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 =__Lesson 1 by Heidi Miller__=

1. SOL 5.3 **–** The student will create and solve problems involving addition, subtraction, multiplication, and division of whole numbers. . **.**  2.   21st Century Skill: Learning and innovation skills (creativity and innovation, critical thinking and problem solving, etc.), Media and technology skills, 3.  Tools: Flip Camera 4.  Explanation: Students will create a taped performance of a math problem. The goal will be to illustrate a math problem without seeing numbers. Students will need to dramatize a word problem using addition, subtraction, multiplication or division. The skit must have a beginning, a middle and the solution will be the conclusion. There must be drama in the performance in that it has to appeal to an emotion, and the audience will have to write down and solve the math problem that is embedded in the skit. 5.  An example could be students setting up desks to represent a bus full of people, then they could act as if the bus were driving down the road, but as the bus drives down the road, it crashes and everyone is thrown from their chairs. All the students stay on the floor except one who climbs over everyone and walks out of the wreckage to go look for help. Another example could be a person in his/her front yard with a soccer ball all alone and is sad. He begins juggling the ball. As the person juggles the ball a stranger comes over and joins in. Then another one comes over and another and another until there are 15 people juggling the ball in a big circle, and the sad lonely person now has lots of friends.

=__Lesson 2 by Heidi Miller__= 1. 5.4: The student will find the sum, difference, and product of two numbers expressed as decimals through thousandths, using an appropriate method of calculation, including paper and pencil, estimation, mental computation, and calculators. 2. 21st Century Skill: Global Awareness, Critical Thinking and Problem Solving, Information Literacy 3. Tool: Wikipedia 4. Explanation: The students will divide into groups of approximately 4. They will look up Nantucket, Massachusetts and Martha’s Vineyard on Wikipedia in order to find the answers to the following questions. As a group, they will brainstorm, and sift through the information to find the answers. The group that finds all the correct answers first will win a prize, but they also have to explain to the losing groups how they found the answers. Answers can not be shouted out or the group will be disqualified, they must be submitted on paper so that the teacher can decide when the time is appropriate to go over the assignment. 5. The questions are as follows: a. What is the combined total land mass of Martha’s Vineyard and Nantucket, Massachusetts? (Marth = 87.48, Nan = 47.8 Add them together, 135.28) b. What is the difference in size between the two places? (subtract them, 39.68) c. How many Nantucket’s would fit on Martha’s Vineyard? Your answer must be expressed in decimals rounded to the nearest thousandths. (divide 87.48 by 47.8. The answer is 1.830)

=__Lesson 3 by Heidi Miller__= 1.  SOL 5.7: The student will add and subtract with fractions and mixed numbers, with and without regrouping, and express answers in simplest form. Problems will include like and unlike denominators limited to 12 or less. 2. 21st Century Skill: Critical Thinking and Problem Solving 3. Tool: Gliffy 

Flowchart Example [|Learn more about our online flow chart software] <span style="font-size: 8.5pt; color: #202020; line-height: 115%; font-family: 'Arial', 'sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;"> <span style="font-size: 12pt; color: #202020; line-height: 115%; font-family: 'Arial', 'sans-serif'; msolist: Ignore; mso-fareast-font-family: Arial; msofareastfontfamily: Arial;">4. <span style="font-size: 12pt; color: #202020; line-height: 115%; font-family: 'Arial', 'sans-serif';">Explanation: Students will create a flow chart explaining the process of adding and subtracting mixed numbers. Students will work in pairs. The teacher will give each pair a different problem to work through in a flow chart. This activity has been preceded by several lessons on adding and subtracting mixed numbers and how to create flow charts in Gliffy. The flow charts will then be shared with the class and displayed around the room. The picture above demonstrates a type of flowchart that can be used. <span style="font-size: 12pt; color: #202020; line-height: 115%; font-family: 'Arial', 'sans-serif'; msolist: Ignore; mso-fareast-font-family: Arial; msofareastfontfamily: Arial;">5. <span style="font-size: 12pt; color: #202020; line-height: 115%; font-family: 'Arial', 'sans-serif';">Examples of different items in the flow chart: Students can explain the step-by-step thought process that they go through when they work a problem. They will also explain how to convert a mixed number into an improper fraction and how to reduce the fraction at the end of the problem.

