This programme has been aligned to registered unit standards. You will be assessed against the outcomes of the unit standards by completing a knowledge assignment that covers the essential embedded knowledge stipulated in the unit standards. When you are assessed as competent against the unit standards, you will receive a certificate of competence and be awarded 9 credits towards a National Qualification.
For ease of reference, an icon will indicate different activities. The following icons indicate different activities in the manual.
| Assessment Criteria |
| Notes (Blank) |
| Stop and Think! |
Take note |
| Note! |
| Reflection |
| References |
| Summaries |
| Example |
| Definition |
| Learning Activities |
| Course Material |
| Outcomes |
The essential purposes of the mathematical literacy requirements are that, as the learner progresses with confidence through the levels, the learner will grow in:
People credited with this unit standard are able to:
The credit value is based on the assumption that people starting to learn towards this unit standard are competent in Mathematical Literacy and Communications at NQF level 2
The programme methodology includes facilitator presentations, readings, individual activities, group discussions, and skill application exercises.
This workbook belongs to you. It is designed to serve as a guide for the duration of your training programme and as a resource for after the time. It contains readings, activities, and application aids that will assist you in developing the knowledge and skills stipulated in the specific outcomes and assessment criteria. Follow along in the guide as the facilitator takes you through the material, and feel free to make notes and diagrams that will help you to clarify or retain information. Jot down things that work well or ideas that come from the group. Also, note any points you would like to explore further. Participate actively in the skill practice activities, as they will give you an opportunity to gain insights from other people’s experiences and to practice the skills. Do not forget to share your own experiences so that others can learn from you too.
“A picture is worth a thousand words.” This is certainly true when you’re presenting and explaining data. You can provide tables setting out the figures, and you can talk about numbers, percentages, and relationships forever. However, the chances are that your point will be lost if you rely on these alone. Put up a graph or a chart, and suddenly everything you’re saying makes sense!
Graphs or charts help people understand data quickly. Whether you want to make a comparison, show a relationship, or highlight a trend, they help your audience “see” what you are talking about.
The trouble is there are so many different types of charts and graphs that it’s difficult to know which one to choose. Click on the chart option in your spreadsheet program and you’re presented with many styles. They all look smart, but which one is appropriate for the data you’ve collected?
Can you use a bar graph to show a trend? Is a line graph appropriate for sales data? When do you use a pie chart? The spreadsheet will chart anything you tell it to, whether the end result makes sense or not. It just takes its orders and executes them!
To figure out what orders to give, you need to have a good understanding of the mechanics of charts, graphs and diagrams. We’ll show you the basics using four very common graph types:
First we’ll start with some basics.
To create most charts or graphs, excluding pie charts, you typically use data that is plotted in two dimensions, as shown in Figure 1.
To remember which axis is which, think of the x-axis as going along the corridor and the y-axis as going up the stairs. The letter “a” comes before “u” in the alphabet just as “x” comes before “y”.
When you come to plot data, the known value goes on the x-axis and the measured (or “unknown”) value on the y-axis. For example, if you were to plot the measured average temperature for a number of months, you’d set up axes as shown in Figure 2:
2.3.1 Scatter plot or Scatter graph
Is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data.
The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.[2] This kind of plot is also called a scatter chart, scattergram, scatter diagram or scatter gr
Things to look for:
If the points cluster in a band running from lower left to upper right, there is a positive correlation (if x increases, y increases).
If the points cluster in a band from upper left to lower right, there is a negative correlation (if x increases, y decreases).
Imagine drawing a straight line or curve through the data so that it “fits” as well as possible. The more the points cluster closely around the imaginary line of best fit, the stronger the relationship that exists between the two variables.
If it is hard to see where you would draw a line, and if the points show no significant clustering, there is probably no correlation.
Caution!
There is a maxim in statistics that says, “Correlation does not imply causality.” In other words, your scatter plot may show that a relationship exists, but it does not and cannot prove that one variable is causing the other. There could be a third factor involved which is causing both, some other systemic cause, or the apparent relationship could just be a fluke. Nevertheless, the scatter plot can give you a clue that two things might be related, and if so, how they move together.
Scatter Plot statistics:
For scatter plots, the following statistics are calculated: Mean X and Y: the average of all the data points in the series.
Maximum X and Y: the maximum value in the series.
Minimum X and Y the minimum value in the series.
Sample Size the number of values in the series.
X Range and Y Range the maximum value minus the minimum value.
Standard Deviations for X and Y values Indicates how widely data is spread around the mean.
Line of Best Fit – Slope The slope of the line which fits the data most closely (generally using the least squares method).
Line of Best Fit – Y Intercept The point at which the line of best fit crosses the Y axis.
One of the most common graphs you will encounter is a line graph. Line graphs simply use a line to connect the data points that you plot. They are most useful for showing trends, and for identifying whether two variables relate to (or “correlate with”) one another.
