TOPIC
28
Averages and Charts
Strand:
Strand unit:
Curriculum Objectives
666
667
668
669
670
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.
Use data sets to solve problems.
Looking back: What the 5th class programme covered
1.
2.
3.
4.
Calculating averages of simple data sets.
Compiling data sets and using data sets to solve problems.
Collecting and organising data in simple pie charts.
Reading and interpreting pie charts.
Maths skills used in this topic
1. Communicating and expressing: Communicate and express mathematical ideas, processes
and results in oral and written form.
2. Reasoning: Reason, investigate and hypothesise with patterns and relationships in mathematics.
Concrete materials
Protractor
Vocabulary
Average
Teaching points
1. Most children will readily understand how to compute an average. Some of
them may fail on the task of finding 1 number when given the average and all
but 1 of the numbers. They may forget to work out the total of the numbers.
For example: The average of 4 numbers is 20, 3 of the numbers are 5, 6 and
8. What’s the 4th number? A common mistake is to offer the number 1 as an
answer. Children may reason that 5 + 6 + 8 = 19 and 20 – 19 = 1. Stress the importance of
calculating the total (4 x 20 = 80) first. Then 80 – 19 = 61.
108
2. Pie charts are awkward to construct when the number of elements in a data set do not readily
lend themselves to whole number angles. Consider, for example, the following data set: from
a total of 59 people surveyed, 17 chose red, 27 chose blue and 15 chose green. When we try
to convert these to angles:
17
= 0.288, therefore 360° x 0.288 = 103.7°.
59
The numbers become very unwieldy. Keep the data sets as simple as possible. Choose
numbers such as 12, 24, 36 and 60 for the total number of elements because these numbers
have lots of factors. There are useful photocopiable pie chart templates in this manual.
Oral and mental activities
Fans:
Show the average of the following numbers: (a) 2, 3, 5, 6 and (b) 6, 7, 4, 3. Show the average on
the fan. Make up some more numbers ensuring that they are divisible by the number given.
Target board 1:
Identify any square numbers on the page. Which numbers have only 2 factors? List the factors for
the other others. Round each number to the nearest 10. After rounding, estimate the total of each
row and column.
Topic suggestions
There is a lot of software available for making charts and graphs, much of it free. If the children
have access to computers, they can input data into spreadsheets and tables and use the software
to construct attractive charts and graphs.
Activity A
1. Look at the first grid of numbers. What is the average of the first row of numbers, second
row, first column, second column, numbers on a green background, numbers on a yellow
background, all the numbers, etc?
2. Look at the second grid of numbers. What is the average of the first row of numbers,
second row, third row, first column, second column, numbers on a blue background,
numbers on an orange background, all the numbers, etc?
3. Look at the third grid of numbers. What is the average of the first row of numbers, second
row, third row, first column, second column, numbers on a grey background, a pink
background, a green background, all the numbers, etc?
Differentiation
Lower attainers:
Separate activity sheet
Higher attainers:
1. Separate activity sheet
109
2. The average type discussed in this chapter is the most widely used measure of central
tendency: the mean. There are other ways to compute an average. Two that are not difficult
are as follows:
(a) Mode: This is the most commonly occurring element in a data set. For example, the mode
of the numbers {4, 3, 3, 8, 8, 9, 3, 6, 4, 2, 3, 3, 1, 8, 7, 7, 7, 3, 3, 6, 6} is 3 because it occurs
most often.
(b) Median: This is the point halfway between the highest and lowest elements of a data set.
For example, the lowest and highest elements of {3, 10, 7, 9, 8} are 3 and 10.
The median is 3 + 10 – 3 = 3 + 3.5 = 6.5 (add the lowest number to half the difference).
