âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA

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MOTIVATION FOR RUNNING WORKSHOPThis workshop will definitely address the problems our educators and learners areencountering in the teaching and learning environment concerning the functions andhow to find equation of graphs using a calculator and a computer. Learners will seethe importance of technology and how it will develop their mathematical knowledgeand thinking.PRESENTATIONTo find equation of a line, one can manually apply mathematical knowledge by firstfind the gradient there-after substitute the coordinates of a point with the m -valueinto the formula or or Use a scientific calculator (Casio: Fx – 82ES) or Use acomputer (Micro soft Excel)ACTIVITYFind equation of a straight line using above mentioned techniquesy(0; 4)(- 2; 0) 0xFirst Technique: MathematicalWORKOUTSTEPS(- 2; 0) and (0; 4) Write the coordinatesym =x4 − 0=0 − ( −2)= 2y − y122−−y = 2x+ 4yxy − 4 = 2( x − 0)11= m( x − x ) 1Find m (the gradient)Equation of a lineSubstitution28
Second Technique: Scientific CalculatorThe following key sequences are used with the Casio: Fx-82ES when working outequation of a line if points are given.WORKOUTSTEPSFirst get the calculator in the correctmode[Mode] [ 2: STAT] [2: A + B x]Enter the data for x: 1 [=] - 1 [=][Replay]for y: 6 [=] 2 [=]To find ATo find BPress:[AC][Shift][1][7;Reg][1:A][=]Press:[AC][Shift][1][7:Reg][2:B][=]Third Technique: Computer (Microsoft Excel)WORKOUTSTEPSOpening Excel window[start][All programmes][Microsoft office][office Excel]Enter data A1: x B1: yA2: 1 B2 : 6A3: - 1 B3 : 2Highlight the whole data in ExcelwindowClick left side of the mouse andmove it to the whole data (Data willbe colored)Follow the steps • Click: chard wizard• Click: x y (scatter)• Click: next• Click: column• Click: finishNext steps • Click: on a dot (right click)• Click: Add Trent line• Click: linear• Click: option• Click: display equation on chart• Click: Ok29
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 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
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
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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
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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
Page 118 and 119:
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
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
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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
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•
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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•
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
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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
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• 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
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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.
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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
Page 222 and 223:
1.3 Is there an opportunity here to
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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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