=__Lesson 4 by Kim Doucette__=

<span style="font-size: 80%; font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; msofareastfontfamily: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';"> =<span style="font-size: 80%; font-family: Arial, Helvetica, sans-serif;"><span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">5 .8 The student will describe and determine the perimeter of a polygon and the area of a square, rectangle, and right triangle, given the appropriate measures. = = =  21st Century Skills: Problem solving, creativity, communication Technological Component: Smart Board, computer lab, [] program availability on machines to be used = Explanation: = = = == <span style="font-family: Arial, Helvetica, sans-serif; msobidifontsize: 14.0ptmsoBidiFontSize;">2. First, the site will be used by the instructor with the assistance of an e-beam or smart board to teach the functions: “Bands” is chosen to stretch the rubberbands on the pegs and draw the shape. Next the shape is colored by clicking on one of the paint squares. Finally the area and perimeter can be checked by clicking on the “measures” button. “Clear” clears the board for the next drawing and “delete” takes off one shape at a time. Students will be taken through the exercise with each of the above listed shapes. The area and perimeter will be calculated by the class…then the feature button clicked to tabulate the answer. The answer will be discussed and clarified, if needed. 3. After some work with area/peremeter and the virtual Geoboard has occurred, the computer lab will be used for each child to explore area and perimeter with one-dimensional shapes. 4. Students will not only be able to check their answers, but also see WHY the answer is what it is using the virtual manipulatives. =<span style="font-family: 'Century Gothic'; msobidifontsize: 14.0pt; mso-bidi-font-size: 14.0pt; msospacerun: yes;"> = = __Lesson 5 by Kim Doucette__ = = = 5.9 The student will identify and describe the diameter, radius, chord, and circumference of a circle. 21st century skills: Collaboration, problem solving, using technology and media Explanation: Students will work in teams of two to practice/quiz each other with identifying and describing the components of a circle. Using a real time whiteboard [|www.scriblink.com], the students will use both the virtual white board component to ask and answer questions (illustrations and text). Moreover, the chat component may be used in order to assist each other at coming up with the correct answers, or looking at data differently. Students taking part in this lesson will do so as review, however, this tool is a great one to use in introduction of skills, if the instructor and students are both working on the whiteboard together. There will be two components of the lesson shown in the screen prints below: 1) students will review the terminology/definitions of a circle’s terminology: == 2) The students will take turns asking and answering questions like the ones shown below: (Depending on the level of students, students may either come up with their own question, use their textbook for samples, or use a teacher generated list) == == =__Lesson 6 by Sue Keffer__=
 * 1) This lesson utilizes the Geoboard function at the National Library of Virtual Manipulatives website. The Geoboard will be used to show how to find both area and perimeter of polygons, squares, rectangles, and right triangles…as well as the differences in area and perimeter.
 * SOL 5.10: The student will differentiate between perimeter, area, and volume and identify whether the application of the concept of P, A, or V is appropriate for a given situation.**


 * 21st Century Skill**: Critical Thinking and Problem Solving


 * Tools**: Photo Story or Voicethread

(If done through photo story this could be set up as a center in a classroom with children solving or if done w/voicethread could be interactive as a center)
 * Explanation**: Students will create or download a picture to represent a situation that will involve finding P, A or V. Create and record the problem situation and challenge children to find the solution.

~ You just bought some fish and a fish tank. The measurements of the tank are...if the tank is to be filled 2/3 of the way with water, how much water is needed? Picture would be of the fish tank.
 * Examples of possible problems**:

~ You just got a new puppy and are fencing a portion of the back yard. You must fence the yard (you might include some tricks like a deck to go around, or connecting to a neighbor's fence). What is the distance needed to fence? Picture would be a yard or a diagram of the yard in the problem.

