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Differentiated “TriMind” Learning Task (Based on Sternberg’s framework for differentiating by learning profile introduced during classes and the readings)

Name & Student Number: Lorelle Barton (2073611) Topic: Chance Curriculum Area: Mathematics Year Level: 5 Learning Objectives. As a result of completing the learning task, students will: Understand that (Concepts, principles, “big ideas”) Students will understand that chance experiments involve equally likely outcomes and can be fair and unfair. Students will understand that all events have many outcomes, called sample spaces. According to ACARA:  

• List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

∆ Recognise that probabilities range from 0 to 1 (ACMSP117)

Know (e.g. facts, vocabulary, dates, information) That probability always ranges from 0 to 1. The vocabulary of chance experiments (likely, unlikely, certain, impossible and equally likely). Be able to (do) (Skills, processes)

When and how this task will be used in the context of the lesson and/or unit (e.g., as an introductory “hook” activity for the unit, as a formative or sense-making activity, as a differentiated assessment piece, etc.): This lesson would be held in the morning for the students Mathematics block and would be undertaken later within the unit on chance. The lesson will allow students to explore their topic of chance and use their current understanding on chance, fair and unfair games and sample space to complete an assessment task. This will be the first lesson for the assessment task. The lesson particularly contains:

• A 15-minute teaching introduction to engage students for their mathematics lesson and chance assessment.

• A 60-minute differentiated lesson sequence that is differentiated by student learning profile. This particular sequence is based on the TriMind strategy devised by Sternberg. In this sequence, students will choose an assessment activity based on analytical, creative or practical learning.

• A 5-minute lesson closure that gives students an opportunity to reflect on their learning and write a statement about what they will do next lesson to continue their assessment piece. Students will be given a chance to question and share what they are doing for their assessment tasks.

How students’ work will be evaluated (i.e., How will you know that

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Create an event of chance. Justify why an event of chance may be fair or unfair and what elements of the event suggest this. Show they can explain all probabilities for their task, to show all outcomes. Essential Question/s:

• How can the probability of an event be calculated and recorded?

• What is chance?

• What are some games of chance?

• Are games or events that depend on chance always fair?

students have achieved the objectives through their completion of the task?): At the end of the lesson, students will hand up what they have done so far and will complete an exit card to reflect on what they are doing. Finally, they will write a statement on what they plan to do for the week coming. Overall, this work will be formatively assessed, to check how students are going and whether they may need some extra support in the following lesson. Once this task has been completed over the next few lessons, it will be marked as their summative assessment piece. The assessment checklist for this lesson monitors if students have met all requirements and objectives for the lesson. It allows their work and progress to be evaluated to ensure they are on the right track, to continue their assessment for summative marking. ∆ Students must complete their own pieces of work, although their

tasks will involve a lot of inquiring and collaboration, working with others. It is expected their final assessment piece and their exit cards will be handed up and completed individually.

Assignment Includes: Description of the creative, analytical and practical tasks that make up your TriMind learning activity (see next page) Supplementary materials (e.g., copies of directions, handouts, assessments, etc. provided to students) Evaluation/ assessment criteria (e.g., rubric or checklist used to guide evaluation of student work) Explanation of how your learning task represents an application of Sternberg’s TriMind strategy for

differentiating by learning profile. Make sure you include this explanation, either as a separate narrative section somewhere in the assignment, or by some other means that makes this clear to the examiner.

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Differentiated “TriMind” Learning Task Lesson Sequence Class Management/Support

Lesson Introduction – “Hook” (15 mins) ∆ The tasks within this lesson have been based on pre-assessment throughout

the unit on the learner profiles of the students within the class.

