Lesson 2

At the end of lesson 1, pupils generated a list of factors (variables and measurements) involved in determining whether the batsman in the photograph was IN or OUT.

One way to begin the lesson is by building on pupils’ responses to Homework problem 4. Invite students to present their arguments for the importance of each of the various factors.

Use a guided whole class discussion to reduce and prioritise the list of Background notes on factors (see Advice for Teachers #2.1). Invite pupils to present their arguments for the importance of each of the various factors. Pupils work with distances in this lesson, and while this is a valuable part of their learning, they will realise later that they need to be working with times. It emerges that pupils need to use distance values to calculate times and thereby judge whether the batsman is 'in' or 'out'. In lesson 2 they have worked with just one piece of the problem which by itself will not solve the problem. This is raised at the end of lesson 2 and is the whole focus of lesson 3.

The two factors that can be measured are the distance the bail has fallen and the distance of the bat-tip past the crease-line.

Refer pupils to their solutions for homework problem 2. Briefly review the concepts of scale factor and ratio. Pupils who have completed homework problem 1 can be invited to share their solutions. Ask pupils to explain how they drew their diagrams. These concepts will be used in the next activity.

Pupils first study the photograph and estimate the measurements by eye, giving their answers in an appropriate unit. (Advice for Teachers #2.3)

Pupils will need to determine the scale factors involved (e.g. the ratio of the photo measurement of stump height to the actual measurement) (Standard cricket measures) and then use these to calculate the actual distances. (Advice for Teachers #2.4)

Teaching and Learning Issue 2: The need for hands-on experience

One of the trial teachers commented on how he needed to rethink his instinctive practice of anticipating or immediately fixing problems that arose.

A mathematics teacher’s role includes ensuring that, having learnt a body of knowledge, the pupil is able to use this to calculate the correct solution to a question. After running the recent series of lessons, I found myself being challenged on this second point. Is getting the answer right the most important factor in a mathematics teacher’s job?

There’s a lot to be said for stepping back and letting the pupils solve a problem on their own. I think in mathematics it is against our nature to stand and watch a group of pupils making mistakes and struggling to understand a concept or idea. We can find ourselves providing guidance too quickly and thus taking away the window of opportunity that existed, for a pupil or group of pupils to discover the answer themselves.

I was not the only one to struggle with the concept of allowing the pupils time to struggle with the problem in hand, my teaching assistant was evidently stressed and seemed annoyed that I wasn’t ‘helping’ the students. Was it not more important that the students had the chance to solve a puzzle and get stuck and frustrated whilst searching for a breakthrough? I decided, against the appeals of the teaching assistant, to allow the students the chance to solve the puzzle in their groups. It was time to step back.

It was evident from the plenary and evaluation stages of the lesson that the majority of the pupils had tussled with the calculations and that some had failed to complete all the solutions. So was I to determine this stage of the cycle a failure? I would suggest not. Upon reflection I would have changed a number of questions slightly, but this would have been purely to lower the level of the mathematics slightly. Would I change the way I had supported the pupils in the lesson? No. I had facilitated learning, rather than lead it. By stepping back, I had given the pupils the opportunity of making mistakes, but then also I had given them the chance to discuss the problem amongst themselves so that they could correct they mistakes and solve the problem without my input. This is an important skill for our pupils to learn.

Close Box

Ask pupils to compare their estimates with their calculations and make comments. (Sample calculations)

The homework is designed to introduce students to the relationship between speed and time and have them thinking about distance to time conversions. Without making it obvious, students practise the calculations necessary for the next lesson.

1. There is a well known formula which relates the distance an object has traveled with the speed of its travel and the time taken.

The formula is d = s x t, where d is the distance, s is the speed and t is the time.

a. Use the formula to calculate the distance travelled by a person jogging at the constant speed of 3 m/s for fifty seconds.

b. Suppose you know that a person has been jogging at the constant speed of 4 m/s for 2 hours.

What extra calculation do you need to do before you can use the distance formula?

a. Use the formula to calculate the time taken by a bus to travel 100 km traveling at a constant speed of 60 km per hour.

b. Suppose you know that a bus has traveled 100 km at the constant speed of 60 km per hour.

What extra calculation do you need to do before you can use the formula to calculate the time of the journey?

a. Use the formula to calculate the speed of a cricketer running 20.1 metres in 5 seconds. (Give your answer correct to two decimal places and write the correct unit as part of your answer.)

b. How fast would a cricketer be running if he or she covered 20.1 m in 9 seconds? (Give your answer correct to two decimal places and write the correct unit as part of your answer.)