5 Putting algebra into cricket
The National Curriculum Framework (NCF, 2005) lists one of its principles regarding the approach to knowledge in the curriculum as:
Connecting with the local and the contextualised in order to ‘situate’ knowledge and realising its ‘relevance’ and ‘meaningfulness’; to reaffirm one’s experiences outside school; to draw one’s learning from observing, interacting with, classifying, categorising, questioning, reasoning and arguing in relation to these experiences.
(NCF, 2005, p. 33)
Activity 4 aims to address this. The activity can be used as a consolidation exercise, where students can use their learning from the earlier activities in a different context, one they are likely to be familiar with – cricket.
Video: Using local resources
Activity 4: Runs per over
This activity allows students to become aware of variable quantities in a cricket game.
For this activity the students could go outside and play the game for real. Alternatively, it could be played inside the classroom by throwing a dice for the number of runs that each player gets for each ball. (Let the number five on the dice be zero runs, since you only rarely score five runs from one ball in cricket!) If the dice falls off the desk, they are out!
Say to the students:
- Let’s play a 5–5 cricket match. For this, we are going to create groups of two teams of five students. Each team is to include both girls and boys. For each team, one student will be designated the score keeper (not always the girls!). Each team gets to bowl five overs.
- After six balls have been bowled, add up the score for that over.
- The two scorers jointly fill in Table 1 by recording the number of runs scored in each over: Table 1 Scoring card.
|Over||Team 1||Team 2|
After the match, ask the class to discuss the following questions. In larger classes it works well to ask the students to first discuss these questions in small groups and then share with the whole class.
- Did each team score the same number of runs in each over? Why?
- What is the maximum number of runs that could be scored per over? Why? (Note for the teacher: You can score one, two or three runs if you really run between the wickets, four for reaching the boundary having hit the field first, and six for hitting the ball over the boundary without hitting the field first – so the maximum number of runs is six sixes. This is a case of a variable having limited values that it can take.)
- For each team, is there a visible trend in the number of runs scored in each over? Is the trend the same for both teams? If not, why do you think the trend is different?
- If this was a six-over match, what could have been the runs scored by each team? Would the result of the game be different or the same if each team got six overs?
- Which of the following quantities are variables? In other words, what may have varied during the match?
- number of wickets taken by each bowler
- number of overs bowled by each team
- number of boundaries scored by different batsman
- weight of the ball used in the match.
- What other quantities may have varied during the match? What quantities are constants (which may have remained unchanged during the match)?
Similar to Part 2 in Activity 3, ask the students to use their list of variables and constants to construct their own statements with algebraic expressions.
Video: Involving all
Case Study 4: Mr Kapur reflects on using Activity 4
Cricket being a game very close to all their hearts, the students could really get into the discussion and contribute a lot to the activity. The day before, I asked the students to bring their cricket bats and balls to the school the next day if that was possible.
I have both girls and boys in the class and I thought the girls might feel a bit left out, or the boys might think this would be all about them! So I introduced the activity by saying I had read in the newspaper about the National Indian women’s cricket team and how well they were doing. I mentioned some names such as Mithali Raj, team captain from Rajasthan, and Jhulan ‘Babul’ Goswami, from Bengal, who, like Mithali Raj also has won the government’s Arjuna Award for excellence in the game and had also been team captain in the past.
I also made sure we discussed some rules of the games that they needed to know to complete the activity, so there would be no issues about that. We then went outside and played the games. We had mixed gender teams, we had girls against boys, we had boys against boys and girls against girls – a real mix.
In preparation for the whole-class discussion I decided to make some changes and work on Questions 1 to 3 first, and only then move on the other questions. I thought otherwise the discussion about variables and constants might get lost and it was important that did not happen as that is about the mathematics I wanted them to learn. So I wrote the Questions 1 to 3 on the blackboard and asked the students to discuss these in their teams of five. We then discussed this as a whole class.
I then wrote the Questions 4 and 5 on the blackboard, asked them to discuss these in their teams again and to make a list in their books with ‘Variables and constants in the cricket game’ as the title. I gave them five minutes to do this. We then had a whole-class discussion. I asked them to use the words ‘variable’ and ‘constant’ all the time so they could get used to the vocabulary.
By the end of the lesson I think I can safely say that most of them were confident of what varying quantities were and what was meant by constants. They also could see that even when denoting the varying quantity by a letter, it was a number. Some of the students managed to write their statements in algebraic notation, others could describe the statements in words. I was happy with that differentiation – they had all learned, and moved on their learning from where they were.
At the end of the lesson I told them to now go and discuss ‘variables and constants in the cricket game’ at home and with their friends. I do not know whether they did this, but they seemed to like the idea!
Pause for thought
4 Moving on to write formal algebraic statements and expressions