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Mathematic Unit “Data Measurement for Everyday Life” Year Seven 1 QCT STANDARDS: 1, 2, 3 and 4. Introduction This unit has been specifically designed for a mixed gendered year seven class. The unit ‘Data Measurements for Everyday Life’ has been planned according to the Australian Curriculum, Assessment and Reporting Authorities National Curriculum draft. The topic for this four-week unit will be Statistics, more specifically Data Measures. Links to Other Subjects This topic very easily links to other strands of math’s such as Number: being able to count and order the data accurately in ascending and descending order. Algebra: identifying the patterns that exist within a specific data set. Time: determining amount of time spent collecting data in order to collect an adequate amount Calculation: using mental and calculator strategies to determine mean, median and mode 2 Developments from K - 7 Data Measures is a new concept introduced in year seven however during ‘Summary of Statistics’ in year five students are first introduced to Median and Mode. After this brief introduction, Data Measures do not arise again in the curriculum until year seven. In order for students to effectively complete this unit, there must be a certain degree of scaffolding in the prior years of schooling during the teaching of Data Representation and Investigation. It is assumed that there would be informal discussion during these topics on the range of particular data sets, for example, which has the most or the least. This informal discussion and early introduction in Year Five sets the scene for this unit. 3 Scope and Sequence of Unit UNIT NAME: Data Measurements for Everyday Life YEAR: 7 TIME LINE: Four Weeks / Twenty Lessons CONTENT STRAND: Statistics – Data Measures OUTCOMES AND ELABORATIONS BIG MATHEMATICAL IDEAS PRIOR KNOWLEDGE Data Measures: Determine mean, median The big mathematical idea for this unit is Students need to be able to and range and use these measures to Central Tendency. By the end of this unit compare data sets explaining reasoning students should be able to accurately Construct, read and interpret graphs including using ICT. identify the middle score of a data set. and other simple data displays using technology Elaborations Identify misleading representations Understanding that summarizing data by calculating measures of centre and spread Interpret secondary data often can help make sense of data represented by the media Calculating mean, mode, median and range from listed data and from graphs that show individual data with and without technology Using mean, median and range to compare data sets and explaining how outliers may affect the comparison. Using dot plot or stem plot to identify outliers in a data set, that is the data values that seem to stand out from the majority of data values. 4 KEY: Teacher Aide Lessons Learning Objectives Worksheets Lessons in Computer Room Collection of Assessment Monday Tuesday Wednesday Thursday Friday Week Scan prior Scan prior knowledge Introduction of Mean Check List Assessment Check List Assessment knowledge of of graphing One graphing Concept Map on Gather examples of Explicit Explanation of Discussion of examples Revise Dot Plot, show Statistics graphs from Mean of mean found for H/W students an example newspaper, internet: Mix and Match Graph look at common Discussion: where we With teacher guidance, Individually students to game – written up as features of different see mean/average in as a whole class put collected data onto ‘Stats Glossary’ in graphs real life situations develop a question and a dot plot, work out book collect data using peers mean Develop graphing Develop class definition H/W: List examples checklist, written in and example: put into In pairs, sort and order Collect all students of how graphs are glossary glossary data. work for checklist used in real life. assessment Worksheet #1 H/W: find two examples of mean in the media 5 Week Reintroduction of Consolidate Reintroduction of Mode Practice use of Introduction to types of Median knowledge of Median and Introduction of measurements using surveys Two Range ICT Quiz: Write down six Word Map of KWL Chart about Mode Students to work Word Map of idea’s things you know knowledge of median on butchers papers in through BBC Website about surveys: what, about median? so far groups of four on ‘Data Handling’ why and how. Discussion of Find examples of Explicit demonstration a) Collecting Data Examples of Answers median using, of Range newspaper, magazines b) Representing 1. Cross sectional Explicit explanation and internet Develop class definition Data of median and example for both 2. Longitudinal Develop class and add to glossary c) Averages Discussion: using 3. Time series definition and Students to choose one graphs, what does example: put in In pairs, using a group activity from A, B and C: Discuss how questions the median tell us? glossary of 50 randomly will vary for each type coloured paddle pop revise, complete the Worksheet #2 activity and take the of survey Worksheet #3 sticks or counters will work out range and test. Individually choose mode. Specific colours ‘Low