Patterns and Trends

Unit standard(s): 9009

Summary:

In this activity students identify patterns and trends using scatter plots, broken line graphs and bar graphs. They read values from given graphs and use them to do calculations. They make simple predictions by identifying trends.

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HIV/AIDS estimates

Unit standard(s): 9009

Summary:

In this activity students are given two world maps with estimated figures for HIV/AIDS. They read figures, calculate averages, make comparisons, tabulate data and represent it on a bar graph.

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Collecting Data

Unit standard(s): 9009

Summary:

This is a preliminary activity designed to give learners an opportunity to collect a small amount of raw data and transcribe information from it onto a frequency table. Learners collect information about hairdresser preferences, using a questionnaire. They then construct frequency tables and make various comparisons.

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Getting the picture

Unit standard(s): 9009

Summary:

In this activity learners represent data in three different ways — on a single bar graph, a double bar graph and a pie chart. They work with frequency tables similar to the ones they completed in the previous activity.

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Shampoo

Unit standard(s): 9009

Summary:

This activity introduces the ideas of central tendency, range and spread. Learners calculate the mean, median and mode for ungrouped data. They organise the data into groups and construct a grouped frequency table and histogram of the raw data. They do this to compare shampoo prices, looking at variance and spread.

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Changing the picture

Unit standard(s): 9009

Summary:

In this activity learners read information from existing graphs and identify ways in which these graphs can be used to “manipulate” and/or “distort” the information. They get further practice in drawing their own graphs and changing the scale on the vertical axis to observe the effects.

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Understanding your hair

Unit standard(s): 9009

Summary:

In this activity learners examine information from graphs and tables. They are required to read graphs and tables and understand what is being represented in them. Each of the graphs and tables represents a different context and questions are asked on each graph specifically.

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Thinking about measuring

Unit standard(s): 12444, 8982

Summary:

In this activity students think about what units of measurement and what measuring instruments they would use for measuring different things. The activity also revises the basic units of measurement and gives students ideas about estimation.

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Changing fractions into millilitres

Unit standard(s): 12444, 8982

Summary:

In this activity learners work with fractions of particular pre-packages products. In particular they practise calculating different fractions of 60 ml. They are encouraged to first work out the unit fraction and then multiply by the numerator. They are then asked to generalize this to make fractions of 1 000 ml. They use this to change fractions of products into millilitre amounts. They add newly purchased products to get the new stock balance.

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Colouring hair permanently

Unit standard(s): 12444, 8982

Summary:

This activity extends the work done in Activity 2. Here learners work out product formulations for colouring hair permanently. They calculate how much of each product to use on different clients’ hair and keep a running total of their stock. They use this to calculate stock at the close of day. This in turn is used as a basis for making decisions about reordering stock.

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Making cards using symmetry

Unit standard(s): 12444, 8982

Summary:

In this activity students fold paper and cut out shapes along the fold-line as an introduction to investigating the concept of symmetry.

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Making cards by moving shapes

Unit standard(s): 12444, 8982

Summary:

In this activity students work with transformations of shapes in which the basic shape stays the same but is repeated in different positions and orientations to form complex pictures and patterns.

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Assessment: Colouring hair pemanently

Unit standard(s): 12444, 8982

Summary:

In this assessment students will be working with capacity. Students are asked to calculate their opening stock by converting fractions of packaged products into millilitres. They need to look up information about the formulation of products for permanent colouring and about the total volume of product to mix in Handout 9. They calculate the amounts of product used and use this as a basis for seeing which products they need to re-order.

Organising a cocktail party

Unit standard(s): 12444, 8982

Summary:

In this activity students focus on measuring capacity and budgeting around these measurements. The activity uses the context of preparing for a cocktail party. This requires students to think about capacities of various containers in ways that enable them to estimate the appropriate amounts and to calculate what amounts to order. Students are asked to do calculations based on tables of data and to consider their answers in terms of this specific context.

