Measurement
🎯 In this topic you will
- Estimate and measure lengths in centimetres, metres, and kilometres, rounding to the nearest whole number.
- Understand and use the relationships between different units of length.
🧠 Key Words
- centimetre (cm)
- metre (m)
- kilometre (km)
- rounding
Show Definitions
- centimetre (cm): A unit of length equal to one hundredth of a metre, commonly used to measure small objects.
- metre (m): The standard base unit of length in the metric system, used for everyday distance measurements.
- kilometre (km): A unit of length equal to 1000 metres, typically used to measure long distances such as between towns or cities.
- rounding: A method of simplifying numbers by changing them to the nearest chosen value, such as the nearest whole number.
📏 Measuring Lengths
This section uses measurements of length, including kilometres.
🎯 Estimating and Rounding
You use estimation and rounding when you measure.
🔺 Shapes and Distances
You work with both regular and irregular shapes.
❓ EXERCISES
1.
a. Draw two lines to make this into a square. Estimate and then measure the length of the sides.
estimate = __________
measure = __________
b. Draw three lines to make this into a square. Estimate and then measure the length of the sides.
estimate = __________
measure = __________
👀 Show answer
🧠 Reasoning Tip
$100$ cm $=$$1$ metre
$1000$ m $=$$1$ kilometre
2. Use the tip to help you work out these conversions.
a. $7$ m $=$ ______ cm
b. $250$ cm $=$ ______ m
c. $3\frac{1}{2}$ m $=$ ______ cm
d. $\frac{1}{2}$ km $=$ ______ m
e. $750$ m $=$ ______ km
f. $\frac{1}{4}$ km $=$ ______ m
👀 Show answer
b. $2.5$ m
c. $350$ cm
d. $500$ m
e. $0.75$ km
f. $250$ m
3. Circle the things that would be measured using kilometres.
the distance between two continents
the height of a door
the length of a football pitch
the width of a towel
the length of a train
the length of a whale
the height of a giraffe
the distance of a marathon race
the length of a long journey
Draw or write three more things that would be measured using kilometres.
👀 Show answer
Examples: distance between cities, length of a motorway, flight distance.
4. Round the measurements of the length of the table, the length of the bed and the length measured by the tape.
👀 Show answer
Bed: $275\frac{1}{4}$ cm $=$$275.25$ cm → nearest cm $275$, nearest $10$ cm $280$, nearest metre $3$ m.
Tape: $466$ mm $=$$46.6$ cm → nearest cm $47$, nearest $10$ cm $50$, nearest $100$ cm $0$ cm.
Distance: $16$ km → round up to nearest $10$ km $20$ km, round down to nearest $5$ km $15$ km.
🧠 Think like a Mathematician
Silas and Simon are snails. They live on a wall. They can travel only along the edge of the bricks. Each brick is $30$ cm long and $15$ cm wide.
Silas wants to visit Simon.
Task:
- Calculate the shortest route, keeping to the edge of the bricks.
- Calculate two other routes.
- Record what you have discovered.
Method (work independently):
- Count how many brick lengths and widths Silas must travel.
- Convert each move into centimetres using $30$ cm and $15$ cm.
- Add all distances to find the total route length.
- Try at least two different paths and compare results.
👀 show answer
- Shortest route: Moving mostly horizontally then vertically gives the minimum distance. Counting the grid shows $4$ long edges and $2$ short edges, so $4 \times 30 + 2 \times 15 = 120 + 30 = 150$ cm.
- Route 2: Taking a longer vertical detour gives $4 \times 30 + 4 \times 15 = 120 + 60 = 180$ cm.
- Route 3: Zig-zagging along extra brick edges gives $5 \times 30 + 3 \times 15 = 150 + 45 = 195$ cm.
- Discovery: Different paths give different total distances, but the shortest route always uses the fewest brick edges. The most direct horizontal-then-vertical path is minimal.