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5Th Grade Thinking Skills Worksheets document sample
663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 1 Explanation and Purpose of this file This document was created from a review of ALL submitted SIPlan Action Plans for the 2006-07 school year. Separate documents (computer files) are in the process of being created for each specific th curricular / focus area and grade level. For example, the document that follows is 5 Grade Mathematics. 28 documents / computer files have created from last year’s Action Plans, e.g., th th Language Arts - Early Childhood through 8 grade, Mathematics - Early Childhood through 8 grade, Algebra I, English II, Attendance, Climate / Behavior and Graduation Rate. This document is a “selected / gleaned compilation” of Interventions / Strategies, Instructional Technology Integrated Strategies, Professional Development Citations, Assessment Summaries and Parental Participation Suggestions. “Selected / Gleaned Compilation” means that you will view some of the best written, some of the most detailed, some that take a unique approach, some that walk down a path taken by only a few other buildings and some that may spark a “domino” thought for further development. Is the listing all inclusive of the quality Action Plan components written last year? NO! It is a “starting gate” for all to walk through as the 2007-08 SIPlan process begins. Its purpose is to provide the individual School Improvement Team with “possible” alternatives, additions and/or modifications to their current focused approach to a specific PASS Objective. It is NOT intended as a replacement for the ideas, directions and decisions that currently reside within individual SIPlans. If the document has no value then you are under no obligation to use it. Buildings should review this document and select those components (via cutting, copying, pasting and then inserting in the appropriate Action Plan Template cell) that will enhance the school’s efforts at sustainable school improvement. All copy provided is presented in 10 point Arial font. Adjust the font size as needed. Each document, by grade level and curricular area, is presented in lowest to highest PASS Objective numeric order. Abbreviations have been used sparingly. Abbreviations include: ELL Link = Strategy that may be used with English Language Users IEP Link = Strategy that may be used with Special Needs Students Tech Link = Insertion within Instructional Technology Integrated Strategies cell Note… Although a particular designation may be inserted before the Strategy do NOT interpret the designation as a “cast in stone” use with a particular group. If, upon review, the Strategy would have application / impact on any or all student groups, then place that Strategy into the appropriate cell(s). 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 2 Patterns and Algebraic Reasoning 1.1 Algebra Patterns Patterns & Algebraic Reasoning/Algebra Patterns - 1.1 Fifth grade teachers will use Marzano’s strategy of Nonlinguistic Representations of classroom practices and cooperative learning to enable students to identify a pattern and generalize a rule about a simple design to make predictions about related designs. Patterns & Algebraic Reasoning/Algebra Patterns - 1.1 Fifth grade teachers will teach students to use a variety of methods to describe patterns and solve problems. The teacher will use visual patterns and musical patterns to enable students to identify patterns and generalize rules about a simple design. Students will create their own function machines to play the game “Guess my Rule?” Number cubes, tiles, and beans will be used to produce patterns found in tables and graphs. Patterns and Algebraic Reasoning - 1.1 Fifth grade teachers will use manipulatives (i.e. blocks, marbles, candy, etc.) along with a graphic organizer, to model the use of a function machine to determine the rule / relationship of an algebraic pattern. Students will work in flex groups to create a function machine for another group to decode. Patterns & Algebraic Reasoning/Algebra Patterns - 1.1 Fifth grade teachers will have students use abstract figures to create and solve algebraic patterns and equations. Students will describe rules that produce patterns found in tables, graphs, and models and use variables to solve problems or to describe in general rules in algebraic expression or equation form. Fifth grade teachers will enable the students to use manipulates repeatedly. Patterns & Algebraic Reasoning/ Algebra Patterns -1.1 Fifth grade teachers will provide real life mathematic problems. Students will utilize prior knowledge and personal experience to relate to learning objectives. Teachers will provide repeated exposure to patterns through the use of a manipulatives, direct instruction, cooperative groups and kinesthetic activities to reinforce algebraic patterns. Tech Link - Patterns and Algebraic Reasoning/Algebraic Patterns - 1.1 Fifth grade students will practice pattern activities at: www.mathplayground.com ; www.funbrain.com Tech Link - Patterns & Algebraic Reasoning / Algebra Patterns – 1.1 Students will utilize activities on The University of Utah Educational Network. http://www.uen.org/ Tech Link - Patterns & Algebraic Reasoning / Algebra Patterns – 1.1 Students will log onto the website http://www.matti.usu.edu/nlvm/nav/index.html and practice working on Algebraic Reasoning/Algebra Patterns. Professional Development Link - Patterns & Algebraic Reasoning / Algebra Patterns – 1.1 Fifth Grade teachers will participate in a grade level book study using Teaching the Fun of Math to develop strategies for increasing student achievement in patterns and algebraic reasoning skills. Professional Development Link - Patterns & Algebraic Reasoning / Algebra Patterns – 1.1 - Teachers will participate in in-service at Fulton for Growing with Mathematics. They will meet regularly with the math coach for peer coaching and modeling as needed. They will share student work in weekly team meetings with the math coach, instructional facilitator and the principal. