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Australian Curriculum Year 5 • Apply the enlargement transforma1on to familiar two dimensional shapes and explore the proper1es of the
resul1ng image compared with the original (ACMMG115) • Recognise that probabili1es range from 0 to 1 (ACMSP117) • Pose ques1ons and collect categorical or numerical data by observa1on or survey (ACMSP118) Key Ideas General Capabili8es u Using spa)al reasoning This element involves students in making sense of the space around them. Learners visualise, iden1fy and sort shapes and objects, describing their key features in the environment. u Cri1cal and crea1ve thinking Inquiring–iden1fying, exploring and organising informa1on and ideas-‐Organise and process informa1on Reflec1ng on thinking and processes-‐Transfer knowledge into new contexts. Reflect on processes Resources • FISH • Photos of Erik Johansson www.adobe.com/inspire/2013/02/interview-‐erik-‐johansson.html • Student landscape artwork • Spinners
Vocabulary Certain, uncertain, possible, impossible, unlikely, likely, fantasy, serendipity, real, predic1ng, evidence, survey,
Ac8vity Process: Spinner Learning Inten1on. To iden1fy the shape of a spinner and consider why a circular form is efficient. Ask learners to demonstrate spinning body kinesthe1c-‐circular movement, a rota1on. Ask learners to describe how many degree this involves in a full rota1on.
Spinning can be controlled or random depending on what Is being rotated-‐force and speed are factors.
Ask learners to create a circular spinner-‐ usually this will be a simple circle. Divide the class cohort into groups
and assign a spinner problem
to each group. Underline the probability clue words
Group 1 Wendy wants to make a spinner for a game that will be equally likely to land on A, B or C. Divide and label a blank spinner so that it will work for Wendy’s game.
Group 2 Elizabeth wants to make a spinner for a game that will be twice as likely to land on A or B. Divide and label a blank spinner so that it will work for Elizabeth’s game Group 3 John is making a game that needs a spinner. The spinner must be divided into four parts: A B, C and D. John wants to make it more likely that it will land on B than on C. He also wants to make sure that leber D is the least likely to land on. Divide and label a blank spinner so that it will work for John’s game.
Group 4 Maria wants to make a spinner for a game that will be likely to land on A, B, C, D, E, F, G or H. Divide and a blank spinner so that it will work for Maria’s game. Groups report on the reasonableness of their solu1ons using the FISH process.
Group 5 Daniel is making a game that needs a spinner. The spinner must be divided into five parts: A, B, C, D and E. Daniel wants to make it more likely that it will land on B than on C or D. He also wants to make sure that the leber E is the least likely to land on. Divide and label the spinner so that it will work for Daniel’s game. As each group reaches a reasonable solu1on they indicate with a thumbs up presented against their torso. Ask the group to prepare to present their ideas to the class.
Ques1ons to be considered • Can we explain how we solved the task? • Can we show evidence which supports our thinking and solu1on? • How do we know that our solu1on is reasonable? Groups present their probability clue words and visual solu1on to the whole class.
Ac8vity Process: Spinning About Key Ques)ons to consider: Is the world real or imagined? How do ar1sts represent their world. Ar1sts are free to interpret reality rather than reproduce it. ‘The ar)st does not draw what he sees, but what he has to make others see’ (Edgar Degas (1834-‐1917) A modern ar1st who would agree with this viewpoint is Ton Schulten. He is a Dutch landscape painter who uses bright blocks of colour to express his ideas about nature. Watch hbps://www.youtube.com/watch?v=WAnpIrS1WpE (in Dutch, but ask learners to read sub1tles) Ask learners to watch it a second 1me the ar1sts statement
‘I translate reality in my own way which makes pain)ng an adventure’
Show further examples of his work and discuss what they see in his work. Slide show is available from hbp://www.tes.co.uk/teaching-‐resource/Ton-‐Schulten-‐Landscape-‐ar1st-‐6096489/
The slideshow can then be adapted to include a perspec1ve on geometry reasoning.
Use the sentence stem-‐Ton Schulten uses……….. They should no)ce: His landscapes are semi-‐abstract (a style of pain1ng, in which the subject remains recognizable although the forms are highly stylized). There is a strong sense of visual texture about his work. As a painter he uses a bright, rich colour palebe that look like building blocks of colour intersec1ng ver1cally and horizontally, which create angles which are olen greater than 90 degrees. Link to: Year 5 Visual ARTs Unit-‐Where the Sky Meets the Sea
While his work is recognisably a landscape it would be impossible to see this view looking out of a window and even two ar1st would not see it in the same way in it en1rety.
In collabora1ve groups, viewers are asked to label the colours used by the ar1st in his landscape. Descrip1ve names for the colours are to be encouraged. Each group then creates a spinner based on the colour names and the es1mated amount the colour is represented in the pain1ng.
Spinners are displayed and differences discussed. Groups are asked to discuss whether a pain1ng created from random spins can be considered Art. Ac8vity process: How can a tree diagrams help list all the possible outcomes? Learning Inten1on: Understanding why making tree diagrams and using mul1plica1on is useful
when finding the possible number of outcomes. Ton Schulten has used a warm colour palebe in his landscape. Red and orange are very prominent in the composi1on. What are the possible outcomes of spinning the spinner if we also toss a coin? To keep a record of the experiment, organise and count the outcomes we are going to use a tree diagram. It is called a tree diagram because it looks like the branches of a tree. Could we have worked out the possible outcomes another way? You can also find the number of outcomes by mul1plying.
Ask the class to compare the two outcomes. How is using mul1plica1on similar to using a tree diagram? How is it different? Both methods show the number of possible outcomes but only the tree diagram shows what the different outcomes are. Ac8vity Process: Inves8ga8on Independently choose three colours from the Ton Schulten spinners and assign a 3 leber code to each colour. Present the possible outcomes as a tree diagram. Support the reasonableness of your answer with a mul1plica1on diagram.
Background Probability is the study of chance or the likelihood of an event happening. Directly or indirectly, probability plays a role in all ac1vi1es. Both mul1plica1on and tree diagrams show the number of possible outcomes but only the tree diagram shows what the different outcomes are. When we need to understand the outcome op1ons not just the amount we use a tree diagram as it records all possible outcomes in a clear and uncomplicated manner.
hbp://www.virtualnerd.com/sat-‐math/arithme1c/probability-‐coun1ng/sample-‐space-‐count-‐outcomes-‐using-‐tree Is a video link to a video example of tree diagram that illustrates a real world situa1on in which we might want to consider the kinds of outcomes.
Spinner 1st toss 2nd toss Outcomes
Red
H H Red H H
T Red H T
T H Red T H
T Red T T
Orange
H H Orange H H
T Orange H T
T H Orange T H
T Orange T T
Spinner Outcomes
1st toss Outcomes
2nd toss Outcomes
Total Possible Outcomes
2 X 2 X 2 = 8