Students will be introduced to the learning intention for the lesson: use different learning tasks to produce your assessment piece for ‘chance’. On the IWB students will be timed for 3 minutes to run up one by one and brainstorm everything that they know on the topic chance. Once the timer runs out, students will have a discussion about what they have learnt about chance within the last few weeks. This will allow students to activate their knowledge in preparation for their assessment tasks. Have student’s pair up for 8-10 minutes to play ‘Yahtzee’, a game of chance. Students have played this earlier in the term so they are aware of what needs to be done. (See right for pairing instructions) Bring students back together as a group. Explain the assessment tasks (see lesson sequence below for explanations). Have students consider what options they think they would prefer and ask students to choose there option and begin working. Other important management instructions: ∆ TriMind learning tasks will be situated in 3 different spots around the room that are

colour coded. Analytical tasks will be on Green paper, Creative tasks will be on Purple paper and Practical tasks will be on Orange paper. This will also allow for good flow throughout the class as they transition from one activity to the other.

∆ When students choose the particular learning profile tasks they will undertake, they are asked to also grab their “group button” from the task box. Students will wear the “group button” throughout the lesson so that peers can speak with and ask questions

∆ Ensure that students are sitting at their tables for this introduction activity. When students are participating in a ‘timed gather’ they are asked to stay seated and pass the pen to one another once they have had their turn. This will monitor chaos when brainstorming prior knowledge.

∆ For 8-10 minutes when students are engaging in their learning by experimenting playing a game of chance, have them pair off with their ‘clock buddy/buddies’. Students will pair up with their 6 o’clock buddy to play. This will support ease of flow for students to move into pair work.

∆ Ask two students to go around and collect all the equipment whilst everyone is sitting at their tables.

∆ Make sure there are enough instruction sheets and support materials for each TriMind activity, as students will be choosing their activity within the lesson.

∆ Ensure the class has a “brain break” between this lengthy mathematical lesson. Have students play a quick game of something to break up their learning and to keep them on task.

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to people undertaking the same activity as them for reinforcement. Also, the teacher and any LSOs can see what students should be working on.

∆ Students will be encouraged to use their learning prisms to show how they are doing. These learning prisms have 3 sides to them: I’m working hard, I need help and I’m finished. This will help to manage 3 different groups within the classroom as individual students can display the side they need while they continue working. Teachers can then monitor the students and see who needs help or needs to move onto an anchor activity.

Analytical Task - Differentiated Lesson Sequence (60 mins) (analyse, compare and contrast, evaluate, explain, etc…)

∆ Spend some time initially with this group to discuss any questions on the task and to clarify the task instructions.

Write a blog for a procedure that explains how to play a game of chance. The game must be one similar to one that we have played within class through this unit. You must include the aim of the game, materials needed, the steps to play

for how they are fair or unfair games. At the end of this procedure, explain to your reader why the game is fair, unfair or shows equal chance of all players winning.

Explanation of learning task as a TriMind: According to Sternberg, analytical thinkers are fascinated with the mechanics of knowledge. They prefer to think logically and will choose to know facts, debate, solve problems and prefer work that gives them either a yes or a no answer. Therefore, analytical thinkers are not always the best at accepting open-ended tasks and being creative with their work.

This analytical assessment task has been designed to work with the strengths of these learners whilst also asking them to extend themselves to challenge their thinking creative work. By asking this group to write either a blog or procedure, they are able to still follow structure of a written genre and are able to explain tasks, rather then create new ones. As the class has been working on procedures in class, these students will be able to comfortably produce this piece of work. However, this task is looking at supporting the needs of these learners by asking them to extend themselves further. They are asked to really think about what makes a game of chance. They must really think to figure this

∆ Within the analytical task box there will be a snap lock bag with “hint cards” in them. These cards will give some hints on what games these students could analyse if they are stuck. There will also be reminders of what steps are involved to write a procedure and clues/questions to get them thinking about their mathematical concepts.

∆ By students working on tasks from

specific groups that cater for their learning interests and by using particular colour coded materials with “group button” tags to wear, students are able to support each other with any questions they might have. This will allow the teacher to float throughout the classroom more and not be overloaded with individual questions until a student has asked a friend their question first.