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 3 Patterns and Algebraic Reasoning 1.2 Problem Solving Patterns and Algebraic Reasoning/Problem Solving - 1.2 Using the Marzano Strategy of Nonlinguistic Representation, students will work in small groups with a balance scale and several objects to weigh from each side. Allow time for exploration with the balance scales then provide them with a balanced equation. (i.e. 5 pencils equal one calculator). Write the following problem on the board. C + 4 = 9. The students will place the calculator and 4 pencils on one side of the scale and 9 pencils on the other side. The students will begin removing one pencil from each side to show that the scale remains balanced. After removing 4 pencils, the students will be able to answer for C. Students will then be allowed to try to find different items from the room to balance and create new problems. Patterns and Algebraic Reasoning/Problem Solving - 1.2 Fifth grade teachers will use graphic organizers and t-charts to teach problem solving strategies. Fifth grade teachers will expose their students to “Daily Math Problems” as well as integrate reading. Fifth grade students will also take a “Being There Experience” to the Ropes Course. Patterns &Algebraic Reasoning Problem Solving - 1.2 5th grade teachers will use Marzano’s Cues, Questions, and Advanced Organizers strategy with graphic illustrations to convert metric units to other units within the metric system. Step 1: Students will measure various objects. Step 2: Using the graphic illustrations, students will practice converting to smaller or larger metric units. Step 3: Using Kagan’s Pair Share, students will create a mnemonic device to remember the order of the metric units. Step 4: Students will estimate the measurements and discuss methodologies for discovering approximate values. Step 5: Students will then measure the object or graphic representation to check their prediction. Step 6: Students will then repeat Step 2 and convert these measurements to larger or smaller metric units. Tech Link - Patterns & Algebraic Reasoning/Problem Solving - 1.2 Students will use balances to model an algebraic equation showing that when an item is subtracted from one side it must also be subtracted from the other side. Tech Link - Patterns & Algebraic Reasoning / Problem Solving – 1.2 Students will utilize activities on The University of Utah Educational Network. http://www.uen.org/ Tech Link - Patterns & Algebraic Reasoning/ Problem Solving - 1.2 Teachers will use various computer games to reinforce learning objectives. Teachers will use the Aver Key and computer to model how to use www.aaamath.com to identify how to describe, extend, and predict algebraic patterns. Tech Link - Patterns & Algebraic Reasoning / Problem Solving -1.2 http://math.com/practice/Algebra.html is a credible site for additional practice at home and at school. Professional Development Link - Patterns & Algebraic Reasoning / Problem Solving – 1.2 Teachers will participate in in-service at Fulton for Growing with Mathematics. They will meet regularly with the math coach for peer coaching and modeling if needed. They will share student work in weekly team meetings with the math coach, instructional facilitator, and the principal. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 4 Number Sense 2.1 Fraction / Decimal / Percents Number Sense/Fractions 2.1a and 2.1c Fifth grade teachers will provide manipulatives for children to model place-value, working with fractions and decimals. They will use concrete objects to build an understanding for an abstract thought process. Children will use their knowledge base to apply properties in math problems. Number Sense / Fraction/Decimal/Percent - 2.1 Using Marzano’s strategy of Classroom Practice and Cooperative Learning, students will compare and order whole numbers and decimals to the thousandths place. Teachers will need to have available an 11x18 sheet of construction paper cut in half horizontally and one number cube for each student. The class should be divided into heterogeneous groups of four. Step One: Students will fold their construction paper into five equal sections and will draw a decimal point in the second box from the left. Step Two: Each student will roll his/her number cube and will fill the remaining three spaces on the construction paper in any order he/she chooses. Step Three: The group will work cooperatively to put their four numbers in numerical order paying particularly close attention to the thousandth place. Step Four: Each student in the group will write their numbers down in order on a sheet of paper for assessment purposes. The assignment can be repeated by flipping the construction paper over to the other side. Step Five: Each group will trade all five pieces of construction paper with another group and will practice the assignment with the other group’s set of numbers, recording their answers on their papers to be assessed by the teacher. Step Six: The teacher will lead the students in putting the class set of the number strips in numerical order. Develop a reference sheet of fraction equivalencies for students to keep at desks. Provide practice in fractions and decimals by using computer software programs that give the student immediate feedback. Number Sense/ Fractions/Decimals/Percents - 2.1 Fifth Grade teachers will use metacognitive strategies to teach students how to order fractions, decimals and percents on a number line. Asking students to verbalize their thinking while working helps students become aware of their thinking process and improve problem-solving so that they become aware of the strategies they use. Step 1: On the board, teacher draws a long number line that goes from 0 to 1. Invite a student to write 1/2 on the line where they think it belongs. Ask students how they know if it is marked correctly. (Students should recognize that ½ should show two equal halves on the number line.) Step 2: Continue inviting students to the board to write other fractions on the number line. Ask students to verbalize their thinking after each fraction is placed on the number line. Explain that a good way to check is to think to one’s self: “How many of that fraction will make 1?” So if you put 1/3 there, is there room for three times that distance between the 0 and the 1? Step 3: Ask questions such as: Is 1/4 closer to 0 than 1? How do you know? How far apart are they? You could think that 1/3 is what you get when you share something between 3 and 1/4 is what you get when you share something between 4. So which is less? Invite students to comment or adjust their number line as more fractions are added. Step 4: Add a few fractions with other numerators, such as 2/3 and 3/4. Ask questions such