TASKS 1

What is a Task? -word problem for which there is no obvious answer -students must create the steps for the solution -causes students to think and struggle in the solution -allows various solution pathways -takes time -encourages students to talk with and learn from each other -leads to truly understanding math concepts 2

Team Building 3

I Y C G L Z R Q B V E M W F O S D K U X T Q J N H J 4

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I Y C G L Z R Q B V E M W F O S D K U X T Q J N H J 6

E S V D I W A O Q B Z G N M K J X H U C Y F T L R P 7

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E S V D I W A O Q B Z G N M K J X H U C Y F T L R P 9

Dan Meyer tool-worth-using/ Less is More Dan Meyer “3-Act Plays”

Questioning What makes a good task question? 11

There are three main features of a good task question: 1. It requires more than remembering a fact or reproducing a skill. 2. Students learn by answering the question and teachers learn from the students’ attempts. 3. There may be several acceptable answers. 12

Jane 4 feet 2 feet 13 What is the perimeter of the above shape? What is the area of the above shape? Jane knew the formula for perimeter: 2 bases + 2 heights = Perimeter and area: base x height = square area

More than remembering: I want to make my garden in the shape of a rectangle. I have 30 meters of fence for my garden. What might be the area of the garden? 14

More than remembering: I want to make my garden in the shape of a rectangle. I have 30 meters of fence for my garden. What might be the area of the garden? 15 This task required Comprehension of the task Application of the concepts and appropriate skills Analysis Some synthesis of the two major concepts

Textbook question: What is the average of 6, 7, 5, 8 and 4? Rephrased as a task question: The average of five numbers is 6. What might the numbers be? Or After five games, the goalie had averaged blocking six goals per game. What might be the number of goals he blocked in each game? 16

Question: John and Maria each measured the length of the basketball court. John said that it was 25 yardsticks long, and Maria said that it was 24 ½ yardsticks long. How could this happen? 17

Question: John and Maria each measured the length of the basketball court. John said that it was 25 yardsticks long, and Maria said that it was 24 ½ yardsticks long. How could this happen? Agree on levels of accuracy Agree on where to start and finish, and the importance of starting at the zero on the yardstick. Avoid overlap at the ends of the yardsticks Avoid spaces between the yardsticks Measure the shortest distance in a straight line. The students established for themselves these essential aspects of measurement, and thus learned by doing the task. 18

Another reason for tasks: Differentiation Since correct answers can be given at a number of levels, tasks are particularly appropriate for mixed ability classes. Students who respond quickly at a superficial level can be asked to look for alternative or more general solutions. 19

How to Create Good Task Questions: It is possible to make up your own good questions for any topic and any grade level. The important thing is to plan the question in advance, as creating them is not something that can easily be done on the fly. 20

Method 1: Working Backward Step 1: Identify a topic. Step 2: Think of a closed question and write down the answer. Step 3: Make up a question that includes (or addresses the answer. ie: Step 1: Topic – rounding Step 2: Round 11.7 to the nearest whole. Answer: 12 Step 3: My coach said that I ran 100 yards in about 12 seconds. What might the number on the stopwatch have been? 21

Method 2: Adapting a Standard Question 1.Identify a topic 2.Think of a standard question. 3.Adapt it to make a good question. ie. 1. subtraction (with and without regrouping) = 3. Arrange the digits so that the difference is between 100 and

Dynamic Classroom - where children are involved and engaged in their own learning. 23

Dynamic Classroom - where children are involved and engaged in their own learning. 24 Achieved through: Activities that promote higher level thinking, Cooperative problem solving, Communication

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Anticipate Student Thinking Monitor Student Thinking Select and Sequence Student Thinking Connect Student Thinking 26

Have we activated appropriate background knowledge? Provided enough information while maintaining the problematic nature of the task? When are students ready to move to the discuss stage? What’s next? What are students taking away from the discussion? 27

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Thinking Through a Unit Ideas: What do we want students to know? Strategies: What do we want students to be able to do? Representations: How do we want students to make their thinking visible? How do ideas, strategies and representations differ from the beginning to the end of a unit of instruction? 29

Launch Engage students with a demonstration, a video, a story, access prior knowledge, or simply pose a good task question. Pose the task question. Write it on the board. It’s important to make sure that everyone knows what the question is. Allow some time for students to ask you about the meaning of the task, but don’t give directions or suggestions on how to do it. This is for the students to work out for themselves. 30

Launch We are going on a field trip and we need to order buses to take us. How many buses do we need to take all of our third grade classes? Do you want to ask me any question before you get started? You will need to show your thinking. You will need to justify your thinking by showing at least two different methods.. 31

Explore Let the students work in pairs or small groups. This allows them to communicate their ideas to others. This communication is an important part of learning. Working together can also assist those who may have difficulty starting. If they have to wait for the teacher then organization and attitude problems can arise. 32

Once the groups are working, your task is to monitor their progress. 33

Once the groups are working, your task is to monitor their progress. What do you know? What are you trying to find out? How are you going to start? What strategies will be most helpful for you to solve this problem? Have you ever solved a problem similar to this? Will that always work? What does that number represent? Tell me about it. As they begin to come up with solutions, look for a few students or groups to come up and present their work. You will not need everyone to finish before you begin the discussion. You could give a 5-minute warning so they can tie up loose ends. 34

Explore: Student role: 1. Engage in task 2. Raise “how,” “why,” “what if,” “so what” and “does this make sense” questions 3. Question, explain, and justify individual or group work using proper vocabulary 4. Make connections among the string or related problems, questions, or tasks 5. Make connections with previous learning. 35

Explore Student Role: Reflect on work by asking: - “Is this accurate?” - “Do I understand this?” - “Can I explain this?” - “Where would I use this?” 36

Whole Class Discussion Students will present their solutions and justify them. Make sure this is a positive, non-threatening time. 37

Discuss Teacher role: 1. Ask probing/directed questions to draw out explicit and specific connections 2. Confirm correct thinking 3. Use language, conventions, and symbols of mathematicians. 4. Assess student understanding 5. Help students recognize emerging concepts, algorithms, and tools. 6. Use direct instruction as appropriate. 38

Discuss Student role: 1. Share, explain and justify thinking. 2. Actively participate by listening, describing, complimenting, or comparing student work. 3. Correctly use mathematical language, conventions and symbols. 4. Question to clarify understanding.. 39

After the discussion: Determine the next phase of the learning cycle: - Solidify Understanding phase, or The goal of Solidify Understanding is to examine and extend student ideas, strategies, and representations, which leads to a development of concepts, algorithms, and tools. - Return to Develop Understanding phase with newly surfaced ideas, or - Move to Practice Understanding phase The goal of Practice Understanding is to allow students to refine and acquire fluency with concepts, algorithms, and tools which leads to the development of generalizations, procedures, and models. 40

Solidify Understanding We are going on a field trip and we need to order buses to take us. How many buses do we need if we have parent volunteers in each class? 41

Practice Understanding We are going on a field trip and we need to order buses to take us. How many buses do we need if we invite 2 nd grade to go with us? We’ll need extra parent volunteers this time. 42