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element out. Furthermore, they are asked to explain why the game they have written a procedure for, is fair, unfair or equally likely to win. This means they have to provide their personal opinion and must work on producing an answer that is not technically right or wrong, more so based on personal opinion.

Anchor Activity: Choose from the following anchor options: (these cards will be supplied in the “anchor” class basket)

∆ Create a PowerPoint that shows likely, unlikely, certain, impossible or equally likely scenarios from real life situations.

∆ Test different chance events. Come up with a list of all possible outcomes to an event you have chosen that depends on chance.

∆ Write a song about chance and probability. Be creative and use the mathematical terminology.

∆ Write a book that would teach your Buddy in Reception about chance.

∆ Remind students that their anchor activity work is within the anchor folder in their task box.

Creative Task - Differentiated Lesson Sequence (60 mins) (create, design, imagine, suppose, etc…) Spend some time initially with this group to discuss any questions on the task and to

clarify the task instructions.

Suppose you were a game maker. How would you create either a fair, unfair or game of equal chance of winning? Create a design for and make a board game

based on this. Make sure you give instructions to your game and can explain why your game shows these elements of chance.

Explanation of learning task as a TriMind: According to Sternberg, creative thinkers like to have time to think and behave creatively. They love to be innovative and produce different ideas for creating something based on a topic. Sternberg suggests that these students need more support and guidance to nurture their creativity and channel it into a realistic finished product. They appreciate assignments that support their creative style of learning and allow them to inquire on a topic, through their creations.

Considering the learning profile aspects of a creative learner, their learning task allows

∆ Within the creative task box there will be a snap lock bag with “hint cards” in them. These cards will give some hints on what games these students could create if they are stuck for ideas. It will also have examples of board game instructions and questions to get them considering the mathematical terms for chance they are using in creating their assessment piece.

∆ By students working on tasks from specific groups that cater for their learning interests and by using particular colour coded materials with “group button” tags to wear, students are able to support each other with any questions they might have. This will allow the teacher to float throughout the classroom more and

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them to work creatively, with support and collaboration, to produce their own piece of work. For a creative learner who may not show strengths within mathematics, this assessment activity gives them the option to create whatever board game they like, as long as it is based around chance and has instructions and a justification. Furthermore, the structure of the activity allows these students to still gain support and work with others in their group to support one another in their creative process of mathematical thinking. Students are undertaking creative a task based around their interests, with support.

Anchor Activity: Choose from the following anchor options: (these cards will be supplied in the “anchor” class basket)

∆ Create a PowerPoint that shows likely, unlikely, certain, impossible or equally likely scenarios from real life situations.

∆ Test different chance events. Come up with a list of all possible outcomes to an event you have chosen that depends on chance.

∆ Write a song about chance and probability. Be creative and use the mathematical terminology.

∆ Write a book that would teach your Buddy in Reception about chance.

not be overloaded with individual questions until a student has asked a friend their question first.

∆ Remind students that their anchor

activity work is within the anchor folder in their task box.

Practical Task - Differentiated Lesson Sequence (60 mins) (use, apply, demonstrate, etc…) ∆ Spend some time initially with this group to discuss any questions on the task and to

clarify the task instructions.

Demonstrate how an event can be made to be fair, unfair or have an equal chance of winning. Apply your knowledge on chance and sample space to teach the class a fitness game that is either fair or unfair. This is showing that you can

put your knowledge into practical use for a real life activity. Justify your reasoning in a 200-300 word summary.

Explanation of learning task as a TriMind: According to Sternberg, practical thinkers like to apply their knowledge in more realistic and worldly situations. Through seeing their learning relate to real life situations, practical thinkers are able to connect with their knowledge at a more personal level, allowing them

∆ Within the practical task box there will be a snap lock bag with “hint cards” in them. These cards will give some hints on what types of games students could use as their fitness or brain break game. There will be questions to get them thinking about the mathematical concepts they should be applying in their task and some prompts for how to start writing their justification.