as: Is 3/4 closer to 1 than 2/3? How do you know? You could find equivalent fractions for both of them, with the same denominator. Remind students how to find equivalent fractions by multiplying. Explain: “Look at the two denominators, 3 and 4. If you multiply them together you get 12. That tells you that twelfths is a good denominator to choose. Now 3/4 is the same as 9/12 and 2/3 is the same as 8/12. So which of them is bigger? Yes, 3/4 is bigger than 2/3.” Step 5: Invite the class to work on some questions presented on the board or on an overhead projector. Explain that it is not enough just to look at the diagram on the board. The diagram on the board can help some, however, it is not always very accurate. Tell students they need to compare the fractions by making their denominators the same. Ask questions such as: Is 1/3 or 1/4 closer to 1? Is 1/3 closer to 1 or to 5/6? Continue to ask students to share the answers to each of the questions, giving their reasons. Step 6: For homework, provide pupils with squared paper and tell them to draw a 0–1 number line 24 squares long. (You might want to provide some pupils with the line already drawn.) They should write 12 fractions of their choice on the line in the correct order. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 5 Remind pupils to choose fractions that challenge them, whatever their level of attainment. Step 7: Steps may be repeated using decimals. When using decimals, teacher should point out that decimals may be expressed in monetary amounts. For example 0.5 is the same as $.50, which is half of a dollar or 1, or 0.75 is the same as $.75 or 3/4 of a dollar (1). Using money as a reference activates students’ previous knowledge and helps students use the decimal system efficiently. Number Sense 2.2 Number Theory Number Sense/Number Theory – 2.2 Fifth grade teachers will teach the algebraic properties by using their knowledge of properties (associative, commutative, distributive, identity, and zero) in real-life situations. Number Sense/ Number Theory – 2.2 Using Marzano’s strategy of Classroom Practice students will apply properties of arithmetic, factors, multiples, prime and composite numbers to solve problems. Number Sense/ Number Theory - 2.2 Fifth grade teachers will provide manipulatives to allow students to simulate the associative and commutative properties. They will use concrete objects to build an understanding for an abstract thought process. Students will be able to identify these properties in math problems. Number Sense/Number Theory - 2.2 Fifth grade teachers will provide manipulatives (like tile squares, linking cubes, beans) for children to simulate the commutative, associative, identity, and distributive properties. They will use concrete objects to build an understanding for an abstract thought process. Children will use their knowledge base to then apply properties in math problems. Tech Link - Number Sense/Number Theory – 2.2 To integrate technology, first students will learn about properties of arithmetic and the greatest common factor on http://www.brainpop.com. There the students will watch a video and then take a quiz to assess learning. Next, the students will apply their knowledge of factors by playing the online Factor game against the computer or a friend: http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 Tech Link - Number Sense/ Number Theory - 2.2 Students can be given the opportunity to visit http://www.mrnussbaum.com/dec0210.htm to interactively work with numbers to understand the basic concepts and properties. Professional Development Link - Number Sense/ Number Theory - 2.2 View & discuss the Learning Math: Number & Operation Video Workshop on Session 6 – Number Theory. Teachers will watch video online and then meet to discuss the learned information. http://www.learner.org/channel/courses/learningmath/number/session6/index.html Number Operations / Computation 3.1 Estimation Number Operations / Computation - Estimation - 3.1 Fifth grade teachers will have students solve daily estimation activities involving decimals. Students will use advertisements from various grocery stores along with different shopping list scenarios. They will estimate the closest amount of change they will receive in return for their payments. Students will record their answers in their estimation journals. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 6 Number Operations and Computation/Estimation - 3.1 Fifth grade teachers will provide students will daily mental math activities. Students will be able to apply a variety of estimation and mental math techniques to simplify computations. Number Operations and Computation/ Estimation - 3.1a and 3.1b Fifth grade teachers will provide situations in which students estimate and find solutions to problems involving decimals, percents and fractions. Fifth grade teachers will teach percents and fractions using Marzano’s non-linguistic representation (with pictures, manipulatives, etc.). Number Operations and Computation/ Estimation - 3.1 Fifth Grade teachers will use metacognitive strategies to teach students how to use estimation skills to determine solutions to problems involving decimals, common percents and equivalent fractions. Fifth Grade teachers will use metacognitive strategies to teach students how to order fractions, decimals and percents on a number line. Asking students to verbalize their thinking while working helps students become aware of their thinking process and improve problem- solving so that they become aware of the strategies they use. Step 1: On the board, teacher draws a long number line that goes from 0 to 1. Invite a student to write 1/2 on the line where they think it belongs. Ask students how they know if it is marked correctly. (Students should recognize that ½ should show two equal halves on the number line.) Step 2: Continue inviting students to the board to write other fractions on the number line. Ask students to verbalize their thinking after each fraction is placed on the number line. Explain that a good way to check is to think to one’s self: “How many of that fraction will make 1?” So if you put 1/3 there, is there room for three times that distance between the 0 and the 1? Step 3: Ask questions such as: Is 1/4 closer to 0 than 1? How do you know? How far apart are they? You could think that 1/3 is what you get when you share something between 3 and 1/4 is what you get when you share