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Reading plans for a new hall

Unit standard(s): 12444, 8982

Summary:

In this activity students look at plans of a new church hall. They are asked to interpret the plans, which includes an understanding of scale and ratio. They need to estimate and measure. They are asked to work out how they would arrange furniture in the hall for different functions. Here they need to think not only of space but how it is used differently in different social functions.

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Covering the floors

Unit standard(s): 12444, 8982

Summary:

This activity builds on from Activity 5: students work with the same church hall plans. They are asked to calculate the area of different floor spaces. It is designed to help learners understand the area formula for rectangular surfaces. Learners also need to be able to imagine shapes and surfaces from different perspectives.

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Buying a new fridge

Unit standard(s): 7469

Summary:

This activity deals with buying a new fridge. We look at various ways of financing this venture. This activity could be used as an assessment activity.

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Savings and investments

Unit standard(s): 7469

Summary:

This activity deals with savings and investments. We look at stokvels and a variety of bank accounts. We need to be able to choose the best option for our particular situation. We focus on reading interest rate tables supplied by banks.

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What am I earning?

Unit standard(s): 7469

Summary:

This activity deals with a typical pay slip. We look at the deductions that are taken off monthly and the resulting net income. We also look at the contributions made by a company on behalf of the employee.

Budgeting

Unit standard(s): 7469

Summary:

In this activity we look at budgeting. We classify expenses into fixed, changing and irregular expenses.

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Inflation

Unit standard(s): 7469

Summary:

This activity deals with inflation. We compare prices of commodities over a ten year period and look at economic indicators.

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Contract or prepaid?

Unit standard(s): 7469

Summary:

This activity deals with cell phone contracts. We look at an advertisement for contracts and prepaid options. We look at the best contract for various situations.

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All about interest

Unit standard(s): 7469

Summary:

This activity deals with simple and compound interest. We do calculations to establish what is the best option for a pensioner who has to live off R90 000.

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A pattern with a twist

Unit standard(s): 9007

Summary:

In this activity we work with functions of the form y= ax + b, where a < 0 (both discrete and continuous). Learners work with tables and graphs of these functions and are encouraged to compare them with the other functions studied thus far in the unit.

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Patterns within patterns

Unit standard(s): 9007

Summary:

Over the first six activities we have explored a large number of different situations and ways of describing them. We have seen how the same situation can be represented by means of words, tables, graphs and formulae and we have translated from one representation to another. In this activity we will formally introduce vocabulary to describe what we have explored in the absence of such vocabulary.

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Continuous functions

Unit standard(s): 9007

Summary:

In this activity we study patterns which are different from those of Activity 1. Students will explore continuous functions and try to identify the ways in which these patterns are both different from and similar to those we studied in Activity 1.

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Inverse proportion

Unit standard(s): 9007

Summary:

In this activity learners are introduced to another basic function, namely xy = k (a rectangular hyperbola). This function is useful in situations concerned with describing inverse proportion. The first situation deals with discrete data while the second deals with continuous data. It is easier to think of applications of the discrete function than of the continuous one. For this reason the second part of the activity deals with xy = 64 in the absence of a context.

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Some other patterns

Unit standard(s): 9007

Summary:

In this activity the underlying concept that is addressed is the notion that although there are numbers, there is not by implication a mathematical relationship (rule/function) that relates the numbers to each other. In the first and third of the situations studied in the activity, there is some discernable pattern. Our social knowledge of the situations can give us confidence to make predictions (to interpolate and extrapolate). However, there are no rules/functions that describe the situations. In the second of the situations there isn’t even the possibility of using social knowledge of the context in order to make predictions, since the data are completely unrelated.

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Yet another pattern

Unit standard(s): 9007

Summary:

In this activity we look at functions which behave differently from those studied in the previous activities in that they are not smooth curves. Learners are exposed to interesting situations where we look at functions which are a combination of a constant and a step function (i.e. within each of the clearly visible sections/intervals of the function, it remains constant).

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Discrete functions

Unit standard(s): 9007

Summary:

In this activity we introduce students to discrete functions, namely functions for which the independent variable (input value) can only be a whole number. In particular, we work with the basic functions y = ax and y = ax + b where x is an element of the positive whole numbers.

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