Fi ndi ngal lth eposs ib ili ti es Produce a list or table Lists and tables are commonly used for displaying information in a particular order, organising a lot of information, examining patterns in numbers or compiling possible combinations. They are ways of organising information to be 'user friendly'. Table pro formas (page 19) can be used to support children who find it too difficult or too time consuming to draw tables themselves. Displaying information in a particular order Children need to be aware that the way information is organised in a table can affect the way it is used. In this table, race results are set out in position order. Results of class 4 400 m race Name Position Time Sanjay 1st 1 min 25 secs Rick 2nd 1 min 27 secs Nathan 3rd 1 min 30 secs Shane 4th 1 min 31 secs Demonstrate how to extract information from the table by using a ruler. Who came third? What was the time of the runner who came fourth? Organising a lot of information Four friends have several pets each. Sam has 3 cats, a dog and 2 hamsters; Jane has 3 rabbits, 3 cats and a hamster; Jamie has 4 dogs and 2 rabbits and Alice has a dog, 4 cats and a rabbit. Once this information is in a table it can be read more easily, flexibly and accurately. The four friends pets Cat Dog Rabbit Hamster Sam 3 1 0 2 Jane 3 0 3 1 Jamie 0 4 2 0 Alice 4 1 1 0 Which friend doesn't have a rabbit? How many pets does Alice have? 1
Produce a list or table Examining patterns in numbers Setting the information out in a table enables the reader to see the rule more quickly. A function machine Input Output 3 5 5 7 10 12 17 19 What is the rule for this function machine? What is being added to each input number to give the output number? Compiling possible combinations For school dinner Danny can choose fish fingers or burgers with mashed potato, chips or hash browns. List the combinations Danny could have. Fish fingers and chips Fish fingers and mashed potato Fish fingers and hash browns Burger and chips Burger and mashed potato Burger and hash browns. This list is a systematic way of ensuring that all possibilities are included. Example teaching sequence 1 Bob and Amy are climbing down a mountain. They start at a height of 2000 metres. They take one hour to climb down 300 metres, two hours to climb down the next 400 metres and another hour to climb down to 800 metres. How far do they travel in the fourth hour? 2
Produce a list or table Key steps Identify whether a table or list is needed. Identify the heading for each column. Complete the table using the information provided in the question. Read information from the table to solve the problem. Identifying whether a table or list is needed Display the question on an OHP. Ask the children to read the question as a class. What is the information in the question telling us? Will they be higher than 2000 metres when they have travelled for four hours or lower? How do you know? Ask the children to read the question again and identify the key information. Choose children to come out and underline the key information in the question for the rest of the class to see. How could we organise all this information so that it is easier to read? Explain that it could be laid out in a table, so that the key information can be read easily. Point to examples of time and distance. Identifying the heading for each column Explain that the units of measurement in the question will be the headings for the table. What are the two units of measurement used in the question? (Hours and metres) Draw a table with two columns and ask the children what the headings should be before writing them in. What should be the heading of the first column? (Time travelled) What unit of measurement is used for this? (Hours) What should be the heading of the second column? (Height) Which unit of measurement is used? (Metres) Completing the table Tell the children they are going to put the information from the question into the table. Complete the table by asking children questions so that they can extract information from the original question. At the start how long have Bob and Amy been climbing down? Where in the table will 0 hours be written? How high are they are the start? Where should that information be written in the table? Reading the information to solve the problem Read the original question back to the class. What is the question asking? Where will we find the information in the table? Explain that using the information they know that they were at 1300 metres after 3 hours. Demonstrate using a ruler to read across from 3 hours to 1300 metres in the table. They need to get to 800 metres (point to this in the table). How far down will they need to climb in the fourth hour? (500 metres) 3
Produce a list or table Plenary Unpicking common difficulties Identifying column headings Show the children a problem and ask them to identify appropriate column headings from a given set. Ask them to consider which are or are not appropriate, and why. Putting all the information into the table Show children a problem with a partially completed table, and ask them to identify whether all the information has been included in the table. Demonstrate how to work through it systematically by crossing off information that has been included. Identifying relevant information in the table to answer a given question Look at several questions relating to the same table. Ask the children to identify which column in the table the information will come from and how they know. Demonstrate how to read across or down using a ruler. Example teaching sequence 2 Shaq makes his own lunch. Today he can make a cheese sandwich or a ham sandwich. He can use white or brown bread. How many different kinds of sandwich can Shaq make? Key steps Identify whether a table or list is needed. Identify a starting point for the list. Complete the list for one of the options. Complete the list for the other options. Check that no combinations are repeated and then count the number of combinations. Identifying whether a table or list is needed Give each pair of children the question on a slip of paper. Ask pairs to read the question together and then discuss it. What is the question asking? (How many different types of sandwich Shaq could make) Give me an example of a sandwich that Shaq could make. How could we record the different types of sandwich so that we include all of them? Explain that they are going to use an organised list. 4
