Maths-Whizz Investigations Paper-Back Book

Transcription

1 Paper-Back Book are new features of our Teachers Resource to help you get the most from our award-winning software and offer new and imaginative ways to explore mathematical problem-solving with real-world objects that students see or use almost every day. Title: Paper-Back Book Description: Investigate a paper-back book and calculate some attributes of the book the paper it is printed on, the number of words in the book, etc. Topic Coverage:, Shape and Space, Ratio & Proportion, Curriculum Coverage: Key Stages 2 and 3 Equipment: - 1 (or more) paperback novels (i.e. all text, or almost all text). For comparison, find two different editions of the same paper-back novel, published at similar times (Try using adult and child editions of Harry Potter or His Dark Materials series) NB only a paper-back book is suitable for this investigation, a hard-back book will skew some measurements and calculation Data Gathering: The first stage of the investigation is gathering information about the object. Encourage your students to list all the discoverable features of the book, and its contents. Discoverable features can be measured directly or determined from information on the cover. Table of information: Attribute Method MW help Unit(s) Mass of book (x) Measure (scales) Year 3 B-3 Year 4 g Year 5 B-2, C-5 Width of book (w) Height of book (h) Measure (ruler) Year 3 Year 5 Year 7 A-1 cm Depth (thickness) of book (d) Price of book (y) Read.p Number of pages Count Number of leaves (z) Halve the number Year 4 Rapid Recall division C-2,4,6 of pages Number of printed pages (not including index, notes, etc) (p) Count Number of lines per page Count

2 Number of words per line (find at least 5 different lines on different pages) Frequency of each letter of the alphabet (sample the same 5 lines counted earlier) Number of sentences per full page of text (s) Chart (use a frequency table, or tally chart) Count one page; treat as representative sample Year 3 A-1 Year 4 A-4 Year 7 A-2

3 Solving Problems: Ask students to list all the attributes of the book that can be calculated or inferred from the data gathered earlier. The table below suggests some such attributes, units for writing those attributes and methods for calculating them. # Attribute Unit(s) Calculation Method What is the total area of paper used? How many sheets of A4 paper is the area in #1 equivalent to? What is the GSM (grams per square metre), or quality, of the paper used? What is the average thickness of the paper used? Which is the modal (most common) letter? What is the mean (average) word length? Estimate the number of words in the whole book. Estimate the total area of all the full stops in the book m 2 Multiply the number of leaves (see Tips below) by the area of the book s front, convert answer to m 2. Measure area of an A4 sheet, divide the answer to #1 by the result of this measurement. Be careful to use consistent units! g/m 2 Divide x by the answer to #1 (in m 2 ). mm cm 2 Divide d (in mm) by z including the covers. Analyse frequency table. Divide the total number of words in the sentences sampled by the number of sentences sampled. Multiply P by the number of lines per page; multiply the result by the average number of words per line. Assume all sentences end in a full-stop. Estimate the area of a full stop (around 0.01mm 2 ), call this f. Estimate the number of sentences in the book, by multiplying s by p. Multiply the result by f [NB if you take f=0.01mm 2 this calculation is equivalent to just dividing by 100]. Convert, then, to cm 2. Tips: If your students are struggling with decimal area calculations, instruct them to convert cm to mm. Remind them to convert their answers back into centimetres, noting that they must divide by 100 to find the number of cm 2 from mm 2, or divide by 1,000,000 to find the number of m 2 from mm 2! Students should be careful of the distinction between pages and leaves of paper. There are, of course, two pages to each leaf (in fact, there are generally four, depending on how the book is bound, but students should count each leaf as if it is no bigger than the book s overall dimensions.)

4 Whizz Education has produced interactive Excel spreadsheets to make calculating the answers to these attributes using the information above a snap. Our interactive tool will help you make quick comparisons with students (e.g., whether children s books have longer words, etc). Click HERE to login to your account page and download an interactive spreadsheet. (or visit and login via the login panel at top-right, click the Teachers button first)

5 Lessons The table below indicates which lessons should be used to teach the principles and methods necessary for solving the problem. Problem Year 4 Year 5 Year 6 Year A-1;;C-1;D-1 Ex-1,2,3,4 Ex-1 ; C-1,2; D-1,2 Ex-5,6,7,8,9 Ex-1,D-1,2 A-1,,2,3, D-1 Ex-1,2,3,4,5 Ex-1,4,5 ; D-1,2 All Ex-1,4,5 A-1; ; D-1 C-1,2; Place Value C-6 Ex-1,2,3,4 Ex-1,2,3 A-1; Ex-5,6 B-2 C-2,3 A-1,2 Ex-1,2 Ex-1,4,5 A-1; B-2 Ex-1,2 3 All Ex-6 4 C-1,2,3,4,5 Ex-2,3,4,5,6 C-1,4 All Ex-2,3 C-1,2 A-1; Ex-5,6 Ex-1,2

6 5 A-1,4,5; C-1 Ex - 1,2,3,4 Ex-1 D-1,3 Ex-1,2 A-2;,2,4; D-1 Ex- 1,2,3,4,5 6 C-1,2;D-1,2 D-1,3 A-1,2; D-1 Ex-1 Ex-5 Ex-1,2 Ex- 2,3,5 7 D-1 A-1,2 Ex-1,2 8 MCS Multiplication Ex-10,2,3 Ex-2,3,4 Ex-2 A-1; D-1 C-1,2 Ex-1,3 Ex-1,2 A-1,2 Ex-1,2

7 Further Investigation Some of your students will find the problems presented above easy. For extension, or further investigation, here are some more open-ended questions we suggest you ask your students. As above, you should prompt the students first to discuss (either in small groups or all together) how they might determine the answers and if a numerical answer can be determined have students calculate the answers and compare results. How might you get a more accurate estimate of the book s word count? (If you have more than one edition of the novel) Why are the different editions priced differently? Which edition is better value? (If you have more than one edition of the novel) Use similar sampling methods to determine word count of each. Do they differ by much? If so, why? How could you go about estimating how long it might take you to read the whole book? Investigate mean word length in different types of book. Which type of book might have the longest and shortest words? Use a wide range of books to help your investigation. How much paper in a typical paperback book does not have anything printed on it? In other words, how much paper is wasted?