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Annotated Lesson Plan Form
Description and Annotated References 50Analysis 23 Reflection 23Grade 96
I’ve included my comments in the document using the commenting feature. You should see them in the margins. You did an excellent job on this lesson!
Name: Ms. Jennifer J. Smith
A. Description of Lesson Plan
Academic Subject(s): Math Lesson - Write and interpret numerical expressions
Grade Level(s): Fifth Grade
Standards Integrated into the Lesson Plan: Maryland State Department of Education (MSDE) standards for Fifth Grade mathematics
Student Content Standards: Maryland Common Core Curriculum Frameworks. 5.OA.2 -Write and interpret numerical expressions Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8+7). Recognize that 3x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. (Maryland Common Core Curriculum Frameworks, 2014)
National Educational Technology Standards for Students (2007): Critical Thinking, Problem Solving, and Decision Making Standard(4). Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students:
a. identify and define authentic problems and significant questions for investigation.b. plan and manage activities to develop a solution or complete a project. c. collect and analyze data to identify solutions and/or make informed decisions. d. use multiple processes and diverse perspectives to explore alternative solutions. (International Society for Technology in Education, 2007)
Learning Objectives for Lesson Plan: Student Students will learn the process of Algebraic thinking through the order of operations with numerical expressions, after this lesson student (s) will demonstrate the ability to write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them. Students will also know how algebra is used outside of the classroom. Within groups students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. (International Society for Technology in Education, 2007)
Estimated Duration: Two hours and thirty minutes Class size: 17 - ((9) students have iPads, and (4) have iPhones)
Featured Technologies SMARTboard InteractiveWhiteboard Five classroom desktop computers Interactive clickers for assessments Students are allowed to use mobile technology within classroom settings To make sure technology is available and working: Students are required to
charge mobile devices the night prior to quiz or test days, however if they are not charged they may charge them upon entering the classroom for fifteen minutes (chargers will be on hand). The desktop computers will be setup prior to class start time by the teacher
Other Necessary Materials: Teacher’s tools & software: SMARTboard notebook lesson file,
Algebraic Expressions Millionaire Game Order of Operations Four Game -Web based software, Socrative (software preinstalled on desktops),
IXL web-based software (class room portal created prior to lesson)
($60 play cash – $20 per group, and Student Rubrics for the math Problem of the Month: Digging Dinosaurs)
Student’s tools: Fifth Grade Math Text book
BYOD is allowed: Socrative (software preinstalled on mobile device prior to lesson)
Prerequisite Student Skills After having full understanding on addition, subtraction, multiplication and division, and exponents students will learn the process of Algebraic thinking with numerical expressions. Computer literate students are able utilize their mobile devices (iPads, iPhones, etc.); however if a child is without a personal technology device and/ or computer skill accommodations (such as provided clickers for the Socrative exercises, in class desktop computers, documented assignment worksheets, and teacher and/or peer assistance) will be providedmade to ensure that he/she is able to learn on an equal level with peers. *Note technical training will be provided after class hours if needed.
Brief Overview of Lesson: This lesson is in the middle of the Operations and Algebraic Thinking unit. The material covered throughout this lesson provides exercises that build upon and reinforce each other as we model our Algebraic thinking skills in the classroom; students through understanding the numerical expression concept, the Order of Operations PEMDAS. and Ttechnology as it is applied with hands on exercises utilizing
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the following: Interactive WhiteBoard (operated by the teacher, while learners interact), Socrative’s assessment software (used by students for both assessments), and Real World Problem of the Month world problem (Socrative and virtual tour).Without technology for this lesson students find basic math, vocabulary and practice skills boring; however the technology incorporated into this lesson will enhance teacher and student motivation as it offers attention getting visualsdisplays, immediate feedback, and interaction (Roblyer & Doering, 2013).
Teacher-To-Teacher: The teacher should be familiar with the correct usage of the 5.0A.2 standard because students will need to have an understanding of the basic art of writing and interpreting word and numerical operation problems and the meaning of each term; also as the standard can be applied throughto technology with the use if a interactive whiteboard, and mobile devices to assist the development of the lesson in case student (s) need assistance. Another good idea for teachers to use is the Differentiated approach; by The teacher may also want to dividinge the students into differentiated learning groups (based on their learning abilities as some are more motivated to learn than others) beginning with the “Problem of the month” exercise. Moreover in order for motivated teachers and students to gain rewarding results from these interactive technologies, teachers must be well trained on the software and hardware applications. As a personal skill assessment the teacher may want to attend training seminars and/or return to school.
Procedures/Activities:
Day 1 Introduction (5 min) Warm up!! (Review current knowledge) Please solve the problems below.
1. 3(3) 2. 2⁴3. 9 x 6
4. 3726 ÷ 185. 19 + 266. 15 – 4
7. Then ask the students to “add 9 and 3, and then multiply by 6.” (Review as a class)
Upon completion of the warm up exercise the teacher directly explains that the latter method was a simple written expression that was used for them to record their calculations with numbers, and interpret numerical expressions. Discuss that numerical expressions are combinations of numbers with one or more operation symbols. Explain that there is a process to understanding numerical expressions, through the use of the Order of Operations called PEMDAS which offers a strategic algorithm formula base Please Excuse My Dear Aunt Sally (reference er them to the chart below). After explaining the process to the class, connect it to a couple of daily real life processes, for instance the ability to makeke the great or /good grades ideally is a process, if we don’t study to learn our lessons, don’t turn in assignments, and miss tests; can we then produce the desired result of making good grades? The answer is undoubtedly no! The process of writing and/or interpreting numerical expressions is the very same concept as the making a desiredgood grade; it must be done in the correct order.
(25 min-No prep time needed, completed set-up prior to class)3
A direct lecture will be provided by the teacher, and during the Numerical Expressions lesson students will discover how to: write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them, build upon numerical expression vocabulary (listed below), and the Order of Operations with an emphasis placed on phrase Please Excuse My Dear Aunt Sally algorithm. While using the interactive Whiteboard technology tool and some (explained in the analysis section) of the great Numerical Expressions PowerPoint lesson files by Drewisis, Melissa (2012), which includes the following content: a warm up, definition notes, master key word list generated through her initial warm up, and more problem solving interactive examples. However, I will only utilize the following from slides from the PowerPoint’s ready-made helpful visuals: definitions and interactive slide where the addition and subtraction words are hidden (students can just click in the box to make them appear). Instead of using the suggested order of operations through the analysis of simplified expressions, I will attempt to make it more personable by utilizing the order process from my childhood learning experience with the Please Excuse My Dear Aunt Sally algorithm, which is still being used as means to help learners better understand the Algebraic process. This sequence will help students memorize, because although the writing of numerical expressions can be a simple process it still needs to follow an order to help learners interpret the right answer.
In addition to the content provided and discussed during the whiteboard lecture, the following table and vocabulary are for notes only (unless asked a question): Explain that in interpreting numerical expressions the sequence detail order we follow is Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction P.E.M.D.A.S. Perform the operations inside a parenthesis first, and then exponents, then multiplication and division-from left to right, and finally addition and subtraction- both from left to right.
For example: Write each phrase as a numerical expressionParenthesis, Exponents, Multiplication, Division, Addition, Subtraction
P.E.M.D.A.S.
