Robots. Reasoning in the classroom. Year 7. Support materials for teachers

Transcription

1 Robots Reasoning in the classroom Support materials for teachers Year 7

2 Year 7 Reasoning in the classroom Robots These Year 7 activities encourage learners to use their reasoning skills within the context of movement. Robots Learners use their reasoning skills to find when the robots meet. Includes: Robots questions Markscheme Robots on grids They extend their thinking to consider robots moving on square grids and then produce a simple proof. Includes: Explain and question instructions for teachers Whiteboard Robots on grids Reasoning skills required Identify Communicate Review They choose their approach, breaking problems down into simpler steps. They consider how to present their work clearly and give detailed explanations. They consider and justify their findings, giving a simple proof. Procedural skills Simple understanding of speed, in terms of distances moved each hour Introduction

3 Robots

4 Activity 1 Robots or Outline This activity requires learners to use information about the distances travelled by two robots in one hour. You will need Q Robots questions One page for each learner M Markscheme Activity 1 Robots Outline

5 Q The orange robot takes 1 hour to move 200m. The blue robot takes 1 hour to move 100m. At 4 the robots stand at opposite ends of a straight line, 600m apart. 2m At 4 the next day they start again, 600m apart. 2m Robots Activity 1 Robots Questions

6 M Activity 1 Robots Markscheme Q Marks Answer i 2m 6 Or 1m States explicitly that the time taken is 2 hours (units must be present) Or Shows 400 and 200 Or Shows Number of metres moved by each robot Total number of metres moved in one hour ii 2m Justifies their answer of 10 by stating or implying that the time taken is 6 hours Or 1m Shows or implies the time taken is 6 hours e.g. 6 hours identified as the total time 3 hours for the orange robot to get to where the blue was, then double that time Or Creates their own method that shows both robots positions for at least the first four hours, e.g. Activity 1 Robots Markscheme

7 M Activity 1 Robots Exemplars 400 Takes 2 hours 200 Takes 2 hours 6 Part i, correct; 2 marks At 4 the next day they start again, 600m apart. Moved 1200m in 6 hours 600m Moved 600m in 6 hours 10 Part ii, correct; 2 marks The justification, 6 hours, is explicit. They meet at 400m orange robot will be at 200m in 1 hour bluerobot will be at Part i, correct; 2 marks At 4 the next day they start again, 600m apart. 200m 400m 600m orange 3 hours 3 10 Part ii, correct; 2 marks The justification, 6 hours, is implicit by the markings on the diagram. 1 hour 1 hour 1 hour 1 hour It will take the robots two hours till they meet 6 Part i, correct; 2 marks At 4 the next day they start again, 600m apart. 1 hour 1 hour 1 hour 1 hour 1 hour At what time do they meet? Show 400 how you 600 know It will take them 5 hours till they meet Part ii, shows both positions; 1 mark The diagram shows understanding but the learner has lost track of where each robot is and when. 9 Activity 1 Robots Exemplars

8 M Activity 1 Robots Exemplars (continued) 2 x 200 = x 100 = 200 Part i, shows 400 and 200; 1 mark At 4 the next day they start again, 600m apart. 8 Common error The answer 8 is a common error. It comes from learners forgetting that the robots move simultaneously Part ii, incomplete; 0 marks Only the positions for the first three hours are shown Part i, incorrect; 0 marks This learner appears to have added the distance travelled in one hour by the orange robot to the distance that the robots are apart. At 4 the next day they start again, 600m apart Part ii, incorrect; 0 marks Common error Although the time of 10 is correct it has been found by adding the time to the distance. Sadly, this is a common error which is why a correct method must be shown. 1 for 200m = 600m 1 for 100m = 300m 5 Part i, incorrect; 0 marks At 4 the next day they start again, 600m apart. because you just double the first one Part ii, not justified; 0 marks Although 10 is the correct time, there is no evidence to support understanding therefore no marks can be given. 10 Activity 1 Robots Exemplars

9 Robots on grids

10 Activity 2 Robots on grids or Outline This activity is designed to carry on from Activity 1 Robots, but could be presented as a stand-alone activity if wished. Learners work in pairs to play a simple game, then produce reasoned arguments to support their thinking. You will need WB Whiteboard Robots on grids Squared paper Counters (optional) Activity 2 Robots on grids Outline

11 Activity 2 Robots on grids Show Robots on grids on the whiteboard and explain that learners are going to work in pairs. One will be the orange robot. The other will be the blue robot. The aim is for the orange robot to catch the blue robot. Explain Give these rules: The robots take it in turns to move, starting with the blue robot. One edge of a square on the grid is one step. Robots cannot retrace their steps. Remind learners that the orange robot moves two steps at a time, then check understanding by asking where each robot could be after one move, i.e. Now ask them to play the game several times, writing down how many moves each robot takes before the orange robot catches the blue robot. Then ask: can they prove that the orange robot will always be able to catch the blue robot after each robot has taken four moves? (The diagram shows where the blue robot could be after four moves For each of these positions it is possible to find a route for the orange robot such that it is in the same place after four moves.) Are you being systematic? How? How could you make it clear to someone else which grid intersection you were referring to? (For example, by using coordinates.) Question Can you convince me that it is not possible for the orange robot to catch the blue robot in fewer than four moves? (The blue robot can always move in such a way that it escapes all possible positions for the orange robot.) Extension What if the size of the grid were to change? Activity 2 Robots on grids Explain and question

12 WB The orange robot moves 2 steps at a time. The blue robot moves 1 step at a time. Robots Activity 2 Robots on grids Whiteboard