GRADE 12 MATHEMATICAL LITERACY TEACHER NOTES
SENIOR SECONDARY IMPROVEMENT PROGRAMME 201 3GRADE 12MATHEMATICAL LITERACYTEACHER NOTES1The SSIP is supported by(c) Gauteng Department of Education, 2013
TABLE OF CONTENTSTEACHER NOTESSESSION3TOPIC1. Drawing graphs of real life situationsPAGE32: Drawing and interpreting more than one graph ona system of axes41: Grids, maps, compass202: Use and interpret scale drawings, build scalemodel s5Self Study1. Compare, summarise and display data – describetrends392. Probability and misuse of statistics in society2(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)SESSION 3: TOPIC 1: GRAPHS IN REAL LIFE SITUATIONSTeacher Note: When learners scan through a newspaper, there are many pages that havegraphs to illustrate visually the information that the articles are about. It is important forlearners to grasp the concept of graphs in real life situations. Sketching and reading graphs isthe key to understanding the information around you.LESSON OVERVIEW:1.2.3.Introduce session:5 minutesTypical exam questions: 30 minutesReview/solutions/memo: 25 minutesSECTION A: TYPICAL EXAM QUESTIONSQUESTION 1A cell phone contract is set up such that the subscriber has to pay R2,80 per minute.a. Complete the table of values for the above contract.MinutesCost12.8025.603411.20(2)5146b. Sketch a graph showing the cost of the contract.(5)c. Set up an equation that represents the above relationship.(3)[10]QUESTION 2The graph on the following page represents the break-even analysis for ABC FlowerDistributors. The fixed cost per month is R250,00. The variable cost is R25,00 per bunchof flowers. The shop breaks even when they sell 10 bunches of flowers.a)b)c)Label the lines that represent fixed costs, total costs (fixed and variable) andincome for the bunches of flowers.(3)Label the axes.(2)What are the co-ordinates of the break-even point?(2)[7]3(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)250.00QUESTION 3Fred and George run the 1000m. Below is a table of values, which shows their relativeposition after a given amount of time. Both runners finish at exactly the same time.Time 700690a. On the given set of axes, sketch both sets of points.14085084016510001000(4)4(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONDistance (m)MATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER 3012011010090807060504030200100Time(s)5(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYb)c)SENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)d)During which time is Fred ahead of George. Indicate on the graph?(2)At what distance other than the start or the finish have the two boys docked thesame time? Indicate on your graph where you got your reading. Label this point A.(2)metersspeed sec ondsUse the formula above to calculate George‟s speed for the first 75 seconds.(2)e)During which interval did Fred run the fastest?(2)[12]SECTION B: SOLUTIONS AND HINTSQUESTION 1a)The complete table:Minutes1Cost2.8025.6038.40 411.20514616.8 (Note: Learners must look at the top value and multiply it by the R2,80)b)(2) For scale and CostR16.8014 11.208.405.602.80 00123456 Min(Note: Learners must take note of the ticks and where marks are allocated. They mustknow what graph is expected of them and that the right values are on the right axes)(5)6(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYc)m SENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)y 2 y1(Or cost per minute); c 0 x2 x1Thus, y m*x c becomes y 2.80x (3)[10]QUESTION 2a)Income Total Cost 250Fixed (Note: look at the mark allocation to ensure learners add everything that is required)(3) (2)b) x-axis: 1 unit per squarey-axis: 50 units per squarec) Read off: (10 ; 500 )(2)[7]7(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)QUESTION 3a)Answer is below after (e).(4)b)c)Show on the graph: Fred is ahead of George for the last 90 seconds orFred is ahead of George from 75 to 165 seconds The label A on the graph should be at (75 ; 420 )(2)(2)d)speed e)Between 75 and 90 seconds Fred ran the fastest. Read off from table orfrom graph. 