Phrase Consider the determining factors for PEMDAS
Interpret Numerical Expression Results
Three less thanthe quotient of 8 and 2
Less than, Difference, Decrease (-)Quotient ()
8 2 – 3
Twice as much asthe difference of 8 and 3
Twice as much (x),Difference, Decrease, Less than (-)
2 × (8 – 3)
Eight more than the product of 3 and 2
More, Increase, In addition to, Sum (+)Product (x)
8 + 3 × 2
The sum of 8 and 3 divided by 2
Sum, More, Increase, In addition to (+)()
(8 + 3) 2
Five less than the quotient of 6 and 2
Less than, Difference, Decrease (-)Quotient ()
(6 2) – 5
Vocabulary terms to know:4
• numerical expression • parentheses• order of operations • brackets
(During this time the teacher will discuss the lesson, and interact with the class by providing opportunities for them to ask questions verbally, and interact with the whiteboard in response to questions similar to the ones listed above - the teacher also is observant of students responses to material, and updates personal student/teacher observation rubric - while students are seated and required to record notes on either the mobile technology, or with paper and pencil)
(15 min – no prep time needed)At this time students will play a game called Algebraic Expressions Millionaire Game on the whiteboard (Technology needed). This game is reinforcement to help them recognize and interpret numerical expressions without evaluating them, and fully understanding how to multiply, add, subtract and use exponents well will be very beneficial in this learning phase.
(Students are still seated and encouraged to participate in the game by a show of hands – to answer questions on the Whiteboard, meanwhile the teacher is operating the interactive software)
(20mins –includes 5 min prep)Have students use the IXL Learning mathematics software that would enhance the lesson on use of order of operations. Students are to practice answering questions from the Algebra section: (Q.1 Simplify expressions using order of operations and parentheses, and/or Q.4 Write equations to represent word problems if they finish early) (IXL Learning, 2014). During this time the nine students who have personal iPad’s maybe ustilize them, since the IXL will be easier to use on a desktop or iPad, so five students will use the in class desktops while the other three will work on an Numerical Expressions worksheet which is also encouraged (without technology- sheet attached below)
(Students are completing individual assignments, peer assisting is allowed, and used in conjunction with one on one teacher time walks the aisles to answer questions and assist as needed)
Issue student notes, and homework assignment over the Numerical Expressions Chapter (Read chapter summary and answer and show work for (20) questions - due by the following class period - no technology necessary)
Day 2 Project Fun Day (50 min – WhiteBoard (clicker users) & Socrative software needed)The students desks will be prearranged dividing students into differentiated learning groups (based on the teacher’s observation of their learning abilities as some are more motivated to learn than others); students already know who their group members are based on past group projects. The Real Life “Problem of the Month” (Digging Dinosaurs, and Peer Review rubrics) worksheets will be setup on each student’s desktop (see the attached worksheets). After they are all seated the teacher will explain that this assignment will reinforces their ability to think algebraically and, write and interpret
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simple numerical expressions; as they have acquired these skills from the lecture, activities and homework assignments.
ThisAs it project requires each team to write a numerical expressions with the information provided in the word problem. They can decide if they want to answer the word problem questions individually (then all decide on the best rate), or work through the questions as a unit and (then decide on the best Museum Summer Rate plan) from the ( Level C, Problem of the Month: Digging Dinosaurs word problem) worksheet. This process will evoke student’s cCritical thinking, communication, problem solving, and decision making skills (International Society for Technology in Education, 2007). Explain that they will each utilize the Socrative software to record their group’s best rate answer choice, and while they are collaborating I will pass out twenty dollars - play money to each group for their project. The twenty dollars will be used as proof, “real life proof” that their group successfully interpreted the best rate from the following choices: Plan A, Plan B, or Plan C on the worksheet. Finally groups will present and briefly share their findings with the class. The peer review sheets were given in order to rate each group member based on each individual’s act of group participation during the collaboration efforts and presentation (see the attached rubric). After interpreting the best Plan rate each student will submit the following: individual Digging Dinosaurs worksheets (show work!) and rubrics (show work!), Socrative responses, and the presented cash (recorded as a group), based on the group choice interpreted Plan rate.
As an added bonus to the “Problem of the Month” Digging Dinosaurs word problem, the teacher will then take students on a “real life visit” to the Smithsonian Museum Virtual Tour (Whiteboard technology needed)
(During this time students are in group settings problem solving – their direct responses are required on the pre-installed Socrative technology software within the classroom. The thirteen students who have working mobile devices ((9) iPads, (4) iPhones) will remain seated, while the other four students are allowed to use the classroom clickers. The teacher is observant of student’s responses to material, and updates personal student/teacher observation rubric for the group presentation assessment - as students they complete the task and would be glad to assist as needed).
(5-10 min only if time permits)Students are to remain in their groups as each person is required to select a problem from their text book over the Numerical Expressions chapter, and take turns adding their questions onto a sheet of paper. Student generated quiz/test are often deemed to test what has been taught, and students report that they learn more from reviewing the learning items covered to decide what merits entry into the evaluative task, than from taking the test itself. Ozdeniz,(, (2012).
(During this time while students are inremain in group settings selecting questions, and taking turns to adding their questions onto a sheet of paper for an upcoming quiz, the teacher observes and directs students as they complete the task and assists as needed.)
Issue homework assignment worksheet over Writing Numerical Expressions (attached below). Encourage students to: STUDY (review lecture& IXL/worksheet notes), STUDY (review homework assignments), and STUDY (Practice)!!
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Day Three(Timed 30 min quiz)To measurably assess students numerical expression writing skills, this quizzed assessment will cover students/teacher pre - selected multiple choice, and true/false word problems, and short answer quiz questions on the Socrative software(as the questions will be manually uploaded into the Socrative Teachers portal). Two sheets of scratch paper will be provided for students to show their work. All answers will be recorded onto the teacher’s Socractive portal excel spread sheet. *If a student doesn’t do so well he/she will be given another opportunity to take the assessments, the teacher may need to reteach lesson. Moreover students may also need to attend tutorial session(s) or stay after class for more one on time on the lesson with the teacher and/or peers.
(During this time students will utilize the preinstalled Socrative technology software within the classroom. The thirteen students who have working mobile devices ((9) iPads, (4) iPhones) will remain seated, while the other four students are allowed to use the classroom clickers. The teacher is observant as students calculate their responses; the personal student observation rubric is updated)
Bring lesson to a closure by thanking them for doing their BEST with the project, game and quiz. Let them know how greatly you appreciate their cooperation with their
Numerical Expression Lesson.&
Start the final unit lesson 5.0A.3 (remainder of class time)
Student Assessment and Evaluation
TThe group real life project “Problem of the week” and the quiz (final multiple choice, and true/false word problems, and short answer) are both formal techniques that quiz questions will utilize theon Socrative software, which which is a student response system that makes creating/grading individualized authentic quiz, or test assessments easy for teachers; morehowoever these assessments will prove that the students have met the lesson objectives and have shown growth toward meeting the standard 5.0A.2. TMoreover to determine rather or not tThe selected Digging Dinosaur Real Life Problem of the Month (with Virtual Tour), and the Socrative web-based content software were both formally techniques ; while Algebraic Expressions Millionaire Game, and the IXL web based software and/or Numerical Expression Matching (worksheet below) all informal techniques activities promotes standard growth, will be determined through student (s) interaction with the game and the graded software/worksheet assignment. the Algebraic Expressions Millionaire game, The teacher will also observe the and student (s) ability and/ or /desire to peer assist during the individual practice portion (provided that he/she completed their own work). which utilized the IXL web based software/ Numerical Expression Matching (worksheet below) were all informal techniques used for the teacher to use and assess each students interaction with the lesson.