something between 4. So which is less? Invite students to comment or adjust their number line as more fractions are added. Step 4: Add a few fractions with other numerators, such as 2/3 and 3/4. Ask questions such as: Is 3/4 closer to 1 than 2/3? How do you know? You could find equivalent fractions for both of them, with the same denominator. Remind students how to find equivalent fractions by multiplying. Explain: “Look at the two denominators, 3 and 4. If you multiply them together you get 12. That tells you that twelfths is a good denominator to choose. Now 3/4 is the same as 9/12 and 2/3 is the same as 8/12. So which of them is bigger? Yes, 3/4 is bigger than 2/3.” Step 5: Invite the class to work on some questions presented on the board or on an overhead projector. Explain that it is not enough just to look at the diagram on the board. The diagram on the board can help some, however, it is not always very accurate. Tell students they need to compare the fractions by making their denominators the same. Ask questions such as: Is 1/3 or 1/4 closer to 1? Is 1/3 closer to 1 or to 5/6? Continue to ask students to share the answers to each of the questions, giving their reasons. Step 6: For homework, provide pupils with squared paper and tell them to draw a 0–1 number line 24 squares long. (You might want to provide some pupils with the line already drawn.) They should write 12 fractions of their choice on the line in the correct order. Remind pupils to choose fractions that challenge them, whatever their level of attainment. Step 7: Steps may be repeated using decimals. When using decimals, teacher should point out that decimals may be expressed in monetary amounts. For example 0.5 is the same as $.50, which is half of a dollar or 1, or 0.75 is the same as $.75 or 3/4 of a dollar (1). Using money as a reference activates students’ previous knowledge and helps students use the decimal system efficiently. Tech Link - Number Operations & Computation/Estimation - 3.1 Fifth grade teachers will provide manipulatives such as tiles and linking cubes to demonstrate the commutative, associative, identity, and distributive properties. Students will practice these skills on Study Island and www.mikids.com Tech Link - Number Operations and Computations/ Multiplication - 3.1 Estimate and find the product of 2- and 3-digit numbers to solve application problems. Teachers will allow students to use the website http://www.dositey.com to improve their multiplication skills through fun games. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 7 Tech Link - Number Operations and Computation/Multiplication – 3.1 Students will use www.aplusmath.com to practice multiplication concepts. Tech Link - Number Operations & Computation/ Estimation - 3.1 For technology reinforcement, students will practice their math skills at these sites: www.coolmath-games.com/numbermonster/index.html; www.funbrain.com/tictactoe/index.html Tech Link - Number Operations & Computation/ Estimation - 3.1 To integrate technology, the students play the online program Grand Slam Math. The students will be given multiplication and division word problems to answer. If they get the answer wrong, then they will be shown how to solve it and prompted to try the same problem with different values. After the student has solved 12 word problems, their score is displayed. http://www.actionmath.com/GSM2/GSM2wp1.html Tech Link - Number Operations & Computation/ Estimation 3.1 - Students can be given the opportunity to visit http://www.mrnussbaum.com/dec0210.htm to interactively practice ordering numbers written to the hundredths place. Students will be asked to record the numbers they were given and the order in which they put them, and then turn in their paper for assessment by the teacher. Number Operations / Computation 3.2 Whole Numbers / Decimals / Fractions Tech Link - Number Operations and Computation/Multiplication - 3.2b To integrate instructional technology, fifth grade students will practice multiplication activities at: www.mathplayground.com ; www.funbrain.com; www.aaamath.com ; www.aplusmath.com Geometry and Measurement 4.1 Geometric Figure Properties Geometry & Measurement/ Geometric Figures – 4.1 Using Marzano’s strategy of Classroom Practice and Cooperative Learning students will identify and describe the properties of figures. Geometry and Measurement/Geometric Figure Properties - 4.1 Fifth grade teachers will use geometric properties and relationships to analyze shapes and use standard units of customary and Metric measurements to solve problems. Students will use manipulatives and the strategy of “Realia” to solve problems. Teachers will integrate art instruction while teaching this standard. Geometry & Measurement/Geometric Figure Properties 4.1 5th Grade teachers will use Marzano’s Nonlinguistic Representation to illustrate properties of solid objects, define vocabulary and identify patterns. Step 1: Students will identify vertices, faces and edges on 3-dimentional manipulatives. Step 2: Students will create a chart to show the pattern of faces, vertices and edges. Step 3: Students will be able to identify the number of vertices, edges, and faces on a 2-dimentional representation of the 3-dimentional manipulative using their previous knowledge and the chart that was created in step 2. Step 4: Students will be able to determine the name of each solid by these properties. Tech Link - Geometry & Measurement/Geometric Figure Properties 4.1 Fifth grade teachers will utilize the computer lab and the computers in their classroom to expose their students to technology, e.g., the National Library of Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 8 Professional Development Link - Geometry & Measurement/Geometric Figure Properties 4.1 View & discuss the Teaching Math: Geometry (Classroom Case Studies, K-5) video workshop on using a Venn diagram to categorize geometry figures using mathematical vocabulary terms. Teachers will watch video online and then meet to discuss the learned information. http://www.learner.org/channel/courses/learningmath/geometry/session10/35video.html Geometry and Measurement 4.2 Perimeter / Area Geometry & Measurement/Perimeter/Area - 4.2 5th grade teachers will use direct instruction and Marzano’s massed and distributed practice to teach students how to find the perimeter of simple polygons and the area of a rectangle. Step 1: Begin by explaining that students will learn