Mensuration Starters:Area Two: How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines? Bizarre Triangle: By how much would the area of this triangle increase if its base was enlarged to 8cm? Christmas Tables: Which of the two shapes has the largest area? You will be surprised! Cross Perimeter: Calculate the distance around the given shape Goat Grazing: Find the loci of the goat's position as it eats the grass while tethered to the rope. Missing Lengths: Introduce linear equations by solving these problems about lengths. Missing Square Puzzle: The missing square puzzle is an optical illusion used to help students reason about geometrical figures. Oblongs: Find the dimensions of a rectangle given the perimeter and area. Quad Areas: Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid. Shopping List: A quick quiz about five items on a shopping list written 40 years ago. Stair Perimeter: Use the information implied in the diagram to calculate the perimeter of this shape. Step Perimeter: Is it possible to work out the perimeter of this shape if not all the side lengths are given?
Small images of these Starters :: Index of Starters Mensuration Advanced Starters:Average Cycling Speed: Work out the average speed of two journeys. The obvious answer is not the correct answer. Charging Rhinos: Find the easy way to solve this kinematics problem involving a fly and two rhinos. Cuboid: Find the dimensions of a cuboid matching the description given Fence Optimisation: Find the length of a rectangle enclosing the largest possible area. Hands Together: The hands of a clock are together at midnight. At what time are they next together? Paper Ratio: Calculate the ratio of the sides of an A4 sheet of paper without any measuring. Paper Surprising Perimeter: Find the perimeter of a folded sheet of A4 paper as described in this short video. Piece of String: Find where a piece of string should be cut to form a circle and a square of equal areas. Pizza Slice: A problem which can be solved by considering the areas of a triangle and a sector of a circle. Road Connections: Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads. Rosie's Cube: How many of the small cubes does Rosie need to complete the big cube? Speed Circles: Find the diameters of the circles in the corners of the square. Sphere Hole: Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it. Square in Rectangle: Find the area of a square drawn under the diagonal of a rectangle
Curriculum for Mensuration:Year 5Pupils should be taught to convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) more... Pupils should be taught to understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints more... Pupils should be taught to measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres more... Pupils should be taught to calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes more... Pupils should be taught to estimate volume [for example, using 1 cm^{3} blocks to build cuboids (including cubes)] and capacity [for example, using water] more... Year 6Pupils should be taught to solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate more... Pupils should be taught to solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison more... Pupils should be taught to use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places more... Pupils should be taught to convert between miles and kilometres more... Pupils should be taught to recognise that shapes with the same areas can have different perimeters and vice versa more... Pupils should be taught to recognise when it is possible to use formulae for area and volume of shapes more... Pupils should be taught to calculate the area of parallelograms and triangles more... Pupils should be taught to calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres and cubic metres, and extending to other units more... Years 7 to 9Pupils should be taught to understand and use place value for decimals, measures and integers of any size more... Pupils should be taught to change freely between related standard units [for example time, length, area, volume/capacity, mass] more... Pupils should be taught to derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) more... Pupils should be taught to use scale factors, scale diagrams and maps more... Pupils should be taught to calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes more... Pupils should be taught to draw and measure line segments and angles in geometric figures, including interpreting scale drawings more... Pupils should be taught to use compound units such as speed, unit pricing and density to solve problems. more... Pupils should be taught to use standard units of mass, length, time, money and other measures, including with decimal quantities more... Pupils should be taught to use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D more... Years 10 and 11Pupils should be taught to convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts more... Pupils should be taught to calculate arc lengths, angles and areas of sectors of circles more... Pupils should be taught to calculate surface areas and volumes of spheres, pyramids, cones and composite solids more... Feedback:Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks." Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia: "Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students  all trying to reach their highest level and competing with their peers while also learning. Thank you very much!" Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources  thanks. Is the collection available on CD? Are solutions available?" Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy: "3 NQTs in the department, I'm new subject leader in this new academy  Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!" Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai: "It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages." Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich: "My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource  thanks a million." Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc  in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is  my pupils love it! 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My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun." Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College: "Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities. Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School: "Really good site. Lots of good ideas for starters. Use it most of the time in KS3." 
