. For example: "This is ________, This is __________, This is NOT __________, This is NOT __________, This is ____________. Show me __________"

Rotation Triangle rotated one hundred eighty degrees


Reflection Triangle reflected across y axis of coordinate plane

Translation Triangle translated diagonally across coordinate plane

Floating on Air

close up of one hot air balloon with a second floating in the distance

Before you can begin teaching students to use reflections, rotations, and translations of figures in the coordinate plane, you must have a deep understanding of these mathematical concepts. Some of these concepts may be familiar to you. Below is a list of skills that should be covered at each grade level in the mathematical strand of measurement. For more complicated concepts, please view the accompanying PowerPoint that will walk you through an example as well as make some suggestions for instruction.

Elementary School

In elementary school skills include:

  • 4.GM.1j1 Recognize a point, line and line segments, rays in two-dimensional figures
  • 4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures
  • 5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures
  • 5.GM.1a1 Recognize properties of simple plane figures

Properties of Plane Figures PowerPoint

  • 5.GM.1b1 Distinguish plane figures by their properties
  • 5.GM.1c1 Locate the x and y axis on a graph
  • 5.GM.1c2 Locate points on a graph
  • 5.GM.1c3 Use order pairs to graph given points

Middle and High School

In middle school skills include:

  • 6.GM.1c4 Locate points on a graph
  • 6.GM.1c5 Use order pairs to graph given points
  • 6.GM.1c6 Find coordinate values of points in the context of a situation

Graphing in the Coordinate Plane PowerPoint

  • 6.GM.1c7 Use coordinate points to draw polygons
  • 7.GM.1e Construct or draw plane figures using properties
  • 8.GM.1f1 Recognize a rotation, reflection, or translation of a figure
  • 8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates

Rotations in the Coordinate Plane PowerPoint

Reflections in the Coordinate Plane PowerPoint

Translations in the Coordinate Plane PowerPoint

  • 8.GM.1g Recognize congruent and similar figures

Insert congruent vs. similar figures PowerPoint here

  • H.GM.1b Use definitions to demonstrate congruency and similarity in figures
  • H.GM.1c Construct, draw, or recognize a figure after its rotation, reflection, or translation

(See rotations, reflections, and translations PowerPoints)

  • H.GM.1d Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles

(See rotations, reflections, and translations PowerPoints)

  • H.GM.1e Make formal geometric constructions with a variety of tools and methods
Note: In high school transformations in the coordinate plane are presented within word problems and students must determine which transformations (e.g., rotations) need to be performed. Also in middle and high school, students are expected to perform combinations of transformations in the coordinate plane.

Great! Now that you have viewed the PowerPoints most useful to you, the next section will provide some ideas to consider when planning for universal design for learning

Sharethesky.jpg

Sharing the Sky

UNIVERSAL DESIGN FOR LEARNING

Visual Impairment or Deaf/Blind Physical Impairment:

Little/ No Hand Use

Lacks Basic Numeracy Concepts Motivational/ Attention Issues
Representation Use graphs and coordinate planes with raised lines and textures Use computer representation of figures that can be manipulated with switch; create a grid (coordinate plane) on a large surface on the floor that the student can walk over or ride over in wheelchair to find ordered pairs Color code equations and corresponding parts of a graphing calculator to support students correctly entering equations Incorporate technology including computer representations, videos, animations, and talking calculators
Expression Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer Student scans and selects points on a graph that represent ordered pairs; use a switch to indicate correct answers; use an eye gaze board to select answer; phrase questions so that they require a "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc. Student selects graphs versus drawing them; selection of correct answer is done after a model; student answers "yes/no" questions regarding slope, quadrants, etc. Have students create graphs using high interest manipulative (e.g. stickers for ordered pair coordinates)
Engagement Teach students to use their hands to scan the raised graph or parts of the coordinate plane Use a computer with AT where the student can click to answer; use figures that are large enough to accommodate the movements that the student is able to make; pair student with another student without a physical impairment and have them work together Student uses talking calculator and graphing calculator

Prepare for Landing

a h ot air balloon in the distance preparing to land

Below you will find ideas for linking graphing and transformations in the coordinate plane to real-world applications, the college and career readiness skills addressed by teaching these concepts, module assessments for elementary, middle school, and high school teachers, sample general education lesson plans incorporating Universal Design for Learning framework, blog for teachers to share their ideas, and a place to upload and share lesson plans from teachers who completed this module. Teaching a variety of strategies for using the coordinate plane may seem like a lot of work and developing creative, yet concrete demonstrations can be difficult. One way to help assist in a special educator's development within this curricular area is through collaboration with other teachers in your building. Often these skills are practiced outside of a math classroom in other curricular areas like art. Some activities with real world connection include:

  1. Make a snowflake reflection.
  2. When creating patterns, slides and flips are used by the Kuba people of the Congo (Zaire) region of Africa. Look at some samples of Kuba cloth.
  3. Take students outside and allow them to trace reflections of themselves using sidewalk chalk.
  4. Using construction and tissue paper, make a mock quilt using reflections, rotations, and transformation of different shapes (have different quilts for different polygons).
  5. Use amalgamations to make an art project.
  6. Cut a picture of a preferable object in half. Use the second half to demonstrate a reflection (putting the two sides together) and a rotation (put the pictures together with one side upside down).
  7. Use examples which incorporate home décor. For example, a student might have to use a reflection to show where the next picture should be hung on the wall to complete a grouping of pictures. Or, students may use the vocabulary terms like "rotate" to describe where to put furniture in a home decorating layout.
  8. Use a photo program and have students orient the pictures correctly.

In addition to the real-world applications of these concepts, skills taught within this content module also promote the following college and career readiness skills.

Communicative competence: Students will increase their vocabulary to include concepts related to "coordinate plane, rotations, reflections, and translations" In addition, they will be learning concepts such as: "up", "down", "left", "right", "positive", and "negative".

Fluency in reading, writing, and math: Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to the "coordinate plane" such as number recognition, counting, and one-to-one correspondence.

Age appropriate social skills: Students will engage in peer groups to solve problems related to the coordinate plane that will provide practice on increasing reciprocal communication and age appropriate social interactions. For example, students might work together with their peers to find ordered pairs to graph the translation of a quadrilateral.

Independent work behaviors: By solving real life problems related to the coordinate plane, students will improve work behaviors that could lead to employment such as locating items on a map.

In addition to collaborating with other educational professionals in your building, the following list of resources may also help provide special educators with ideas for activities or support a more thorough understanding of the mathematical concepts presented in this content module

Additional Resources

Module Assessments

Below are links to assessments for the purpose of self-checking your understanding of the content in this module. After answering the assessment questions, you may want to review the key to check your work.

Elementary Assessment

Elementary Assessment Key

Middle and High School Assessment

Middle and High School Assessment Key

Sample General Education Lesson Plans

Insert developed lesson plans here

Have an idea: Upload the lesson plans you've created here

Insert link for teachers to upload lesson plans

Teacher's Corner: Blog with other teachers

Up for a Challenge

Insert forum or blog for teachers to share ideas


Adapt the following general education lesson plan; adapt, and upload. These lesson plans may be shared with higher education professionals developing strategies to provide meaningful academic instruction in mathematics to students with severe disabilities. Insert blank lesson plan form with UDL chart here Insert link for teachers to upload lesson plans

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