SUPPORTING NOTES FOR LESSON 5 |
Pupils will need to begin with the values calculated in Lesson 2. Incremental values greater than and less than these values will be used in the investigations.
The estimated speed of the batsman.
The distance the bat tip is past the crease line.
The time that the bat tip has been past the crease line.
The distance that the bail has fallen.
The time that the bail has been falling.
Two examples (Example 1; Example 2) are provided to show how pupils might use spreadsheets to investigate the relationship between the variables. Note: As before, these examples are not intended to prescribe the ‘correct’ method, but to provide an example of how the mathematical analysis could be performed.
In one trial, the teacher noted a student who had a spreadsheet done already in the fourth lesson, arrived at the fifth lesson with three more spreadsheets done. The teacher asked him to have a go at making a table in Excel that varied the batsman’s speeds vertically and time the bails had been off horizontally. He assumed distance of the bat-tip across the crease-line to be 0.95 m. This was based on the fact that distance across the crease was probably his most accurate prediction. The values in the cells represented how much earlier the bails came off compared to the time the bat-tip had crossed the line. A function in Excel allows negative values to be shown in red and hence red values indicated the batsman being “in”. This was able to give a very good representation of a variety of combinations that would result in the batsman being in. This was quite challenging programming requiring some complex equations and fixed addressing in the cells.
Table 1 shows the spreadsheet formulas and table 2 shows the calculated values.
Table 1
Speed (m/s) | Time bails off (sec) | |||||||||
=B2+0.05 | =C2+0.05 | =D2+0.05 | =E2+0.05 | =F2+0.05 | =G2+0.05 | =H2+0.05 | =I2+0.05 | =J2+0.05 | =K2+0.05 | |
2 | =C$2-(0.95/$A4) | =D$2-(0.95/$A4) | =E$2-(0.95/$A4) | =F$2-(0.95/$A4) | =G$2-(0.95/$A4) | =H$2-(0.95/$A4) | =I$2-(0.95/$A4) | =J$2-(0.95/$A4) | =K$2-(0.95/$A4) | =L$2-(0.95/$A4) |
=A4+0.5 | =C$2-(0.95/$A5) | =D$2-(0.95/$A5) | =E$2-(0.95/$A5) | =F$2-(0.95/$A5) | =G$2-(0.95/$A5) | =H$2-(0.95/$A5) | =I$2-(0.95/$A5) | =J$2-(0.95/$A5) | =K$2-(0.95/$A5) | =L$2-(0.95/$A5) |
=A5+0.5 | =C$2-(0.95/$A6) | =D$2-(0.95/$A6) | =E$2-(0.95/$A6) | =F$2-(0.95/$A6) | =G$2-(0.95/$A6) | =H$2-(0.95/$A6) | =I$2-(0.95/$A6) | =J$2-(0.95/$A6) | =K$2-(0.95/$A6) | =L$2-(0.95/$A6) |
=A6+0.5 | =C$2-(0.95/$A7) | =D$2-(0.95/$A7) | =E$2-(0.95/$A7) | =F$2-(0.95/$A7) | =G$2-(0.95/$A7) | =H$2-(0.95/$A7) | =I$2-(0.95/$A7) | =J$2-(0.95/$A7) | =K$2-(0.95/$A7) | =L$2-(0.95/$A7) |