Notes:Mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume. It is linked closely to the topic of Estimation and related to the topics of Angles, Shape and Shave (3D). Mensuration Teacher Resources:Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes. Memorable Measures: This is a visual aid and printable cards to introduce a homework activity about measures. Mensuration Activities:Area and Perimeter of a Rectangle: Questions on the areas and perimeters of rectangles which will test your problem solving abilities. Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters. Measuring Angles: Measure the size of the given angles to within two degrees of their actual value. Area of a Triangle: Calculate the areas of the given triangles in this self marking quiz. Area and Perimeter of a Parallelogram: Many different ways to practise your skills finding the areas and perimeters of parallelograms. Algebraic Perimeters: Questions about the perimeters and areas of polygons given as algebraic expressions. Reading Scales: A self marking exercise on the reading of scales of different types. Area and Perimeter of a Kite: A short exercise to practise using the formulae for area and perimeter of a kite. Area of a Trapezium: Check that you can find the area of a trapezium and use the trapezium area formula for problem solving. Area and Perimeter: Show that you know the area and perimeter formulas of basic shapes. Area Maze: Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams. Area Two: How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines? Mileometer: Practise converting between miles and kilometres with this self marking quiz. Quad Areas: Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid. Scale Drawings: Measure line segments and angles in geometric figures, including interpreting scale drawings. Volume: Use formulae to solve problems involving the volumes of cuboids, cones, pyramids, prisms and composite solids. Measuring Units: Check your knowledge of the units used for measuring with this selfmarking quiz about metric and imperial units. Sorting Units: Order the ten containers according to their value (money, length and weight) Metric Units Pairs: Find the matching pairs of equivalent metric units in this interactive online game. Circles: Practise using pi to calculate various circle measurements. There are six levels of difficulty. Screen Test: Memorise the mathematical facts in the video then answer the ten quiz questions. Volume Equals Surface Area: Find the cuboids with integer side lengths where the volume is numerically equal to the surface area. Areas of Composite Shapes: Find the areas of combined (composite) shapes made up of one or more simple polygons and circles. Map Scales: Test your understanding of map scales expressed as ratios with this self marking quiz. Imperial Units: Learn about common imperial units and how they relate to other units of measurement. Inequalities: Check that you know what inequality signs mean and how they are used to compare two quantities. Includes negative numbers, decimals, fractions and metric measures. Imperial Units Pairs: Find the matching pairs of equivalent imperial units in this interactive online game. Formulae to Remember: The traditional pairs or pelmanism game adapted to test recognition for formulae required to be memorised for GCSE exams. Formulae Pairs: Find the matching pairs of diagrams and formulae for basic geometrical shapes. Converting Standard Units: Converting measurements of length, mass, volume and time from one unit of measure to another. Cylinders: Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions Bottles, Boxes and Cans: Estimate the capacity of the bottles, boxes and cans in the photograph and answer questions about volume. Surface Area: Work out the surface areas of common solid shapes in this collection of exercises. Compound Units: Practise using compound units such as speed, unit pricing and density to solve problems. Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world. Alternatively, for the more advanced student, there is an evergrowing collection of ExamStyle Questions with worked solutions on the topic of Mensuration. Mensuration Investigations:Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters. Area shapes: Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed. Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes. Rectangle Perimeters: The perimeter of a rectangle is 28cm. What could its area be? Maxvoltray: Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation. Mensuration Videos:Metric System: Ted Talk: Why the metric system matters  Matt Anticole Area And Perimeter Video: Calculate and solve problems involving perimeter and area of rectangles, triangles, parallelograms, trapezia, kites and composite shapes. Parallelogram: Instructional video showing how the area of a parallelogram can be determined. Volume Video: There are simple formulas that can be used to find the volumes of basic threedimensional shapes. Circle Facts Song: A free trial lesson from Math Upgrade dot com. Circles Area and Circumference Video: The circumference and area of a circle can be found if the radius or diameter are known. Pi Song: Kate Bush sings the digits of pi (audio only). Surface Area Video: Finding the surface are of three dimensional shapes can involve some interesting formulae. Pi and Four Fingers: Why is The Simpsons not in Base 8? In this video Simon Singh talks about Pi and Maths in The Simpsons cartoon. Formulae for GCSE: These are the formulae candidates need to know for the GCSE(91) Maths exams. Mensuration Worksheets/Printables:Measuring Lines and Angles: Practice using a ruler and protractor on this worksheet with answers provided. Memorable Measures Notes: These are the printable cards to go with the activity called Memorable Measures. Mensuration External Links:Links to other websites containing resources for Mensuration are provided for those logged into 'Transum Mathematics'. 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CNN,
Monday, December 10, 2018
"Metric mishap caused loss of NASA orbiter. (CNN)  NASA lost a $125 million Mars orbiter because a Lockheed Martin engineering team used English units of measurement while the agency's team used the more conventional metric system for a key spacecraft operation, according to a review finding released Thursday.Sep 30, 1999"