420 mmeters 5.6 m So for George: speed s75ssec onds(2)(2)8(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)SECTION C: HOMEWORKTeacher Note: As the learners attempt the homework, they must look at the mark allocationsand time themselves to ensure they can answer the questions in the given time. If theycannot, or get the answers wrong, the learners must attempt the homework again as this isgood practice.QUESTION 1:10 minutesThe South African Revenue Service (SARS) is responsible for collecting taxes from taxpayerson behalf of the government. The following graph shows how the government spent some ofthe money it received from taxes in the 2002/3, 2003/4, 2004/5 and 2005/6 financial years.a) How much more was spent on education in the 2005/6 financial year thanin the 2002/3 financial year?(2)b) Analyse each of the amounts spent on education, health and socialdevelopment over the four financial years listed. What trend do you notice?Explain your observations.(4)c) What is the percentage increase on the expenditure of social developmentbetween 2002/3 and 2005/6?(2)d) What was the average increase on the expenditure of social development overthe four years?(2)[10]9(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYQUESTION 2:GRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)25 minutesFig 7Again in the line graph above, the exact values have been shown at the points plotted.We are now going to work through possible questions that assess other skills as welland may be more challenging.Please refer to Fig 7 above which gives the diesel prices per litre from 2002 to May 2008.a)b)c)d)e)f)What was the price difference per litre between 1 January 2002 and1 January 2008?(3)Determine the average increase per year from 1 January 2002 until1 January 2008.(7)Determine the price increase, as a percentage, over the first 4 months of2008.(Round your answer to the nearest whole number)(3If the price of diesel was to increase at the same rate it has done for the first 4months of 2008, calculate the expected diesel price for the end of 2008?(6)Why do you think the price of diesel increased so drastically in the beginning of2008? Give two possible reasons.(2)If the graph above had no numbers along the vertical axis and no numbers ontop of each point that has been plotted, it would still be possible to determinewhich year had the highest fuel increase. Explain how this would be possible.(2)[23]10(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)SECTION E: SOLUTIONS TO HOMEWORKQUESTION 1a) R62 – 44 billion R18 billionb) More is spent each year with the most being spent on social development. This isprobably due to funds being spent on developing sport in previously disadvantagedareas.c) (42 – 21) 21 X 100 100 %d) Average increase 3 8 10 7 Billion per year3QUESTION 2a.b.This is an easy question. (Read off from the graph and subtract the values)725 – 327 398 cents R3,98Here we have to work out the increase for each year, i.e. subtract the valuesgiven for each year, then find the average of these values.360 – 347335 – 360 13-25(3)Note: price went down. It is important to include thenegative sign398 – 335 63518 – 398 120551 – 518 33725 – 551 174Now average these amounts: 13 -25 63 120 33 1746c. 378 63 cents per year.6Do you remember how to work out percentage increase?Final price – original priceOriginal priceX 100 1009 – 725 X 10072539%(7)(3)11(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYd.SENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)According to the previous answer the price increases by 39% in 4 months.To reach the end of the year it must thus go through another TWO 4 month periods,increasing by 39% twice.May - Aug1009 X 39 100 393,511009 393,51 1402,51Sept - Dec1402,51 X 39 100 546,98546,98 1402,51 1950 centsTherefore, the expected diesel price, would have been R19,50 at the end of 2008.Note: only round off the FINAL answer to be more accurate.If number of decimals is not specified, keep to the same as in the question.(6)e.f.Here you are giving your own opinion, but of course it must make sense.(2)Yes, it would be the highest value point on the graph, i.e. where the graph peaks.