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Chance, Statistics and Graphs

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Prim-Ed Publishing

0031窶的RE REV10/02

Foreword

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Data Handling plays an important part in today's society. People are placed in chance situations all the time and meet statistics wherever they turn. This book is designed to give pupils a relative and practical introduction into this area of mathematics. Data is a specific strand in the mathematics curriculum, with strand units on 'Representing/Interpreting Data' and 'Chance'. Data Handling provides a variety of opportunities for pupils to develop data handling skills, including to: • collect, classify, organise and represent data using concrete materials and diagrammatic, graphical and pictorial representation • read, interpret and analyse tables, diagrams, bar charts, pictograms, line graphs and pie charts • appreciate, recognise and express the outcomes of simple random processes • estimate and calculate using examples of chance • use acquired concepts, skills and processes in problem-solving All activities have been based on experiences familiar to children. Each activity can be extended to provide more difficult situations or problems.

Contents

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Hair Colours Hair Colours 2 Eye Colours Car Colours Travelling to School Favourite Sport Favourite Fruit Spelling Test Birthdays House Numbers Pets Absent Amazing Dice

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Curriculum Links

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14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

Data Handling

Noughts and Crosses Coloured Squares Square Lines Circle Maze Counter Target Dice Target Dice Numbers Two Dice Domino Pick Up Bar Graph Master 1 Bar Graph Master 2 Graph Master 1 Graph Master 2

27i

Curriculum Links Book

Class

Strand

Strand Unit

Content Objectives

Lower

1st/2nd

Number

Counting/Numeration

• count the number of objects in a set

Comparing/Ordering

• compare equivalent and non-equivalent sets

Operations (Addition)

• add without and with renaming • know and recall addition facts

Number Data

Middle 1st/2nd

Number

Measures Data 3rd/4th

Operations (Addition)

Representing/Interpreting • collect, organise and represent data using pictograms, block graphs, bar charts Counting/Numeration

• count the number of objects in a set

Comparing/Ordering

• compare equivalent and non-equivalent sets

Length

• estimate, measure and record length using metre and centimetre

Representing/Interpreting • represent, read and interpret simple tables, charts and block graphs

Number

Operations (Multiplication)

Measures

Length

• develop and recall multiplication facts within 100 • estimate, compare, measure and record lengths

Representing/Interpreting • collect, organise and represent data using block graphs and bar charts • read and interpret tables, bar charts and simple pie charts • use data sets to solve and complete practical tasks and problems

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Data

• add without and with renaming • know and recall addition facts

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3rd/4th

Representing/Interpreting • represent, read and interpret simple tables and charts (pictograms) • represent, read and interpret simple block graphs

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Data

Upper 3rd/4th

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Chance Number

Operations (Addition)

• know and recall addition facts

Operations (Multiplication)

• develop and recall multiplication facts within 100

Number patterns/ Sequences

• explore, recognise and record patterns in number

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Algebra

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Data

5th/6th

Number Data

Representing/Interpreting • collect, organise and represent data using block graphs and bar charts • read and interpret tables, bar charts and simple pie charts • use data sets to solve and complete practical tasks and problems

Chance

• use vocabulary of uncertainty and chance • identify and record outcomes of simple random processes

Number Theory

• identify simple prime numbers • identify common multiples

Representing/Interpreting • collect, organise and represent data using pie charts and trend graphs • read and interpret trend graphs and pie charts • compile and use simple data sets • explore and calculate averages of simple data sets Chance

Prim-Ed Publishing

• use vocabulary of uncertainty and chance • identify and record outcomes of simple random processes

• identify and list all possible outcomes of simple random processes • construct and use frequency charts and tables

Data Handling

28 ii

Hair Colours This is a block graph showing the hair colour of the children in first class. Answer the questions under the graph.

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black

blonde

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red

brown other

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red hair?

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1. How many children in the class have

brown hair?

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black hair?

2. What colour hair is the most common?

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3. What colour hair is the least common? 4. How many children are in this class?

Five new children joined the class at the start of term. Three had red hair, one had brown hair and another had blonde hair. Add these children to your graph. Colour your graph so that it is easier to understand. Prim-Ed Publishing

Data Handling

1

Hair Colours 2 How many children in your class have:

black hair?

brown hair?

red hair?

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blonde hair?

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Colour the boxes below to show the answers. Each box shows one person's hair.

Blonde Prim-Ed Publishing

Black

Brown Data Handling

Red 2

Eye Colours How many children in your class have:

green eyes?

brown eyes?

other colours?

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blue eyes?

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Colour the boxes below to show the answers. Each box shows one person's eye colour.

Blue Prim-Ed Publishing

Brown

Green Data Handling

Other 3

Car Colours The 2nd class children did a survey on the colour of their family car. They made a tally of their results. Colour white red blue green

llll ll llll lll llll l lll ll llll lll llll l

Total

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yellow

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The tally is not finished. You will need to finish it before you answer the questions below.

brown

orange black grey

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1. Which is the most popular colour?

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Is there a reason for this?

2. Which is the least popular colour? Is there a reason for this?

3. How many families are there in 2nd class with a family car? Prim-Ed Publishing

Data Handling

4

Travelling to School

Bus

Car

Bicycle

Walk

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A class of pupils did a survey to find out how each child travelled to school each day. To show the results of their survey they produced the following pictogram. Answer the questions about this pictogram.

