Name Semester 2 Major Assessment Task: Four Bean Mix Investigation Subject Mathematics: Statistics and Probability Year Level 8 Due Date Conditions Students will get 2 hours of class time and will be given approximately a week after this to finish this task at home. Curriculum links Statistics and Probability Data representation and interpretation Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation (VCMSP297) Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (VCMSP298) Explore the variation of means and proportions of random samples drawn from the same population (VCMSP299) Investigate the effect of individual data values including outliers, on the range, mean and median (VCMSP300) Chance Purpose Identify complementary events and use the sum of probabilities to solve problems (VCMSP294) Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and' (VCMSP295) Represent events in two-way tables and Venn diagrams and solve related problems (VCMSP296) Students will increase their confidence in mathematical modelling of real life scenarios. Students will become more familiar with the measures of centre and spread Students will calculate expected values of probabilities Students will develop their mathematics communication skills. This page has intentionally been left blank Your class has been contracted by Woolworths investigate the percentages of each bean in their cans of “Woolworths Four Bean Mix” https://www.woolworths.com.au/shop/productdetails/663580/woolworths-four-bean-mix-noadded-salt-can Note: ingredients are usually listed from highest percentage of total weight to lowest percentage. Marking Rubric Extended Abstract Explains how to create a Venn diagram and two-way table Synthesises all information (survey, tables, cost) to create an evidence backed report to Woolworths Relational Creates Venn diagram and two-way table Multistructural Creates column graphs with appropriate features Explains claims made in report using evidence (mean, median, mode) Refers to evidence in report Unistructural Uses tables Makes claims Prestructural Indicative behaviors Insufficient evidence Represents data Insufficient evidence Interprets data Capabilities Assessment Task Subject Marks: _______ / 20 Comment: Explains how to create two way tables and Venn diagrams using union and intersection symbols or terminology Uses probability notation such as Pr(C) Discusses measures of centre in relation to can label information Demonstrates an algebraic understanding of expected value Shows working/evidenc e for calculations Calculates expected number of chickpeas Presents probabilities in appropriate format (simplified fractions or % or decimal with number of decimal places rounded to communicated) Includes units, % signs, etc in appropriate places Insufficient evidence Uses correct notation and terminology Finds mean, median and mode for bean number and weight Calculates probabilities from two-way table or Venn diagram Communication Finds mean, Calculates median or mode probability of for bean number chickpea from or weight data Insufficient Insufficient evidence evidence Calculates Calculates measures of probabilities centre Problem solving Four Bean Mix Year 8 Mathematics calculated from the above rubric, one mark per criteria You are to create a report (by hand or on iPad) that has the following information. Each part must be clearly indicated with an appropriate title. Part 1: A photo/sketch of all the beans from one can organised by type – this needs to be well labelled so the reader knows what they are looking at A table which summarises the following information for at least 10 cans of beans. You will need to collect data from your classmates. Total number of beans, total number of each bean, for example: Can Number of Number of Number of Number of Total chickpeas Red Green Borlotti number of Kidney Baby Lima beans all beans beans beans 1 2 3 … 10 Total The mean, median, mode and range for frequency of each type of bean and the total number of beans (show working) The percent of number of beans for each type of bean (show working) A column graph which communicates the mean number of each type of bean in each. Appropriate scale, title, axis labels are required Same as above, but for weight of beans Can Weight of Weight of chickpeas Red Kidney beans 1 2 3 … 10 Total Weight of Green Baby Lima beans Weight of Borlotti beans Total weight of beans The mean, median, mode and range for total weight of each type of bean (show working) The percent (of total) in weight of beans for each type (show working) A column graph which communicates the mean weight of each type of bean Research the cost of each type of bean (on its own). Compare the costs using evidence (links). Summarise your findings in an appropriate format. Survey at least 10 people, what is their favourite and least favourite type of bean out of these four? Summarise the data in an appropriate format. Write a short paragraph summarising the data collected, your findings on cost and consumer preferences to report back to Woolworths. Discuss: does the number and weight order data you have match the listed order of ingredients on the can label? Part 2: One customer likes only chickpeas out of these four beans. They accidentally bought hundreds of cans of “Woolworths Four Bean Mix” and now need some help figuring out how many chickpeas they actually have. Answer the following questions using the class data, show working: On average, what is the probability of any one bean selected being a chickpea? On average, what is the probability of any one bean selected NOT being a chickpea? If they have 100 cans, how many individual chickpeas would they expect to have? If they have 1070 cans, how many individual chickpeas would they expect to have? If they have x cans, how many individual chickpeas would they expect to have? Write an expression for your answer using x Part 3: Do a survey on your at least 20 people to find out if they: Like (or dislike) chickpeas Like (or dislike) red kidney beans Represent this information visually: Create a Venn diagram to represent this information Create a two way table to represent this information How many people did you survey in total? How many people liked neither chickpeas nor red kidney beans? How many people surveyed like chickpeas? How many people like both red kidney beans and chickpeas? How many people like chickpeas or red kidney beans (or both)? For a randomly selected person, calculate the probability that they: liked neither chickpeas nor red kidney beans? like chickpeas? like both red kidney beans and chickpeas? like chickpeas or red kidney beans (or both)? Write a brief paragraph explaining how to create a Venn diagram and two-way table step-bystep, as if you were teaching someone else to do it.