= __Lesson 7 by Kim Doucette__ =

<span style="font-size: 13pt; font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">5.12 The student will determine an amount of elapsed time in hours and minutes within a 24-hour period. <span style="font-weight: normal; color: black; font-family: 'Century Gothic'; mso-bidi-font-weight: bold;">21st Century Skills : Creativity, communication, problem solving, collaboration Internet Tool: an online planner program like the free Zoho planner ([|www.planner.zoho.com]), smart board or e-beam Explanation: <span style="color: black; font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">1. Students will work in small groups on the online planner to make a “day in the life of Joe Student”. They will write times and tasks for a twenty-four hour period and save them. <span style="color: black; font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">2. Example:



3. Next, students will print their planner page (print screen function).

4. These planner pages will be re-distributed to another group of students who will write elapsed time questions for the events/times listed on the planner they’ve received. Sample questions will be given to ensure correct format. ie: Jenny wakes up at 7:30 and her bus comes to pick her up at 8:12. How much time will Jenny have to get dressed, brush her teeth, and eat her breakfast? Or Jose gets home from school at 4:37. His mom comes home at 6:00. He is to spend 45 minutes on his homework before she comes home – and make dinner. How much time does Jose have to prepare dinner? 5. Once questions are written, the original group will receive their planner back…along with the questions written….to answer together. 6. * The use of a smart board to do steps 1-4 together as a group, before this activity is performed alone would be a great tool. <span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">6. The stem and leaf plot will be copied (ctrl/c) and pasted (ctrl/v) to become the next slide on the PPT. Just as before, students will use the text feature to describe this slide. <span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">7. Students will present their PPT presentations in groups to the class…classmates are encouraged to ask questions, as this will assist everyone in learning the steps taken/kinds of data collection. = __Lesson 8 by Kim Doucette__ =

5.14 The student will classify a) angles as right, acute, obtuse, or straight; and b) triangles as right, acute, obtuse, equilateral, scalene, or isosceles 21st Century Skills: Problem solving, creativity, communication Technological Component: digital cameras, photo sharing software, like Flickr, printer, projector Explanation: <span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">1. This lesson is a REVIEW lesson, which can be used as an extra-credit at home type assignment, or could be completed in class to use in making games or centers for classroom exploration. <span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">2. Students will use digital cameras to take pictures at home/at school of angles and triangles in their home/school. Each picture taken will be loaded onto a picture sharing site (Flickr) to be shared with classmates. <span style="font-family: 'Century Gothic'; mso-bidi-font-family: 'Century Gothic'; msobidifontfamily: 'Century Gothic'; msolist: Ignore; mso-fareast-font-family: 'Century Gothic'; msofareastfontfamily: 'Century Gothic';">3. The teacher may use the photos in one of the following ways for student review: <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Photos may be printed, sorted, and pinned up to create bulletin boards in the classroom <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Photos may be used as a class sort to be laminated and put into a center. (Students will pour out the laminated pictures from a large envelope, and sort them by type of angle or triangle. A triangle game and an angle game may both be made!) The headings “right, acute, obtuse, or straight” etc. will be laminated for use as well. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Students may receive extra credit for finding triangles/angles in their community and uploading them to the class Flickr page. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· A BINGO game may be created by pasting the pictures into a blank graph….this could be used as a center or a whole class review game. =**__Lesson 9 by Sue Keffer__**=
 * 5.17: The student will **
 * a) solve problems involving the probability of a single event by using tree diagrams or by constructing a sample space representing all possible results; **
 * b) predict the probability of outcomes of simple experiments, representing it with fractions or decimals from 0 to 1, and test the prediction; and **
 * c) create a problem statement involving probability and based on information from a given problem situation. Students will not be required to solve the created problem. **
 * 21st Century Skills: **Creativity, communication, solve problems, judgments and decisions, collaboration..