You can only use line graphs when the variable plotted along the x-axis is continuous – for example, time, temperature or distance.
| Note: When the y-axis indicates a quantity or percent and the x-axis represents units of time, the line graph is often referred to as a time series graph. |
| Example:
ABC Enterprises’ sales vary throughout the year. By plotting sales figures on a line graph, as shown in Figure 3 .It is easy to see the main fluctuations during the course of a year. Here, sales drop off during the summer months, and around New Year. |
While some seasonal variation may be unavoidable in the line of business ABC Enterprises is in, it may be possible to boost cash flows during the low periods through marketing activity and special offers.
Line graphs can also depict multiple series. In this example you might have different trend lines for different product categories or store locations, as shown in Figure 4 below. It’s easy to compare trends when they’re represented on the same graph.
Another type of graph that shows relationships between different data series is the bar graph. Here the height of the bar represents the measured value or frequency: The higher or longer the bar, the greater the value.
ABC Enterprises sells three different models of its main product, the Alpha, the Platinum, and the Deluxe. By plotting the sales each model over a three year period, it becomes easy to see trends that might be masked by a simple analysis of the figures themselves. In Figure 5, you can see that, although the Deluxe is the highest-selling of the three, its sales have dropped off over the three year period, while sales of the other two have continued to grow. Perhaps the Deluxe is becoming outdated and needs to be replaced with a new model? Or perhaps it’s suffering from stiffer competition than the other two?
Of course, you could also represent this data on a multiple series line graph as shown in Figure 6.
Often the choice comes down to how easy the trend is to spot. In this example the line graph actually works better than the bar graph, but this might not be the case if the chart had to show data for 20 models rather than just three. It’s worth noting, though, that if you can use a line graph for your data you can often use a bar graph just as well.
The opposite is not always true, when your x-axis variables represent discontinuous data (such as different products or sales territories), you can only use a bar graph.
In general, line graphs are used to demonstrate data that is related on a continuous scale, whereas bar graphs are used to demonstrate discontinuous data.
Data can also be represented on a horizontal bar graph as shown in Figure 7. This is often the preferred method when you need more room to describe the measured variable. It can be written on the side of the graph rather than squashed underneath the x-axis.
| Note: A bar graph is not the same as a histogram. On a histogram, the width of the bar varies according to the range of the x-axis variable (for example, 0-2, 3-10, 11-20, 20-40 and so on) and the area of the column indicates the frequency of the data. With a bar graph, it is only the height of the bar that matters. |
Everyday life would be quite difficult if you had no knowledge of mathematics whatsoever. On a basic level one need to be able to measure, estimate and calculate. Mathematics is used as a problem solver in every field of science and is playing a very important role in our daily lives. In fact mathematics is involved directly or indirectly wherever we go and every thing that we may use. Living your day to day life without maths would be extremely difficult. Even if you were a nomad in the desert you would want to count your goats wouldn’t you?
Measurement is how we determine the exact capacity of something that is in solid, liquid or gas form. It is the process or the result of determining the ratio of a quantity. Estimating is a process of defining the quantity of the imaginary things .For example we estimate for the cost of production of anything which will be completed (ready) later but we have imagined that it’s cost will reach to this figure.
Why do we measure?
We measure to find out something about an object in order set objectives and planning work schedules. For example a carpenter needs to know the length of a piece of wood. It has to be right size.
1.2 MEASURING INSTRUMENTS
In the past, each culture used their own system of measuring things. You might have come across some of them, and you may be using some even today. Eventually, people decided that there must be an international measurement system where all ranges can be measured according to an agreed standard. For each type of measurement, there is a particular measuring instrument which is most suitable to do the job. It will be impossible to list all the possible measuring instruments, thus we will look at the most common instruments and welcome your knowledge and experience to enhance understanding of this section. When using any measuring instruments, ensure that measurement is: accurate, precise and viewed squarely off the scale of the measuring instrument.
A ruler is an instrument used in geometry, technical drawing, printing and engineering/building to measure distances and/or to rule straight lines. It contains calibrated lines to measure short, straight lines (linear lines). We can measure millimeters and centimeters with a ruler. If you need to measure using a ruler, you will place the 0cm measurement at the start of the line and read the measurement at the end of the line on the comparative point on the ruler. In engineering, we use millimeters as the common measurement. Centimeters are more often used for domestic purposes. A type of ruler used in the printing industry is called a line gauge. These may be made from a variety of materials, typically metal or clear plastic. Units of measurement on a basic line gauge usually include inches, agate, picas, and points. More detailed line gauges may contain sample widths of lines, samples of common type in several point sizes, etc.
Take care when reading measurements:
A measuring tape is used when a ruler is too short to measure the distance or length. We use the measuring tape to measure short distances in meters. Measuring tapes are usually gradated in millimeters, centimeters and meters. Measuring tapes come in different styles. For measuring rooms, or large areas, the heavy duty style, in a case that pulls open and snaps shut is often used. Measuring tapes also come in soft material, used for the dress maker, or to measure a hem and everything in between. Understanding what measurement it shows is important in any project.
The distance between each measurement with a red dot.
The distance between each mark with a red dot.