(2)[23]12(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)SESSION 3: TOPIC 2: DRAWING AND INTERPRET MORE THAN ONE GRAPH ON ASYSTEM OF AXESLESSON OVERVIEWTeacher Note: Learners must ensure that they understand the basic concepts of graphsbefore trying to interpret them.1.2.3.Introduce session:Typical exam questions:Review/solutions/memo:5 minutes30 minutes25 minutesSECTION A: TYPICAL EXAM QUESTIONSQUESTION 1:5 minutes(From Cluster Prelim Exam 2008)The graph below illustrates the ratio between wage settlement rates (line graph) and theconsumer price inflation(bar graph) that were achieved during collective bargainingagreements for the period 1990 to 20051. During which year was the lowest wage settlement rate achieved?2. During which year(s) does the consumer price inflation exceed the wagesettlement rate?3. Study the wage settlement trend from 1995 to 2001. Is it generally increasing ordecreasing?4. In which year is the largest percentage gap between the consumer price inflationand the wage settlement?5. During which year(s) was the wage settlement rate and consumer price inflationalmost on par?(1)(1)(1)(1)(1)[5]13(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYQUESTION 2:15 minutesGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)(From June Examination 2008)NOTE: Learners must look at how negative values are interpreted.The graph below shows the annual percentage change in Gross Domestic Product(GDP) for South Africa over the period 1980 to 2006.There are four bars for each year, i.e. each bar represents one financial quarter:January to March, April to June etc.The line represents the annual percentage change in the rate of inflation from 1982 to2006.1.2.3.4.In what year did GDP growth reach its lowest level?What is the highest rate of inflation since the turn of the century?Explain why there are two quarters „missing‟ in 1991 GDP graph.Describe what was happening to South Africa‟s GDP from the second halfof 1991 through until the middle of 1993.5. In a short paragraph, describe the differences in South Africa‟s GDP growthfor the two periods 1980 to 1993 and 1994 to 2006.6. Identify and explain the relationship that exists between GDP growth andinflation over the period 1982 to 1992.(1)(1)(1)(2)(6)(2)7. Making specific reference to the period 2001 to 2006, explain why a very low rate ofinflation is not beneficial for the general economy.(2)[15]14(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)QUESTION 3:10 minutesThe graph below shows the average maximum temperature and rainfall figures forTown X, in Africa, in 2007.a) Give the highest and lowest temperatures recorded.(2)b) Is Town X in the northern or southern hemisphere? Give a reason for your answer.(2)c) In which month is the highest rainfall recorded?(1)d) In which season does Town X have the most rainfall?(2)e) Determine the total rainfall for Town X for 2007and hence find the average monthlyrainfall for Town A in 2007.(3)[10]SECTION B: SOLUTIONS AND HINTSQUESTION 1:Note: Learners must read off the graph carefully.1. 2005. 2. 1992 and 2002 3. decreasing 4. 1997 5. 1993 QUESTION 21.1983 (highest negative value) 2.Values not known, no records of GDP for this time OR 312,5 or 12,6 % Value of GDP was zero(1)(1)(1)(1)(1)[5](1)(1)(1)15(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACY4.5.6.7.GRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)There was negative growth in GDP i.e. the GDP decreased steadily during thisperiod to approx -2,6 % in first quarter of 1993 and then took a turn to end up atzero growth in middle of 1993. 1980-93 Growth fluctuated - upwards followed by downwards , periods ofnegative growth 1994 -2006 All positive growth , general upwards trendpossible reason end of apartheid and sanction against SA) As inflation increases, GDP growth decreases - As prices increase, less isspent and GDP growth decreases. During this period, inflation was low in comparison to earlier and as it droppedso did GDP growth. As it increased so did GDP growth. QUESTION 3a) Highest temp – 29 degrees C , lowest temp 18 degrees C b) Southern H, close to the equator . Temperatures are hot. c) August d) Winter e) ) 5 15 14 25 35 62 98 105 62 22 12 5 (1M for adding all thetemperatures)12 (1M for dividing by 12) 