 * Internet tool:** Power point, a flip camera and either a prescribed web site or clip art for pictures.

<span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Creation of a problem situation that can be solved using a tree diagram or sample space and the solution (student can use the web site [|www.images.com], or clip art if available, to search for images for the diagram or sample space). For example, students could present the situation where they are fixing lunch with the available options of ham, turkey, cheddar cheese, provolone cheese, lettuce, tomato, wheat bread, and white bread. They would then create either a tree diagram or sample space using images to show all possible combinations. This can be simplified or complicated to meet all children’s needs depending on the number of options specified by the teacher. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Students will choose an experimental situation (flipping coins, shooting baskets, spinning a spinner, choosing candy from a bag, etc.) and predict the outcome of the situation represented as a fraction. Students will then use the flip camera to video tape the testing of the prediction. This video will be included in the power point presentation. Students will compare their prediction to the actual outcome and comment on the comparison. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Each group will create a problem statement based on a given situation. These situations will be created by the students to represent a situation where an outcome is likely and one where the outcome is impossible. <span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· In order for students to present their power points (including video) the presentation will be limited to no more than 10 slides lasting no more than 10 minutes. This will mean that students will have to make group decisions about how the presentation will be organized and what part of the video to include.
 * Explanation:** Students will work in groups of 3-4 students to create a power point presentation, including a video representing the testing of their prediction in step # . The presentation will include the following:


 * Sample tree diagram:

Caroline is making an ice cream sundae. She has a choice of vanilla, chocolate, or strawberry ice cream; she may have chocolate syrup or caramel syrup, and she may choose to have sprinkles or gummy bears on top. How many different sundaes could Caroline make?** Caroline could make 12 different ice cream sundaes with the given choices (see tree diagram below).

=__Lesson 10 by Sue Keffer__= **SOL Covered:** 5.18: The student will, given a problem situation, collect, organize, and display a set of numerical data in a variety of forms, using bar graphs, stem-and leaf plots, and line graphs, to draw conclusions and make predictions.


 * 21st Century Skills:** Creativity, reason effectively, access and evaluate information, use and manage information, create media products, solve problems, judgments and decisions, collaboration.

<span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Students will collect survey information and create a bar graph, line graph and stem and leaf plot (bar and line graphs can be created either using Power Point or Excel). Sample graphs**:** <span style="font-size: 12pt; font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">
 * Internet Tools:** Survey Monkey, Power point (can be used to present and to create graphs), Excel (for purposes of organizing information collected and producing graphs), Create a Graph website (used to create graphs): []
 * Explanation:**<span style="font-size: 80%; font-family: Arial, Helvetica, sans-serif;">Students will work in groups of 3-4 to create a survey using Survey Monkey on a topic of their choice, approved by the instructor. The class will report to the lab to take the surveys created by the other groups and each group will solicit an additional sample (if all fifth grade classes are doing the same project, they will simply all take a survey other than their own).

<span style="font-family: Symbol; mso-bidi-font-family: Symbol; msobidifontfamily: Symbol; msolist: Ignore; mso-fareast-font-family: Symbol; msofareastfontfamily: Symbol;">· Students will then draw conclusions and make predictions based on the data displayed in the graphs. <span style="font-size: 12pt; font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">Each group will create a short presentation explaining their process, conclusions and prediction. **__SOL__**
 * __ Lesson 11 by Jesse Blackburn __**