how to find the perimeter of simple polygons and the area of a rectangle. Define perimeter (the distance around the outside of a polygon) and area (the amount of space enclosed in the polygon.) Connect to prior knowledge by explaining that the perimeter is like the fence that goes around the edge of a yard and area is the yard itself. Write the definitions on the chalkboard or an anchor chart for reference during the lesson. Step 2: Using the chalkboard or overhead, draw a rectangle. Explain that the rectangle represents a backyard. While labeling the rectangle, explain that the length of the backyard is 12 feet and the width of the backyard is 8 feet. Step 3: Model for students how to determine the length and width of the unlabeled sides. For example, “I know that the length of this side is 12 feet. I know that a rectangle has opposite sides congruent. Therefore, this side must also be 12 feet.” Label the opposite sides as you think aloud. Step 4: Repeat the definition of perimeter. Think aloud as you model how to find the perimeter of the rectangle. For example, “Perimeter is the distance around the outside of a polygon. So the perimeter is the length of this side – 12 feet – and the width of this side – 8 feet – and the opposite sides – 12 feet and 8 feet again. So if I add all of the sides together, I will have the perimeter. 12 + 8 + 12 + 8 = 40. The perimeter of this backyard is 40 feet.” Increase difficulty by pointing out the geometric formula 2L + 2W = P for rectangles and squares. Step 5: Provide massed practice by having students solve perimeter problems using various polygons the teacher provides. Invite students to the chalkboard or overhead to solve perimeter problems while others solve the problems on erasable white boards or in their math notebook. Vary the linear units used, such as centimeters, yards, inches, etc. Step 6: Increase difficulty by providing the perimeter measurement and having students work backward to find the sides. For example, “The perimeter of a regular hexagon is 18 cm. How long is one side?” (s=18/6, s=3.) Step 7: Repeat steps using area. For example, “Area is the space inside the polygon. We find the area of a rectangle by multiplying the length by the width. So if the length is 12 feet and the width is 8 feet, I can multiply 8 x 12 which equals 96. Area is expressed in square units. The area is 96 square feet.” Step 8: Summarize the lesson by asking students to explain how to find the perimeter and area. Display the definitions and reread together orally. Have students write the steps for finding area and perimeter in their math notebooks. Step 9: Provide distributed practice in homework and daily review, lengthening the time between practice sessions as students gain mastery. Geometry & Measurement / Perimeter / Area - 4.2 5th Grade students will use Marzano’s strategy of Non-linguistic Representations to explore and calculate the perimeter and area of polygons. Step 1: Differentiate and compare perimeter and area. Step 2: Students will be given a graphic illustration of various polygons and will use the inductive method to determine how perimeter and area were derived. Step 3: Class will discuss. Step 4: Students will create their own polygons and find the perimeter and area of each. Step 5: Students will use timed pair share to figure out the perimeter and area of their partners polygons. Step 6: Students will discover and write the formulas for calculating perimeter and area of polygons. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 9 Geometry & Measurement / Perimeter / Area - 4.2 Fifth grade teachers will use Marzano’s Nonlinguistic Representations to explore and calculate the perimeter and area of rectangles. Step #1, after discussing the definition of area (the surface of a solid plane measured in square units) and the definition of perimeter (the length of a boundary of a plane figure), the teacher will distribute graph paper to each student. Step #2, instruct the students to cut out a square that is 25 cm by 25 cm. Step #3, have the students find the perimeter and area and ask them to record their findings on a separate sheet of paper. Step #4, ask students to cut a square that is 10 cm by 10 cm, from the top right corner of their 25cm by 25cm square and then find the perimeter and area of the small square. Step #5, have the students find the perimeter and area of the new shape that was formed when the smaller square was removed and then record their findings. Step #6, ask each student to write a brief reflection on the comparison of the three shapes. Geometry & Measurement / Perimeter / Area 4.2 -- Fifth grade teachers will use Marzano’s strategy of Nonlinguistic Representations to explore and calculate the perimeter and area of rectangles. Step #1, discuss the definition of area (the surface of a solid plane measured in square units) and the definition of perimeter (the length of a boundary of a plane figure). Step #2, the teacher will instruct the students to use graph paper to make as many shapes as possible with an area of 25 square centimeters. Encourage students to be creative when making their shapes, but remind them that each shape must be connected. Step #3, instruct students to label the dimensions of each shape and color each. Step #4, instruct the students to find the perimeter of each. Step #5, the teacher will ask students to record their findings on a separate sheet of paper. Step #6, have the students write a brief reflection on what they learned about the differences between area and perimeter. ELL Link - Geometry & Measurement / Perimeter / Area - 4.2 Teachers will structure ample opportunities to actually measure perimeter and area. Fifth grade teachers will draw two rectangles on the board and label the sides of each with whole-number centimeter dimensions. Have students draw these rectangles on grid paper. The teacher will model what the students should draw on the board to help the ELL students. Then ask, what is the area of each rectangle? How do you know? They are going to use Marzano’s Cooperative Learning strategy with a partner to develop a rule or formula for finding the area of a rectangle. Encourage a variety of responses and list them on the board. Tech Link - Geometry & Measurement / Perimeter / Area - 4.2 To integrate instructional technology, fifth grade students will play Bucky’s Geometry Workshop. First, the students need to click “play” under the Workshop