The Digging Dinosaur real life “Problem of the Month” (with Virtual Tour) group project was used to assess students overall understanding of the 5.0A.2 standard objective. This form of assessment meets my purpose as it reinforces their ability to think algebraically, write and interpret simple numerical expressions; and recognize that 2 x (182 + 191) is three times as large as 182 + 191, without having to calculate the indicated sum or product, .as they have acquired these skills from the lecture, activities and homework assignments; in that they each had to apply their Please Excuse My Dear Aunt Sally
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algorithm to interpret the most cost effective rate plan. Moreover this assessment has met the chosen International Society for Technology in Education (2007), standard as it is reflected in student’s ability to use critical thinking skills (through the interpreting the word problem’s the best rate plan), ability to plan and conduct research (as a group each student is responsible for collecting and analyze data to identify solutions), manage projects (groups are responsible for deciding if they want to answer the word problem questions individually then all decide on the best rate, or work through the questions as a unit), solve problems (as it requires each team to write a numerical expressions with the information provided in the word problem), and to make informed decisions using appropriate digital tools and resources (students can use the Socrative software, to record their group’s best rate answer choice). While tThe purpose of the quizis assessment is to measurably assess students numerical expression writing skills, this quizzed assessment will cover students/teacher preselected multiple choice and true/false word problems and short answer quiz questions on the Socrative software (as the questions will be manually uploaded into the Socrative Teachers portal). This assessment meets my requirements as the Socrative web-based content software is utilized as a convenient aid to assess all students’ ability to meet the requirements of the 5.0A.2 standard objective, as well as in preparation for the No Child Left behind standardized multiple choices, true/ false test.
When asked what can a teachera teacher can do beyond testing and implementing project based learning assessments to determine the degree of which students have mastered the standard objectives?objectives. Smith (2014) replies by stating “Reference a personal student/teacher observation rubric, which can be used as means to determine the degree ofto which your students have mastered your objectives” (personal communication, April 5, 2014). (personal communication).” Moreover Smith’s quality learning advice has been adapted throughout the lesson as I made note of what the teacher will be doing each section (generic rubric attached). Moreover The peer review sheets which were provided to students in order for them to rate each group member based on each individual’s act of group participation during the collaboration efforts and presentation (see the attached rubric) must be submitted, and a quiz grade of ninety or above will also useful in determining which students have mastered my objectives. Moreover the final determinant of mastery which covers not only this lesson, but for entire fifth grade mathematics level is the No Child Left behind standardized test as this assessment applies to both the teacher and student.
I would know if I need to makeHowever mid-course corrections will be needed if the learner(s) is/are s not responding very well with the numerical expression content through the individual learning drill, and/or the group project. I am always concerned when learners are only able to connect with the lesson in group settings and not individually. Candy (2014) suggested “a clean copy of lecture notes for students who cannot write, or have a hard time deciphering their own writing” (personal communication, April 5, 2014)(personal communication.).’ I adapted this suggestion into the lesson plan by creating a lecture note sheet (attached).
SMoreover students may also need to refer to the PEMDAS notes hand out below, make, make arrangements to attend tutorial sessions and/or stay after class for more one on time on the lesson with the teacher and/or peers. Furthermore the teacher can also reassess the lesson presentation by referencing the student/teacher observation rubric to ensure that the lesson delivery is accurate. For future lessons I will suggest to students at the end of each lesson to be proactive and prepare for the next lesson by reviewing it over the weekend before the start of lesson.
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B. Analysis (Rationale)
Rationale for Activities
The use of technology is very useful within autonomy class setting assetting as motivated student interaction activities should be implemented throughout all lesson plans. Incorporating technology can be very helpful to as there are sundries software available for lessons to make the lesson planning process less time consuming. Through quality preparation with the use of visual aids, learner’s memory will be enhanced, while the project “Problem of the Month” with the assistance of the teacher will also allow students to become more excited about working and learning with fellow classmates. ve, Interactive Whiteboards will draw learners' attention, help them concentrate on learning more, and motivate them to learn through the use of graphics, pictures and color which influence learning. Interactive whiteboards and project-based learning like the real world “Problem of the Month” encourage students to work in small groups to practice problem solving together. While covering this lesson content and meeting state standards, these small groups can collaborate to create math word problem presentations, math games and much more! Through quality preparation with the use of visual aids, learner’s memory will be enhanced and with the assistance of their teacher and peers, students will also become more excited about working and learning with fellow classmates as they may also be given an opportunity to judge each other based on a rubric scale. In implementing a well-defined technology integrated lesson plan requires the use of standards, a rationale for activities, and an explanation of technology integration.
This lesson plan reflects upon thee Statestate of Maryland, and ISTE standards which provides a great blueprint for constructing lesson plans. The Maryland Common Core Curriculum Frameworks 5 OA.2: Write and interpret numerical expressions- write simple expression that record calculations with numbers, and interpret numerical expressions without evaluating them; standard was implemented throughout this lesson. The 5.0A.2 standard was met as used the standard’s mathematical practice recommendation with this I made sense of problems and preserve in solving them as demonstrated through the warm up and the Order of Operations PEMDAS model, as I reasoned abstractly and quantitatively this was demonstrated through the use of Socrative responsive software “Problem of the Month” question interpretation, and for the quizzed assessment, I model with mathematics through the use of the PEMDAS model as well, used appropriate tools strategically this includes the use of the Whiteboard PowerPoint to teach and play games, I was attentive to precision with the one method rule of PEMAS, as I looked for and made use of structure by using IXL Learning software and prepared Numerical expression worksheets, and I looked for and expressed regularity in repeated reasoning by utilizing similar word and numerical expressions questions w/ different numbering, reiterated through teaching, and hands on game with the interactive white board.
Moreover the National Educational Technology Standards for Students (2007): Indicator (4) Critical Thinking, Problem Solving, and Decision Making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. This standard has enhanced the “Problem of the Month” word problem. standard as it is reflected in student’s ability to use critical thinking skills (through the interpreting the word problem’s the best rate plan), ability to plan and conduct research (as a group each
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student is responsible for collecting and analyze data to identify solutions), manage projects (groups are responsible for deciding if they want to answer the word problem questions individually then all decide on the best rate, or work through the questions as a unit), solve problems (as it requires each team to write a numerical expressions with the information provided in the word problem), and make informed decisions using appropriate digital tools and resources (students can use the Socrative software, to record their group’s best rate answer choice).
The chosen activities are appropriate for my students as each meets the 5.0A.2 standard mathematical practices suggestion. Moreover technically my teaching theory is based on the merging approaches of objectivists and constructivists teaching/learning strategies. And I believe that education helps promote self-confidence, after completing a challenging task a learner may become more confident in his/her ability and willing to take on the next task. Roblyer and Doering (2013) state that the Scaffolding Learning Theory encourages finding out where a child is in his/her development, and tailor learning exercises to each student’s individual needs and preferences. As it pertains to the direct Numerical Expressions lesson lecture provided in the beginning of the lesson plan, I have also proved that through the “Problem of the Month” word problem project based learning exercise allow the students to actively make their own decisions.
