âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA

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Calculate the relative frequency of:1) Obtaining a Head on the coin and an even number on the die ……2) Obtaining a Tail on the coin and an odd number on the die ………3) Obtaining a Head on the coin and a 6 on the die ………………….4) Obtaining a 6 on the die …………………………………………...A TWO-WAY TABLEWe can draw a two-way table to find all the possible outcomes when rolling a die andtossing a coin. The following table shows all the possibilities clearly:DIECOINHEADS TAILS1 1 H 1 T2 2 H 2 T3 3 H 3 T4 4 H 4 T5 5 H 5 T6 6 H 6 TFrom the two-way table, we can list the possible outcomes:1 H, 2 H, 3 H, 4 H, 5 H, 6 H, 1 T, 2 T, 3 T, 4 T, 5 T, 6 TUse the two-way table to calculate the probability of:1) Obtaining a Head on the coin and an even number on the die …….2) Obtaining a Tail on the coin and an odd number on the die ………3) Obtaining a Head on the coin and a 6 on the die ………………….4) Obtaining a 6 on the die …………………………………………...Another way to find the set of all the possible outcomes is by drawing a TREEDIAGRAM.36
Activity 3:Use the tree-diagram to list all the possible outcomes from throwing a die and tossinga coin.Use the tree diagram to calculate the probability of:1) Obtaining a Head on the coin and an even number on the die ……2) Obtaining a Tail on the coin and an odd number on the die ………3) Obtaining a Head on the coin and a 6 on the die ………………….4) Obtaining a 6 on the die …………………………………………...ConclusionWe can use either a two-way table or a tree diagram to list outcomes and todetermining relative frequency or probability of a compound event occurring.References1. Prof North D (2006), Probability Component of Data Handling in the SeniorPhase, University of KwaZulu Natal.2. Department of Education (2002), NCS Policy DocumentGrade R – 9 Mathematics3. Laridon et al (2005), Mathematics <strong>for</strong> the Classroom Grade 9, Heinemann37
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 20 and 21: 2) Use the information given in the
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 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
Page 88 and 89: In a survey, 50 people were asked t
Page 90 and 91: At the end of the first “branches
Page 92 and 93: Let A denote an odd and even number
Page 94 and 95:
ADD THE ANGLE TO THE 2- and 3- DIME
Page 96 and 97:
……………………………
Page 98 and 99:
Enlarge the following objects90
Page 100 and 101:
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
Page 110 and 111:
a Now complete the table below:pris
Page 112 and 113:
27 Now look at the different spatia
Page 114 and 115:
elationships algebraically; and rep
Page 116 and 117:
• How do analytical and global th
Page 118 and 119:
Adults must not be shy about asking
Page 120 and 121:
In fact, if a pupil asks a research
Page 122 and 123:
INVESTIGATING BALANCING POINTS OF P
Page 124 and 125:
DATA HANDLING IN THE FOUNDATION PHA
Page 126 and 127:
NUMERACY ASSESSMENT STANDARDS AND M
Page 128 and 129:
FUNCTIONS AND INVERSES IN CONTEXTMa
Page 130 and 131:
ARRIVE ALIVE!!!When a motorist brak
Page 132 and 133:
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
Page 138 and 139:
table. Then press [AC]. The screenc
Page 140 and 141:
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
Page 150 and 151:
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
Page 158 and 159:
Grade R Grade 1 Grade 2 Grade 3•
Page 160 and 161:
3.2Grade R Grade 1 Grade 2 Grade 3R
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have a lid that can roll, andPeople
Page 164 and 165:
Grade R Grade 1 Grade 2 Grade 3•
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
WORKSHOP: TWO HOURSTARGET GROUP: GR
Page 172 and 173:
PROBLEM SOLVINGFOUNDATION PHASE MAT
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5. Guess the number I stand for.•
Page 176 and 177:
ASTROS? OR SMARTIES? ASTROS? OR SMA
Page 178 and 179:
It is important to note that volume
Page 180 and 181:
Part 1: The Great Bicycle Race (30
Page 182 and 183:
IDEAS AND ACTIVITIES TO MAKE YOU A
Page 184 and 185:
WHAT IS THINKING? (15 MIN)An import
Page 186 and 187:
EXPLORING GRAPHS THROUGH TABLESDORY
Page 188 and 189:
• Use the constant -3 to decide o
Page 190 and 191:
Explain the error in line 7.6. Draw
Page 192 and 193:
SOLVING EQUATIONS & FACTORISING AN
Page 194 and 195:
Simple GrowthYear Amount1 R11000234
Page 196 and 197:
3. Solve for x :3 24x - 4x - 7x - 2
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2) QUARTILESA quartile is any of th
Page 200 and 201:
‣ The lower quartile corresponds
Page 202 and 203:
ACTIVITY:Answer the following quest
Page 204 and 205:
SETTING A MATHS LITERACY EXAMINATIO
Page 206 and 207:
are soup tins usually cylindrical?.
Page 208 and 209:
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
Page 214 and 215:
3.Fig. 1 Fig. 2 Fig. 34.Fig. 1 Fig.
Page 216 and 217:
2. Another brick wall:Repeat questi
Page 218 and 219:
2.1 Are the methods of all three le
Page 220 and 221:
2.3 Is there an opportunity here to
Page 222 and 223:
1.3 Is there an opportunity here to
Page 224 and 225:
Investigate whether the following i
Page 226 and 227:
Kieran, C. 1989. The early learning
Page 228 and 229:
Motivation for doing the workshopOu
Page 230 and 231:
• 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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