Expressions Content Module
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=Plot the Course= | =Plot the Course= | ||
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==The rationale== | ==The rationale== | ||
| − | The act of simplifying complex tasks into smaller, simpler steps is a skill that has implications both inside and outside the classroom. Whether you're trying to determine if you have enough money to see a movie and buy snacks or you need to buy materials to build a flowerbed, these complex tasks often require the combining or | + | The act of simplifying complex tasks into smaller, simpler steps is a skill that has implications both inside and outside the classroom. Whether you're trying to determine if you have enough money to see a movie and buy snacks or you need to buy materials to build a flowerbed, these complex tasks often require the combining or simplifying of similar terms. |
==Module Goal== | ==Module Goal== | ||
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| + | =Time for Take Off= | ||
| + | [[File:Timefortakeoff.jpg|thumb|A flame used to lift hot air balloon]] | ||
| − | + | Understanding the vocabulary used within simplifying expressions 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. | |
| − | Understanding the vocabulary used within simplifying expressions 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. Expressions 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. | 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. Expressions 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. | ||
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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). | 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). | ||
==Vocabulary== | ==Vocabulary== | ||
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| − | + | {{Def|Terms | expressions that are separated by a plus or minus sign (e.g., 2t-3b{{Equals}})}} | |
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| + | {{Def|Like terms |terms that have the same variable (e.g., 2t and 3t are like terms)}} | ||
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| + | {{Def|Coefficients |a number multiplied by a variable (e.g., In the term 6y, 6 is the coefficient).}} | ||
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| + | =Floating on Air= | ||
| + | [[File:Floatingonair.jpg|thumb|A close up of one hot air balloon with a second floating in the distance]] | ||
Before you can begin teaching simplifying expressions, 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 presentation that will walk you through an example as well as make some suggestions for instruction. | Before you can begin teaching simplifying expressions, 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 presentation that will walk you through an example as well as make some suggestions for instruction. | ||
==Middle and High School== | ==Middle and High School== | ||
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In middle and high school skills include: | In middle and high school skills include: | ||
* 6.PRF.2a2 Use variable to represent numbers and write expressions when solving real world problems | * 6.PRF.2a2 Use variable to represent numbers and write expressions when solving real world problems | ||
* 6.NO.1i2 Solve numerical expressions involving whole number exponents | * 6.NO.1i2 Solve numerical expressions involving whole number exponents | ||
* 6.SE.1a3 Write expressions for real-world problems involving one unknown number | * 6.SE.1a3 Write expressions for real-world problems involving one unknown number | ||
| − | + | ||
| + | ::[[Media:Simplifying expressions.pptx| Simplifying Expressions powerpoint]] | ||
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* H.PRF.2a1 Translate an algebraic expression into a word problem | * H.PRF.2a1 Translate an algebraic expression into a word problem | ||
* H.NO.2c1 Simplify expressions that include exponents | * H.NO.2c1 Simplify expressions that include exponents | ||
* H.NO.2c2 Rewrite expressions that include rational exponents | * H.NO.2c2 Rewrite expressions that include rational exponents | ||
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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. | 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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| − | ==UNIVERSAL DESIGN FOR LEARNING | + | |
| + | =Sharing the Sky= | ||
| + | [[File:Sharethesky2.jpg|thumb|bottom|Two hot air balloons in the distance]] | ||
| + | <font size=3>UNIVERSAL DESIGN FOR LEARNING</font> | ||
{|border=1 | {|border=1 | ||
| − | | | + | | colspan=5|'''Some examples of options for teaching expressions to students who may present instructional challenges due to:''' |
|- | |- | ||
| − | | | + | | width = "500"| |
| − | | | + | | width = "500"|'''Visual Impairment or Deaf/Blind''' |
| − | | | + | | width = "500"|'''Physical Impairment:''' |
'''Little/No Hand Use''' | '''Little/No Hand Use''' | ||
| − | | | + | | width = "500"|'''Lacks Basic Numeracy Concepts''' |
| − | | | + | | width = "500"|'''Motivational/Attention Issues''' |
|- | |- | ||
| − | | | + | ||'''Representation''' |
| − | | | + | ||Add corresponding textures (e.g., Velcro) to manipulatives representing each term in the expression. |
| − | | | + | ||Student scans an array of possible options and uses a switch to select the appropriate terms, coefficients, or exponents. |
| − | | | + | ||Use objects to represent numbers in the expression; color code similar terms within the expression. |
| − | | | + | ||Create personally-relevant word problems or stories to pair with expressions. |
|- | |- | ||
| − | | | + | ||'''Expression''' |
| − | | | + | ||Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer. |
| − | | | + | ||Uses a switch to indicate correct answers; uses an eye gaze board to select answer; "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc. |
| − | | | + | ||Student selects numbers or terms versus writing them; selection of correct answer is done after a model. |
| − | | | + | ||Student simplifies expressions using computer software or other technology. |
|- | |- | ||
| − | | | + | ||'''Engagement''' |
| − | | | + | ||Add corresponding textures (e.g., Velcro) to manipulatives representing each term in the expression. |
| − | | | + | ||Use a computer with AT where the student can click to answer; use manipulatives that are large and easily manipulated; pair student with another student without a physical impairment and have them work together to simplify expressions. |