In addition to the order in which I’ve applied the lesson was strategic as the TPACK model and my teaching theory were applied to meet the learning needs of each student. The introducAs the tionintroduction into the lesson through the “Warm up!” served as a refresher- that all of what they have learned in the past is still relevant. My equations of choice for that brief activity were appropriate for this fifth grade group of magnet students, because I referenced the Order of Operations (Please Excuse my Dear Aunt Sally) algorithm. I then mentioned the process of making good/great grades is the very same way as interpreting/ solving equations- it must be done in the correct order! The PowerPoint lecture was covered next as means to directly explain the Numerical Expression lesson as only a teacher would do, and skillfully provide examples utilizing the Order of Operations (PEMDAS) model. Within my PowerPoint lecture I would have used some of Drewisis, Melissa (2012) great SMARTboardSMART board lesson file ideas. However instead of using all of the material Drewisis, Melissa (2012), presented I will instead use nine different -well formatted questions from our class text book to emphasis on throughout the lecture, and students will be provided with opportunities to interact with the whiteboard during the lecture. Those same questions will be reintroduced to students during the following game, and in their homework assignment to reiterate the lesson. Also an emphasis will be placed on introducing the Order of Operations phrase Please Excuse My Dear Aunt Sally algorithm, although some mathematicians don’t agree, as they may say the algorithm confuses learners; however the method is still used widely by teachers and has proven to model math. The game will immediately following the lecture also reinforces the knowledge gained through the previous lecture with similar questions as students are already in interacting with the Whiteboard. The Algebraic Expressions Millionaire Ggame, (2014) will be a success as it provides students with more interactive hands on experience, which in particular is appropriate for this group of learners. As some students may be more motivated by assessments that are presented via video, White/SmartboardSMART board, PowerPoint or collaborative game formats (Barlow & Wetherill, 2005; Mounce, 2008). The IXL Learning software is used last for day one because it is usefulbut for more so though interpreting numerical word problems. Since teachers have limited time for correcting students’ individual practice items IXL drill and practice software can be used as a an
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teachersteacher’s aide in providing feedback to students immediately with well definedwell-defined explanations; thus freeing teachers for work with students (Roblyer & Doering, 2013). The Problem of the Month: Digging Dinosaurs assessment was chosen next because it requires more time to complete. This assessment requires each team to write numerical expressions with the information provided in the word problem. They can decide if they want to answer the word problem questions individually then all decide on the best rate, or work through the questions as a unit and then decide on the best Museum Summer Rate plan from the (Level C, Problem of the Month: Digging Dinosaurs word problem) worksheet. This process will evoke student’s Critical thinking, communication, problem solving, and decision making skills (International Society for Technology in Education, 2007). Finally is used to measurably assess student’s numerical expression writing skills, this quizzed assessment will cover students/teacher pre - selected multiple choice and true/false word problems and short answer quiz questions on the Socrative software.
With seventeen students in my class within a culturally diverse Technology and Engineering (STEM) magnet school setting I may have one or more learners who may be from another country. To accommodate my learners from a wide array of backgrounds I would need to find out if the school offers any resources like reading material to better educate myself on the child’s cultural background such as: their communication, language, food, and /or use of technology. For instance some the behaviors displayed in some cultures are very strict about not making eye contact, and I would also have to consider communication between student and the parent. Moreover, if I should find that the school’s resources are limited I will utilize my school based Personal Learning Network (s) which may include but is not limited to sources like Edmodo, or The Educators PLN for some professional suggestions/tips on their cultural background from colleagues on how to help make my young foreign student (s) feel a part of the class and/or lesson for their optimum learning experience, otherwise I may use a social media network like Twitter. Moreover to accommodate a learner(s) who didn’t quite understand the lesson I will review a few expressions with him/her individually to target the PEMDAS process area he/she didn’t understand; if it’s the math process we are using I will identify the issue then explain the formula again or try another formula that he/she may understand better. Furthermore I may encourage Peer Learning in class which will be beneficial to both children as it will reinforce the lesson for both the child explaining, and the child who’s having trouble. If the applied accommodation doesn’t help the learner gain a better understanding of the material, then his/her parent and/or guardian will be informed that the child will need tutoring.
Past generation teachers have allowed their student suggested quiz/ test questions were generated from a book, and/or lesson notes then written down onto paper then the hardcopy would be submitted to the teacher. Through the integration of technology- Socrative’s teacher portal allows sstudentsstudents to personally add their multiple choice, true /false questions utilizing both aspesctsaspects of the technology software, thereby helping student (s) take standardized tests that comply with the mandates of No Child Left Behind. Moreover, Ozdeniz (2012) states that student generated test questions covers what has been taught, and students report that they learn more from reviewing the learning items covered to decide what merits entry into the evaluative task, than from taking the test itself this can be preformedperformed through a shared teacher’s Socarative portal.Theportal. The problem I solved through technology integration is the lack of enthusiasm for learning; moreover even teachers are more engaged with lessons where technology is involved. This lesson can be covered with or without technology in
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fact a backup lesson plan should also be implemented in case the technology devices fail – I could reference the teacher’s math work book and highlight content areas I would like to discuss and write on the standard white board for examples, as well as utilize worksheets (some of which I have attached below). However without technology for this math lesson Roblyer & Doering , (2013), states “students find basic math, vocabulary and practice skills boring; however when technology is incorporated it will enhance teacher and student motivation as offers attention getting displays, immediate feedback, and interaction.” Technology also saves time, and money print documents while covering lessons. Moreover added value is that the No Child Left Behind Act (2012) also emphasizes the improvement of student achievement in academics with the use of technology in elementary and secondary schools through integration initiatives, building access, accessibility, and parental involvement.
The technology covered throughout this lesson augments student learning; I believe this to be so, as each technology tool used builds upon and reinforces the next, as students learn to model algebraic thinking skills; students will gain a thorough understanding of the numerical expression concept. For example the interactive whiteboard not only provides visuals throughout the teacher’s Numerical Expression content lecture but it also engages students with its interactive touchscreen capabilities during the lecture and after for the Math Play’s Algebraic Expressions Millionaire game a supplement that requires students to identify the correct mathematical expression that models a given word expression. The IXL Learning software provides content drills and practice games can be used as a teacher’s aide in providing great feedback to students immediately with well-defined explanations. While the real world “Problem of the Month’ requires students to collaborate and solve problems (as it requires each team to write a numerical expression with the information provided in the word problem) and make informed decisions using the Socrative software, to record their group’s best interpreted answer. The Socrative response software is also used as a true/false word problems and short answer quiz supplement on mobile devices for this lesson its purpose is to measurably assesses student’s ability to write and interpret numerical expressions. The Socrative response software has made an impression on many teachers as it is transforming the way old way of administering test with hardcopies – as this software saves time and makes the assessment process a lot easier.
Even though all schools have not adopted the use of technology devices; there are many software applications that can be used within computer labs and/or on desktop computers that may prove to be beneficial also. Children often learn through their peers by sharing personal devices for use beyond games and social media. Teachers should not be intimidated by incorporating content area tools. Technology is real life to most of today’s generation of students as it relates to communication and learning. As the generation millennials is extremely dependent upon technology, classroom settings need to be a space that emulates a real-life environment thereby students will have a more positive attitude toward school and student achievement will increase as a result of incorporating technology devices.
C. Reflection
21st Century learners can progress in this technology-driven era through with valuable subject knowledge and the use of technology software, mobile devices, and Interactive Whiteboards and more. The material used in this lesson plan was numerical
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expression content with the aid of the Order of Operations-PEMDAS model, and technology as it is applied through hands on exercises utilizing the following: interactive whiteboard (operated by the teacher, while learners interact), Socrative’s assessment software (used by students for both assessments), and real world “Problem of the Month’ (Socrative and virtual tour) which were all utilized to meet learners needs at any learning level to improve progression. Although I found my first lesson plan challenging, I also consider it to have been an enriching journey as it relates to learning about teaching technology and teaching, my personal future explorations, and learning from peers. I especially like the fact that teachers are able to maneuver creatively their lesson plans around the required State and International Society for Technology in Education (ISTE) standards.