46012 38,33 (2)(6)(2)(2)[15](2)(2)(1)(2)(3)[10]SECTION C: HOMEWORKQUESTION 1The CPFI (Consumer Price Food Index) is a measure of the inflation rate of our country.The BCI (Business Confidence Indicator) is a measure of the level of confidence thatbusinesses (both local and foreign) have in the economy of our country.Local businesses need to feel confident about our country‟s economy if they are to spendmoney on expansion (growing bigger).Foreign businesses also need to feel confident about our country‟s economy if they are toinvest their money in our country. They will only do so if they feel that our country‟s economyis healthy and growing. If not, they would rather invest their money elsewhere.16(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)Graph 1CPFI and BCIGraph 2a) Consider GRAPH 1. What trend would you hope to see the CPFI graph follow?Is this possible? Justify your answer.b) Consider GRAPH 1. When the CPFI climbs steeply, what does the BCI do?Do you expect this to happen?c) Consider GRAPH 2. Graph 2 is based on the same data as Graph 1 yet looksvery different. Which would be more beneficial to us as consumers: the CPFIbeing positive (above the 0) or the CPFI being negative (below the 0)? Justifyyour answer.(3)(3)(4)17(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION 3(TEACHER NOTES)d) A foreign business is considering investing in our country, but he needs someconvincing. Use, and refer to each of the graphs, to discuss how you wouldconvince foreign investors to invest in South Africa.(4)[14]QUESTION 2Study the graph above and then answer the following questions:a) What was the highest and what was the lowest rand/dollar exchange rate duringthe time period illustrated?b) What was the highest and what was the lowest rand/euro exchange rate duringthe time period illustrated?c) Both rates fluctuate a lot over the period, but show an overall trend which can beseen in spite of the fluctuations. What is this trend?d) During the period illustrated on the graph, was the dollar or euro worth more inrand?e) On 15 May 2006, the exchange rates were as follows:1 US 6,42652 ZAR,and 1 Euro 8,27310 ZAR. Compare these exchange rates with those between2000 and 2002, as shown on the graph. What is different about the 2006 rates incomparison to the 2000 to 2002 rates?(2)(2)(3)(2)(3)[12]Teacher Note: As learners attempt the homework, they must take careful note of the timelimits and marks awarded. It is important that they know what is being asked.18(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION 3(TEACHER NOTES)SECTION D: SOLUTIONS TO HOMEWORKQUESTION 1a) Trend – CPFI be low and remain lowIs possible if food prices remain low.(3)b) BCI increases as the CPFI increases.Expect this to happen because it shows that the economy is growing(3)c) The CPFI would be beneficial if it was above the line as this shows that theeconomy is growing and businesses would invest(4)d) Graph 1 – Since Jan „03, CPFI has stabilised and BCI has grown steadily.That trend is likely to continueGraph 2 – Whenever the graph shows that there is a positive increase in CPFI,foreign investment increases rapidly. The graph tends towards the positive towardsthe end.(4)[14]QUESTION 2a)b)c)d)e)Highest R125 / dollarLowest R62 / dollar(2)Highest R111 / euroLowest R60 / euro(2)Both exchange rates increase gradually. There was a rapid increase at end of 2001with a peak in 2002. There after the exchange rates decrease.(3)In 2001, 2002 a person was receiving more rands per dollar than rand per euroand in 2006 a person is receiving more rands per euro than rands per dollar.(2)Both rates are substantially less in 2006, which means that the rand has becomestronger.(3)[12]19(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYSENIOR SECONDARY INTERVENTION PROGRAMMEGRADE 12SESSION (TEACHER NOTES)SESSION : TOPIC 1: GRIDS, MAPS AND THE COMPASS - LOCATION AND RELATIVEPOSITIONTeacher Note: Make sure learners know and understand how to (a) use grids to locateplaces (b) read and use maps (c) use a compass to determine bearing and direction. Makesure learners know how to use a grid, map and / or compass to locate and describe therelative position of a place.LESSON OVERVIEW1.2.3.Introduce session:Typical exam questions:Review/solutions/memo:5 minutes55 minutes30 minutesSECTION A: TYPICAL EXAM QUESTIONSQUESTION 1:13 minutes(Taken from DoE/Preparatory Exam 2008 Paper 1)Shop AN1S2CompanyGardens3CShop BABCD1.1 The grid reference of Shop B is A3. Write down the grid reference for Shop B.(1)20(c) Gauteng Department of Education, 2013
