Plan and pursue an enquiry; present evidence by collecting, organizing and interpreting information;
suggest extensions to the enquiry
(Objective repeated in Block C Units 1, 2 & 3)
; Show the class a large dice with the faces numbered 1 to 6. Q Which number is the most likely to turn up when this dice is rolled? Discuss children‟s answers and agree that as the dice is fair then the numbers are equally likely. ; Explain to the class that you will roll the dice and as you do, they are to sum the numbers you get until you get 20 or more. Before you do ask: Q How many times must we roll the dice so that we get a total of 20 or more? Collect children‟s suggestions and record them on the board. Roll the dice and have the children total the numbers, and keep track of the number of rolls needed to get a score of 20. Repeat the experiment a few times, and record the results on the board. ; Compare the number of rolls taken with the children‟s predictions. Ask: Q Is it possible to predict the number of rolls needed to get a total of 20 or more? Discuss the behaviour of the numbers on the dice, the way they occur and how these cannot be predicted so neither can the total. Explain that the occurrence of the numbers is random. Q Suppose we put the number 3 on each face, could we predict how many rolls we would need to get a total of 20 or more? Establish that it would require 7 rolls. This time we can predict the numbers that occur, as the numbers we get are not random but are always 3s. ; Say that this time the total is 24 or more and ordinary dice are to be used so the numbers 1 to 6 will occur at random. Q What could the greatest number of rolls be to get a score of 24 or more? What could the fewest number of rolls be? Collect answers and establish that it could take 24 rolls, getting a 1 each time, or just 4 rolls with a 6 each time. Give out the dice and ask the children to work in pairs, and conduct the experiment 10 times. Each time the pair is to record the number of rolls they needed to get a score of 24 or more. ; When the children have completed their experiments ask: Q Did anyone get a 24 in exactly 24 rolls or in exactly 4 rolls? Say that you want to record the results of the whole class and represent them on a chart. Q How can we collect and display the class‟s results? Draw children towards use of tally charts and bar charts. Discuss methods and demonstrate how to record tallies for some of the data. In groups of 8 to 10 children set them the task of collecting all their experimental results using tallies and counting up the different numbers of rolls taken. Discuss the results of the different groups and establish that it is possible to take between 4 and 24 rolls. Show OHT Y5 1. Explain that you are going to write the results from each group in the middle column to collect the class‟s results. When all the results have been collected get the children to record the totals for each of the number of rolls 4 to 24. With the class, complete the totals column and the Grand Total box at the end.
; Explain that you want the class to do some experiments using dice to solve a problem. Write the sequence 2, 3, 5 on the board and establish the numbers are increasing. Add 1 to the sequence and explain that at this point the sequence has started to decrease so it stops. There are 4 numbers or terms in this sequence. Q Can you give me other sequences that increase then stop when they start to decrease? Record some on the board e.g. 3, 3, 5, 6, 1 together with the length of the sequence, in this case 5. Establish that repeats are allowed but once the number decreases it stops. ; Explain that the children are going to generate sequences like this using dice. With the class use dice to generate some sequences, ensuring children understand the stopping rule. Q What is the shortest sequence we could have? Ensure children recognise these might only have 2 terms and ask them for examples e.g. 6, 1; 4, 2. Q What is the longest sequence we could have? Establish the sequence could be very long if we keep getting repeats. Ask for examples such as 1, 1, 2, 2, 2, … . ; Tell the children that you read in a book that „more than half the time the sequences will have 4 or less terms‟. Write this on the board.
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Q Do you think this is true? Collect their ideas and get a class view. Give out dice and ask every child to generate 20 sequences using the stopping rule „when it decreases stop‟. They are to list their sequences and the length of their sequences. ; Organise the class into groups of 5 children and get them to poll their results, using tallies for the lengths of the sequences. When they have polled their results ask: Q What was the longest sequence in your group? Record this sequence on the board to confirm it is correct. Q Do the results in your group suggest that the statement on the board is true or not? Have your views changed? Discuss the results and the children‟s views. ; Say you want to collect and display the results of the whole class. Q What table should we use? Confirm the table needs to cover the numbers 2 to the largest number of terms in the longest sequence already written on the board. Agree a table. Collect the results and total the frequencies. Explain that you want to display it as a bar line chart where the bars become lines. Q Will there be gaps between the lines? Establish there will be as you can only have a whole number of terms in a sequence. Give out squared paper for children to draw the bar line chart using the whole-class data set.
; Show OHT Y5 2. Explain that instead of thick bars as used on a bar chart the bars are lines, so it is called a bar line chart. Say that the chart shows how often each number card was selected from a pack of cards. Q What numbers were on the cards selected? Agree the numbers were 1 to 8. Q What number was selected most/least often? Agree 7 was the least selected, 8 the most selected. Q How many times were cards selected? With the class read the different frequencies and have the children sum them. Agree there were 40 selections. ; Tell the children that there were in fact ten cards in the pack not eight. Q What do you think the numbers were on the ten cards? Discuss suggestions. Establish that it was most likely that there were two cards numbered 4 and two cards numbered 8. Q Was there a fair chance of selecting each number 1 to 8? Remind the children of the language they had used to describe chance earlier in the week. Agree that the chance of selecting a 4 or an 8 was greater than a 1, 2, 3, 5, 6 or 7. ; Say that you want the children to conduct an experiment. They are to work in pairs. Each pair is to take six 6 numbered cards 1 to 6. They can add two more cards, e.g. a 2 and 5 or two 3s, so they have eight cards to work with. They are to shuffle their eight cards, select a card at random, note down the number, return the card, shuffle the pack and then repeat until they have selected 40 cards. They then organise their data and draw the bar line chart. Say that each pair must be the only ones to know what the numbers on their eight cards are. Give out cards and sheets of squared paper for the children to gather their data and represent it as a bar line chart. ; Show the first graph on OHT Y5 3. Say that it is called a line graph. The points represent temperature measurements which are joined up to show the changes in temperature over the day. Q When was the temperature highest? Agree it was at 10:30 when the temperature was about 19ºC. Q When was it coldest? Establish this was at 09:00 when it was 15ºC. Q When did it warm up the most?
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OHT Y5 1
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OHT Y5 2
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OHT Y5 3
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