I have found that learning about technology and teaching works hand in hand for me, since I am already comfortable with technology as a former Computer Information Systems major, and former substitute teacher. I have also learned that adjusting the lesson to incorporate technology tools requires a lot of practice drills before class, research and networking to meet to ensure that the technology meets the standards, and not a complete waste of time. Once the technology tools are discovered it will be vital for me to become very familiar with the source and have a quick reference Personal Learning Network in place in when personal assistance is needed, as the school’s instructional technology department may not be readily available. Although I have recently tested the Socrative tool personally and it worked really well, however incorporating it within the classroom would be new for me. I choose this tool because it makes administering a test, quiz or game easy and the students will love the opportunity to use their device. This tool requires students to preinstall the software onto their mobile devices in general, and have the devices fully charged so that the battery life will be preserved during classroom response use.
After reviewing the Maryland State Department of Education (MSDE) standard 5.0A.2 for Fifth Grade mathematics, I considered my knowledge on the standard (which was in compliance, but needed a refreshing review of the necessary material) and ways to incorporate it technically within my lesson based upon the TPACK model which will infuses content knowledge, with technological knowledge, and pedagogical knowledge within the my lesson plan for my class .(Roblyer and Doering, 2013). With the TPACK model approach in mind I selected technology an interactive whiteboard as the new technology device along with the following content web based software programs: IXL Learning, Math Play’s- Algebraic Expressions Millionaire Ggame which all would enrich the lesson. The interactive whiteboard and lesson files were specifically new for me; I choose them because they of the interaction capabilities with the learner(s); although it doesn’t seem to be very difficult to operate I would have rather extensive hands on training by taking ActivInspire Training Courses on the device to fully learn all of the capabilities before implementing it within the classroom. Moreover I found that there are Interactive PowerPoint resource files that can referenced by teachers to help build upon in their lesson. With tThe IXL Learning (2014), the multiple choice, true /false drills will help better prepare learners for their tests, Math Play’s Algebraic Expressions Millionaire gameMillionaire Game was also new to me but after reviewing the content I learned that it met the standard requirements and would be interesting to my leaners, as well as self-explanatory provides great feedback if the wrong answer is selected.
This lesson on writing and interpreting numerical expressions has brought back many memories for me as I so enjoyed algebra as adolescent and teenager. However as a
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teacher in this case finding: technical visuals and/or worksheets, determining which devices and/or software would be best suited for the lesson, as well as project based learning references to meet the 5.OA.2 standard was a little difficult for me, as I had to adapt them into my classroom structure. Moreover adjusting Inside Mathematics (2012) the word problem of the month: Digging Dinosaurs to meet the needs of my classroom was a little time consuming but while I preserved the original Museum concept, I adjusted it to seem more real life for my fifth grade class by: adjusting the word problem, issuing play money, and including a virtual tour. I’ve learned that in being time conscious in the development of a well-timed lesson was a bit of a stretch, as I wanted to make sure that I addressed every area of learning for my well-deserved students; this includes being active as the teacher in not only teaching the class directly as a whole but on an individual bases (which sometimes can be a little difficult in larger classroom settings-in this case I will feel comfortable allowing peer- assisting), I also realize that in fact most students require more time to absorb the lesson and/ or technology- so allocating time for “one-on-one” learning time is necessary for me to incorporate as a professional teacher.
I have learned that incorporating technology requires strategic planning. Regardless the of the technology integration strategy they used, teacher’s need a planning approach to ensure their strategy will be successful, the TIP model provides a helpful guide on the procedures and issues to address (Roblyer & Doering, 2013). Within my technology integration strategy I will also have backup lesson plan that does not require technology, because as exciting and motivating technology maybe, is the fact of the matter is that “Technology is great when it works!” “ I’ve applied the differentiation idea from our class discussion in to my lesson plan, with the aid of . I a utilized a personal teacher/student observation rubric assessment to implement the differentiated learning group approach (based on their learning abilities as some are more motivated to learn than others), beginning with the “Problem of the Month” exercise.
In my future explorations I absolutely plan to implement technology within my classroom or as a floating instructional technology specialist. Moreover I will also continue to exercise my research capabilities and continue to locate great content based software which meets the Common Core Curriculum requirements for students, and become a great resource for colleagues, family and friends. The next time I explore a similar lesson I should have the software I would create my very own interactive whiteboard lesson over the standard, and I would like for my students to use the software and Whiteboard to build upon their project based learning assignment(s). Moreover my concern about future implementation of this lesson includes the following questions: Wwill an Interactive Whiteboard be readily available for me to utilize, once I’m working in a school setting? If so will it be in my personal class or will I have to borrow it from the Media center? How many computers will be in my classroom? Will I have a similar class size? Will I more than likely purchase my own classroom technology equipment? The Peer learning review experience has been good for my helping me develop my lesson plan, although I already had a general idea as to how they are formed based on personal experience, and the assignment guidelines. Learning from Peer Review pending below Learning from Peer Review: pending
I valued the opinions of my group members as Janet and Susanne who are both professional teachers were able to offer great advice on forming my lesson plan ____. We all collaborated on Google Docs which is a great source although it had a few formatting glitches in the software with loading images, etc. – furthermore I would use it
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again in the near future. Susanne asked detailed insight in the development of my lesson plan such as: “What would you do if students don’t do so well on the quiz assessment?” After the quiz I noted: If a student doesn’t do so well he/she will be given another opportunity to take the assessment the teacher may need to reteach lesson. Moreover students may also need to attend tutorial sessions or stay after class for more one on time on the lesson with the teacher and/or peers; She also added that “make sure you stick with the content of the standard” as she didn’t want me to get too involved with technology that I lose sight of the actual lesson- I then reviewed my material and updated Day One’s, Warm Up by ensuring that learners were not evaluating but interpreting their answers. I’ve learned about the great uses of commercial building using the iPad and the iMovie application software for her eighth grade language arts standard, Susanne will use her lesson the week of April 7th . While I learned about Voki from LaVon, I’ve learned about the great uses of commercial building using the iPad and the iMovie application software for her eighth grade language arts standard, Susanne will use these Janet suggested “a clean copy of lecture notes for students who cannot write, or have a hard time deciphering their own writing” (personal communication, April 5, 2014). I adapted this suggestion into the lesson plan by creating a lecture note sheet (attached). I learned more about Janet’s interest in the Westward Expansion comes at the end of Unit III Interactions in American History as she utilized a Whiteboard for her presentation as she split students up into groups to visit to the computer the computer lab to each personally view a YouTube video on the content. LaVon offered assistance by editing my plan and asked “What will you do if students can’t stay afterschool?” I then referenced Janet’s advice and issued lecture notes. I learned about LaVon’s choose of technology through the use of Voki’s for his Reading and Special Education lesson plan, which are talking Avatars students must add their voice in order to meet the standards and to demonstrate an ability to be articulate and passionate in persuading someone to go watch a film. I would utilized each of their choices of technology as each choice could be creatively flexible in meeting any standard’s requirement. I generally agree with the process of peer reviews, however in the future I think it would be a good idea to have the suggestions question on the peer review form.