GAUTENG DEPARTMENT OF EDUCATIONMATHEMATICAL LITERACYGRADE 12SENIOR SECONDARY INTERVENTION PROGRAMMESESSION (TEACHER NOTES)1.2 If a truck drives from Shop B in a northerly direction in Longmarket Street1.2.1 In which street should the truck turn east in order to reach Shop A?(2)1.2.2 The scale of the map is 1 : 70 000. Calculate the distance, in km, the trucktravels from Shop A to Shop B as described above.(3)1.3 In which direction should one travel from Shop B in order to reach the CompanyGardens (grid reference A3)?(1)1.4 Peter walks in a northerly direction from Shop B. At Burg Street he turns right andcontinues in an easterly direction until he reaches Prestwich Street. At Prestwich Streethe turns and continues his journey in a northerly direction. He crosses one road and atthe second road he turns right. He continues to the end of this road and reaches hisdestination straight ahead.What is his destination?(2)In what direction would you have to travel from the V&A Waterfront to get to the airport?(2)1.5 Complete the following : „The traffic circle (marked C on the map) liesof Shop A on a bearing of(4)[15]QUESTION 2:22 minutes(Taken from Summary sets f
GRADE 12 . MATHEMATICAL LITERACY . TEACHER NOTES (c) Gauteng Department of Education, 2013 1. . 2013 11. GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME . QUESTION 2: 15 minutes (From June Examination 2008) NOTE .
Traditionally, Literacy means the ability to read and write. But there seems to be various types of literacy. Such as audiovisual literacy, print literacy, computer literacy, media literacy, web literacy, technical literacy, functional literacy, library literacy and information literacy etc. Nominal and active literacy too focuses on
Teacher of Grade 7 Maths What do you know about a student in your class? . Grade 7 Maths. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Primary. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 . Learning Skill
Grade 3, Grade 4 and Grade 5 This collection of mathematical literacy sample materials represents a typical range of mathematics material in ISA tests from Grade 3 to Grade 5. The purpose of this collection is to show teachers examples of the kinds of mathematical literacy that are used in the ISA.
Grade 4 NJSLA-ELA were used to create the Grade 5 ELA Start Strong Assessment. Table 1 illustrates these alignments. Table 1: Grade and Content Alignment . Content Area Grade/Course in School Year 2021 – 2022 Content of the Assessment ELA Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
MATHEMATICAL LITERACY P1 MARKS: 100 TIME: 2 hours This question paper consists of 16 pages including 1 answer sheet and 2 annexures. 2 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2015) . MATHEMATICAL LITERACY P1 MEMORANDUM MARKS: 100 Symbol Explanation M Method A Accuracy
Math Course Progression 7th Grade Math 6th Grade Math 5th Grade Math 8th Grade Math Algebra I ELEMENTARY 6th Grade Year 7th Grade Year 8th Grade Year Algebra I 9 th Grade Year Honors 7th Grade Adv. Math 6th Grade Adv. Math 5th Grade Math 6th Grade Year 7th Grade Year 8th Grade Year th Grade Year ELEMENTARY Geome
7 Grade 1 13 Grade 2 18 Grade 3 23 Grade 4 28 Grade 5 33 Grade 6 38 Elementary Spanish. 29 Secondary. 39 Grade 7 43 Grade 8 46 Grade 9 49 Grade 10 53 Grade 11 57 Grade 12 62 Electives. Contents. Textbook used with Online Textbook used with DVD. Teacher Edition & Student Books. Color Key
Part VII. LIteracy 509 Chapter 16. A Primer on Literacy Assessment 511 Language Disorders and Literacy Problems 512 Emergent Literacy 514 Emergent Literacy Skill Acquisition 516 Assessment of Emergent Literacy Skills 520 Assessment of Reading and Writing 528 Integrated Language and Literacy Skill Assessment 536 Chapter Summary 537