Produce a list or table Identifying a starting point for the list Ask children to discuss with their partner the possible combinations of sandwich. Which sandwich shall we put at the top of the list? Does it matter? Write the sandwich combination on the board, demonstrate how to use abbreviations to make the process quicker, e.g. W + C (for white bread and cheese). Completing the list for one of the options We have got white bread and cheese, what else could we have with white bread? (Ham) How could we write that combination? (W + H) Ask a child to add this combination to the list. Are there any other possibilities? Why not? Completing the list for the other options Point to the two combinations on the board. Explain that the combinations using white bread have been listed and that they now need to list the combinations which include brown bread. What sandwiches can be made using brown bread and the available fillings? (Brown bread and cheese, brown bread and ham) Are there any other combinations? Write the combinations on the board. Checking through the list Point to the list on the board. Have we found all the combinations? Read through the questions again. How many combinations are there? Plenary Unpicking common difficulties Identifying where to start Children need to be clear that it does not matter so long as they are systematic. Write the list systematically with one starting point, e.g. white bread and cheese, then do it again with a different starting point, e.g. brown bread and ham. Being systematic Children need to be encouraged to stick with one option and list all the combinations that can be matched to it before moving on to the next one. Write some combinations on slips of paper, e.g. W + C, B + H, H + B, B + C. Discuss with children why this might be confusing: there is no particular order, the type of bread does not always come first so combinations are repeated. Checking all the combinations have been found Give children slips of paper and ask them to work in pairs. One writes down combinations for one option and the other writes down the combinations for the second option, e.g. W + C, W + H and B + C, B + H. Slips of paper can then be rearranged to check all the combinations have been found, e.g. W + C, B + C and W + H, B + H, etc. 5
High in the sky A plane takes off and climbs into the sky. It climbs 300 metres every minute for the first 4 minutes, 200 metres per minute for the next two minutes and 100 metres per minute for the next 6 minutes. Draw a table to show the information. 1 How far has the plane climbed after 9 minutes? 2 How far does the plane climb in the first 5 minutes? s Daisy days Anne bought 1 white, 3 red, 9 yellow and 5 purple flowers. Tom bought 2 white, 2 red, 7 yellow and 10 purple flowers. Donna bought 8 white, 4 red, 1 yellow and 6 purple flowers. Draw a table to show this information. 1 Who bought the most red flowers? 2 How many more purple flowers than red ones did Tom buy? 3 Who bought the fewest flowers? 6
Election day West Road Juniors held an election for school council. Shay Wilson got 19 votes from 3J, 23 votes from 3H and 14 votes from 3B. Bo Rodriquez got 12 votes from 3J, 17 votes from 3H and 21 votes from 3B. Complete a table to show the election results. 1 How many more votes did Bo get from 3B than Shay? 2 How many votes did Shay get altogether? 3 Who won the election? s Vet variety Roy is a vet. On Monday he sees 6 cats, 9 dogs and 7 rabbits. On Tuesday he sees 8cats, 10 rabbits and 13 dogs. On Wednesday he sees 11 dogs, 10 cats and 6 rabbits. Put this information into a table. 1 How many rabbits does Roy see altogether? 2 How many more cats does Roy see on Wednesday than Monday? 3 Over the three days which sort of animal does Roy see most? 7
Pizza problem On Friday, Pete's Pizza Parlour sold 32 cheese pizzas, 27 pepperoni pizzas and 18mushroom pizzas. On Saturday they sold 23 mushroom pizzas, 35 cheese pizzas and 29 pepperoni pizzas. On Sunday they sold 26 pepperoni pizzas, 31 cheese pizzas and 16 mushroom pizzas. Put all the information into a table. 1 How many more cheese pizzas were bought on Saturday than Friday? 2 On which day were most pepperoni pizzas sold? 3 On which day were most pizzas sold? s More pizza please! At Pete's Pizza Parlour, a medium pepperoni pizza costs 4 50, a small pepperoni costs 3 20, a medium cheese costs 3.80, a small cheese costs 2 50, a medium mushroom costs 4 20, and a small mushroom costs 2 80. Put the information into a table. 1 If you buy a medium cheese and a medium mushroom pizza, how much does it cost? 2 Find a medium and small pizza that cost 7 altogether. 8
Snack time Strategy: Produce a list For his afternoon snack Anton can have biscuits, crisps or popcorn. With his snack he can have juice, milk or cola. Make a list to find all the choices Anton has. 1 How many choices does Anton have? 2 If he was allowed a piece of fruit as one of the snacks how many choices would he then have? s Are you hungry yet? Strategy: Produce a list For lunch Iris buys a piece of fruit and a drink. She can choose an apple, an orange or a pear; for her drink she can choose from milk, juice, squash or hot chocolate. Make a list to find all the possible combinations. 1 How many of the choices include milk? 2 How many choices does Iris have? 9
