Answer a question by identifying what data to collect; organise…

Answer a question by identifying what data to collect; organise… Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate (Objective repeated in Block C Units 1, 2 & 3) Show the children a tally chart like the one below: Colour Red Silver Green Black Ask the children questions like: Q What name is given to this type of chart? Q What do we mean by ‘tally’? Get the children to discuss in pairs questions like: Q What could this chart be representing? Q What could the title of the chart be? Q How many of each colour are there? Q Who might need this information? Ask the children to think of other information that could be collected by tally charts. Take feedback from the children. Establish this tally chart shows the colour of cars that passed my house between 8pm and 8.15pm last night. Tell the children another way of showing this information is by a pictogram. In this example a car picture could represent each car. Discuss how the car picture could represent 2 or 5 cars. Ask the children to draw the pictogram using car pictures. Discuss any difficulties that arise, e.g. how to represent 1, 3 or 4 cars. Pose the question: What is your favourite animal out of these? hamster dog cat tiger dolphin elephant snake Ask the class to vote. Say they can each have 2 votes. Work out how many votes there should be altogether. Collect the results using a tally chart. Discuss what symbol will represent the animals and how many animals the symbol represents. Ask the children to draw the pictogram. 1 Display the top half of OHT Y4 9 showing the number of books read by reading groups over a term. Reading group Badgers Tigers Peacocks Elephants Pigs Spiders Get the children to find the frequency for each group, interpreting the tally marks. Explain that the frequency means how many and the table is called a frequency table. Show the children how to change this into a pictogram by using a symbol to represent 2 books. Ask the children: Q How would we represent 8 books, 3 books, etc.? Display the bottom part of OHT Y4 9. e.g. Badgers Tigers Peacocks Elephants Pigs Spiders represents two books Q Is this a good way to present this information? Q What other number could we suggest stand for? Establish that if stands for 4 we would have to draw fewer symbols but for 3 becomes more difficult and so on. Ask the children to work in pairs to find a symbol that could represent 5 books. How could is also show 4, 3, 2 or 1 book? Take feedback on the symbols children have devised and discuss how easy or difficult they are for others to understand. Encourage children to redraw the pictogram using a symbol for five books and compare results. Q What makes a good choice for a pictogram symbol? Take feedback, establishing that a clear, simple picture that can easily be divided makes a good choice. 2 Show the children the frequency table on OHT Y4 10 which shows the number of drinks sold in a school in one week. Day of week No. of drinks Monday 41 Tuesday 29 Wednesday 38 Thursday 7 Friday 11 Draw axes on the board. Take the children through the following: Decide on a title for the bar chart. Ask: Q Where do we put ‘Days of the week’? Q Where do we put ‘Number of drinks sold’? Q Where do we put ‘Monday, Tuesday’ etc.? Ask the children which of the following scales we should use on the vertical axis and why. A B C D 5 25 50 100 4 20 40 80 3 15 30 60 2 10 20 40 1 5 10 20 0 0 0 0 Emphasise that the best way to choose is to look at the biggest/greatest frequency or the most common, i.e. 41. Since this is 41, the axis must be C or D, but D is too large. With the children, construct the bar chart on the board. Highlight the vertical scale, the gaps between the bars, and get children to interpret the resulting card. Ask the children to complete the work on frequency tables in Activity sheet Y4 11. They should then choose one table and complete the following task: a) construct a bar chart; b) think of a title; c) write two statements about the information. Q. What do I need to think about and include when I draw a bar chart? Take feedback to establish that scale, labels, and a title are key features. Highlight gaps between the bars (as data is discrete, bars have no relationship to each other). Explain that today’s work will involve them collecting and presenting data about two statements. Ask for suggestions to ensure children are interested in finding out an answer, for example: Many Y4 children have a dog as a pet. More Y4 children like fruit more than crisps or sweets. Encourage them to plan how they can collect data to help them decide. Model drawing a table, with up to six choices. Tally marks can then be added to the model table. This could be repeated to answer the second question. Direct the children to draw one bar chart. Remind them of how to construct bar charts. Let them choose the vertical axis scale. Children should ensure the chart has a title then write two statements and questions about the information on the chart. 