∆ By students working on tasks from specific groups that cater for their learning interests and by using particular colour coded materials with “group button” tags to wear, students

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to engage more with the task. Practical thinkers have been thought to be workers that show great leadership qualities and have more of a “go-getter” type personality. Because these types of learners have been classified as liking more hands-on activities, activities that connect to the world and are often good leaders, their task has been adapted to suit this learner profile.

The students are asked to “plan” and “teach” a fitness lesson to either a small group or the class. By doing this, students are able to apply their knowledge in a practical situation, which would be more relevant to them as fitness is actually something they would do most days of the week at school and in daily life.

Anchor Activity: Choose from the following anchor options: (these cards will be supplied in the “anchor” class basket)

∆ Create a PowerPoint that shows likely, unlikely, certain, impossible or equally likely scenarios from real life situations.

∆ Test different chance events. Come up with a list of all possible outcomes to an event you have chosen that depends on chance.

∆ Write a song about chance and probability. Be creative and use the mathematical terminology.

∆ Write a book that would teach your Buddy in Reception about chance.

are able to support each other with any questions they might have. This will allow the teacher to float throughout the classroom more and not be overloaded with individual questions until a student has asked a friend their question first.

∆ Remind students that their anchor

activity work is within the anchor folder in their task box.

Lesson Closure (5 mins) Have students place their “group button” and task cards back into the correct task box. One student from each group can place these boxes away on the resource shelf for next lesson. Instruct other students to move back to their tables whilst handing out the exit cards. Ask students to complete an exit card that will be used along with the assessment sheet to test that students have understood what was expected of them for the lesson and assessment so far. This knowledge will help to monitor students for their next lesson working on these assessment tasks.

∆ Select individual students to

collect materials back into boxes to control the transition to the closure section of this lesson.

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References

Sternberg’s TriMind Strategy: Sternberg, R., & Grigorenko, E. (2005). Styles of thinking as a basis of differentiated instruction. Theory into Practice, 44(3)

ACARA: Australian Curriculum Assessment and Reporting Authority, Australian Curriculum, ‘Mathematics: Foundation to Year 10’, Accessed April 2013, URL: http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10

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Appendix A: Analytical Thinkers Task Sheet

Chance Task:

Write a blog for a procedure that explains how to play a game of chance. The game must be one similar to one that we have played

within class through this unit. You must include the aim of the game, materials needed, the steps to play for how they are fair or unfair

games. At the end of this procedure, explain to your reader why the game is fair, unfair or shows equal chance of all players winning.

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Appendix B: Creative Thinkers Task Sheet

Chance Task:

Suppose you were a game maker. How would you create either a fair, unfair or game of equal chance of winning? Create a design for and make a board

game based on this. Make sure you give instructions to your game and can explain why your

game shows these elements of chance.

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Appendix C: Practical Thinkers Task Sheet

Chance Task:

Demonstrate how an event can be made to be fair, unfair or have an equal chance of winning. Apply your knowledge on chance and sample space to teach the class a fitness game that is either fair or unfair. This is showing that you can put your knowledge into practical use for a real life

activity. Justify your reasoning in a 200-300 word summary.

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Appendix D: Student Exit/Reflection Card

Exit Card ∆ What task (colour) are you working on? ∆ What is your plan for next lesson on this task? ∆ Do you have any questions about chance or your task? Would you like a

conference?

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Appendix E: Assessment Sheet for Lesson This assessment sheet can be used to check that students have understood the lesson and have met the learning intention. It will also be used to show how far along with the assessment students have progressed. This will also be added to after the next lesson.

Chance “TriMind” Task Formative Assessment Checklist Components Yes No Comment

Student has completed all sections of their TriMind task.

Student has used correct terminology for chance.

Student has justified their reasoning as to why their event is a fair, unfair or equal chance of winning activity.

Student has demonstrated knowledge on sample space.

Student has used knowledge about probability to show that probabilities can range from 0 to 1.