Clothes shopping Strategy: Produce a list Lisa went shopping for new clothes. She bought a yellow top and a white jumper. She also bought a pair of blue jeans, a pair of faded jeans and a pair of black trousers. Make a list of the different outfits Lisa could wear (an outfit is trousers and a top). 1 How many outfits include a pair of jeans? 2 How many outfits are there altogether? s Gymnastics get-up! Strategy: Produce a list Paige has pink, blue, yellow and black shorts for gymnastics. She also has pink or black gym shoes. List the different gym outfits she could wear. 1 How many outfits have an item of pink clothing in them? 2 How many outfits have no black in them? 3 How many outfits altogether? 10
School colours Strategy: Produce a list Thorpe School sells school uniform polo shirts, trousers and sweat shirts. Each comes in blue or grey. Make a list to find the different combinations of outfits. An outfit is a polo shirt, a pair of trousers and a sweat shirt. 1 How many outfits have grey trousers? 2 How many outfits consist of only one colour? 3 How many outfits are there altogether? s Bicycle buy Strategy: Produce a list Amanda is buying a new bike. She can have one with 3 gears or 5 gears; it can be blue, green, silver or black. Make a list to find the possible combinations. 1 How many bicycles with three gears can she choose from? 2 How many green bicycles can she choose from? 3 How many bicycles can she choose from altogether? 11
More shopping Strategy: Produce a list Van went shopping for new clothes. He bought a red shirt, a striped shirt and a denim shirt. He also bought a pair of blue jeans, a pair of black jeans and a pair of green board trousers. Here are some of the outfits he could wear: Red shirt and green board trousers Striped shirt and blue jeans Black jeans and red shirt Denim shirt and blue jeans Green board trousers and denim shirt 1 How many more outfits could he wear which include a striped shirt? 2 List all the other outfits he could wear. 12
On the menu Strategy: Produce a list Misao and her friends are trying out a new café. From the set menu they can order a veggie burger, chicken burger, or hamburger. With the burger they can have either coleslaw, chips, salad or potato wedges. 1 Which of these combinations can the friends not order? Veggie burger and coleslaw Hamburger and chips Chicken burger and chips Veggie burger and hamburger Chips and coleslaw Chicken burger and potato wedges 2 If all the friends have something different, and between them have all the possible combinations, how many friends are there? 13
Car purchase Strategy: Produce a list or table Adam is buying a new car. He goes to two different car showrooms. In Jones Cars he looks at 5 red cars, 3 blue cars and 6 green cars. In Smith's Cars he looks at 7 blue cars, 8 green cars and 3 red cars. Organise this information clearly, either in a list or a table. 1 How many more green cars did Adam look at in Smith s Cars than Jones Cars? 2 How many more blue cars did he look at than red cars? 3 In which car showroom did he look at the most cars? s More car buying Strategy: Produce a list or table Anita is buying a car. The car she wants comes in red, blue or green. She can have black, grey or brown seats. Organise this information clearly, either in a list or table. 1 How many different seat colours can she have with a red car? 2 How many combinations can she have with black seats? 3 How many combinations can Anita choose her car from? 14
Ice cream sundae Strategy: Produce a list or table The ice cream van stocks 4 different flavours of ice cream: vanilla, chocolate, strawberry and mint. A two-scoop ice cream can be made from two scoops of the same flavour or one scoop each of two different flavours. Organise this information in a table or list. 1 How many two-scoop ice creams will have ice creams of just one flavour? 2 How many two-scoop ice creams will include ice cream of two flavours? 3 How many different types of two-scoop ice cream are there? s More ice cream Strategy: Produce a list or table The ice cream van sells 200 ice creams in five hours. After one hour 70 ice creams have been sold, in the second hour another 50 are sold, after three hours 150 have been sold and 25 are sold in the fourth hour. Organise this information in a table or list. 1 How many ice creams are sold in the third hour? 2 How many ice creams are left after four hours? 3 During which hour are the most ice creams sold? 15
Three of a kind Debbie, Dave and Donna are triplets. One has blonde hair, one has red hair and one has brown hair. Debbie does not have red hair. The boy has dark hair. Complete this table putting a cross in a box where the combination is not possible, e.g. Debbie/Red and a tick where it is certain, e.g. Dave/Brown. Debbie Dave Donna Blonde Red Brown 1 What colour hair does each of the triplets have? 16
Who's who? Mr Jackson, Miss Morales and Mrs O'Hara work at Southdene School. One is the headteacher, one is the caretaker and one is the Year 4 class teacher. Mr Jackson told the headteacher that Miss Morales was in the hall putting out the chairs. Miss Morales isn't the Year 4 class teacher. Complete the table using the clues. Mr Jackson Miss Morales Mrs O Hara Headteacher Caretaker Y4 teacher 1 Which job does each person do? 17
Best lessons Anne, Ben, Chris and Diana each have a favourite school subject. Anne likes finding out about the past. Ben does not like learning dates or doing calculations. Chris enjoys finding out about other places. Anne Ben Chris Diana Maths History Geography Literacy Complete the table using the clues. 1 Who likes which subject? s Best hobbies Ed asked his friends Fred, Gary, Helen and Ian what their favourite hobbies were. Helen does her hobby inside. Ian doesn't like running but enjoys being outdoors. Gary often goes to the library for his hobby. Draw up a table using these column headings. Reading Football Snooker Cycling 1 Who likes which hobby best? 18
Table A Table B Table C 19