# The Bowland Maths assessment tasks

School closed?These problems are more interesting than your typical test! Look on page 2-3 of the PDF for the problem - don't read on until you have tried to solve it.

Bowland Maths includes over thirty tasks designed to help you assess your pupils' achievements and progression against the Key Processes defined in the Key Stage 3 National Curriculum. To help you with this assessment, each task comes with sample pupils' work, and a "progression table" showing how pupils' work on this task can provide evidence of their progress with the four Key Processes. These self-contained tasks take between twenty minutes and an hour.

These materials are also ideal for *formative
assessment* that concentrates on providing the
types of rich feedback that have been proven to help
pupils improve their reasoning.

Although titled 'Assessment', these tasks have been designed to be just as rich and engaging as the longer 'Case Studies'. If you are new to Bowland and unsure about taking on a 3-4 lesson project, one of these shorter tasks would make a great basis for a lesson.

# List of Assessment Tasks

# 1. 110 Years On

Time 45min

Level 5-8

Pupils use mathematical reasoning to estimate the number of descendants a girl who lived 110 years ago might have today.

# 2. Bunting

Time 45-60min

Level 5-8

Pupils work out how much material is needed to make bunting to go round a garden.

# 3. Candle Box

Time 30-60min

Level 4-6

Pupils design a 2D net for a box, given a 3D picture of the box.

# 4. Cats and Kittens

Time 45-60min

Level 5-8

Pupils work out how many descendents one female cat could produce in 18 months.

# 5. Counting Trees

Time 30-60min

Level 4-7

Pupils devise a method for estimating the numbers of trees in a plantation then use their method to estimate the numbers of two different kinds of tree.

# 6. Day Out

Time 30-60min

Level 4-5

Pupils are asked to choose the best trip using survey data and then cost it.

# 7. Fares not Fair

Time 45-60min

Level 6-8

Pupils determine whether the rates for taxi fares, set by a local council, are fair in relation to the changing cost of fuel.

# 8. Fish Dish

Time 30-60min

Level 5-6

Pupils plan when they should start preparing a meal in order to have it ready by a stated time.

# 9. Fruit Pies

Time 60min

Level 6-8

Pupils use their knowledge of area of circles and rectangles to solve a problem.

# 10. Geoboard Squares

Time 30-60min

Level 6-7

Pupils Investigate patterns in the number of nails on a geoboard used to form a square.

# 11. German or English

Time 45min

Level 4-7

Pupils use pie charts to decide whether a code is more likely to be in German or English.

# 12. Golden Rectangles

Time 30-60min

Level 4-6+

Pupils work out how adventurers can maximise the area in which they can dig for gold given a fixed perimeter.

# 13. Hilbre Island

Time 30-60min

Level 4-7

Pupils determine the optimum time to visit Hilbre Island, taking account of given considerations.

# 14. Hot Under the Collar

Time 20-40min

Level 7-8

Pupils compare two rules for converting Celsius to Fahrenheit, one accurate and one approximate.

# 15. Ice Cream

Time 30-60min

Level 5-6

Pupils plan quantities they will buy in order to maximise their profit from selling ice creams at a school event.

# 16. Lottery

Time 20-40min

Level 5-6

Pupils decide whether or not a lottery will be a good way to raise money.

# 17. Magic Sum Puzzle

Time 30-60min

Level 5-7

Pupils analyse a numerical puzzle, solve some examples and then deduce that a further example is impossible.

# 18. Mobile Phones

Time 20-40min

Level 6-7

Pupils compare two different mobile phone tariffs and decide when one is cheaper than the other.

# 19. Olympic Cycling

Time 30min

Level 3-6

Pupils interpret and apply data through devising questions (and answers) relating to lap times in a cycling race.

# 20. Patchwork Cushions

Time 30-60min

Level 6-7

Pupils are asked to find a method for calculating the number of triangles and squares that are needed to make cushions in different sizes.

# 21. Problem Page

Time 45-60min

Level 6-8

Pupils interpret the graph provided to give advice on the statistical “acceptability” of age gaps in relationships.

# 22. Public Transport

Time 30-45min

Level 5-8

Pupils analyse a newspaper article, evaluating its (mathematical) claims and identifying its flaws.

# 23. Rods and Triangles

Time 30min

Level 4-7

Pupils work with the properties of triangles through combining a range of rods to make different types of triangle.

# 24. Royal Liver Clock

Time 45min

Level 6-8

Pupils apply their knowledge of circles and show their ability to estimate appropriately.

# 25. Security Camera

Time 30-60min

Level 4-7

Pupils select the best position to put a security camera in a shop.

# 26. Smoothie Box

Time 30-60min

Level 6-6

Pupils measure a bottle and then design a box that will hold 12 bottles.

# 27. Soft Drinks

Time 30-60min

Level 5-6

Pupils compare two sets of data with different sample sizes and consider how the testing procedure could be improved.

# 28. Speedy Santa

Time 30-60min

Level 4-7

Pupils determine the amount of time Santa can spend at each house in the UK when delivering presents on Christmas Eve.

# 29. Spinner Bingo

Time 30-60min

Level 6-8

Pupils analyse a simple game and plan a winning strategy.

# 30. Sports Bag

Time 20-40min

Level 5-6

Pupils design a sports bag, and show all the measurements they will need to make. They also plan how they will waste the least material.

# 31. Taxi Cabs

Time 20-40min

Level 5-5

Pupils plan a trip for a large party using two kinds of taxi cab. They try to decide how many of each cab they need to minimise the overall transport costs.

# 32. The Z Factor

Time 45-60min

Level 3-8

Pupils determine how long it would take a panel of judges if they saw every act that auditioned for the “Z factor” programme.

# 33. Three of a Kind

Time 30-60min

Level 3-8

Pupils use their knowledge of geometry to describe a pattern.

# 34. Tuck Shop

Time 30-60min

Level 4-5

Pupils are asked to draw graphs to represent data and to critique an erroneous interpretation of the data.

# 35. Youth Hostel

Time 30-60min

Level 5-6

Pupils work out the best way of allocating dorms at a Youth Hostel to a group of children and adults.