The Yakkety Yak About A Yak In A Kayak

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The yak even took a shower … watching the weather, hour after hour. Once, the yak even went out in the rain, but he quickly slipped and fell in a drain.  Perhaps a boat was what was needed, to ensure he won every race, completely unseeded. The yak yaketty – yacked with everyone, but no – one really knew, where he could find a kayak big enough, to fit both the yak and the gnu, too.

The yak looked around, by the riverside, to find a suitable log, that could be used for a river ride, that wasn’t too wide. He carved the log a bit, so there was a place to sit. All the other woodland creatures came to admire it. Everyone thought that the yak was drunk, wobbling about inside a tree trunk ! Once, the log, afloat, almost hit a skunk.

The yak yakkety – yacked some more, until the makeshift kayak wobbled and the yak fell out onto the floor. Whilst the yak was still yakety – yakking, the gnu, complained about the noise and sent him packing. Of course, it may be that he was back – tracking … but the yak still never could river ride without his face cracking. In fact, he yakkety – yacked till he was blue in the face, but still, the yak, found he was stuck in one place. 

Mud ! Mud ! Glorious Mud !

Game 1 – The following measurements show the yak’s journey along the muddy riverside. Work out how deep the mud was that the yak was stood in. How deep does he have to dig, for his kayaking to begin ? Give your answer in cm.
Height of The Yak           Amount of Yak (Visible)           Depth of Mud
4 m                                             3.8 m                                    20 cm

4 m                                             3.1 m                                      ……

4 m                                             2.9 m                                      ……

4 m                                             1.7 m                                      ……

4 m                                             2.6 m                                      ……

4 m                                             2.4 m                                       ……

4 m                                             3.2 m                                       ……

4 m                                             3.3 m                                       ……

4 m                                             2.5 m                                       ……

4 m                                             1.8 m                                       ……

4 m                                             1.25 m                                     ……

4 m                                             2.9 m                                       ……

4 m                                             3.4 m                                       ……

4 m                                             2.8 m                                       ……

4 m                                             3.5 m                                       ……

Game 2 – If the mud is deeper than the yak, look what happens …

Height of The Yak           Depth of Mud           Amount Of Yak Visible

4 m                                           7.8 m                            3.8 m

Complete the table, using the data above. What do you notice about the two sets of figures, above ? Give a definition to explain this maths phenomenon. Give one algebraic equation in your answer.

Game 3 – When the yak stood on a rock or a log, his height was above the depth of the mud and the original subtraction sum turns around to become an addition, as follows. Give your answer in m.

Height of The Yak           Depth Of Mud            Total Height

4 m                                        3.8 m                          7.8m

4 m                                        3.1 m                           ……

4 m                                        2.9 m                           ……

4 m                                        1.7 m                           ……

4 m                                        2.6 m                           ……

4 m                                        2.4 m                           ……

4 m                                        3.2 m                           ……

4 m                                        3.3 m                           ……

4 m                                        2.5 m                           ……

4 m                                        1.8 m                           ……

4 m                                        1.25 m                         ……

4 m                                        2.9 m                           ……

4 m                                        3.4 m                           ……

4 m                                        2.8 m                           ……

4 m                                        3.5 m                           ……

© Jacqueline Richards 2008

Game 1 Answers : 90 cm ; 110 cm ; 230 cm ; 140 cm ; 160 cm ; 180 cm ; 170 cm ; 250 cm ; 220 cm ; 275 cm ; 110 cm ; 60 cm ; 120 cm ; 50 cm
Game 2 Answers : As above – Just like a cake being cut into three unequal pieces, the values of two of the pieces allows us to measure the other missing piece. This is how algebra works – to give a method of working out what we don’t know from what we do.

 

Ga

me 3 Answers : 7.8 m ; 7.1 m ; 6.9 m ; 5.7 m ; 6.6 m ; 6.4 m ; 7.2 m ; 7.3 m ; 6.5 m ; 5.8 m ; 5.25 m ; 6.9 m ; 7.4 m ; 6.8 m ; 7.5 m

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