Bowland Maths
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Bowland Charitable Trust  
Case study problems and lessons designed to develop thinking, reasoning and problem solving skills in UK math pupils ages 1114. In particular, download series of standalone assessment items that challenge students to estimate the number of descendants a girl who lived 110 years ago might have today; work out how much material is needed to make bunting to go round a garden; design a 2D net for a box, given a 3D picture of the box; devise a method for estimating the numbers of trees in a plantation, then estimate the numbers of two different kinds of tree; choose the best trip using survey data and then cost it; determine whether the rates for taxi fares, set by a local council, are fair in relation to the changing cost of fuel; plan when to start preparing a meal in order to have it ready by a stated time; investigate patterns in the number of nails on a geoboard used to form a square; use pie charts to decide whether a code is more likely to be in German or English; work out how prospectors can maximise the area in which they can dig for gold given a fixed perimeter; compare two rules for converting Celsius to Fahrenheit, one accurate and one approximate; plan quantities to buy in order to maximise profit from selling ice creams at a school event; decide whether or not a lottery will be a good way to raise money; analyse a numerical puzzle, solve some examples and then deduce that a further example is impossible; compare two different mobile phone tariffs and decide when one is cheaper than the other; interpret and apply data through devising questions (and answers) relating to lap times in a cycling race; find a method for calculating the number of triangles and squares that are needed to make cushions in different sizes; interpret the graph provided to give advice on the statistical acceptability of age gaps in relationships; analyse a newspaper article, evaluating its (mathematical) claims and identifying its flaws; work with the properties of triangles through combining a range of rods to make different types of triangle; measure a bottle and then design a box that will hold 12 bottles; analyse a numerical puzzle, solve some examples and then deduce that a further example is impossible; determine the amount of time Santa can spend at each house in the UK when delivering presents on Christmas Eve; analyse a simple game (bingo) and plan a winning strategy; design a sports bag, showing all the measurements needed to make it and planning how to waste the least fabric; plan a trip for a large party using two kinds of taxi cab, deciding how many of each cab they need to minimise the overall transport costs; draw graphs to represent data and to critique an erroneous interpretation of the data; work out the best way of allocating dorms at a Youth Hostel to a group of children and adults; and more. Bowland also provides five professional development modules about the main pedagogical challenges of investigative problem solving, and two further modules directly addressing issues around assessment, each built around problems similar to the case studies: tackling unstructured problems; fostering and managing collaborative work; using computer resources effectively; questioning and reasoning; involving students in self and peer assessment; and more. Also available from http://www.bowland.org.uk/.  


Levels:  Middle School (68) 
Languages:  English 
Resource Types:  Video, Lesson Plans and Activities, Problems/Puzzles 
Math Topics:  Basic Algebra, Estimation, Factors, Fractions/Decimals/Percents, Measurement, Number Sense/About Numbers, Patterns/Relationships, ProblemSolving, Communicating Math, Euclidean Plane Geometry, Data Analysis 
Math Ed Topics:  ProblemSolving, Staff/Prof Development 
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