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Year 8 Spring 2 Lesson 4: nth term Venn DiagramsObjectiveTo classify nth terms into Venn DiagramsAimStudents use their knowledge of nth terms to sort sequences into the different regions of Venn Diagrams. This gives them the opportunity to practice their reasoning skills as they must describe why they are placing the nth terms into each region, or why no nth term can be placed there.ResourcesPowerpointTemplates for plastic wallets (students draw over the top of them)Slides 8 - 10 printed as an A5 booklet if students are working individually.Slides 11 and 12 as a challengeActivity 1: This activity is a recap of the work from last lesson, but with a few questions that will help them with the Venn Diagram activity.These should be answered on whiteboards.Questions for progressionWhat is the common difference in all three of the sequences?On your whiteboard, can you show me an expression that would also give me a common difference of 4?And anotherWrite down an nth term would give the multiples of 3.Can you show me a different nth term that would give another sequence with an common difference of 3? Can you show me an expression that would give me a decreasing sequence with a common difference of 5? Do any of the sequences above contain a term of 20?Which sequence definitely does not contain the term 536? How do you know?None of the three sequences have any of the same terms. Why is that?Activity 2: This activity is just to get used to using the Venn Diagram template, and shouldn’t take more than a couple of minutes.Students sort the digits 1-9 into the Venn Diagram on their plastic wallets following the rules on the sheet – Numbers in the sequence 2n and numbers in the sequence 3n.Pick out any incorrect ones and ask students where they should go.Questions for progressionWhich numbers are in the intersection? Why are they there?Which numbers are in the sequence 2n, but not in the sequence 3n? Where can you find them in the diagram?Which numbers are neither?Activity 3: Students answer slides 5 – 7 as a class using their plastic wallets. Pick a variety of answers to go in each region. Questions for progressionWhy did you choose that nth term?How did you know it would go there?How do we know what the common difference is from the nth term?How can you find the first term?Activity 3: Now in their pairs, they work through the Venn diagrams on slides 8 - 10Little progressStuck on slides 8 - 10Questions for progressionCan you write me down any nth term?Do the numbers increase?Does it contain the term 20?How do you know?Where would that nth term go in the Venn DiagramWhere can you see the common difference in an nth term.How can you check what the 3rd term of your sequence is?Some progressStuck on slides 11 - 12Questions for progressionWhat property would a sequence have in this region? (Choose one of the intersections)Write down any linear nth term. Where would it go in the Venn Diagram?Substantial progressStuck Finished all three and written up in their booklet.Questions for progressionWhich was the easiest region to complete, and which was the hardest?Which region has the most possible examples, and which has the fewest?What would you change a circle label to, to make the task harderCreate your own Venn Diagram on this topic where it is possible to fill in all the regionsCreate your own Venn Diagram on this topic when it is impossible to fill in just 1 of the regions. How about one where it is impossible to fill in 2, 3, 4, etc regions?-62865129540Acknowledgement: Venn Diagram tasks adapted from tasks on 0Acknowledgement: Venn Diagram tasks adapted from tasks on ................
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