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2.2 Use squared paper similar to the previous e x ercise. Carefully plan what the numbers on the axes must be to fit the values in this table, and plot the coordinates from the table as dots.
2.3 For this graph it is wrong to try joining the dots with a straight line. This graph has to go up in steps. The reason is that the gardener will charge the same amount for working, say, two hours 10 minutes, two hours 25 minutes, two hours 40 minutes and three hours. Complete the graph by making the appropriate shape of the steps.
2.4 From the completed graph, read off how much it will cost if the gardener works for 6½ hours.
| Learning outcomes(LOs) |
| LO 1 |
| Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems |
| Assessment standards(ASs) |
| We know this when the learner: |
| 1.2 recognises, uses and represents rational numbers (including very small numbers written in scientific notation), moving flexibly between equivalent forms in appropriate contexts; |
| 1.3 solves problems in context including contexts that may be used to build awareness of other learning areas, as well as human rights, social, economic and environmental issues such as: |
| 1.3.1 financial (including profit and loss, budgets, accounts, loans, simple and compound interest, hire purchase, exchange rates, commission, rental and banking); |
| 1.3.2 measurements in Natural Sciences and Technology contexts; |
| 1.4 solves problems that involve ratio, rate and proportion (direct and indirect); |
| 1.7 recognises, describes and uses the properties of rational numbers. |
| LO 2 |
| Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. |
| We know this when the learner: |
| 2.1 investigates, in different ways, a variety of numeric and geometric patterns and relationships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in nature and cultural forms and patterns of the learner’s own creation; |
| 2.2 represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using: |
| 2.2.1 verbal descriptions; |
| 2.2.2 flow diagrams; |
| 2.2.3 tables; |
| 2.2.4 formulae and equations; |
| 2.3 constructs mathematical models that represent, describe and provide solutions to problem situations, showing responsibility toward the environment and health of others (including problems within human rights, social, economic, cultural and environmental contexts); |
| 2.4 solves equations by inspection, trial-and-improvement or algebraic processes (additive and multiplicative inverses, and factorisation), checking the solution by substitution; |
| 2.5 draws graphs on the Cartesian plane for given equations (in two variables), or determines equations or formulae from given graphs using tables where necessary; |
| 2.6 determines, analyses and interprets the equivalence of different descriptions of the same relationship or rule presented: |
| 2.6.1 verbally; |
| 2.6.2 in flow diagrams; |
| 2.6.3 in tables; |
| 2.6.4 by equations or expressions; |
| 2.6.5 by graphs on the Cartesian plane in order to select the most useful representation for a given situation; |
| 2.8 uses the laws of exponents to simplify expressions and solve equations; |
| 2.9 uses factorisation to simplify algebraic expressions and solve equations. |
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