Creating a technology integrated lesson plan is a process that required a well-defined plan, as it is also important in preventing unnecessary problems from occurring during a lesson. Although the technology and standards used throughout this lesson can be applied differently, the 21st century magnet school students can fair well with the material and structure of this lesson over Numerical Expressions. Moreover, having this detailed plan in the classroom, will also help me stay organized and prevent procrastination. Moreover having an opportunity to ideally teach technology, share my personal future explorations, and learn from my peers was a valuable experience. In conclusion pending
Once your colleagues have given you feedback on your lesson plan, please add to your reflection the following:
Learning from Peer Review: pending
I valued the opinions of my group member as Janet and Susanne are both professional teachers were able to offer great advice on forming my lesson plan ____. We all collaborated on Google Docs which is a great source although it had a few formatting glitches in the software with loading images, etc. – furthermore I would use it again in the near future. I learned about Voki from LaVon, I’ve learned about the great uses of
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commercial building using the iPad and the iMovie application software for her eighth grade language arts standard, Susanne will use these
What did you learn from the peer review process? o How did you change your lesson plan in response to the comments of your
classmates? If you rejected aspects of the peer review feedback, explain. (Be specific.)
o What did you learn about using technology from reviewing your colleagues’ lesson plans? (Be specific.)
And finally, from experiencing the peer review process, what suggestions do you have about for peer reviews in the future? (Remember to include the peer review comments you made with your lesson plan.)
D. References and Annotated Referencees
Barlow, C. L., & Wetherill, K. S. (2005). Technology + Imagination = results. T.H.E. Journal 33, 20-22, 24. 26. Retrieved fromhttp://www.thejournai.com/articles/17431_l
The following is used to reinforce learning:(reinforce)The Algebraic Expressions Millionaire Game, (2014) will be a success as it provides students with more interactive hands on experience, which in particular is appropriate for this group of learners. As some students may be more motivated by assessments that are presented via video, White/SMART board, PowerPoint or collaborative game formats (Barlow & Wetherill, 2005; Mounce, 2008).
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Big Ideas. (2014). Writing Expressions. Retrieved from http://www.bigideasmath.com/protected/content/ipe_cc/grade%206/01/g6_01_02.pdf
The following is used to reinforce learning:Issue student notes, and homework assignment over the Numerical Expressions Chapter (Read chapter summary and answer and show work for (20) questions - due by the following class period - no technology necessary)
J. Candy, Janet (personal communication, April 4, 2014). (2014). EDTC 600, Group Colleague’s advice.The following is used to reinforce learning:“AA clean copy of lecture notes for students who cannot write, or have a hard time deciphering their own writing would be useful?” I adapted this suggestion into the lesson plan by creating a lecture note sheet (attached).
Drewisis, Melissa. (2012). Grade 5 Common Core Numerical Expressions SMARTboard lesson. Teachers pay Teachers an open marketplace for educators. Retrieved from http://www.teacherspayteachers.com/Product/Grade-5-Common-Core-Numerical-Expressions-SMARTboard-lesson-372849
The following is used to reinforce learning:While using the Interactive Whiteboard technology tool and some(explained in the analysis section) of the great Numerical Expressions PowerPoint lesson files by Drewisis, Melissa (2012), which includes the following content: a warm up, definition notes, master key word list generated through her initial warm up, and more problem solving interactive examples. However I will only utilize the following from slides from the PowerPoint’s ready-made visual: definitions and interactive slide where the addition and subtraction words are hidden (students can just click in the box to make them appear). instead the using the suggested order of operations through the analysis of simplified expressions, I will attempt to make it more personable by utilizing the order process from my childhood learning experience with the Please Excuse My Dear Aunt Sally algorithm, which is still being used as means to help learners better understand to the Algebraic process. This sequence will help students memorize, because although the writing of numerical expressions can be a simple process it still needs to follow an order to help learners interpret the right answer. I will also incorporate nine different -well formatted questions from our class text book to emphasize on during the Whiteboard lecture instead the suggested lesson file problems. Those same questions will be reintroduced to students during the following game, and in their homework assignment to reiterate the lesson. Although many may contend that the general PEMDAS algorithm technique has caused misconceptions and confusion for students thereby suggesting students to discover the order through an analysis of simplified expressions which will not covered in this lesson as it is covered in other teacher lessons. Moreover instead the using the suggested order of operations through the analysis of simplified expressions, I will attempt to make it more personable by utilizing the order process from my childhood learning experience with the Please Excuse My Dear Aunt Sally algorithm, which is still being used as means to help learners better understand to the Algebraic process. This sequence will help students memorize, because although the writing of numerical expressions can be a simple process it still needs to follow an order to help learners interpret the right answer.
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Image. (2010). Retrieved from http://www.mahalo.com/pemdas/The image is a visual to reinforce learning this is located on the (attached) lecture notes document.
Inside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
The following is used to reinforce learning:This was Real life problem was utilized in day two of my lesson plan I used it as an assessment. I adapted and changed the a substantial amount of information on this, while preserving the Museum and word problem concept I wanted become more real life for my students so I revised the original word problem (per the attachment), I incorporated play money, and a virtual tour for students.
International Society for Technology in Education. (2007). NETS for Students 2007. Critical Thinking, Problem Solving, and Decision Making. Retrieved from http://www.iste.org/standards/standards-for-students/nets-student-standards-2007
IXL Learning. (2014). Retrieved from http://www.ixl.com/math/grade-5 (reinforce)The following is used to reinforce learning:Have students use the IXL Learning mathematics software that would enhance the lesson on use of order of operations. Students are to practice answering questions from the Algebra section: Q.1 Simplify expressions using order of operations and parentheses, and/or Q.4 Write equations to represent word problems if they finish early (IXL Learning, 2014).
Maryland Common Core Curriculum Frameworks. (2014). Mathematics Grade 5. Retrieved from
http://www.mdk12.org/instruction/commoncore/index.html
National Board for Professional Teaching Standards. (2003). Early adolescence and young adulthood English language arts portfolio. Arlington, VA: AuthorNo Child Left Behind. 2012 Retrieved from http://www.ed.gov/legislation/ESEA02/
Also emphasizes the importance of incorporating technology: Technology also saves time, and money print documents while covering lessons. Moreover added value is that the No Child Left Behind Act (2012) also emphasizes the improvement of student achievement in academics with the use of technology in elementary and secondary schools through integration initiatives, building access, accessibility, and parental involvement.
Ozdeniz, D. (2012). Apps for Learning with iPads. Perspectives (TESOL Arabia), 19(3), 28-30.
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The following is used to reinforce learning:
Past generation teachers have allowed their student suggested quiz/ test questions were generated from a book, and/or lesson notes then written down onto paper then the hardcopy would be submitted to the teacher. Through the integration of technology- Socrative’s teacher portal allows students to personally add their multiple choice, true /false questions utilizing both aspects of the technology software, thereby helping student (s) take standardized tests that comply with the mandates of No Child Left Behind. Moreover, Ozdeniz (2012) states that student generated test questions covers what has been taught, and students report that they learn more from reviewing the learning items covered to decide what merits entry into the evaluative task, than from taking the test itself this can be performed through a shared teacher’s Socarative portal. (reinforce)
Pennsylvania Department of Education. (2014). Writing and Interpreting Numerical Expressions. Retrieved from http://www.pdesas.org/module/content/resources/6136/view.ashx
The following is used to reinforce learning:The writing numerical expressions and expression matching worksheets (attached below) will aid students for an in class assignment (without technology), as well as a homework assignment.
