Publishing book. Reasoning in the classroom. Year 8. Support materials for teachers

Transcription

1 Publishing book Reasoning in the classroom Support materials for teachers Year 8

2 Year 8 Reasoning in the classroom Publishing book These Year 8 activities are based around the context of book publishing. Learners use real data to estimate costs and profit. Publishing book Learners read and interpret graphs to solve a problem. Includes: Publishing book question Markscheme Will I make any money? They consider the selling price needed for the author to break even. Includes: Explain and question instructions for teachers Whiteboard My profit Reasoning skills required Identify Communicate Review Learners choose the relevant mathematics to solve problems. They interpret graphs that describe real-life situations and explain their methods. They interpret their answers and draw conclusions from their data. Procedural skills Reading and interpreting graphs Percentages Rounding Numerical language Estimate Profit/loss Break-even point Year 8 Reasoning in the classroom: Publishing book Introduction

3 Publishing book

4 Activity 1 Publishing book or Outline This activity focuses on reading and interpreting graphs to estimate the cost of publishing a book. It is based on real data, from You will need Q Publishing book question Two pages for each learner, must not be printed double-sided M Markscheme Year 8 Reasoning in the classroom: Publishing book Activity 1 Publishing book Outline

5 Q Den has written a book containing words. She will pay to have her book designed. Then she will pay a fee for each copy printed. She wants 500 copies of her book. Use the information on the opposite page to estimate how much she will pay altogether. 4m Publishing book Activity 1 Publishing book Question

6 Q Stage 1: Estimate the number of pages 300 Number of pages Number of words Stage 2: Estimate the design costs 800 Total cost in Number of pages Stage 3: Estimate the printing cost for each copy Cost in for each copy Number of pages Publishing book Activity 1 Publishing book Question

7 M Activity 1 Publishing book Markscheme Marks Answer 4m 2640 Or 3m Shows both 640 and 4 (accept 644) 7 Has read all graphs correctly Or Shows Total printing cost Or Answer The only error is to pay the design cost for all 500 copies Common error Or Answer Scale on stage 2 graph misread as 620 Common error Or 2m Shows 640 Or Links 225 to 4 on the stage 3 graph Or 1m Shows or implies 225, e.g. by marking on either or both of the stage 2 and stage 3 graphs Year 8 Reasoning in the classroom: Publishing book Activity 1 Publishing book Markscheme

8 M Activity 1 Publishing book Exemplars words is 225 pages. 225 pages is 640 for design. It s 4 for printing but that is each copy so altogether it is = Correct; 4 marks This numerical communication is strong for cost in each copy For total cost is Shows 644; 3 marks Common error This learner reads the graphs correctly but forgets that the printing cost is per copy. This is a common error. Number of pages is Design cost 650 Print each copy 4 x 500 = Shows 2000; 3 marks Common error The only error is to misread the scale on the stage 2 graph. This is another common error. Stage 1: Estimate the number of pages 300 Number of pages Number of words Stage 2: Estimate the design costs 800 Total cost in Number of pages Stage 3: Estimate the printing cost for each copy Cost in 4 for 3 each 2 copy Number of pages Shows 640 and 4; 3 marks This learner s numerical communication is weak: there is no indication of how the answer 1090 has been found. However, 640 and 4 are clearly shown on the graphs. calculator for the answer 1090 stage pages stage 2 book 745 stage 3 book 4.60 Incorrect; 0 marks Common error For each stage, this learner has tried to read the end point of the graph. This is another common error. Year 8 Reasoning in the classroom: Publishing book Activity 1 Publishing book Exemplars

9 Will I make any money?

10 Activity 2 Will I make any money? or Outline This activity continues the theme of publishing introduced in Activity 1 Publishing book. Learners consider different selling prices of the book in order to estimate the author s profit or loss. You will need WB Whiteboard My profit The use of a spreadsheet is highly recommended. Year 8 Reasoning in the classroom: Publishing book Activity 2 Will I make any money? Outline

11 Activity 2 Will I make any money? Explain Ask learners if they know what the selling price of a paperback novel is likely to be. (Of course this varies, but 6.99 to 8.99 is a reasonable estimate.) Of this selling price, how much do learners think goes to the author? (If a wholesaler is used as well as a book store, the author may receive only about 45% of the selling price.) Show My profit on the whiteboard and ask learners to work in groups/pairs to find the profit. Once learners realise there is a loss (of ) ask them to work out what the selling price would need to be for this author to break even. (The break-even point is % of the total selling price will equal Therefore, the total selling price of the 500 books must be and the selling price of each book is = , i.e Other ways to find this value include trial and improvement, or drawing a graph. For both of these, the use of a spreadsheet is highly recommended.) How are you working out 45% of an amount? What is 45% as a decimal? How does that help? Question What calculations did you do to find the loss when she sells for 7.99 each? Have you set them out so that someone else can understand your working? What is a break-even point? What method did you use to find the selling price? Can you think of another method that you could have used? Year 8 Reasoning in the classroom: Publishing book Activity 2 Will I make any money? Explain and question

12 WB I paid 2640 for 500 copies of my book. If I sell all my books for 7.99 each, and I get 45% of the selling price, will I make a profit? Publishing book Activity 2 My profit Whiteboard