Achievers’ to work type of survey and should be given a with Teacher Aide develop a relevant particular value. question H/W: use constructed survey on family members and friends 6 Week See where the gaps Explanation of Introduction of Outliers Identifying Outliers Identifying Outliers in students Assessment using dot plots Three knowledge are Revision of ways of Discuss task and Students use Each student is given a Look at dot plots working for each explain criteria dictionaries and page out of the local constructed from internet to search for newspaper, they have previous lesson: Card Game Break students into definition to cut out an article and identify Outliers groups (speaker, highlight a paragraph Worksheet #4 director, manager) Using students heights Work out mean and which is eight lines as data set, collect long. mode, median of Run through data measurements collected data collection procedure – Table of alphabet and visit tuck shop to Spot the outliers tally of how many times Evaluate: How do the practice the letters arises in the outliers affect the mean H/W: How do outliers and mode? What does paragraph. affect data? this mean for data sets? Group One to Students to organise How do dot plots help Tuck Shop data and put onto dot us identify outliers? plot Group Three to Group Two to Tuck Shop Tuck Shop Week Relationships Sorting and sharing of Use ICT to create pie Work out mean, Completion of between percentages collected data from chart of results median, mode and Assessment Task Four and pie graphs Tuck Shop range for data set Explicit explanation In data collection ‘How to’ Power point Students work Finishing touches: title and examples of how groups, students sort individually and silently and contents page to be 7 percentages work out their data. Students have a go at to work out added to report with pie graphs putting their As a class, students information into pie Mean Type up justification Discuss formula construct a graph representation on the Median Complete any Develop a definition white board that will Students will also work unfinished elements of and example for Mode and the report best collect their out their percentages glossary shared data for each, showing all Range All students to hand in working out Work Sheet #5 Each group presents assessment. Write up justification Group Four to their data to the class, for the data they have Tuck Shop adding to the found representation on the white board ‘Low Achievers’ to work with Teacher Aide. Students add representation to workbook (please note, this lesson needs to take place after lunch so all data can be collected) Group Five to Tuck Shop 8 Resources Literacy Demands Mathematical Language Computer Rooms: Internet, Macintosh This unit requires students to translate Mean Word and Excel, information often from a worded problem into mathematical terms and symbols. It Median Classroom Computers also requires students to justify their Range Newspapers, Magazines mathematical answer with a worded explanation. Students need to be able to Mode ‘Mix and Match’ A4 cards comprehend the questions in order to give appropriate answers. Data Sets Novelty Card Pack Outliers ‘How To’ power point Skewed Work Sheets Reasoning Coloured paddle pop sticks or counters Giant Protractor Tape Measures Catering for Diverse Learners Teacher Aide Support Assessment Opportunities Visual Impairments will be catered for by Teacher Aide hours are first period every Throughout this unit there are two being seated up the front of the class, second Thursday. For this unit, Teacher opportunities for assessment. Firstly there worksheet will have bigger font and all Aides will work specifically with low level is an assessment at the end of week one, to computer work will have the view of the achievers, helping them mostly with determine any gaps in the basics of data screen enlarged by 100%. For lessons assessment pieces. representation: the unit will be altered where being seated up the front may not slightly according to these gaps. Secondly give the best vision, the student will be there is an assessment in week four so the 9 given enlarged hand outs of what is students can demonstrate the knowledge happening, for example a power point. and skills they have learned throughout the unit. This also will demonstrate if the Auditory Processing Disability will be students have reached the unit objectives catered for by being seated up the front, or not. simple explicit language and hand signals will be used when explaining content or giving directions and directions on cue cards card’s will be given out where possible. Unit Evaluation How effective was my sequence? Did I cater for my diverse learners? Could I change my resources? Overall, was my unit successful? Why/why not? 10 Lesson Plan A Lesson: Measurement Card Game Date: Time: Week Three, Lesson Eleven Year: 7 Unit Outcomes Calculating Mean, Median, Mode and Range from listed data and from graphs that show individual data with and without technology. Learning Objectives Throughout this lesson student‟s knowledge of how to measure data sets will be consolidated and reinforced through the use of hands on materials. Students Prior Knowledge Students