Measurement

Lesson 1 · B7.3.2.1.1 · about 45 min

Perimeter of Shapes with Mixed Units

A carpenter in Kumasi measures a table as 1 m 75 cm long, and a farmer at Techiman measures a cocoa plot in metres and centimetres. Real measurements often come in two units at once. In this lesson you will learn to add them correctly and find the perimeter of any shape, whatever mix of units it is given in.

Lesson 2 · B7.3.2.1.2 · about 50 min

Circumference of a Circle and the Meaning of Pi

Every trotro wheel, every roundabout at Kaneshie and every bowl of fufu is a circle. How far does a wheel roll in one turn? How long is the fence round a circular pond? In this lesson you will measure circles, discover for yourself why the circumference is always a little more than three diameters, and use the number pi to calculate it.

Lesson 3 · B7.3.2.1.3 · about 45 min

Drawing Rectangles and Triangles on a Square Grid

Architects, kente weavers and surveyors all start with a plan drawn on a grid. In this lesson you will draw rectangles and triangles of given sizes on square and dot grids, change their sides to make the area bigger, and discover how many different triangles share the same area.

Lesson 4 · B7.3.2.2.1 · about 50 min

Deriving the Area of a Triangle

Roofs, flags, road signs and the pieces of a kente pattern are often triangles. How much cloth or paint does a triangle need? In this lesson you will not just be handed a formula. You will see that every triangle is exactly half of a rectangle or a parallelogram, and then work out the formula for yourself.

Lesson 5 · B7.3.2.2.2 · about 50 min

Calculating the Area of Triangles

Now that you know a triangle is half of a rectangle, it is time to use the formula to solve real problems: the gable of a roof, a triangular plot of land, a flag or a road sign. You will learn to choose the right base and height, to work backwards to find a missing length, and to find the area of shapes made from triangles and rectangles.

Lesson 6 · B7.3.2.3.1 · about 45 min

Bearings: Giving Direction with Three Digits

When a driver in Techiman asks the way to Kintampo, the answer is not 'go that way' but a direction everybody agrees on. Surveyors, pilots, ship captains and the Ghana Armed Forces all describe direction with a **bearing**. In this lesson you will learn to read, measure and draw bearings with a protractor.

Lesson 7 · B7.3.2.3.2 · about 45 min

Back Bearings: Finding the Way Home

If you leave Accra for Cape Coast on one bearing, what bearing must you follow to return? The answer is the **back bearing**. Ship captains, hunters and hikers use it to retrace a route without getting lost. You will learn a very short rule and understand exactly why it works.

Lesson 8 · B7.3.2.3.3 · about 45 min

Scalar and Vector Quantities

Some measurements, like the mass of a bag of cement, need just a number and a unit. Others, like the wind blowing over Cape Coast, need a size **and a direction**. In this lesson you will learn to sort quantities into scalars and vectors, and to draw a vector from its length and bearing.

Lesson 9 · B7.3.2.3.4 · about 50 min

Column Vectors: Writing Vectors as East–North Components

A bearing and a distance tell you how to travel. A **column vector** tells you the same thing in a different way: how far to go East (or West) and how far to go North (or South). This lesson shows you how to change a vector like (5 km, 030°) into a column vector using a graph and using trigonometry.

Lesson 10 · B7.3.2.3.5 · about 55 min

From Column Form to Magnitude and Bearing (and Back)

A pilot flying from Accra to Tamale reads her instruments as 'so many km east and so many km north'. The control tower wants the journey as 'so many km on a bearing of such and such'. Converting between the two forms is the final skill in this strand. It uses Pythagoras' theorem for the length and a little trigonometry for the direction.

Ready? Take the sub-strand quiz