Hitting Four

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Purpose

This is a level 4 measurement and number activity from the Figure It Out theme series.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
GM4-4: Interpret and use scales, timetables, and charts.
Student Activity

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Specific Learning Outcomes

interpret information from a table

find fraction of a whole number

solve problems involving addition and multiplication

Required Resource Materials

FIO, Levels 3-4, Theme: Sport, Hitting Fours, page 24

Activity

The scoring wheel shown on this page is a little different from those shown on TV. In TV broadcasts, the “wagon wheel” is compiled as if the batter hit shots from only one end. This is done so that patterns can be found in the areas the batter scores in.
The wheel on this page shows the runs scored from each bowler. For example, 4K means a hit for four from R. King’s bowling and 1W means a single taken from C. Walsh’s bowling.
The students can work out the score from Mathew Sinclair’s innings fairly easily because he hit a large number of boundaries (fours). They should use multiplication to work out the total of the fours. Mathew hit 22 fours for a total of 88 runs. Similarly, they can find the number of runs scored from twos and threes by multiplying.
To estimate the distance that Mathew ran during his innings, the students will need to recognise that he ran 18 metres for every non-boundary run he scored (ones, twos, threes), that is, 126 lengths of 18 metres, which is 2 268 metres. For each four he scored, Mathew may have averaged about one and a half lengths running, which gives 22 x 11/2 x 18, which is 594 metres. (You may need to remind the students that when Mathew hits a four, he would run until he was sure that the ball had hit the boundary.) The students also need to take into account that Mathew was not always
facing the bowler and that he had to run when the other batter was scoring runs. The batters at the other end during Mathew’s innings may have scored fewer runs in total than he did, so the students might consider that doubling 2 268 + 594 to get 2 832 x 2 = 5 664 metres is an exaggerated estimate. It is interesting to reflect that this distance was covered at sprinting pace while carrying a bat and wearing protective gear!

Answers to Activity

1. You can work this out from the totals line in the table:

table.
(He scored a total of 214 runs.)
2. 88 out of 214 runs came from boundaries (fours). This is just over 2/5 or 40% of his runs.
3. Mathew ran the whole length of the pitch for every single, two, or three that he scored. That was a distance of (58 + 56 + 12) x 18 = 2 268 m. For each boundary, Mathew may have run only one or two lengths of the pitch, a distance of between 22 x 18 = 396 m and 44 x 18 = 792 m.
If the other batters during Mathew’s innings had scored the same runs as he did, the total distance he would have run is between (2 268 + 396) x 2 = 5 328 m and (2 268 + 792) x 2 = 6 120 m.
However, as the other batters probably scored fewer runs than Mathew, it would be more realistic to base your estimate on the lower figure of 5 328 m.
 

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Level Four