will need prior knowledge of data sets and the ways of working for mean, median, mode and range. Resources A deck of cards per students (must bring in more incase some students don‟t bring in) A large set of novelty cards for demonstration Record Sheet (See Worksheets) Blue Tack Calculator and Pen per student Printed simplified rule cards for diverse learners Lesson Procedure Introduction (10 minutes) 1. Students will be seated at their desks 2. Discussion about ways of working for mean, median, mode and range. Concept map will be drawn up on board to help aid discussion and remind students throughout game. 3. Record Sheets handed out 11 Lesson Content and Procedure (30 minutes) 4. Rules of game are explicitly taught: students are given a particular hand they must pull out of their deck of cards. From that hand, students will work out the measurements during allotted time frames. There are four measurements to work out: if correct student receives 5 points for each, if incorrect received 0 points. Students must show their working on the record sheet. The winner is the student with the highest number of points at the end of the four rounds. 5. Value of picture cards and aces are written up on white board 6. Using the novelty cards blue tacked to the whiteboard, show students the hand they must pull out of their deck. 7. Allow 3 minutes for all except mean, which should allow 4 minutes. 8. When all four have been worked through, work out correct answers and winner. Conclusion (10 minutes) 9. If time permits, play another round with a new hand. 10. Get students to glue record sheets into workbook and hand in 11. Pack up Assessment/Evaluation The student‟s work can be evaluated by looking at their working out of each round. This evaluation will allow the content and teaching to be adjusted in order to fill in the gaps of the student‟s knowledge. Adaption’s for Diverse Learners Visual Impairment – Student will be given a set of large playing cards and the font will be enlarged to size 16 on the record sheet. Auditory Processing Disability – Student will be given a laminated card that has a set of simplified rules and instructions for the game. 12 Teacher Reflection/Evaluation Learning Objectives? Did the students meet the objectives? Why or Why not? What could be improved to enable students to meet objectives? Self as a teacher? Where my resources effectively used? Did I cater for my diverse learners appropriately? How was my classroom management during this learning experience? Overall, how did my lesson go? 13 Lesson Plan B Lesson: Pie graphs on ICT Date: Time: Week Four, Lesson Eighteen Year: 7 Unit Outcomes (Curriculum) Calculating mean, mode, median and range from listed data and from graphs that show individual data with and without technology Learning Objectives Use ICT to create a pie chart which will effectively represent collected data from the „Tuck Shop‟ Investigation Resources Computer Lab Projector “How To” Power point USB Sticks Collected surveys and data from previous lessons Students work books Students Prior Knowledge Students will need prior knowledge of the data which will need to be transferred onto a graph. They will also need knowledge of what they want their finished pie graph to look like. Lesson Procedure Introduction (10 minutes) 1. Students will be seated at individual computers in computer room 2. Aim for lesson will be discussed: Students to put collected „Tuck Shop‟ data onto a pie graph using word. 3. Explicit explanation how to make graph using word: power point is shown on projector 14 Lesson Content and Procedure (45 minutes) 4. Students told to log on 5. Open „How To‟ power point on their individual screens 6. Students to make their own graph following the prompts: teacher to be walking around room, answering questions. 7. Work out percentages for each section of data using appropriate formula (See glossary of work book if cannot remember) Conclusion (5 minutes) 8. All students to either print completed graph or save to USB. 9. Log off and pack up equipment Assessment/Evaluation The completed graph will be added to a portfolio that will be evaluated and marked at the end of the unit. Adaption’s for Diverse Learners Visual Impairments - Students will be seated at the front of the classroom and their individual computer screen‟s view will be increased. The font will also be enlarged for them. Auditory Processing Disability - Students will be seated up the front of the class with a clear view of teacher. A simplified set of instructions will be given out at the beginning of the lesson and a printed version of the power point will be given to them. Teacher Reflection/Evaluation Learning Objectives? Did the students meet the objectives? Why or Why not? What could be improved to enable students to meet objectives? Self as a teacher? Where my resources effectively used? 15 Did I cater for my diverse learners appropriately? How was my classroom management during this learning experience? Overall, how did my lesson go? 16 Worksheet #1 A farmer has his cows, sheep and chickens separated into a number of different paddocks. Help him work out the mean for each animal. 