NZ Level 6 (NZC) Level 1 (NCEA) Units resulting from a formula or Graph
Lesson

In all our years of learning maths, we've learnt how to make all kinds of calculations. However, if I told you the answer is $42$42, your initial response may be, "$42$42 what?" That's why units of measurement are really important!

We can use units of measurement to define any physical phenomenon, such as quantities, weights, lengths, areas, volumes and rates. Let's look at some different units of measurement now. ## Measurements of Length

Length (distance) is a measurement of one dimension. For example, we could measure from one point to another

Units of measurements for length include millimetres ($mm$mm), centimetres ($cm$cm), metres ($m$m) and kilometres ($km$km).

## Measurements of Area Area is a measure of two dimensions: length and width. Hence, it is measured in square units.

Units of measurements for area include square millimetres ($mm^2$mm2), square centimetres ($cm^2$cm2), square metres ($m^2$m2) and hectares ($ha$ha). ## Measurements of Volume

Volume is a measure of three dimensions: length, width and height. Hence, it's measured in cubed units.

Units of measurements for volume include millimetres cubed ($mm^3$mm3), centimetres cubed ($cm^3$cm3), metres cubed ($m^3$m3)

## Measurements of Mass Units of measurement for mass include grams (g), kilograms (kg) and tonnes (t).Mass is a measure of how heavy something. We often refer to the mass of an object as its weight. ## Measurements of Capacity

Capacity is a measure of how much something holds, such as how much liquid will fit in a bottle.

Measures of capacity include millilitres (ml) and litres (l).

## Measurements in Rates A rate is a ratio between two measurements with different units. There are any number of combinations of measurement units for rates, such as dollars per kilogram ($/kg), kilometres per hour (km/h) and so on. ## Units from Formula Any formula whose components are measurements will have units attached to each of the pronumerals. Here is a formula we a familiar with, the speed of an object is a measure of the distance traveled per unit of time.$S=\frac{d}{t}$S=dt The units for Speed in the formula are derived from the units used for distance and time. So if the distance is measured in kilometres and time is measured in hours, then the$\text{Speed (unit) }=\frac{\text{distance (units) }}{\text{time (unit) }}$Speed (unit) =distance (units) time (unit)$\text{Speed (unit) }=\frac{\text{kilometres }}{\text{hour }}$Speed (unit) =kilometres hour$\text{Speed (unit) }=\text{kilometres / hour }$Speed (unit) =kilometres / hour #### Worked Examples ##### Question 1 The area of a rectangle is given by$A=l\times w$A=l×w, where$l$l is the length and$w$w is the width. Both length and width must be of the same units when performing the multiplication to find the area. 1. What would the unit for area be if the length and width are in millimeters? m2 A cm-km B mm2 C mm D m2 A cm-km B mm2 C mm D ##### Question 2 Adam plotted a point to represent material purchases ($x$x) and the costs involved ($y$y). When Adam bought$140$140cm of material, it cost$\$2.20$$2.20. Loading Graph... 1. What unit is the$x$x-axis using? cost in dollars of material purchased per meter A cost in dollars of material purchased per sale B meters of material purchased C centimeters of material purchased D cost in dollars of material purchased per meter A cost in dollars of material purchased per sale B meters of material purchased C centimeters of material purchased D 2. What unit is the$y\$y-axis using?

cost in dollars of material purchased

A

centimeters of material purchased

B

cost in cents of material purchased

C

meters of material purchased

D

cost in dollars of material purchased

A

centimeters of material purchased

B

cost in cents of material purchased

C

meters of material purchased

D

### Outcomes

#### GM6-2

Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures

#### 91030

Apply measurement in solving problems