Poly Plug, Proportion & Percent Years 3 - 6

Summary Everyone in the class turns over the same number of plugs in a yellow board. For example, if they turn over 14, then 14 out of 25 are turned over. One child comes to the front to show this. Then they are joined by another child to show two examples of 14 out of 25, or one example of 28 out of 50. Kate's comment below shows just how powerful this activity is when threaded. Materials One Poly Plug per child One calculator for each child (for extension) Acknowledgement Many thanks to Kate Thureau, Gagebrook Primary School, Tasmania, Australia who has told us below of the success this activity brought to her Grade 5/6. The value of this activity would be improved further if it included children's work from your classroom.

Procedure Use the yellow/blue board and ask each child to turn over the same number of plugs, eg: 12. Ask the children for the number of plugs in their board and the number turned over. Record this on the white board, eg: 12 in every 25 are turned over. Walk around the room asking several children: Johnny, how many plugs have you turned over? and expecting the response: 12 in 25. Summarise with the statement: So, 12 in every 25 are turned over. Bring two children to the front with their boards, and ask for the number of plugs altogether and the number turned over altogether. Suppose we all paired up like this, would it be true that each pair would show 24 out of every 50? Record this on the board below the original statement and comment: So, 12 in every 25 can be rearranged to become 24 in every 50.

Content decimal calculations decimal interpretation decimal representation of a fraction fraction calculations fractions as a partition of a whole multiples, factors & primes multiplication pattern interpretation pattern recognition percentage ratio & proportion recording - calculator recording - written times tables visual and kinaesthetic representation of number visual representation of fractions

6. Bring two more children to the front and ask the same questions again until you can add the following to the white board list of proportional statements:

   48 in every 100 are turned over.

7. Ask children to record these statements in their books. Add some incomplete statements such as these to the list and challenge them to fill the gaps:

   96 in every ___ are turned over.
   ___ in every 400 are turned over.
   ___ in every 300 are turned over.
   72 in every ___ are turned over.
   36 in every ___ are turned over.

8. Discuss the reasoning children used to fill the gaps. There are several valid ways of thinking to complete each one.
9. Ask the children to think up some more statements which belong in this list. As they work, move around the class asking individuals to justify the statements they are adding to the list.
   
   • Who is thinking them out using a brain picture of children regrouping?
   • Who is thinking them out by using the numbers in the statements previously recorded?

Summary

48 in every 100 are turned over ... and explain that another way of saying this is ... 48% are turned over.

From The Classroom

Gagebrook Primary School Kate Thureau, Grade 5/6 As part of my Changing Places professional development course we were asked to choose an activity from Calculating Changes and run that activity three times a week for approximately four weeks. I selected Poly Plug, Proportion & Percent and approached it with a certain amount of trepidation. Firstly I felt the topics of proportion and percentages would cause some problems for my 5/6. Secondly I was using the Poly Plugs for the first time - with an older group that would be interesting.

Wangaratta Primary School, Victoria Tim M's teacher, transcribed these examples from his book. He seems to have picked up the power of proportional reasoning in this list of other comparisons which he developed from 12 in every 25 are turned over. 54 in every 112.5 are turned over. 9 in every 19.75 are turned over. 60 in every 125 are turned over. 120 in every 250 are turned over. 240 in every 500 are turned over. 480 in every 1000 are turned over. 960 in every 2000 are turned over. 1920 in every 4000 are turned over. But are they all correct? (See Extensions below.)

I started the first lesson and put a yellow/blue Poly Plug board on the desks and asked the children to work in pairs. For the first 10 minutes the children were asked to experiment with these previously unseen boards. They enjoyed this exploration time and were well occupied. They were then happy to proceed with the lesson.

I followed the instructions described in the activity. The children turned over 12 in 25, then a group came up the front and we recorded it on the board. We got a little carried away and continued till we reached 400, it was all recorded. The next lesson the children turned over 6 plugs and we did it as a class activity and then they were asked to fill in the missing spaces, as seen in the lesson plan above, eg: 6 in every 25 are turned over 12 in every __ are turned over etc. Soon I was getting explanations such as: All you need to do is double both numbers to get the next numbers. To get the answer for 100 all you need to do is to times by 4.

Once they were able to visualise the problems, looking at equivalent fractions and percentages became remarkably easy. It was like a journey that we all approached together because we were all students; it became extremely enjoyable and a very valuable learning experience. The children were keen to do these activities and even the repetition made them feel more secure and none of them complained.

By this stage the children were more easily able to visualise the problem and were doing away with the Poly Plugs and the calculators. It was great seeing the children's reactions when all of a sudden they had the 'aha' moment when everything fell into place.

Once they were able to visualise the problems, looking at equivalent fractions and percentages became remarkably easy.

It was like a journey that we all approached together because we were all students; it became extremely enjoyable and a very valuable learning experience. The children were keen to do these activities and even the repetition made them feel more secure and none of them complained.

With the use of a poly plug the children were able to see that:

This is 14 out of 25 turned over.

Now we have 28 out of 50 turned over.

This makes 42 out of 75 turned over.

We record like this ... Suppose we had four boards ...

They were asked every day when a certain number of plugs were inverted what percentage was turned over. It was amazing how quickly they were able to work out the equivalent fractions and determine the percentage.

I am amazed at how a topic that I thought would cause a huge amount of difficulty turned into an extremely valuable and enjoyable unit. The children did not feel threatened and it was wonderful to observe them when they understood the concepts and were happy to help each other.

Extensions

1. If your school is a member of Maths300, this activity will lead into Lesson 9, First Principles Percent.
2. The question of whether all of Tim's list is correct suggests a way to use the calculator as part of this activity. Begin the extension lesson with the white board list of correct responses derived in the previous lesson.

   The one we started with was '12 in every 25 are turned over'. How could we represent 12 in every 25 on the calculator?

   Link this to 12 out of 25 and using the division button. Make sure everyone agrees that 12 ÷ 25 = 0.48 is the calculator result. Invite the children to do a similar calculation for each item in the white board list from the previous lesson. They are likely to be surprised that in each case the result is 0.48.

   So, now we have another way of checking our thinking in this type of problem. If we have figured out our 'in everys' correctly they will all come out the same on the calculator.

   Here is an opportunity to check Tim's list (or another one constructed for the purpose).
   Ask the students to especially notice the result for '48 in every 100 are turned over'.

   So '48 in every 100' are turned over is the same as 48% and 0·48. Can you explain to me why 'in every 100' is important?

   Return to this activity frequently with different numbers of plugs turned over each time. The steps are:
   1. Ask the children to turn over a given number of plugs.
   2. Record this on the board.
   3. Ask them to tell you some ways of combining plug boards to produce new 'in everys'.
   4. Record these on the board.
   5. Ask the children to record the white board list and add ten more of their own.
   6. Ask them to tell you which one of these is the percentage result and to record this as an 'in every', a fraction, a decimal and a percent.

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