3 Show the children Activity sheet Y4 12/OHT Y4 12. ? 35 Tuesday ? Wednesday 10 ? 20 Friday 45 Saturday ? ? 70 40 M T W T F S S Children work in pairs to complete the chart and the graph. Ask them to: decide what information can be gained from each display; give the graph a title; make up true/false statements for the graph. Encourage children to use ICT programs to construct their bar chart, for example ‘Handy Graph’ from the NNS ICT pack or the NNS animation ‘Bar Chart’ or a similar graphing program. Present the problem: I’m thinking of a number. If I add 11 to my number, I get 19. What is my number? Q What did you do to find my number? Discuss responses. Draw attention to the use of addition and subtraction as inverse operations. Ask similar questions and talk about how to answer them, e.g. 14 more than my number is 27. What is my number? 19 less than my number is 14. What is my number? If I increase my number by 26 and get 53, what is my number? If I decrease my number by 32 and get 51, what is my number? Ask children to pose similar questions to a partner. Q Which questions were easier/harder? Why? Using one of the examples above, demonstrate to the children the related facts that can be derived 51 + 32 = 83 32 + 51 = 83 83 – 32 = 51 83 – 51 = 32 Ask the children to give the related facts for: 84 + 17 = 101 76 + 74 = 150 38 – 26 = 12 97 – 69 = 28 Remind children that inverse operations and related facts can be used to check calculations. Give some calculations and ask children to work out which are correct, e.g. 47 + 17 = 54 42 – 18 = 24 45 + 16 = 61 54 – 19 = 35 Q How are you working out if these calculations are correct? 4 Show how an empty number line can be used to answer questions, e.g. write on board: What is 20 minutes later than 9.50am? Explain the am notation if necessary. Draw empty number line and talk through steps. Show on large teaching clock analogue and digital. 10 minutes 10 minutes 9.50am 10.00am 10.10am Answer 10.10am. Repeat with different example for earlier than. Give the children a page from a TV guide and ask them to: a) find the length of some programmes of their choice; b) rewrite one channel’s listing for 20 minutes earlier. A television programme starts at 3.50pm and finishes at 4.15pm. How long is the programme? 10 minutes 15 minutes 3.50pm 4.00pm 4.15pm Answer 25 minutes: Allow children time to practise finding the lengths of TV programmes using the number line. Lay a large sheet of paper on the floor where the children can see it, and place a label ‘all numbers’ just outside the sheet. Using large number cards, quickly agree with the children that they are all examples of the set of ‘all numbers’. Now place a single sorting hoop on the sheet, labelled ‘numbers less than 50’. Ask the children to come up and place cards either inside, or outside the hoop. Q What is the name of the region outside the hoop? (numbers 50 or more). Take off the label and the cards and replace ‘numbers less than 50’ with ‘even numbers’. Repeat the exercise: agree the outer region is now ‘not even numbers’ (or ‘odd numbers’). Remind the children that a one-criterion sort simply decides whether an item does, or does not, match the given property. Give the children examples of a criterion and ask the name of the ‘not’ region, for example: red (not red); even (not even). Consider 10 or less. Q Can you decide the ‘not’ set? With the first loop still labelled ‘even’, place a second hoop on the sheet (not overlapping) and with it, the original ‘numbers less than 50’ label. With the children’s agreement, place (say), 3, 17, 25 in that hoop. Q Where am I going to place… 20? Agree that it matches both properties; and the only way to make it fit is to overlap the hoops and place it in the centre. Check that all the cards are in the correct position. Provide other numbers, so there are examples in all four regions, including the outer region. Q What is the name for this outer region? (not even and not less than 50). Q Can you describe this outer region in another way? Emphasise that this is the area where neither property is matched. Ask the children to draw on large paper a diagram to represent the two hoops and the sorted numbers. Invite the children to draw the Venn diagram with the correct title and labels. Sort the same numbers using different properties, e.g. ‘multiples of 5’ and ‘multiples of 2’. Repeat similar questions to first example. The children work in pairs. Each pair is given a set of number cards. Display OHT Y4 13 which gives a set of number properties. Children choose two properties at a time and draw a Venn diagram with one property for each circle. They then sort the number cards onto the diagram. Repeat with other number properties. Each pair decides on their favourite Venn diagram to show in plenary. 