| − | | | + | ||Use objects to represent numbers in the expression; color code similar terms within the expression. |
| − | | | + | ||Include personally-relevant contexts for simplifying the expressions. |
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|} | |} | ||
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=Prepare for Landing= | =Prepare for Landing= | ||
| + | [[File:Prepareforlanding.jpg|thumb|A hot air balloon in the distance preparing to land]] | ||
Below you will find ideas for linking simplifying expressions 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. | Below you will find ideas for linking simplifying expressions 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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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: | 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: | ||
* Estimating costs at the grocery store by combining same priced objects; and | * Estimating costs at the grocery store by combining same priced objects; and | ||
* When counting money (25 quarters, 10 dimes, 15 nickels 25 pennies) and then when you come across 15 more nickels, you would put the nickels together when counting the coins. | * When counting money (25 quarters, 10 dimes, 15 nickels 25 pennies) and then when you come across 15 more nickels, you would put the nickels together when counting the coins. | ||
| − | 25 Q + 10 D + 15 N + 25 P + 15 N... combine N so now you have 30 N | + | ::25 Q + 10 D + 15 N + 25 P + 15 N... combine N so now you have 30 N |
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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. | ||
<u>Communicative competence</u> | <u>Communicative competence</u> | ||
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Students will increase their vocabulary to include concepts related to "simplification" and "expressions". In addition, they will be learning concepts such as: "terms", "coefficient", and "exponent". | Students will increase their vocabulary to include concepts related to "simplification" and "expressions". In addition, they will be learning concepts such as: "terms", "coefficient", and "exponent". | ||
<u>Fluency in reading, writing, and math</u> | <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 "expressions" such as number recognition, counting, and grouping similar things. | Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to "expressions" such as number recognition, counting, and grouping similar things. | ||
<u>Age appropriate social skills</u> | <u>Age appropriate social skills</u> | ||
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Students will engage in peer groups to solve problems related to "simplifying expressions" that will provide practice on increasing reciprocal communication and age appropriate social interactions. | Students will engage in peer groups to solve problems related to "simplifying expressions" that will provide practice on increasing reciprocal communication and age appropriate social interactions. | ||
<u>Independent work behaviors</u> | <u>Independent work behaviors</u> | ||
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By working with real life problems related to "simplifying expressions" 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, and other construction 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. | By working with real life problems related to "simplifying expressions" 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, and other construction 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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<u>Skills in accessing support systems</u> | <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 "simplifying expressions" 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. | At times, students will need to ask for assistance to complete activities related to "simplifying expressions" 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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* [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). | * [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). | ||
* [http://www.purplemath.com/modules/simpexpo.htm http://www.purplemath.com/modules/simpexpo.htm] - This website provides examples and extra resources simplifying expressions with exponents. | * [http://www.purplemath.com/modules/simpexpo.htm http://www.purplemath.com/modules/simpexpo.htm] - This website provides examples and extra resources simplifying expressions with exponents. | ||
| − | * [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 | + | * [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| Use of Manipulatives powerpoint] - This website provides a webinar about how to adapt materials for students who have visual impairments. |
==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:Expressons assessment.pdf| Expressions Assessment pdf]] | ||
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| + | :[[Media:Expressions assessment with answers.pdf| Expressions Assessment with answers pdf]] | ||
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| + | :[[Media:Simplifying expressions.pptx| Simplifying Expressions powerpoint]] | ||
==Sample General Education lesson plans== | ==Sample General Education lesson plans== | ||
| − | + | :[[Media:General education challenge lesson plan.pdf| General Education Challenge lesson plan pdf]] | |
| − | + | <!-- | |
==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== | ||
| − | Insert forum or blog for teachers to share ideas | + | Insert forum or blog for teachers to share ideas --> |
| + | [[File:Upforachallenge.JPG|500px|center|Up for a Challenge]] | ||
| + | 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 link for teachers to upload lesson plans --> | ||
| − | + | :[[Media:UDL expressions lesson plan.pdf| Expressions Content Module - Simplifying Expressions Lesson Plan pdf]] | |
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Latest revision as of 09:23, 10 September 2015
BACK TO Content Modules
Contents |
[edit] Plot the Course
[edit] The rationale
The act of simplifying complex tasks into smaller, simpler steps is a skill that has implications both inside and outside the classroom. Whether you're trying to determine if you have enough money to see a movie and buy snacks or you need to buy materials to build a flowerbed, these complex tasks often require the combining or simplifying of similar terms.