=A7+0.5 | =C$2-(0.95/$A8) | =D$2-(0.95/$A8) | =E$2-(0.95/$A8) | =F$2-(0.95/$A8) | =G$2-(0.95/$A8) | =H$2-(0.95/$A8) | =I$2-(0.95/$A8) | =J$2-(0.95/$A8) | =K$2-(0.95/$A8) | =L$2-(0.95/$A8) |
=A8+0.5 | =C$2-(0.95/$A9) | =D$2-(0.95/$A9) | =E$2-(0.95/$A9) | =F$2-(0.95/$A9) | =G$2-(0.95/$A9) | =H$2-(0.95/$A9) | =I$2-(0.95/$A9) | =J$2-(0.95/$A9) | =K$2-(0.95/$A9) | =L$2-(0.95/$A9) |
=A9+0.5 | =C$2-(0.95/$A10) | =D$2-(0.95/$A10) | =E$2-(0.95/$A10) | =F$2-(0.95/$A10) | =G$2-(0.95/$A10) | =H$2-(0.95/$A10) | =I$2-(0.95/$A10) | =J$2-(0.95/$A10) | =K$2-(0.95/$A10) | =L$2-(0.95/$A10) |
=A10+0.5 | =C$2-(0.95/$A11) | =D$2-(0.95/$A11) | =E$2-(0.95/$A11) | =F$2-(0.95/$A11) | =G$2-(0.95/$A11) | =H$2-(0.95/$A11) | =I$2-(0.95/$A11) | =J$2-(0.95/$A11) | =K$2-(0.95/$A11) | =L$2-(0.95/$A11) |
=A11+0.5 | =C$2-(0.95/$A12) | =D$2-(0.95/$A12) | =E$2-(0.95/$A12) | =F$2-(0.95/$A12) | =G$2-(0.95/$A12) | =H$2-(0.95/$A12) | =I$2-(0.95/$A12) | =J$2-(0.95/$A12) | =K$2-(0.95/$A12) | =L$2-(0.95/$A12) |
=A12+0.5 | =C$2-(0.95/$A13) | =D$2-(0.95/$A13) | =E$2-(0.95/$A13) | =F$2-(0.95/$A13) | =G$2-(0.95/$A13) | =H$2-(0.95/$A13) | =I$2-(0.95/$A13) | =J$2-(0.95/$A13) | =K$2-(0.95/$A13) | =L$2-(0.95/$A13) |
=A13+0.5 | =C$2-(0.95/$A14) | =D$2-(0.95/$A14) | =E$2-(0.95/$A14) | =F$2-(0.95/$A14) | =G$2-(0.95/$A14) | =H$2-(0.95/$A14) | =I$2-(0.95/$A14) | =J$2-(0.95/$A14) | =K$2-(0.95/$A14) | =L$2-(0.95/$A14) |
=A14+0.5 | =C$2-(0.95/$A15) | =D$2-(0.95/$A15) | =E$2-(0.95/$A15) | =F$2-(0.95/$A15) | =G$2-(0.95/$A15) | =H$2-(0.95/$A15) | =I$2-(0.95/$A15) | =J$2-(0.95/$A15) | =K$2-(0.95/$A15) | =L$2-(0.95/$A15) |
=A15+0.5 | =C$2-(0.95/$A16) | =D$2-(0.95/$A16) | =E$2-(0.95/$A16) | =F$2-(0.95/$A16) | =G$2-(0.95/$A16) | =H$2-(0.95/$A16) | =I$2-(0.95/$A16) | =J$2-(0.95/$A16) | =K$2-(0.95/$A16) | =L$2-(0.95/$A16) |
=A16+0.5 | =C$2-(0.95/$A17) | =D$2-(0.95/$A17) | =E$2-(0.95/$A17) | =F$2-(0.95/$A17) | =G$2-(0.95/$A17) | =H$2-(0.95/$A17) | =I$2-(0.95/$A17) | =J$2-(0.95/$A17) | =K$2-(0.95/$A17) | =L$2-(0.95/$A17) |
=A17+0.5 | =C$2-(0.95/$A18) | =D$2-(0.95/$A18) | =E$2-(0.95/$A18) | =F$2-(0.95/$A18) | =G$2-(0.95/$A18) | =H$2-(0.95/$A18) | =I$2-(0.95/$A18) | =J$2-(0.95/$A18) | =K$2-(0.95/$A18) | =L$2-(0.95/$A18) |
=A18+0.5 | =C$2-(0.95/$A19) | =D$2-(0.95/$A19) | =E$2-(0.95/$A19) | =F$2-(0.95/$A19) | =G$2-(0.95/$A19) | =H$2-(0.95/$A19) | =I$2-(0.95/$A19) | =J$2-(0.95/$A19) | =K$2-(0.95/$A19) | =L$2-(0.95/$A19) |
=A19+0.5 | =C$2-(0.95/$A20) | =D$2-(0.95/$A20) | =E$2-(0.95/$A20) | =F$2-(0.95/$A20) | =G$2-(0.95/$A20) | =H$2-(0.95/$A20) | =I$2-(0.95/$A20) | =J$2-(0.95/$A20) | =K$2-(0.95/$A20) | =L$2-(0.95/$A20) |
=A20+0.5 | =C$2-(0.95/$A21) | =D$2-(0.95/$A21) | =E$2-(0.95/$A21) | =F$2-(0.95/$A21) | =G$2-(0.95/$A21) | =H$2-(0.95/$A21) | =I$2-(0.95/$A21) | =J$2-(0.95/$A21) | =K$2-(0.95/$A21) | =L$2-(0.95/$A21) |
