5:01 Drawing Tables Use the picture to fill in the two-way table. Buttons Red Blue Green Use the table above to fill in this simpler table. Buttons Red Blue Green Show the data from Question 1 on a graph. Fill in this table using data about your family and friends. Me Name ge Male or Female Use the table above to fill in this simpler table. Large Small Buttons Large Small You can use these tables to draw graphs. Use the dice to complete the table. Number of Times Thrown Graphing the Weather Mon Tue Wed Thur Fri 1 2 3 4 7 8 9 10 11 14 15 16 17 18 For the next month record the weather like this. t the end of the month cut up the calendar. Glue the pieces to make a graph like this. 16 15 10 14 9 11 8 7 2 Use the graph to describe the month s weather. 4 3 1 Data representation and interpretation: Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values. 147
5:02 Chance Without looking, Min must choose one card. a Is she more likely to choose red or black? b Is she certain to choose an ace? c Is there an even chance to choose red? d The chance of choosing black is 1 out of. e The chance of choosing red is 2 out of. The spinner can land on any colour. a Which colour is it most likely to land on? b Which colour is it least likely to land on? c Which colour has an even chance of occurring? d What is the chance of spinning pink? e The chance of landing on red is out of 8. f The chance of landing on blue is out of 8. g The chance of landing on yellow is out of 8. Order these events from 1 (least likely) to 4 (most likely). The principal will visit our classroom tomorrow. It will be sunny tomorrow. Our class will use books tomorrow. The next person to visit our room will be a female. R Y R B B R B R Write three things that might happen tomorrow. Order each event from 1 (least likely) to 3 (most likely). Heads or Tails? Toss a coin 50 times and keep a tally of the number of heads and tails. Discuss the experiment and which results you think are most likely. 148 Chance: Describe possible everyday events and order their chances of occurring. Identify events where the chance of one will not be affected by the occurrence of the other.
5:03 Chance Write these events in order from least likely to most likely. n equal chance of picking or n even chance of picking or least likely most likely The principal will come to school on Monday with no shoes on. B It will be sunny tomorrow. Here, each ball has the same chance of being selected. 2 4 5 1 3 6 More chance of picking than C If I drop a glass it will break. D If I toss a coin it will be a head. E Our next teacher will be from Mars. 3 1 2 4 5 6 To decide who works together, two numbers will be taken from the jar at the same time. In a random selection each Does each number have the same chance of number has the same chance being chosen? of being chosen. Carry out this experiment in your classroom. Record the results: 6 is matched with, with and with. Choose a label to answer each question. In Question 2, what is the chance that: a the numbers 6 and 7 are picked? b the numbers 1 and 2 are picked? c two numbers less than 10 are picked? d when lf is chosen, he will be working with a girl? e at least one of the pairs will be two girls? impossible not likely even chance very likely certain Chance: Describe possible everyday events and order their chances of occurring. Identify everyday events where one cannot happen if the other happens. 149
5:04 Using Graphs Rhonda graphed the number of calls made each day last week by her family. a How many calls were made on Monday? b On what day was the greatest number of calls made? c On what day was the least number made? d What is the difference between the number of calls made on Saturday and the number made on Thursday? e What is the total number of calls made for the week? f Why do you think more calls were made on Sunday and Saturday? Rhonda kept this tally of calls made by her children. Use the tally to draw the graph. Name lana Rachel Naomi Luke Heather Number of calls Number of Calls 14 12 10 Calls Made lana Rachel Naomi Luke Heather 0 2 4 6 8 10 12 14 16 8 6 4 2 0 Sunday Monday Number of Calls Telephone Calls Tuesday Wednesday Thursday Friday Saturday When columns are drawn across, it is called a bar graph. Trees were planted in a row. rabbit sat in each space. How many rabbits would there be between: Draw a picture. a 3 trees? b 7 trees? c 10 trees? 150 Data representation and interpretation: Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values. Evaluate the effectiveness of different displays in illustrating data features including variability.
5:05 Reading Graphs Bottles Brought to School Number Collected 8 6 4 2 0 ªn the graph 3 is between two lines. lan nne Bev Don Ella Gia Ian Jan Jill Ken Lana Luke Pam Ron Sam Tim a How many bottles were brought to school by: i lan? ii Luke? iii Jan? b How many people brought bottles? c How many bottles altogether were brought by lan, nne and Bev? d How many bottles were brought to school altogether? e If all these bottles were brought to school during the first week, how many bottles do you think would be brought during the first two weeks? How did you get your answer? Sport Chosen by Class 4R a Which was the most popular Volleyball sport? b How many students made a Basketball choice? Tennis c How many sports were chosen? 0 2 4 6 8 10 12 SPORT Number of Students d What is the title of this graph? Tally Marks Tally marks used in South merica and sia also have five lines. With a partner, create your own five-line tally marks. Discuss: When would tally marks be useful? Sth merica sia 1 2 3 4 5 Data representation and interpretation: Evaluate the effectiveness of different displays in illustrating data features including variability. 151
5:06 Ordering Events Choose the label you think best for each part below. impossible unlikely even chance very likely certain a My first throw of the dice will be a one. b I will throw a zero on a dice. c When I throw a dice the number will be greater than one. In this jar are 3 red and 3 yellow marbles. Blindfolded, I draw one out. Which label from above is best for each of these statements? d I will draw out a coloured marble. e I will draw out a blue marble. f I will draw out a yellow marble. Ms Banner placed two red and two blue counters in a hat. She had two more red and two more blue counters. Which two counters must she put into the hat so that she would be: a more likely to draw out a red than a blue counter? b more likely to draw out a blue than a red counter? c equally likely to draw out a blue or a red counter? B C D E F The spinners above stop on either red or yellow. a Which spinners are equally likely to stop on red as on yellow? b Which spinners are more likely to stop on red than on yellow? c Which spinners are more likely to stop on yellow than on red? Here is the head and tail of an old ustralian penny. a If I toss a coin in the air, would a head be more likely to show than a tail? b If two coins are tossed, what could result? 152 Chance: Describe possible everyday events and order their chances of occurring.