Popovici, Doina. (2010). Math Play. Algebraic Expressions Millionaire. Retrieved from
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions- millionaire.html
The following is used to reinforce learning:This Algebraic Expressions Millionaire game is used as reinforcement and will be played online alone in two teams. For each question students will have to identify the correct mathematical expression that models a given word expression.
L.D. Smith , Lynise. (personal communication, April 5, 2014). Retired Teacher’s veteran advice.
The following is used to reinforce learning:Refer to a personal observation rubric, which can be used as means for you to determine the degree to which your students have mastered your objectives. I have adopted this idea throughout the lesson in the as I mentioned in each section that “the teacher also is observant of students responses to material, and updates personal student/teacher observation rubric” as we covered the lecture, game, individual web based learning, project based learning and finally on the quiz
Smithsonian National Museum of Natural History. (201) Retrieved from http://paleobiology.si.edu/dinosaurs/interactives/tour/main.html
The Tour was used to reinforce learning in attempts of making the “Problem of the Month” become more real life.
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Socrative. (2014). Retrieved from http://www.socrative.com/compatibility
(software installed on mobile devices and desktops) This software is installed on mobile devices and desktops in order to provide deeper learning enrichment for students to utilize their personal technology devices, or provided clickers within the classroom. Socrative software is used during the assessment portion of the lesson plan.deeper enrichment
Robllyer, M. D., & Doering, A. H. (2013). Integrating Educational Technology into Teaching. New York: Pearson.
The following is used to reinforce learning:Technology as it is applied with hands on exercises utilizing the following: Interactive WhiteBoard (operated by the teacher, while learners interact), Socrative’s assessment software (used by students for both assessments), and Real World Problem of the Month world problem (Socrative and virtual tour).Without technology for this lesson students find basic math, vocabulary and practice skills boring; however the technology will enhance teacher and student motivation as it offers attention getting visuals, immediate feedback, and interaction (Roblyer & Doering, 2013).
The problem I solved through technology integration is the lack of enthusiasm for learning; moreover even teachers are more engaged with lessons where technology is involved. This lesson can be covered with or without technology in fact a backup lesson plan should also be implemented in case the technology devices fail – I could reference the teacher’s math work book and highlight content areas I would like to discuss and write on the standard white board for examples, as well as utilize worksheets (some of which I have attached below). However without technology for this math lesson Roblyer & Doering (2013), states “students find basic math, vocabulary and practice skills boring; however when technology is incorporated it will enhance teacher and student motivation as offers attention getting displays, immediate feedback, and interaction.”
After reviewing the Maryland State Department of Education (MSDE) standard 5.0A.2 for Fifth Grade mathematics, I considered my knowledge on the standard (which was in compliance, but needed a refreshing review of the necessary material) and ways to incorporate it technically within my lesson based upon the TPACK model which will infuses content knowledge, with technological knowledge, and pedagogical knowledge within the my lesson plan for my class (Roblyer and Doering, 2013). With the TPACK model approach in mind I selected technology an interactive whiteboard as the new technology device along with the following content web based software programs: IXL Learning, Math Play’s- Algebraic Expressions Millionaire Game which all would enrich the lesson.
The IXL Learning software is used last for day one because it is useful for interpreting numerical word problems. Since teachers have limited time for correcting students’ individual practice items IXL drill and practice software can be used as a teacher’s aide in providing feedback to students immediately with well-defined explanations; thus freeing teachers for work with students (Roblyer & Doering, 2013).
I have learned that incorporating technology requires strategic planning. Regardless of the technology integration strategy used, teacher’s need a planning approach to ensure
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their strategy will be successful, the TIP model provides a helpful guide on the procedures and issues to address (Roblyer & Doering, 2013). Within my technology integration strategy I will also have backup lesson plan that does not require technology because as exciting and motivating technology maybe, the fact of the matter is that “Technology is great when it works!”
Rubistar. (2008) Create Rubrics for your Project-Based Learning Activities RetrievedActivities. Retrieved from http://rubistar.4teachers.org
This rubric can be used to help differentiated group member assess their peers.
TeachThought. (2014). Building Rubrics. Retrieved from http://www.teachthought.com/wp-content/uploads/2013/09/rigor-rubric-fi.jpg
This is used as the teacher’s personal guide to assess student’s mastery of a lesson.
http://www.learningfarm.com/web/demoExpired.cfm?&CFID=3286304&CFTOKEN=2b0740852a480815-27270E60-C598-8893-47A5A3CFACFA8A31
Drewisis, Melissa (2012) Also I will incorporate nine different -well formatted questions from our class text book to emphasize on during the Whiteboard lecture instead the suggested lesson file problems. Those same questions will be reintroduced to students during the following game, and in their homework assignment to reiterate the lesson.
Although many may contend that the general PEMDAS algorithm technique has caused misconceptions and confusion for students thereby suggesting students to discover the order through an analysis of simplified expressions which will not covered in this lesson as it is covered in other teacher lessons. Moreover instead the using the suggested order of operations through the analysis of simplified expressions, I will attempt to make it more personable by utilizing the order process from my childhood learning experience with the Please Excuse My Dear Aunt Sally algorithm, which is still being used as means to help learners better understand to the Algebraic process. This sequence will help students memorize, because although the writing of numerical expressions can be a simple process it still needs to follow an order to help learners interpret the right answer.
E. Preview of Lesson Plan Implementation
I am not a teacher yet.
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References
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Student Lecture Notes
For example: Write each phrase as a numerical expression
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Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction P.E.M.D.A.S.
Phrase Consider the determining factors for PEMDAS
Interpret Numerical Expression Results
Three less thanthe quotient of
8 and 2
Less than (-)Quotient (/)
8/ 2 – 3
Twice as much asthe difference of 8 and 3
Twice as much (x),Difference (-)
2 × (8 – 3)
Eight more than the product of 3 and 2 More (+)Product (x)
8 + 3 × 2
The sum of 8 and 3 divided by 2 Sum (+)(/)
(8 + 3)/ 2
Five less than the quotient of 6 and 2 Less than (-)Quotient (/)
(6/2) – 5
Vocabulary terms to know:• numerical expression • Parentheses• order of operations • Brackets
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Day 1 game:Popovici, Doina. (2010). Math Play. Algebraic Expressions Millionaire. Retrieved from
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions- millionaire.html
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Day one - In class worksheet. This can be used for additional (take home) practice.Pennsylvania Department of Education. (2014). Writing and Interpreting Numerical Expressions.
Retrieved from http://www.pdesas.org/module/content/resources/6136/view.ashx
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Day one - In class worksheet. This can be used for additional (take home) practice.Pennsylvania Department of Education. (2014). Writing and Interpreting Numerical Expressions.
Retrieved from http://www.pdesas.org/module/content/resources/6136/view.ashx
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Day one - In class worksheet. This can be used for additional (take home) practice.Pennsylvania Department of Education. (2014). Writing and Interpreting Numerical Expressions.
Retrieved from http://www.pdesas.org/module/content/resources/6136/view.ashx
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Writing Numerical Expressions
Augusto earned $50 last month mowing lawns. Peiyi earned $40 less than twice as much as Augusto. How much did Peiyi earn?
Jeanna has a 3-year-old brother and a 5-year-old brother. Jeanna is four years older than the sum of the ages of her brothers. How old is Jeanna?