18 18 15 18 18 14 4 21 Mean = 94 96 84 69 70 105 Mean = 23 1 31 18 10 7 3 17 Mean = How many animals does he have altogether? What is the mean of all the farm animals? 17 Assessment Tool A Check List Assessment Students can or cannot accurately complete each stage with appropriate working. Students Collect Sort Organ Interp Work Comments Names Data Data - ise - ret out the Data Data Mean of onto the Dot data plot 18 Worksheet #2 MEDIAN Q1. The Smith Family Drove from Sydney to Cairns for their family holiday. On the way they stopped seven times to fill up their car with petrol. They paid $1.69, $1.99, $1.10, $2.05, $1.30, $1.23, $1.44. What is the median price they paid?? Q2. The salaries of eight McDonald‟s employees are listed below. $30 000, $40 000, $32 000, $29 000, $43 000, $31 000, $35 500, $27 000. What is the median salary? Q3. A family of five members runs the Bridge to Brisbane 10 km event. They do it in 55 minutes, 1 hour and 18 minutes, 38 minutes, 44 minutes and 1 hours and 25 minutes. What was the median time for the family? Q4. James is always being told he plays too much Xbox so he decides to record how many hours he plays over a four week period. 8hrs, 3hrs, 1hr, 2hrs, 4hrs, 1hr, 6hrs, 4hrs, 4hrs, 3hrs, 1hr, 2hrs, 3.5hrs, 2hrs, 7hrs, 2.5hrs, 3.5hrs, 3.5hrs, 6hrs, 4hrs, 1hr, 1hr, 2hrs, 2.5hrs, 3hrs, 9hrs, 3.5hrs, 2hrs, 1hr, 4hr. a) What is the total number of hours he played during that month? b) What is the mean number of hours played? c) What is the median hour James played? 19 Worksheet#3 WORK OUT THE MEDIAN FOR a) 3, 6, 4, 14, 35, 7, 7, 5, b) 35, 76, 55, 45, 44, 56, 43, 48, 46, 46, 46, 46, c) 50, 87, 88, 130, 109, 126, 77, 87, 109, 109, 123 d) 209, 405, 366, 560, 309, 299, 325, e) 687, 1098, 999, 789, 875, 545, 1001, 779 f) Tim is travelling around the USA. He decides he is going to have the same burger: beef pattie, onion rings, cheese, lettuce, tomato with mustard and ranch sauce in all the 52 states he is visiting. The amount Tim paid for each burger is below: $4.50, $2.50, $3.00, $5.95, $5.00, $7.00, $6.05, $3.75, $2.50, $6.00, $1.95, $3.75, $4.50, $4.25, $6.00, $5.95, $4.80, $3.95, $4.50, $3.50, $6.50, $7.85, $9.05, $8.75, $3.80, $2.50, $4.25, $4.80, $5.60, $5.60, $7.80, $3.50, $5.25, $5.20, $6.80, $4.85, $5.00, $7.50, $3.75, $2.95, $7.20, $6.85, $5.30, $6.60, $4.45, $12.00, $2.95, $7.50, $6.85, $4.50, $4.50, $4.50 1. What is the average price Tim paid? 2. What is the median price Tim paid?? 20 Worksheet #4 Record Sheet for Card Game… Hand: Working Answer Points Mean Median Mode Range Total 21 Assessment Tool B Question: The Tuck Shop is revising its menu and has decided it needs to take out two items that are their lowest sellers. They cannot decide between The sausage roll The baked bean jaffle The ham, mustard and onion sandwich The almond cookie The potato and green pea pie Your job is to develop a formal report which includes 1. Collection of the appropriate data: you will be broken up into groups of three and will spend one 10 minute period during the hot lunch time at the Tuck Shop surveying the items bought. 2. Sort out data and share results so all members of the class have the same data 3. Use ICT, to represent the collected data on a pie chart 4. Work out the mean, median, mode and range. Identify any outliers and evaluate how they might skew the data. 5. Write a justification about which items you believe need to be taken off the menu. Reminder: Steps 1, 2 and 3 are to be done in groups, Steps 4 and 5 must be done individually. 22 A B C D E Translated problem Translated problem Translated problem Developed a Little or no into appropriate into question and into question and survey. Collected attempt to develop question and developed survey. developed a survey. and attempted to survey. Collected developed survey. Collected data and Collected data and sort data using data. Some Collected data and sorted using sorted using graphical attempt to sorted using graphical graphical graphical representation. represent data representation: tally, bar graph. Using ICT, representation: representation. Using ICT using ICT. Little or correctly represented tally. Using ICT, Using ICT, attempted to no attempt at data as pie chart and correctly represented data as represent data as working out mean, converted data sets represented data as pie chart. Worked graphical median, mode and to percentages. pie chart. Worked out mean, median, representation. range. Correctly worked out out mean, median, mode and range. Some attempt to Justification was mean, median, mode mode and range Justification was work out mean, not present. and range using using appropriate present. median, mode and appropriate formulas. formulas. range. One or two Justification was in Justification was in sentences as depth and referred to depth. justification. data. 23 Worksheet #5 At the local high school, 60 year seven students were asked to choose their summer sport. The results were as follows: Swimming 20 Cricket 15 Dance 12 Canoeing 3 Tennis 10 Draw a pie graph of the results. (Show all working in your exercise book) Work out the percentage of the choices and don‟t forget to clearly label the graph. a) Which sport had the highest percentage? b) Which sport had the lowest percentage? 24 25