5:07 Chance Used in Games Caroline tossed a coin many times. She kept this tally of the results. a How many times did she toss the coin? b What fraction of the time did she toss: i a head? ii a tail? Tossing a Coin Tossed Tally Total Heads Tails When playing cricket, we toss a coin to see who will bat first. How would you describe the chance that our team will win the toss? 100 tickets were sold in a raffle. John bought 70 of the tickets, Peta bought 25, Jeremy bought 2 and lan bought none. Choose a label that describes the chance that the winner will be: a John c lan e none of the four people mentioned b Peta d Jeremy dice is rolled. Jack wins if an odd number is rolled. Emma wins if a 6 is rolled and Luke wins if a 2 or 4 is rolled. a Write their names in order from most likely to win, to least likely to win. b Which person has an even chance of winning? What s My ge? sk friends to write the month in which they were born. (1 for January, 2 for February, 3 for March, etc.) Tell them to multiply this number by 5, then add 2, then multiply by 20, then add their age in years, impossible even chance very unlikely Try this on your friends. then subtract 40. sk the person their answer. Solution The last two digits of the answer give you the age. The other digits give you the month of birth. For example, 714 means the person is 14 and was born in July (the 7th month). likely unlikely certain Chance: Describe possible everyday events and order their chances of occurring. Data representation and interpretation: Evaluate the effectiveness of different displays in illustrating data features including variability. 153
5:08 Surveys Who will you vote for in the election? Jared chose as his survey topic: The time students go to bed. He asked everyone in his class. Jared s Survey Tick the box next to the time you went to bed last night. before 8 pm between 8 pm and 9 pm between 9 pm and 10 pm between 10 pm and 11 pm after 11 pm How many students went to bed: a before 8 pm? Jared s Results b between 9 pm and 10 pm? c after 11 pm? d before 9 pm? e before 11 pm? f What was the most popular bed time? Surveys are used to discover information, to give us a general view of a situation or to check predictions. If everyone is surveyed from the group we wish to study, we have carried out a census. before 8 pm between 8 pm and 9 pm between 9 pm and 10 pm between 10 pm and 11 pm after 11 pm g How many students were surveyed altogether? Was this a census? h Make up a question of your own that could be answered using these results. Write down a topic that you would like to use in a survey of your class. Write two questions you would like to ask about this topic. a b 154 Data representation and interpretation: Select and trial methods for data collection, including survey questions and recording sheets.
5:09 Tally Marks Tally the Colours Start on any white square. Throw a dice and move that many spaces clockwise. Each time record the colour you land on, as a tally mark. Throw the dice 50 times. Before you start, try to guess which colour will appear the most. Green Red Blue White Colour Tally Total White Blue Red Green Yellow Orange Yellow Use squared paper to graph your results. Blue Red Green Eric asked 300 people to name their favourite sport. He made this tally of their answers. Sport Tally Total Tennis thletics Swimming Hockey Red White 0range Yellow a Complete the Total column. b What was the most popular sport? c How many more people chose swimming than athletics? Basketball Cricket Football Other sk 50 people to name their favourite sport. Keep a tally, like the one above, of their answers. Before you begin, estimate how many out of 50 will choose each sport. d ltogether, how many chose athletics and tennis? e Name two sports which might have been included in other. nyone for tennis? Data representation and interpretation: Select and trial methods for data collection, including survey questions and recording sheets. 155
5:10 Constructing Spinners im: Construct and test spinners with 3, 4, 5, 6 and 8 sides. B C D E Step 1: Use a program such as Microsoft Word to create these shapes. (Go to Insert, then Shapes, select the shape and hold the shift key to give the shape equal sides.) Step 2: Print these shapes onto cardboard. Divide the spinners into sections (as above) and colour one section of each. Step 3: Make these shapes into spinners with one section coloured. Experiment Spin each spinner 20 times. Keep a tally of coloured spins for each. a Which spinner do you think will have most coloured spins? b Which spinner do you think will have least coloured spins? c Carry out the experiments. Spinner Tally of Coloured Spins B C D E d Which spinner had most coloured spins? e Which spinner had least coloured spins? From your results, on which spinner is a colour: f most likely to be spun? g least likely to be spun? h If we combined the results of many students, would we have a better idea of the answers to parts f and g? Why or why not? i Put to E above in order, from most likely to spin a colour to least likely to spin a colour. 156 Chance: Describe possible everyday events and order their chances of occurring. Data representation and interpretation: Select and trial methods for data collection, including survey questions and recording sheets.