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Ideas for teaching chance, data and interpretation of data

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These activities have been designed specifically for Year 3 students according to the Australian Curriculum guidelines. However, they can be adapted to meet other standards or year levels.

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Ideas for teaching chance, data and interpretation of data

1. 1. Chance, Data and Interpretation Unit created by Joanne Villis Year 3 Australian Achievement Standard: Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables. Year 3 Australian Content Descriptors: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067). Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068) Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069) Interpret and compare data displays (ACMSP070)
2. 2. ENGAGE (iDEA 1): Task: Brainstorm a list of words that could be used to describe the chance of an event occurring (ie likely, unlikely, impossible etc). Ask students if they have heard numbers being used to describe chance? Discuss as a class. Create a class probability line. Ask students to sort words along the line (ie impossible, rarely, certain, likely, unlikely, uneven chance,) then on different coloured card numbers to represent chance (e o, ½, 1 and o, 50% and 100%). Task: Invite students to think of an event, write the event on a post it note and then stick it to the probability line. Allow students time to read each others responses.
3. 3. ENGAGE (iDEA 2): Task: Create scenarios like the ones below for students to consider: a) I overheard my mum telling our neighbor that on the weekend we would definitely so something but I could not hear what it was. What might it be? b) I heard the teach say, ‘It is… that all of the children in this class will watch television tonight’ but I didn’t hear one of the word. What might the missing word be? What is something that is more likely to happen than what the teacher is talking about? c) Someone asked the teacher a question and she replied ‘Maybe’. What might the question be? d) Sydney went ice skating for the first time, stood up and… What might have happened next? e) A family has three children We know that at least one of the children is a girl. Draw what the other family might look like. f) A class wrote down some things that they felt were impossible. What might they have written? Source: Sullivan, P & Lilburn, P (2008) Open-ended math activities, Second Edition, Oxford Press, p. 100-101.
4. 4. ENGAGE (iDEA 3): Task: Play the fair race game. You can play this game outside with boxes of dress up clothes or small bean bags. a) Place students in teams of 4. b) Ask students to line up in their team so that your class is in 4 lines. c) Place clothes (or bean bags) in 4 boxes opposite each team. The task is for team members to take it in turns to run to the box of clothes, put on a garment, run back and tag the next person in the line (ie like a relay race). The first team with no clothes left in their box is the winner. NOTE: For the first race use an even number of items in each box. Then for the next race change the number of items in each team’s box so that some have more than others. Race and then ask students if the game was fair? Discuss why or why not?
5. 5. EXPLORE (iDEA 1): Task: This activity is a modified version of an Indigenous Australian Game known as ‘kal-ka-doon kee-an’ . Background: “In areas of north Queensland, a game of throwing skill was played. A large bone, such as an emu shinbone (with twine attached to it) was thrown over a net (used to catch emus) into a pit or hole. Considering the distance to the hole, great skill was required to correctly aim the bone and ensure that it did not touch the net” (Australian Sports Commission, 2009, p.64). Language: “The game is called kee’an, which means ‘to play‘ in the Wik- Mungkan language of north Queensland. The Kalkadoon people from around the Mount Isa area also played a game similar to the one outlined and their connection has been recognised as part of the name of this game” (Australian Sports Commission, 2009, p.64). Australian Sports Commission (2009), Yulunga Traditional Indigenous Games, p.1-107 Retrieved from: ausport.gov.au/isp
6. 6. Tasks: 1.Ask students to list all of the possible outcomes which could occur if they threw their object. For example: (1) player 1’s object and player 2’s object will land inside the target (2) player 1’s object will land inside target but player 2’s will not (3) player 2’s object will land inside the target but player 1’s will not (4) neither of the player’s targets will land inside the target. 2. Model on an IWB or whiteboard how to rule up a table in order to record results. 3. Model how to record using the tally system. Inform students that they will need to use the tally system in order to record the results of their game after each pair has thrown their object. 4. Students play the game and record their results. 5. Demonstrate to students on an IWB or whiteboard how to draw a column graph. Students can follow the instructions step by step in their books as this may be the first time students have drawn graphs in their current year level. Remember to encourage students to name the axis of the graph (ie possible outcomes and throw results). 6. Repeat step 5 using a bar graph.