heading, and when prompted to register, click “Maybe later”. Next, click on the small button titled, “Choose a Challenge topic”. For this activity, instruct the students to choose #5 “Perimeter and Area”. Finally, instruct the students to click “Give Me a Challenge!” The computer will now generate an area or perimeter problem. If the student is unable to solve the problem, it will show them how to think it through. http://www.iknowthat.com/com/App?File=GeometryWorkbench.htm&Type=D&App=GeometryWor kbench&SkipGuestWarning=true Tech Link - Geometry & Measurement/ Perimeter/Area - 4.2 To integrate instructional technology, fifth grade students will explore perimeter and its relationship to the corresponding area. Using the online Area Explorer, students will choose the desired perimeter using the slide at the bottom of the grid applet. Next, the students will type in the correct area and click “Check Answer”. Then, they will click the button “Draw a New Shape”. Students can click “Show Score” to keep a record of their explored perimeters and areas. http://www.shodor.org/interactivate/activities/perm/index.html 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 10 Tech Link - Geometry & Measurement / Perimeter / Area - 4.2 Additional practice using perimeter and area may be assigned using the online website www.mathplayground.com Tech Link - Geometry & Measurement / Perimeter / Area - 4.2 http://emints.org/ethemes/resources/S00001227.shtml http://emints.org/ethemes/resources/S00000278.shtml Geometry and Measurement 4.5 Convert Measurements Geometry & Measurement/Convert Measurements - 4.5 Fifth grade teachers will use Marzano’s Cues, Questions, and Advanced Organizers Strategy to assist students in converting from one unit of metric measure to another within the metric system. Discuss that an easy way to remember the sequence of metric units from largest to smallest is using this mnemonic device: King Henry Died Unexpectedly Drinking Chocolate Milk. (kilo, hecto, deca, base unit, deci, centi, milli) Geometry and Measurement / Convert Measurements – 4.5 Fifth grade teachers will introduce tools of measurement. Teachers will use Marzano’s strategy of CooperativeL and Generating and Testing Hypothesis to allow students to manipulate various types of measurement tools (ie. Thermometers, rulers, meter sticks, balances, and scales, etc.) and complete tasks involving graphing temperatures, measuring set areas and weighing amounts. Students will be given opportunities to measure temperatures in Fahrenheit and Celsius scales to become proficient. Students will measure distances with meter and yard sticks (i.e. flights of paper airplanes, hallway distances, etc.) Students will be given opportunities to use pan balances to weigh different items and compare weights. ELL Link - Geometry & Measurement/Convert Measurements - 4.5 Fifth grade ELL teachers will use Marzano’s cooperative learning strategies to have students determine actual conversions. They will work in pairs to find the dimensions and volume of their two boxes. Using Marzano’s Cooperative Learning strategy helps the ELL students. When pairs have calculated the volume of their boxes, the teacher will have them measure the amount of beans that fills each of their boxes. The students will use a Marzano categories chart to write the capacity of each box. When partners have finished, the teacher will lead a class discussion about the results. Tech Link - Geometry & Measurement/Convert Measurements - 4.5 To integrate instructional technology, fifth grade students will practice converting metric measurement using the interactive game of “Memory” to reinforce the use of the skill. http://www.harcourtschool.com/activity/con_math/g05c14.dcr Tech Link - Geometry & Measurement/Convert Measurements - 4.5 http://www.aaaknow.com/geo.htm Tech Link - Geometry & Measurement/Convert Measurements – 4.5 Teachers will send small groups or pairs to computers to visit http://www.hbschool.com/elab/act_3_24.html where they will practice measuring using a virtual ruler. They will print off the recording sheet for the activity and turn it in to the teacher. Tech Link - Geometry & Measurement / Convert Measurements - 4.5 Fifth grade teachers will use Marzano’s Nonlinguistic representation with the customary units of measurement to build a Gallon Man from rectangular pieces first and then the class will create a gallon man from actual containers. First the students will create the gallon man located at the 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 11 following website: http://home.att.net/~clnetwork/math/mrgallon.pdf Once they understand that there are four cups representative of the feet, and hands, 8 pints represent the two bones in the bottom of the legs and arms and 4 quarts represent the large bones in the upper arms and legs and the gallon represents the torso of the body. The students will explore with sand or water using Gallon, quarts, pints, cups to determine where the containers go to create a real gallon man. Data Analysis and Probability 5.1 Data Analysis Data Analysis - 5.1 The teachers will incorporate a daily graph in the class, e.g., students will graph on both a bar and circle graph lunch choices and other questions of the day. Resources to be used include the following books: Graph A Day and Great Graphs and Sensational Statistics. Data Analysis/ Selecting Table or Graph - 5.1b Fifth grade teachers will use Marzano’s strategy of Nonlinguistic Representations and Cooperative Learning to enable students to manipulate and organize data. Explain to the students that a part of the study of probability is learning permutations and combinations. It is the study of choices and the arrangement of those choices. For elementary math, students will not need to learn the difference between permutations (order of the elements in a set is important) and combinations (order of the elements in a set is not important). For each activity, the teacher will state whether or not order matters. For example: If you were deciding what topping to put on a sandwich and you had these choices: (M) mayonnaise or (C) cheese to go on either a (T) turkey or (H) ham sandwich, would order matter? The options would be MT, MH, CT, CH. Would it matter whether it was listed as MT or TM? In this case, no it is not important. So, this is really a combination problem, rather than a permutation problem because order does matter in the study of