There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Mensuration. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### 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?

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.

Rope Around The World: Imagine a long rope wrapped around Earth's equator - One metre longer than it needs to be.

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

#### Area and Perimeter of a Rectangle

Questions on the areas and perimeters of rectangles which will test your problem solving abilities.

Transum.org/go/?to=oblongs

### Curriculum for Mensuration:

#### Year 5

Pupils 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 (cm2) and square metres (m2) and estimate the area of irregular shapes more...

Pupils should be taught to estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water] more...

#### Year 6

Pupils 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 9

Pupils 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 2-D 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 3-D more...

#### Years 10 and 11

Pupils 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...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

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### 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).

It is essential for pupils to have an understanding of the units used to measure which include both the more common metric units and the Imperial units still in common usage. We have found a good teaching strategy is to ask each of the pupils to "Bring to the next Maths lesson some visual aid which will help the rest of the class remember the size of a unit of measurement". See Memorable Measures below for the printable resources. This activity provides an association with a unit, a visual aid and a known person which is a great memory enhancer.

### 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.

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.

Algebraic Perimeters: Questions about the perimeters and areas of polygons given as algebraic expressions.

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 self-marking 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.

Animal Records: Match the values and the units to the animal world records.

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 ever-growing collection of Exam-Style 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:

Transum's Mensuration Video

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 three-dimensional 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(9-1) 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.

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#### Compound Units

Practise using compound units such as speed, unit pricing and density to solve problems.

Transum.org/go/?to=compound_units

### Teaching Notes:

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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"

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