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1. Which is the most popular method of travel to school?

2. Which is the least popular method of travel to school?

3. How many children are there in the class? 4. Why do you think some methods are more popular? Prim-Ed Publishing

Data Handling

5

Favourite Sport

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Survey your class to find out each person's favourite sport from those listed. Football Cricket Rugby Netball Swimming

Swimming

Netball

Rugby

Cricket

Football

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Record your results as a pictogram. Make your own symbols for each sport.

Which is the most popular sport? Prim-Ed Publishing

Data Handling

6

Favourite Fruit

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Survey your class to find out each person's favourite fruit from those listed. Apple Orange Banana Grape Pear

Pear

Grape

Banana

Orange

Apple

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Record your results as a pictogram. Make your own symbols for each fruit.

Which is the most popular fruit? Prim-Ed Publishing

Data Handling

7

Spelling Test In a class spelling test the teacher recorded the results on a block graph. The teacher has started but you will need to finish the graph and answer the questions. The results for each child are Mary (8), John (9), Susan (9), Simon (7), Deb (10), Anne (8), Karl (7), Cliff (10) and Brian (6).

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mark out of 10

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Brian

Cliff

Karl

Anne

Deb

Simon

Susan

John

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Mary

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1. Which children had the best results?

2. Which children had the worst results?

3. Do you think the teacher would by happy with the results?

Prim-Ed Publishing

Data Handling

8

Birthdays

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Graph the number of people born in each month of the year in your class.

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sept.

Oct.

Nov.

Dec.

Which month has the greatest number of birthdays?

Prim-Ed Publishing

Data Handling

9

House Numbers What is your house number? What are the house numbers of the children in your group? house number

Name

house number

Name

house number

Name

house number

Name

house number

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Name

Name

house number

Name

house number

Name

house number

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Try to answer these questions.

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1. Which digit is used most?

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2. Which digit is used least? 3. What is the largest house number?

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4. What is the smallest house number? 5. How many '1s' are there in all the house numbers? 6. Take the smallest house number from the largest. What is the difference? 7. Are there any consecutive house numbers?

Prim-Ed Publishing

Data Handling

10

Pets Below is a bar chart that shows the number of pets the children in Sunny Beach 2nd class have. Can you answer the questions below?

10

5

;; ;;

Dogs Mice Cats

Birds Rabbits Fish

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15

;; ;;

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;; ; ;; ;;;; ;; ; ; ; ; Pet Numbers

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Which animal is the most popular pet? Which animal is the least popular pet?

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How many animals are owned by the class? Put the pets in order from most popular to least popular.

How many dogs and cats are there? How many birds and rabbits are there? Prim-Ed Publishing

Data Handling

11

Absent Below is a graph that shows the number of children absent in the first six months of a 2nd class at Sunny Beach School. Try to answer the questions below.

; ;; ; ;; ;; ; ; ;;; ;; ; ; ; ;;; ;; ; ; ; ;;; ;; ;;;

9 6 3

1

2

3 4 Months

5

1. 2. 3. 4. 5. 6.

January February March April May June

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Numbers absent

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Children Away

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Which months had the lowest number of children absent?

In which month were the most children absent? How many days were the children absent altogether? In which months of the year do you have school holidays?

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Data Handling

12

Amazing Dice

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With a partner, throw a die. Move only if you throw a 1, 3 or 6. Try to find your way through the maze and win.

Start

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Finish

Data Handling

13

Noughts and Crosses

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Throw a die to move around the board. If you land on a nought, move ahead two spaces. If you land on a cross, move back two spaces. Can you beat your partner?

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Data Handling

14

Coloured Squares

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With a partner, throw a die. If you throw more than a three, colour in a square. After five minutes, count the squares each person has coloured. The winner is the person who has coloured the most squares.

Prim-Ed Publishing

Data Handling

15

Square Lines

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With a partner, throw a die. If you throw less than a four, colour in a square. The winner is the first person to make a line of six squares going across or down the page.

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Data Handling

16

Circle Maze

âž”

Finish

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Start

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Throw a die with your partner and see who can find a way into the circle maze first. If you land on a shaded square, go ahead an extra two places.

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Data Handling

17

Counter Target Throw a counter onto the target five times. Add up the total score. If the counter crosses a line, count the larger number.

2

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5

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What is the highest score you could get?

6

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9 9 10 9 9

1

7

3

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8 4

Data Handling

18

Dice Target Throw two dice. You must try to throw the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12. When you throw any of these numbers, colour in a part of your target. But, you can only use a number once!

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How many throws did it take you to colour in the whole target?

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Data Handling

19

Dice Numbers Throw a die. Colour in a box under the number you throw. Do this forty times.

2

3

4

5

6

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Which number was thrown most often? Compare with a friend. Prim-Ed Publishing

Data Handling

20

Two Dice Throw two dice and add them together.

Do this twenty times. Colour in a matching square for each answer.

3

4

5

6

7

8

9

10 11 12

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What is the total?

Which number was thrown most often? Can you explain why?

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Data Handling

21

Domino Pick Up Pick up ten dominoes, one at a time, from a pack. Colour in a matching box each time you pick up a number. Which number came up most often?

2

3

4

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Try this activity several times. Are the results the same each time?

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Data Handling

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Bar Graph Master 1

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Data Handling

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Data Handling

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Bar Graph Master 2

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Graph Master 1

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Data Handling

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Graph Master 2

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