7. 7. Tasks continued… 7. Use Microsoft Word Charts to create a pie graph. a) Go to Microsoft Word, Insert, Chart. Select the chart you require.
8. 8. Tasks continued… b) Enter the data into the EXCEL part. This will automatically adjust the data being displayed in the graph.
9. 9. EXPLORE (iDEA 2): Task: Ask students to consider the scenarios below and provide them with the equipment needed in order to test their thoughts. a) 2 dice Scenario 1: Two students were playing a dice game. One student tossed two dice together and when they landed one was 6 and one was 4. What other combinations might the students have tossed? Scenario 2: Zac threw two dice and when they landed he subtracted one number from the other and wrote down the answer 1. What might the numbers on each dice have been? Equipment: 2 dice b) Bag of coloured paper Scenario: In a bag there are some coloured pieces of paper. I draw one piece of paper and it is red. I put it back and draw again. This time the paper is black. I put it back. After ten draws, I have drawn out three red and seven black. How many pieces of paper might there be in the bag and home many might be black? Equipment: Red and black pieces of paper and a zip lock back. Source: Sullivan, P & Lilburn, P (2008) Open-ended math activities, Second Edition, Oxford Press, p. 101-103.
10. 10. EXPLORE (iDEA 3): Tasks: 1. Show students a jar with a packet of jelly beans inside. Ask students to record all of the possible outcomes which could occur if they put their hand into the jar and selected a jelly bean (ie red, green, blue etc). As students to record all possible outcomes using a list. 2. Invite students to predict how many red, blue etc jelly beans there are in the jar and record their predictions in the their book. 3. Tip an additional bag of jelly beans into the jar and ask student to predict how many of each colour are now in the jar. 4. Ask students to calculate the total of their number of jelly beans for 1 bag and then two bags of jelly beans. 5. Ask students to record their thinking or mathematical reasoning. 6. Let students test their calculations of total jelly bean numbers using a calculator. Note: I used 3 packets and this task took too long. Therefore, I suggest that 2 packets are used instead.
11. 11. Tasks continued… 7. Model/demonstrate how to draw a table in order to record the outcomes of the investigation. 8.Allow students to pull 2 jelly beans out of the jar at a time a demonstrate how to record results on an IWB or whiteboard using the tally system. Invite students to call out their colours in a loud and clear voice so that peers can hear.
12. 12. Tasks continued… 9. Once all jelly beans have been removed from the jar, invite students to tall their results. If there are inconsistencies amongst students, this doesn’t matter. The focus if for students to record their own data. 10. Invite students to analyse their data using chance language (ie greater than, equal, least likely). This process should require about 4 sentences.
13. 13. Tasks continued… 11. Ask student to draw a jar and inside draw their own jelly beans which they have collected from the previous activities. 12. Discuss various ways of explaining chance (ie words and percentages). Introduce students to the idea o representing probability using fractions. For example, the bottom number tells me how in total and the top number tells me how many I am talking about. If I had 9 jelly beans and 4 of them were red, the probability of me selecting a red would be 4/9.
14. 14. Extension: I worked on the following activities with a student whilst a student teacher (Madeleine Hunter) was teaching. Once the data of the jelly bean numbers had been recording I asked the student to: 1. Consider how she could work out the percentage of each colour of jelly bean compared to the total. 2. I asked her to record her calculations. 3. She calculated her percentages rounding to the nearing 0.5. This resulted with a total of 115%.She then decided to calculate the percentages to the nearest 10 which resulted with an overall total of 98% (we thought this was close enough). 4. The student was then asked to draw a pie graph to represent her data. 5. Then I gave her a challenge. For example, draw a pie graph combining the totals red, blue, green , orange and black and white jelly beans.
15. 15. Tasks continued… 13. Ask students to create a column graph using a scale of 5 and then an picture bar graph where 1 jelly bean represents 10 jelly beans.
16. 16. EXPLORE (iDEA 3): Tasks: 1. Give each student a Minite. 2. Show students how to rip a Mintie wrapper to create a piece as long as they can. 3. Ask students to measure the length of their Mintie wrapper and round the length of the wrapper to the nearest 5cm. 4. Students record the length of their Mintie wrapper and the data is collated as a class using a table. 5. Ask students to draw a picture graph to represent the various lengths of Minitie wrappers. Each Mintie on the picture graph needs to represent 5cm of length.
17. 17. Tasks continued… 6. Using EXCEL students enter their Mintie data and then create a column and bar graph to represent their data.
18. 18. Tasks continued… 7. Students interpret the data displayed in their graphs. For example, what was the greatest length and the shortest length? What is the total length of the class Mintie wrappers combined? (students may need to use a calculator). As an extension, students may calculate the average length of the class Mintie wrappers.