Length

Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 2.0 Measurement | Sub-Strand 2.1 Length (14 Lessons)

Lesson objectives

By the end of this topic, you will be able to:

• Use the millimetre as a unit of measuring length
• Establish the relationship between millimetres and centimetres
• Convert, add, subtract, multiply, and divide lengths in centimetres and millimetres
• Determine the circumference of a circle practically
• Identify the relationship between circumference and diameter
• Appreciate the use of length in real life

Length

Length measures how long something is. In Grade 6 we add the millimetre, the smallest unit on your ruler.

a) The millimetre

Look at a ruler. Between each centimetre mark there are ten small lines. Each small space is one millimetre.

So 1 cm = 10 mm.

Use millimetres for small things. The thickness of a coin. The width of a pencil lead. The size of a seed.

b) Converting

To change centimetres to millimetres, multiply by 10.

To change millimetres to centimetres, divide by 10.

A check: millimetres are smaller, so there are more of them. An answer in mm that is smaller than the cm figure means you divided by mistake.

c) Adding and subtracting

Change both lengths to the same unit first.

To add 6 cm and 45 mm, change 6 cm to 60 mm. Then 60 + 45 = 105 mm, which is 10.5 cm.

Say which unit your answer is in. A number on its own is not an answer.

d) Multiplying and dividing

Multiply or divide the number, keeping the unit the same.

Four pieces of 35 mm come to 4 × 35 = 140 mm. That is 14 cm.

Cut a 96 mm strip into 6 equal pieces. Each is 96 ÷ 6 = 16 mm.

e) Measuring a circle

You cannot measure round a circle with a straight ruler. Use a piece of string.

Wrap the string once round, mark where it meets, then straighten it against a ruler. That length is the circumference.

Now measure straight across the middle. That is the diameter.

f) The special number

Divide the circumference by the diameter. You get about 3.14.

Try it with a tin, a cup and a bucket. Every time, the answer is about 3.14.

That number is called pi, written π. It never changes, however big or small the circle is.

So the circumference is always a little more than three times the diameter.

g) Where this is used

A tailor measures cloth. A carpenter marks wood in millimetres. A mechanic measures a bolt. Anyone fitting a band round something round uses the circumference.

Words to know

• Millimetre (mm) — a unit of length; 10 mm = 1 cm.
• Circumference — the distance around the outside of a circle.
• Diameter — a straight line across a circle, through its centre, from edge to edge.
• Pi (π), approximated as 22/7 — the constant relationship between a circle's circumference and its diameter.

:::checkpoint Check yourself

1. How many millimetres are in 1 cm?
2. Change 12 cm into millimetres.
3. Change 65 mm into centimetres.
4. What do you get when you divide any circumference by its own diameter? :::

Bridge to practice

Try the exercises below — converting, adding, subtracting, multiplying, and dividing cm/mm lengths, plus working out circumference from a diameter.