permutations. However, for elementary students, this distinction is irrelevant. Select a type of table or graph to document the results. Students work cooperatively to justify their selection. Using clipart from Microsoft Word or from other sources, the teacher will print off enough pictures of a hamburger, French fries, and a pop so that each group will have one. Then, divide the class into small groups. Instruct each group that they will find out how many combinations of items that you could buy if the menu only had three items. Imagine that you went to McDonald’s or Burger King and the menu only offered a hamburger, a small fries, and a medium drink. You could not choose to change the sizes and you could not order two or more of the same item. You could however choose to buy nothing. How many possible combinations could you make? Tell them that order does not matter: a hamburger with fries is the same as fries with a hamburger. After experimenting with the picture props, the students will make a chart that explains their process of thinking and shows how they obtained their answer. For the chart, they could use pictures or a variable representing each item (H-hamburger, F – Fries, D – Drink). The student groups will then share their posters with the class. The students should come up with 8 possible combinations (, H, F, D, HF, HD, FD, HFD). Now, repeat this activity, but this time add a salad to the menu. Ask the students how many possible combinations are there if you have four choices. The answer is 16 possible combinations. Finally, you might repeat this process but add an ice cream cone to the menu. The students will find that with 5 choices, they will have 32 possible combinations. If your students are ready, lead them in a discussion of “powers”. With 2 choices, they will have 4 combinations. With 3 choices they have 8 combinations and so on. 2 3 4 5 This can be seen as 2 = 4, 2 = 8, 2 = 16, and 2 = 32. Select a type of table or graph to document the results. Students work cooperatively to justify their selection. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 12 Tech Link Data Analysis - 5.1 To integrate technology students will use virtual manipulatives in the online activity Bobbie Bear. http://illuminations.nctm.org/activitydetail.aspx?id=3 Professional Development Link - Data Analysis and Probability 5.1a Teachers will participate in in-service at Fulton for Growing with Mathematics. They will meet regularly with the math coach for peer coaching and modeling if needed. They will share student work in weekly team meetings with the math coach, instructional facilitator and the principal. Data Analysis and Probability 5.2 Probability Data Analysis and Probability / Probability – 5.2 Teachers will use Marzano’s strategy of Nonlinguistic Representations to enable students to organize data. Using a bean bag toss at a target with differing points, students will analyze all of the possible combinations that they might have thrown. Data Analysis and Probability / Probability – 5.2 The study of probability helps students with problem-solving. It presents a problem, has the student make a mathematical prediction, and then allows the student to experiment to prove or disprove the mathematical prediction. Step 1 -- Instruct the students to take notes as part of Marzano’s note taking strategy. Step 2 -- Explain to the students that probability is a fractional number or percentage that tells how likely it is for a specific result to happen. The closer the probability is to 1, the more likely it is to happen. This is also called the mathematical probability. It is different from experimental probability. The experimental probability is a fractional number or percentage of times an event actually occurred in the experiment. Probability is measured by adding the total number of favorable outcomes and dividing that by the total number of possible outcomes. The probability is then expressed as a fraction or a percentage. Next, the students will use Marzano’s strategy of Generating and Testing Hypotheses while conducting a coin toss. Step 3 -- Instruct the students to take out a sheet of paper and label it “Probability of Flipping a Coin”. Then, have them draw four T-charts with the labels “Heads” and “Tails” on each. Step 4 -- Tell the students to predict and write down the probability of a coin landing on heads or tails. Remind them to write the probability as a fraction and a percent. Step 5 -- Have the student choose a partner and give each team a coin. Step 6 -- Instruct each team to flip a coin 10 times and record the results on a tally chart. Step 7 -- Have the students write down their experimental probability as a fraction and percentage. Step 8 – Monitor the students for re-teaching needs. Step 9 -- Tell the students to repeat this process with flipping the coin 25 times, 50 times, and 100 times. Step 10 -Ask the students to write their observations on the back of the paper. Specifically, ask them what they noticed was happening with their results. Finally, reinforce that with experimental probability, the more times that the students flipped their coin, the closer the results came to the mathematical probability. Data Analysis and Probability / Probability – 5.2 Fifth grade teachers will use Marzano’s Strategy of Cooperative Learning to explore the concept of probability. Step 1 -- The teacher will divide the students into groups of four, and then give each group two paper sacks (labeled “A” and “B”) containing varying amounts of two colored tiles. Step 2 -- Tell all of the students that they are not to look into their bags. Step 3 –Give each group a piece of paper describing what their bags contain. For example: one group might be given two bags and this information: One bag has 2 green tiles and 18 red tiles. The other bag has 12 green tiles and 8 red tiles. (See following page) Step 4 -- Have the students calculate the mathematical probability for each color and each bag’s description. Remind the students that they need to write the probability as a fraction and a decimal. Step 5 -- Tell the students, “You are going to conduct a probability experiment. Probability helps with making predictions. Meteorologist use probability to find patterns and make predictions about the weather. Today, 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 13 you will use probability to make a prediction about the contents of your paper sack without looking