âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA

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2) Use the in<strong>for</strong>mation given in the table to draw an ogive (cumulative frequencygraph or diagram).NOTE:i. The ogive or cumulative frequency graph starts at the point where the cumulativefrequency is zero.ii. For a cumulative frequency curve of continuous data, the first element of the ordered pair is the upper limit of the interval. the second element is the value of the cumulative frequency.iii. When you join the points on the graph you are assuming that the items are evenlyspread throughout the groups. However, data items are not necessarily evenlyspread on a graph so any reading from a frequency curve is an estimate, not anexact reading.iv. The ogive or cumulative frequency curve allows you to read off the numbers oflearners who are less than a certain height. If you wanted to know how manylearners were 102 cm or were shorter than 102 cm, you can read up from 102 cmon the horizontal axis and find that there are about 20 learners who are shorterthan or equal to 102cm.v. Always draw lines on the graph to show where you took the readings3) Use the ogive to find the approximate values of the following:a) Median ……………………………............................................12
) Lower quartile (Q 1 ) …………………………………………….c) Upper quartile (Q 3 ) ……………………………………………..ACTIVITY 2The following ogive or cumulative frequency diagram shows the test marks out of100 obtained by learners in a test.1) Use the ogive to find approximate values ofa) The median ………………………………………………………b) The upper quartile (Q 1 ) ………………………………………….c) The lower quartile (Q 3 ) ………………………………………….2) Complete the following sentences:a) Half of the learners achieved a mark lower than ………………..b) A quarter of the learners achieved a mark lower than …………..c) 75% of the learners achieved a mark lower than ………………..3) Using the cumulative frequency diagram, what other facts can you conclude aboutyour original data set? ……………………………………………..13
Page 1 and 2: Proceedings of the15 th Annual Cong
Page 3 and 4: Foreword“Mathematical Knowledge f
Page 5 and 6: ContentsHow I teachAuthor Title Pag
Page 7: Scheiber, JackieThe interpretation
Page 10 and 11: SKETCHING A CUBIC FUNCTIONTRADITION
Page 12 and 13: of the first computer games, Pong,
Page 14 and 15: Although this genre of computer gam
Page 16 and 17: He played on and off all day until
Page 18 and 19: [10] Butgereit, L, “Thumb Tribe M
Page 22 and 23: ConclusionSince these terms were fa
Page 24 and 25: EXAMPLE: The table below represents
Page 26 and 27: Five-number summaryMinimum = …; Q
Page 28 and 29: ACTIVITYIn an experiment to measure
Page 30 and 31: Conclusion:I hope that learners wou
Page 32 and 33: ACTIVITYBelow is a summary of a cir
Page 34 and 35: REFERENCESScheiber, J. 2003. Data h
Page 36 and 37: MOTIVATION FOR RUNNING WORKSHOPThis
Page 38 and 39: CONCLUSIONThese are not the only te
Page 40 and 41: n(E)• P(E) = 1 if event E is cert
Page 42 and 43: DETERMINING PROBABILITIES OF COMPOU
Page 44 and 45: Calculate the relative frequency of
Page 46 and 47: HOW I TEACH SCATTER PLOTSDUNGILE MA
Page 48 and 49: • It is clear from the above grap
Page 50 and 51: A STATISTICAL INVESTIGATION INTO HU
Page 52 and 53: • Does the activity relate to han
Page 54 and 55: MEASURES OF CENTRAL TENDENCYTHABANI
Page 56 and 57: 1) Determine the mean, mode and med
Page 58 and 59: HOW I TEACH MATH USING VIRTUAL MANI
Page 60 and 61: The Balloon ModelIs this game fair?
Page 62 and 63: Virtual manipulatives can be both s
Page 64 and 65: References• Moyer P., Bolyard,J.