[edit] Module Goal
The goal of this module is to provide detailed instruction on the more difficult concepts of simplifying expressions 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.
[edit] Module Objectives
After viewing the content module, teachers will:
- Identify similar terms within an expression
- Complete all the steps to simplify an expression in its simplest form using the commutative, associative, and distributive properties
- Translate word problems into an expression
[edit] Time for Take Off
Understanding the vocabulary used within simplifying expressions 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. Expressions 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).
[edit] Vocabulary
- Terms - expressions that are separated by a plus or minus sign (e.g., 2t-3b=)
- Like terms - terms that have the same variable (e.g., 2t and 3t are like terms)
- Coefficients - a number multiplied by a variable (e.g., In the term 6y, 6 is the coefficient).
[edit] Floating on Air
Before you can begin teaching simplifying expressions, 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 presentation that will walk you through an example as well as make some suggestions for instruction.
[edit] Middle and High School
In middle and high school skills include:
- 6.PRF.2a2 Use variable to represent numbers and write expressions when solving real world problems
- 6.NO.1i2 Solve numerical expressions involving whole number exponents
- 6.SE.1a3 Write expressions for real-world problems involving one unknown number
- H.PRF.2a1 Translate an algebraic expression into a word problem
- H.NO.2c1 Simplify expressions that include exponents
- H.NO.2c2 Rewrite expressions that include rational exponents
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.
[edit] Sharing the Sky
UNIVERSAL DESIGN FOR LEARNING
| Some examples of options for teaching expressions to students who may present instructional challenges due to: | ||||
| Visual Impairment or Deaf/Blind | Physical Impairment:
Little/No Hand Use |
Lacks Basic Numeracy Concepts | Motivational/Attention Issues | |
| Representation | Add corresponding textures (e.g., Velcro) to manipulatives representing each term in the expression. | Student scans an array of possible options and uses a switch to select the appropriate terms, coefficients, or exponents. | Use objects to represent numbers in the expression; color code similar terms within the expression. | Create personally-relevant word problems or stories to pair with expressions. |
| Expression | Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer. | Uses a switch to indicate correct answers; uses an eye gaze board to select answer; "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc. | Student selects numbers or terms versus writing them; selection of correct answer is done after a model. | Student simplifies expressions using computer software or other technology. |
| Engagement | Add corresponding textures (e.g., Velcro) to manipulatives representing each term in the expression. | Use a computer with AT where the student can click to answer; use manipulatives that are large and easily manipulated; pair student with another student without a physical impairment and have them work together to simplify expressions. | Use objects to represent numbers in the expression; color code similar terms within the expression. | Include personally-relevant contexts for simplifying the expressions. |
[edit] Prepare for Landing
Below you will find ideas for linking simplifying expressions 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.
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:
- Estimating costs at the grocery store by combining same priced objects; and
- When counting money (25 quarters, 10 dimes, 15 nickels 25 pennies) and then when you come across 15 more nickels, you would put the nickels together when counting the coins.
- 25 Q + 10 D + 15 N + 25 P + 15 N... combine N so now you have 30 N
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 "simplification" and "expressions". In addition, they will be learning concepts such as: "terms", "coefficient", and "exponent".
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 "expressions" such as number recognition, counting, and grouping similar things.
Age appropriate social skills
Students will engage in peer groups to solve problems related to "simplifying expressions" that will provide practice on increasing reciprocal communication and age appropriate social interactions.
Independent work behaviors
By working with real life problems related to "simplifying expressions" 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, and other construction 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.
Skills in accessing support systems
At times, students will need to ask for assistance to complete activities related to "simplifying expressions" 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.
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.
[edit] Additional Resources
- http://www.algebrahelp.com/calculators/expression/oops/ - Allows students to enter an expression and the website will simplify automatically. Great place for students to check their answers.
- 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.
- http://mathforum.org/ - Website specifically for teachers which provides a variety of ideas and activities to use in your classroom.
- 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).
- http://www.purplemath.com/modules/simpexpo.htm - This website provides examples and extra resources simplifying expressions with exponents.
- Use of Manipulatives powerpoint - This website provides a webinar about how to adapt materials for students who have visual impairments.
[edit] 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.
[edit] Sample General Education lesson plans
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.