into them.” Step 6 -- Instruct the groups that they will need to choose two students to be recorders (one for sack “A” and one for “B”) and two students to draw out the tiles. The student that draws out the tile will show the recorder and then put the tile back into the bag. He/she will repeat that process 30 times. The recorder will tally the results of the draws on a T-chart. After the students have completed the 30 draws and recorded the results on the T-chart for both sacks “A” and “B”, they will determine the probability of each color on both T-charts. Step 7 -- The students should be able to accurately determine the contents of their bags based on their probability statistics. Using the paper which described the bag contents, the students will identify which description belongs with each bag and label it “Bag A” or “Bag B”. They will also write the experimental probability underneath the mathematical probability. Data Analysis and Probability / Probability – 5.2 Fifth grade teachers will use Marzano’s Strategy of Representation and Classroom Practice to increase the students’ understanding of probability. Step 1 -- Before beginning the activity, ask the students if they have ever played rock/paper/scissors and then have the students explain the rules for the game. The students should state that there are three hand configurations: closed fist for rock, flat palm for paper, and two fingers that form scissors. With a closed fist, each person will hit the palm of their hand twice. On the third hit, each person forms either a rock, paper, or scissors hand configuration. Step 2 -- Ask the students “How many favorable outcomes there will be?” The answer is 3 (rock wins, paper wins, or scissors win). A tie is not a favorable outcome, because no one wins. Step 3 -- Make a tree diagram on the board or overhead projector to show the total possible outcomes. Have the students count the total number of outcomes. (See example 1.) Step 4 – Lead the students to calculate that since there are three favorable outcomes and nine total possible outcomes, then the mathematical probability of each outcome is 1/3. Step 5 -- Divide the students into pairs and instruct them to play 27 rounds of rock/paper/scissors. Step 6 – Have the students keep a tally chart of the outcome of the experiment and subsequently find the experimental probability of each outcome. Step 7 – Finally, instruct the students to create a poster about their experiment depicting the results to share in class. Tech Link - Data Analysis and Probability / Probability – 5.2 To integrate technology, the students will use the Internet to conduct research and then create a slide show using MS PowerPoint about their chosen topic. The students can choose from researching the history of the game, “Rock, Paper, Scissors” (which in Japanese is called, Jen Ken Pon), the history of probability, an explanation of probability, the importance of probability in our every day lives, or occupations that use probability. The students should be divided into small groups and instructed to make a slide show with a minimum of three slides: title slide, topic slide, and concluding slide. Tech Link - Data Analysis and Probability / Probability – 5.2 To integrate technology, students will find the fractional probability of fish in a fish tank. To use the following website, http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html you must have shockwave installed on your computer. The game has three levels of play. On level one, the students use drop-down boxes to choose the fractional probability. On levels two and three, the students use fish nets to add fish to make the predetermined probability. Tech Link - Data Analysis and Probability / Probability – 5.2 To integrate technology, students will use virtual manipulatives in the online activity Bobbie Bear http://illuminations.nctm.org/activitydetail.aspx?id=3, to find all of the possible combinations of outfits that Bobbie can wear. Tech Link - Data Analysis and Probability / Probability – 5.2 To integrate technology, use the probability spinner on the electronic interactive whiteboard. From the number of equally divided sections, the students can determine the mathematical probability. Then, using the digital spinner, the students can find the experimental probability of a specific colored section. 663c2835-edc4-4abc-a9c5-1016e66bfa82.doc – page 14 Assessments Daily and Weekly: Teacher observations of daily participation/work and flexible group work will give an informal view of student development. Teacher-made tests will be administered as needed. Periodic: Standard District Curriculum Assessments will be administered quarterly (at a minimum). Semester: Student portfolios will be compiled for parent/teacher conferences. Yearly: The OCCT test will be administered as directed by the state. Parental Participation Communication: Fifth grade teachers will send Thursday folders home with updates of academic objectives. Fifth grade teachers will send home a monthly newsletter with information that may include current objectives test schedule, and other pertinent academic information Math teacher will hold phone conferences to communicate areas that need extra work to attain the objective or areas that have improved. Daily agendas will provide daily communications of student’s math development and progress. Parents shall receive assistance in understanding such topics as the state’s academic content and achievement standards, the assessments being used and how to monitor their children’s progress and work with educators to improve their achievement. (Parenting, Learning at Home) Parent Facilitator will coordinate and integrate parental involvement programs, such as resource centers, that support parents in more fully participating in the education of their child. Schools shall ensure that information related to school and parent programs, meetings and other activities is sent to the parents of participating children in a format, and, to the extent practicable, in a language the parents can understand. Learning at home: Multiplication fact fluency will be emphasized with student fact cards taken home and ardently practiced. Homework that reinforces math objectives will be completed at home. Schools shall provide materials and training, such as literacy training and training on how to use technology, to help parents work with their children to improve achievement. (Parenting)