5 Q What is a Carroll diagram? Give the pupils maths dictionaries to find a definition. Discuss how it is used in data handling for sorting and representing information in rows and columns. Draw a Carroll diagram on the board: In the x 4 table Not in the x 4 table Numbers that have three 10s Numbers that do not have three 10s Talk through the properties and ‘not’ properties for each category. Point out how the four regions represent one ‘yes both’ region, two ‘one but not the other’ regions and one ‘not either’ region. Write the numbers 24, 32, 36, 38, 16, 25, 33, 17, 38 on the board. Demonstrate to the children how to use the Carroll diagram to sort the numbers, talking through the criteria for selecting a particular box for a particular number. Q What other number could we put into the box that is in the x 4 table and has three 10s? Discuss why there are no other numbers to fit in. Q What number could I put into… this box? Point to any other box. Change properties, for e.g. to x 5 table and a number that is even or is odd. Can they sort related numbers, e.g. 20, 48, 30, 16, 53, 25, 40, 46, 38, 40? Use whiteboards to record. Discuss why they have put the numbers where they have. Q Why do none of the numbers in the ‘2 even numbers’ and ‘x 5 table’ box have a 5 digit at the end? Allow the children the opportunity to decide their own properties in small groups and select the numbers, then give to another group to sort. Have a set of properties on the board for pupils to choose from, e.g. four-digit, three-digit, two-digit numbers; multiples of 2, 10 or 5; greater or less than 83, etc. 6 Show the children a pack of cards. Remind them if necessary of the four suits, their names, and the ‘royal’ cards. Discuss and list on the board properties that could be used to sort them, for example: black (not black) royal (not royal) odd (not odd – decide if royal counts as not odd) less than 8 (8 or over) hearts (not hearts) Choose the two properties: black/not black, hearts/not hearts. On a large sheet of paper, draw the Carroll diagram and invite the children to choose cards and place them in the correct region. Q Which region is getting no cards? Q Can you explain why? Point out how there cannot be a group with ‘black hearts’ in it. Shade it over. Black Not black suits suits Hearts Not hearts Leave the paper where it is, and lay out a fresh sheet. Explain that the same sort is going to be used for a Venn diagram. Repeat the activity, placing cards into the correct regions. Shade over the ‘overlap’ region. hearts black suit Q Which region is getting no cards? Why? Point out that the four regions of the Carroll diagram are exactly the same as the four regions of a Venn diagram. Explain how the information they put in a Venn diagram can also fit into a Carroll diagram. Give the children a copy of Activity sheet Y4 14/OHT Y4 14. Discuss and complete. Q Are the numbers grouped the same way in the two diagrams? They should be! Discuss any that have gone astray on the children’s sheets and check that the children can see what led to the mistake. Display the pictogram OHT Y4 15 on books borrowed from library. Draw attention to the key showing one picture of a book represents ten books. Q How many books were borrowed on Monday? How do you know? Q On which day were most books borrowed? Why do you think this is? Q What do you think the ‘half book’ on Thursday represents? How many books were borrowed on Thursday? Q How many books were borrowed altogether over the week? Show the children the data on OHT Y4 16. Say you want to represent the data on a pictogram. Q What symbol could we use for the pizzas? Q How many pizzas should each symbol represent? Q How could we represent Wednesday and Thursday if one symbol represents 20? (demonstrate). Q Tell me one thing about ‘Dial-a-Pizza’. Give ready data (Activity sheet Y4 17) to the children to represent as a pictogram on acetate sheets (some could use ‘Dial-a-Pizza’ data). Once they have drawn a pictogram, ask them to develop a series of questions to ask others. 7 OHT Y4 9 8 OHT Y4 10 9 ACTIVITY SHEET Y4 11 10 ACTIVITY SHEET Y4 12 / OHT Y4 12 11 OHT Y4 13 12 ACTIVITY SHEET Y4 14/ OHT 14 13 OHT Y4 15 14 OHT Y4 16 15 ACTIVITY SHEET Y4 17 16