(how they change or grow) and express the relationship, using words, tables, graphs, or a mathematical sentence. Concrete materials and calculators will be used.
 * 5.20 The student will analyze the structure of numerical and geometric patterns

a) investigate and describe the concept of variable; b) use a variable expression to represent a given verbal quantitative expression involving one operation ; and c) write an open sentence to represent a given mathematical relationship, using a variable. Critical Thinking and Problem Solving, Collaboration and Communication Illuminations.nctm.org; Chairs Around the Table applet; Excel Students will be presented with a problem such as: At a new restaurant in town, there are 24 square tables. One chair is placed on each side of a table. How many customers can be seated at this restaurant? Once the problem has been discussed, the teacher can use tables in the classroom, draw diagrams on the board, or even use manipulatives to show how the chairs could be organized around a table. In the end they should understand that only 4 chairs can fit around the square table.
 * 5.21 The student will
 * __21st Century Skill__**:
 * __Technology Tool:__**
 * __Explanation:__**

The questions then can be posed that if we have 4 chairs around 1 table how many chairs can fit around 24 tables. Students should be able to realize the correlation between the question and multiplication. If not, take the opportunity to show how this situation can lend itself to the use of simple multiplication. A chart can be used to show the pattern From this chart students should be able to see that the number of chairs is equal to 4 times the number of tables. You can take the opportunity to introduce the concept of a variable at this time. For example if there are X amount of tables then you could express the number of chairs that would be present as 4X. Meaning that whatever number X is, you can simply multiply that number by 4 to determine the number of chairs that would be present.
 * Tables || Chairs ||
 * 1 || 4 ||
 * 2 || 8 ||
 * 3 || 12 ||
 * 4 || 16 ||
 * 5 || 20 ||

As an extension, the question can be posed that for large groups of people tables would have to be pushed together in order to accommodate seating. Remind them that only 1 chair can be place at each side of the table. Then ask them how many tables would be needed to accommodate 24 people. Students should begin to see that when tables are pushed together they begin to lose the number of spaces available for chairs. They should soon realize that for most tables only 2 chairs will fit, while the tables on the end will be able to hold 3


 * [[image:http://illuminations.nctm.org/Lessons/Chairs/Chairs-TwoTables.jpg]] ||



At this point, students should be broken up into small groups and asked to explore different table designs to accommodate the amount of people given. This activity should be done using the Chairs Around the Table applet. ( [] ) This applet allows students to manipulate the design of tables and chairs, so that they have an opportunity to answer the question in their own way. During this activity students should keep an organized record of the data they are collecting. This data should show the relationship between the number of tables present and the number of seats available. This table could be done using Excel. You can continue your extension of variables by using mathematical expressions when the students are using words to describe their findings. For example: If a student says, "You find the number of chairs by multiplying the number of tables by 2, and then adding 2," then you might write either of the following on the overhead projector: chairs = 2 × tables + 2 or //c// = (2 × //t//) + 2 Diagrams can also be used to show the expression so that all can see the correlation.


 * [[image:http://illuminations.nctm.org/Lessons/Chairs/Chairs-OneEachEnd.jpg]] ||



Once students have a good understanding of this, you can begin changing the numbers. Students should then be able to come to an answer using words, variables, as well as, using an open sentence to represent the mathematical relationship.

__** Lesson 12 by Jesse Blackburn ** __ 5.22 The student will create a problem situation based on a given open sentence using a single variable.
 * __SOL__**

Critical Thinking, Problem Solving, Communication, Collaboration
 * __21st Century Skill__**:

Photo Story, Power Point
 * __Technology Tool:__**


 * __Explanation:__**

Students will be asked to create and share a story using Photo Story, Power Point, or any other programs that is pre approved by the teacher. The story must include graphics and will be presented to the class. The story will demonstrate the students’ ability to take a mathematical problem and relate it to a real world situation

Example:

A group of students will be given an equation such as “N x 6” or “N + 6”. The group will then create or find images to make a story using one of the programs listed above. For instance, the group may find pictures showing the Farmer Joe has some chickens. They might then say that each chicken lays 6 eggs a day. This would be a situational story for the equation “N x 6”. They could then say that in his other barn he has some cows. At an auction today he bought 6 more. This would be a situational story for the equation “N + 6”. You could use as many equations as you want, or even have them create a story using each of the four operations; addition, subtraction, multiplication, and division.