=A21+0.5 | =C$2-(0.95/$A22) | =D$2-(0.95/$A22) | =E$2-(0.95/$A22) | =F$2-(0.95/$A22) | =G$2-(0.95/$A22) | =H$2-(0.95/$A22) | =I$2-(0.95/$A22) | =J$2-(0.95/$A22) | =K$2-(0.95/$A22) | =L$2-(0.95/$A22) |
=A22+0.5 | =C$2-(0.95/$A23) | =D$2-(0.95/$A23) | =E$2-(0.95/$A23) | =F$2-(0.95/$A23) | =G$2-(0.95/$A23) | =H$2-(0.95/$A23) | =I$2-(0.95/$A23) | =J$2-(0.95/$A23) | =K$2-(0.95/$A23) | =L$2-(0.95/$A23) |
=A23+0.5 | =C$2-(0.95/$A24) | =D$2-(0.95/$A24) | =E$2-(0.95/$A24) | =F$2-(0.95/$A24) | =G$2-(0.95/$A24) | =H$2-(0.95/$A24) | =I$2-(0.95/$A24) | =J$2-(0.95/$A24) | =K$2-(0.95/$A24) | =L$2-(0.95/$A24) |
Table 2
Speed (m/s) |
| Time bails off (sec)
| |||||||||
| 0.050 | 0.100 | 0.150 | 0.200 | 0.250 | 0.300 | 0.350 | 0.400 | 0.450 | 0.500 | 0.550 |
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2 | -0.425 | -0.375 | -0.325 | -0.275 | -0.225 | -0.175 | -0.125 | -0.075 | -0.025 | 0.025 | 0.075 |
2.5 | -0.330 | -0.280 | -0.230 | -0.180 | -0.130 | -0.080 | -0.030 | 0.020 | 0.070 | 0.120 | 0.170 |
3 | -0.267 | -0.217 | -0.167 | -0.117 | -0.067 | -0.017 | 0.033 | 0.083 | 0.133 | 0.183 | 0.233 |
3.5 | -0.221 | -0.171 | -0.121 | -0.071 | -0.021 | 0.029 | 0.079 | 0.129 | 0.179 | 0.229 | 0.279 |
4 | -0.188 | -0.138 | -0.088 | -0.038 | 0.013 | 0.063 | 0.113 | 0.163 | 0.213 | 0.263 | 0.313 |
4.5 | -0.161 | -0.111 | -0.061 | -0.011 | 0.039 | 0.089 | 0.139 | 0.189 | 0.239 | 0.289 | 0.339 |
5 | -0.140 | -0.090 | -0.040 | 0.010 | 0.060 | 0.110 | 0.160 | 0.210 | 0.260 | 0.310 | 0.360 |
5.5 | -0.123 | -0.073 | -0.023 | 0.027 | 0.077 | 0.127 | 0.177 | 0.227 | 0.277 | 0.327 | 0.377 |
6 | -0.108 | -0.058 | -0.008 | 0.042 | 0.092 | 0.142 | 0.192 | 0.242 | 0.292 | 0.342 | 0.392 |
6.5 | -0.096 | -0.046 | 0.004 | 0.054 | 0.104 | 0.154 | 0.204 | 0.254 | 0.304 | 0.354 | 0.404 |
7 | -0.086 | -0.036 | 0.014 | 0.064 | 0.114 | 0.164 | 0.214 | 0.264 | 0.314 | 0.364 | 0.414 |
7.5 | -0.077 | -0.027 | 0.023 | 0.073 | 0.123 | 0.173 | 0.223 | 0.273 | 0.323 | 0.373 | 0.423 |
8 | -0.069 | -0.019 | 0.031 | 0.081 | 0.131 | 0.181 | 0.231 | 0.281 | 0.331 | 0.381 | 0.431 |
8.5 | -0.062 | -0.012 | 0.038 | 0.088 | 0.138 | 0.188 | 0.238 | 0.288 | 0.338 | 0.388 | 0.438 |
9 | -0.056 | -0.006 | 0.044 | 0.094 | 0.144 | 0.194 | 0.244 | 0.294 | 0.344 | 0.394 | 0.444 |
9.5 | -0.050 | 0.000 | 0.050 | 0.100 | 0.150 | 0.200 | 0.250 | 0.300 | 0.350 | 0.400 | 0.450 |
10 | -0.045 | 0.005 | 0.055 | 0.105 | 0.155 | 0.205 | 0.255 | 0.305 | 0.355 | 0.405 | 0.455 |
10.5 | -0.040 | 0.010 | 0.060 | 0.110 | 0.160 | 0.210 | 0.260 | 0.310 | 0.360 | 0.410 | 0.460 |
11 | -0.036 | 0.014 | 0.064 | 0.114 | 0.164 | 0.214 | 0.264 | 0.314 | 0.364 | 0.414 | 0.464 |
11.5 | -0.033 | 0.017 | 0.067 | 0.117 | 0.167 | 0.217 | 0.267 | 0.317 | 0.367 | 0.417 | 0.467 |
12 | -0.029 | 0.021 | 0.071 | 0.121 | 0.171 | 0.221 | 0.271 | 0.321 | 0.371 | 0.421 | 0.471 |