Jeanna’s father is 7 years younger than 9 times the age of her older brother. How old is Jeanna’s father?
To find the age of Jeanna’s grandmother, begin with 100 and subtract the product of the ages of Jeanna’s brothers. How old is Jeanna’s grandmother?
Tao has 48 baseball cards. His friend, Kian, has 93 baseball cards. Lakeo has 14 less than the total that Tao and Kian have. How many baseball cards does Lakeo have?
David says, “I have 3 more than five times as many baseball cards as Tao.” How many baseball cards does David have in his collection?
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Writing Numerical Expressions—KEY
Augusto earned $50 last month mowing lawns. Peiyi earned $40 less than twice as much as Augusto. How much did Peiyi earn?
(2 × 50) – 40 or
2 × 50 – 40
Jeanna has a 3-year-old brother and a 5-year-old brother. Jeanna is four years older than the sum of the ages of her brothers. How old is Jeanna?
4 + (5 + 3) or
(5 + 3) + 4 or
5 + 3 + 4
Jeanna’s father is 7 years younger than 9 times the age of her older brother. How old is Jeanna’s father?
(9 × 5) – 7 or
(5 × 9) – 7 or
9 × 5 – 7
To find the age of Jeanna’s grandmother, begin with 100 and subtract the product of the ages of Jeanna’s brothers. How old is Jeanna’s grandmother?
100 – (3 × 5) or
100 – 3 × 5
Tao has 48 baseball cards. His friend, Kian, has 93 baseball cards. Lakeo has 14 less than the total that Tao and Kian have. How many baseball cards does Lakeo have?
(48 + 93) – 14 or
48 + 93 – 14
David says, “I have 3 more than five times as many baseball cards as Tao.” How many baseball cards does David have in his collection?
(5 × 48) + 3 or
5 × 48 + 3 or
3 + 5 × 48
Day two – homework sheet.Pennsylvania Department of Education. (2014). Writing and Interpreting Numerical Expressions.
Retrieved from http://www.pdesas.org/module/content/resources/6136/view.ashx
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Problem of the Month: Digging Dinosaurs
The Problems of the Month (POM) are used in a variety of ways to promoteproblem‐solving and to foster the first standard of mathematical practice from theCommon Core State Standards: “Make sense of problems and persevere in solvingthem.” The POM may be used by a teacher to promote problem‐solving and toaddress the differentiated needs of her students. A department or grade level mayengage their students in a POM to showcase problem‐solving as a key aspect ofdoing mathematics. It can also be used school wide to promote a problem‐solvingtheme at a school. The goal is for all students to have the experience of attackingand solving non‐routine problems and developing their mathematical reasoningskills. Although obtaining and justifying solutions to the problems is the objective,the process of learning to problem‐solve is even more important.The Problem of the Month is structured to provide reasonable tasks for all studentsin a school. The structure of a POM is a shallow floor and a high ceiling, so that allstudents can productively engage, struggle, and persevere. The Primary VersionLevel A is designed to be accessible to all students and especially the key challengefor grades K – 1. Level A will be challenging for most second and third graders.Level B may be the limit of where fourth and fifth grade students have success andunderstanding. Level C may stretch sixth and seventh grade students. Level D maychallenge most eighth and ninth grade students, and Level E should be challengingfor most high school students. These grade‐ level expectations are just estimatesand should not be used as an absolute minimum expectation or maximum limitationfor students. Problem‐solving is a learned skill, and students may need manyexperiences to develop their reasoning skills, approaches, strategies, and theperseverance to be successful. The Problem of the Month builds on sequential levelsof understanding. All students should experience Level A and then move through thetasks in order to go as deeply as they can into the problem. There will be thosestudents who will not have access into even Level A. Educators should feel free tomodify the task to allow access at some level.
Overview:In the Problem of the Month Digging Dinosaurs, students use algebraicthinking to solve problems involving multiple answers, optimum solutions,variables, and functions. The mathematical topics that underlie this POM areequations, optimization, variables, functions, and linear and non‐linear patterns.In the first levels of the POM, students view a drawing of eight dinosaur feetunder the water. Their task is to determine multiple solutions for answering thequestion of how many dinosaurs are standing in the water. As one continuesthrough the levels, students analyze different rate plans in order to visit a museum.The purpose is to determine the least expensive plan for a given group and thefrequency of their visits. In the final levels of the POM students examine a table ofdata that is linear and then later non‐linear. Students are asked to define a rule forboth situations. In the context of these situations, students focus on algebra andfunctions.
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Inside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
Mathematical Concepts:Algebra is the cornerstone of secondary mathematics. Algebraic thinking is taught inprimary grades with the foundations of algebra taught usually by the end of middleschool. Even though the term algebraic thinking is routinely used, it can not besimply defined. The underpinnings of algebra involve abstractions and language.Identifying the conceptual understandings students must learn about algebra isparamount. One resource is Fostering Algebraic Thinking.A facility with algebraic thinking includes being able to think about functionsand how they work and to think about the impact that a system’s structures has oncalculations. These two aspects of algebraic thinking are facilitated by certain habitsof mind.
Doing –Undoing. Effective algebraic thinking sometimes involves reversibility (i.e.,being able to undo mathematical processes as well as do them). In effect, it is thecapacity not only to use a process to get to a goal, but also to understand the processwell enough to work backward from the answer to the starting point....
Building Rules to Represent Functions. Critical to algebraic thinking is the capacityto recognize patterns and organize data to represent situations in which input isrelated to output by welldefined rules...
Abstracting from Computation. This is the capacity to think about computationsindependently of particular numbers that are used. One of the most evidentcharacteristics of algebra has always been its abstractness. But, just what is beingabstracted? To answer this, a good case can be made that thinking algebraicallyinvolves being able to think about computations freed from the particular numbersthey are tied to in arithmetic – that is, abstracting system regularities fromcomputation....(Driscoll, 1999)
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Inside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
Problem of the Month Digging Dinosaurs Page 1
ORIGNAL COPY
If you and your brother and/or sister want to go to the museum eight times during the three months of summer, which one plan should you use and when should you go to save the most money?
What if you can’t go as you originally planned what other plans might you use?
State when you would attend and the best plan(s) to use. Explain your thinking.
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Day two:
Original CopyInside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from
http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
Level C:
It is spring and you can go to the museum more often. The rates change for spring specials.
Museum Spring Rate Plans
Plan A: $2.75 per person to visit the museum.
Plan B: Monthly membership is $7.50 for each person, but you can go as many times as you like during the month.
Plan C: A class group membership for a month is $15.25. Everyone in your class group can go as often as they like for a month.
If you and your group member and/or another group member want to go to the museum eight times during the three months of spring, which one plan should you use and when should you go to save the most money?
What if you can’t go as you originally planned what other plans might you use?
State when you would attend and the best plan(s) to use. Explain your thinking.
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Inside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
Day two Jennifer Smith’s Adjusted Copy:Jennifer Smith’s Adjusted CopyInside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdfProblem of the Month Digging Dinosaurs Page 3
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Inside Mathematics. (2012). Problem of the Month: Digging Dinosaurs. Retrieved from http://www.insidemathematics.org/problems-of-the-month/pom-diggingdinosaurs.pdf
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Rubistar. (2008) Create Rubrics for your Project-Based Learning Activities. Retrieved from http://rubistar.4teachers.org
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TeachThought. (2014). Building Rubrics. Retrieved from http://www.teachthought.com/wp-content/uploads/2013/09/rigor-rubric-fi.jpg
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