Page 66 and 67: WHAT ARE MISLEADING BAR GRAPHS?If a
Page 68 and 69: CONCLUSION:It is a well known fact
Page 70 and 71:
MISLEADING AVERAGESThe mean, median
Page 72 and 73:
e) Do you think any of the averages
Page 74 and 75:
ANALYSIS OF QUESTION 10.2 OF THE NO
Page 76 and 77:
CONCLUSIONThe midpoint curve is TRA
Page 78 and 79:
called a sample. A sample is any su
Page 80 and 81:
This demonstrates that the larger t
Page 82 and 83:
Consider the marks 32 ; 56 ;With 32
Page 84 and 85:
SOLUTIONStep 1: Collect the data in
Page 86 and 87:
HOW I TEACH TALLY TABLES TO LEARNER
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In a survey, 50 people were asked t
Page 90 and 91:
At the end of the first “branches
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Let A denote an odd and even number
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ADD THE ANGLE TO THE 2- and 3- DIME
Page 96 and 97:
……………………………
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Enlarge the following objects90
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MathematicsGrade: 6Learning Outcome
Page 102 and 103:
A B CD E FGMathematicsGrade: 6Learn
Page 104 and 105:
INVESTIGATING 3-D SHAPES: ANALYSING
Page 106 and 107:
When we arrange objects according t
Page 108 and 109:
Sphere:Cube:Prisms, pyramids, cylin
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a Now complete the table below:pris
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27 Now look at the different spatia
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elationships algebraically; and rep
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• How do analytical and global th
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Adults must not be shy about asking
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In fact, if a pupil asks a research
Page 122 and 123:
INVESTIGATING BALANCING POINTS OF P
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DATA HANDLING IN THE FOUNDATION PHA
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NUMERACY ASSESSMENT STANDARDS AND M
Page 128 and 129:
FUNCTIONS AND INVERSES IN CONTEXTMa
Page 130 and 131:
ARRIVE ALIVE!!!When a motorist brak
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BACTERIA!!!Food goes rotten when th
Page 134 and 135:
Suppose we want to make x the subje
Page 136 and 137:
REGRESSION MODELLINGPaul LaridonRAD
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table. Then press [AC]. The screenc
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3.2 The PendulumThe diagram represe
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3.2.5 and comment on how good or ot
Page 144 and 145:
THE VERSATILE USE OF PATTERN BLOCKS
Page 146 and 147:
AN INTRODUCTION TO FUNCTIONAL RELAT
Page 148 and 149:
USE OF MATHEMATICAL GAMES AS AN ALT
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the teacher’s ability to choose t
Page 152 and 153:
method. This will be followed by a
Page 154 and 155:
mathematical concepts, (2) develop
Page 156 and 157:
TEACHING AND ASSESSING SPACE AND SH
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Grade R Grade 1 Grade 2 Grade 3•
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3.2Grade R Grade 1 Grade 2 Grade 3R
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have a lid that can roll, andPeople
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Grade R Grade 1 Grade 2 Grade 3•
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Page 168 and 169:
Page 170 and 171:
WORKSHOP: TWO HOURSTARGET GROUP: GR
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PROBLEM SOLVINGFOUNDATION PHASE MAT
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5. Guess the number I stand for.•
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ASTROS? OR SMARTIES? ASTROS? OR SMA
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It is important to note that volume
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Part 1: The Great Bicycle Race (30
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IDEAS AND ACTIVITIES TO MAKE YOU A
Page 184 and 185:
WHAT IS THINKING? (15 MIN)An import
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EXPLORING GRAPHS THROUGH TABLESDORY
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• Use the constant -3 to decide o
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Explain the error in line 7.6. Draw
Page 192 and 193:
SOLVING EQUATIONS & FACTORISING AN
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Simple GrowthYear Amount1 R11000234
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3. Solve for x :3 24x - 4x - 7x - 2
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2) QUARTILESA quartile is any of th
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‣ The lower quartile corresponds
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ACTIVITY:Answer the following quest
Page 204 and 205:
SETTING A MATHS LITERACY EXAMINATIO
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are soup tins usually cylindrical?.
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Part 4: 30 minutesIn groups: Make y
Page 210 and 211:
DEVELOPING ALGEBRAIC THINKING IN TH
Page 212 and 213:
WORKSHEET 2Activities to develop le
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3.Fig. 1 Fig. 2 Fig. 34.Fig. 1 Fig.
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2. Another brick wall:Repeat questi
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2.1 Are the methods of all three le
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2.3 Is there an opportunity here to
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1.3 Is there an opportunity here to
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Investigate whether the following i
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Kieran, C. 1989. The early learning
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Motivation for doing the workshopOu
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• Paired cards• Crack the code
Page 232 and 233:
• Separate tests were developed f
Page 234 and 235:
Enlighten Education TrustBaseline T
Page 236 and 237:
Enlighten Education TrustSchool Ave
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âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA