Coordinate Plane Content Module
Contents |
Plot the course
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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, understanding the concepts of graphing on the coordinate plane are also used in games such as Battleship or some of the simulation games where students build amusement parks or entire cities. Other recreation leisure activities such, 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 is 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 should be able to:
- Apply strategies for finding ordered pairs and graphing in the coordinate plane
- Identifying attributes of polygons
- Perform transformations in the coordinate plane
- Apply transformations in the coordinate plane to real-world applications and activities
Time for take off
<Insert Picture here> Before you begin the math lesson, it will be necessary to ensure the students know the vocabulary of the lesson. When choosing which vocabulary to teach it is most important that the teacher selects the most salient, important, or most frequently used vocabulary. 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 also want to consider including pictures or objects to make the instruction more concrete for students with disabilities. 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 axis 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
Congruent Shapes
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Similar Shapes <Insert Shapes>
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
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Reflection
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Translation
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Floating on Air
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
Insert 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 point son 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
Insert graphing on the coordinate plane PowerPoint here
- 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
Insert rotations PowerPoint here Insert reflections PowerPoint here Insert translations PowerPoint here
- 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
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.
Sharing the Sky
Insert Picture here UNIVERSAL DESIGN FOR LEARNING
| Visual Impairment or Deaf/Blind | Physical impairment:
Little/ no hand use |
Lacks basic numeracy concepts | Motivational/ attention issues | |
| Representation | Use a talking calculator when solving equations; use a ruler with raise measurement lines, use objects to represent fractions and decimals; use raised lines to represent portions of the whole object. Use items that are velcroed together to represent the whole and have the student separate the whole into parts. | Count the parts of fractions or decimals using a step by step process which progresses through numbers; student scan an array of possible options and use a switch to select the number to identify the numerator; use computer representation of figures that can be manipulated with switch; place fraction representations on a slant board or eye gaze board; create a grid on a large surface on the floor that the student can walk over or ride over in wheelchair.
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Use fraction and decimal manipulative that can be separated and placed on a number line. Have student use talking calculate to count along. Students can use one to one correspondence to match equal number of parts on representation of fraction or decimals. Color code equations and corresponding parts of calculator to support students correctly entering equations. | Find fractions of motivating objects (e.g. pizza, coloring markers in a box, piece of a Lego set). Incorporate technology including computer representations, videos, animations, and talking calculators. Use token economy system that embeds fractions ("you earned ¼ of your Lego piece, you have ¾ left and then you get Lego time.) |
| Expression | Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer; teach tangible symbols that mean fraction and decimal | Student scans and selects number that represents numerator or denominator; uses a switch to indicate correct answers; use an eye gaze board to select answer; use a blink response to count parts or 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; count parts of fractions out loud having student move in some voluntary way (e.g., nod head, tap hand, tap foot) to count along | Student selects numbers versus writing them; selection of correct answer is done after a model; student points to each part of a fraction or decimal while teacher or peer counts aloud; student answers "yes/no" questions regarding fractions or decimals after parts have been counted aloud (e.g., 1,2,3,4. There are 4 colored parts. Is this the number we write as the numerator?); matches the parts of a fraction to the correct number (matches 4 to 4). | Have students express fractions using high interest manipulative (e.g. Legos, stickers of favorite characters, a fraction of an IPod, or jewelry beads) |
| 'Engagement' | Teach students to use their hands to scan the raised of each whole item; use talking calculator for computing the area; start with simple, clearly defined fractions; use items that are familiar and reinforcing to students. | Use bright colors to call attention to numerators; 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 to create fraction and decimal representations. | Student uses talking calculator, limit fractions and decimals to numerals less than 10, use bright colors to represent fractions and numerals. | Use token economy system that embeds fractions ("you earned ¼ of your Lego piece, you have ¾ left and then you get Lego time.) |
Insert possible photos of adapted materials
Prepare for landing
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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. 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:
- Make a snowflake reflection
- Take students outside and allow them to trace reflections of themselves using sidewalk chalk
- Using construction and tissue paper, make a mock quilt using reflections, rotations, and transformation of different shapes (have a different quilts for different polygons)
- Use amalgamations to make an art project
- 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)
- 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.
- Use 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
- [www.teachertube.com-http://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)
- [1] 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.
- [2] this SMART board exchange has developed lessons by classroom teachers differentiated by grade level. You can also search by skill and/or state standards.
- [3] this website provides a webinar about how to adapt materials for students who have visual impairments
- [4] website with a lesson plan for using battleship to practice finding ordered pairs in the coordinate plane
- [5] website provides tutorials for graphing that range from easy to hard
- http://commoncoretools.wordpress.com/ - website provides explanation of common core connectors
Module Assessments Insert elementary assessment Insert middle and high school assessment 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 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>