2
Topic
Topic
28
28
1. The average of 2 numbers is 106. What is their total? _____________
1. What is the average of each set of numbers?
(a) 12, 20
________
(d) 15, 18, 24 ________
(g) 40, 58, 64 ________
(b) 13, 37
________ (c) 23, 33
________
2. The average of 3 numbers is 218. What is their total? _____________
(e) 23, 28, 33
________ (f) 31, 42, 53
________
3. The average of 6 numbers is 211. What is their total? _____________
(h) 23, 18, 31, 28 ________ (i) 35, 45, 19, 41 ________
4. The average of 8 numbers is 314. What is their total? _____________
5. The average of 7 numbers is 420. What is their total? _____________
2. What is the average of each set of numbers?
(a) 16, 18, 9, 36, 26 ___
(b) 64, 38, 18, 73, 22 ___
(c) 71, 18, 6, 44, 56 ___
(d) 86, 72, 47, 56, 39 ___ (e) 55, 23, 14, 87, 36 ___
(f) 83, 96, 71, 62, 88 ___
(g) 11, 15, 16, 18, 25 ___ (h) 26, 28, 36, 47, 53 ___
(i) 74, 63, 88, 97, 53 ___
6. The average of 4 numbers is 100. 3 of the numbers are 97, 132 and 144. What is the other?
_____________
7. The average of 5 numbers is 90. 4 of the numbers are 88, 88, 88 and 88. What is the other?
_____________
3. (a) The average of 3 numbers is 20. 2 of the numbers are 18 and 36. What’s the other number?
8. The average weight of three people is 45.1kg. A fourth person joins the group. The average
weight of the 4 people is 44.92kg. What is the weight of the fourth person? _____________
__________________
(b) The average of 3 numbers is 20. 2 of the numbers are 12 and 23. What’s the other number?
9. A supermarket survey examined the prices of a basket of groceries in 4 supermarkets. The
average price was €44.56. If the prices of the basket of groceries in 3 of the supermarkets were
__________________
(c) The average of 3 numbers is 20. 2 of the numbers are 10 and 9. What’s the other number?
€41.99, €43.07 and €48.11, how much were the groceries in the fourth supermarket? _________
__________________
10. The average age of 2 boys is 11.6 years. The average age of 3 girls is 11.7 years. What is the
(d) The average of 3 numbers is 20. 2 of the numbers are 23 and 29. What’s the other number?
average age of a person? _____________
__________________
11. Peter sat three exams in his first year in college and five exams in his second year. He scored an
4. (a) The average of 4 numbers is 25. 3 of the numbers are 20, 32 and 33. What’s the other number?
average of 50 in his first year’s exams and scored and average of 90 in his second year’s exams. Is
__________________
it true that his average score for two years is 70? Why (not)? What is his average score for the two
(b) The average of 4 numbers is 25. 3 of the numbers are 18, 23 and 36. What’s the other number?
years? _____________
__________________
12. Draw a pie chart to show the following information: A group of 48 people were asked to name
(c) The average of 4 numbers is 25. 3 of the numbers are 6, 7 and 10. What’s the other number?
something they would never do. These are their answers.
__________________
Parachute
12
Pick up a mouse 6
(d) The average of 4 numbers is 25. 3 of the numbers are 16, 37 and 40. What’s the other number?
__________________
Bungee Jump
Drive without a seatbelt
(a) What fraction of her money did he save? _________
(f) How much money did he spend on clothes? _________
(g) What fraction of his money did he spend on games? _________
(h) How much money did he spend on games? _________
Name: _______________________________________
Date: ___________________
4
6
© Folens Photocopiables
(b) Which type of movie was least popular? _____________
© Folens Photocopiables
(a) Which type of movie was most popular? _____________
(c) What fraction of his money did he spend on books? _________
(e) What fraction of his money did he spend on clothes? _________
Steal
Learn Japanese
do you most often choose?’
(b) How much money did he save? _________
(d) How much money did he spend on books? _________
4
16
13. This graph shows the answers of a group of 300 people
to the question, ‘When you rent a DVD, what type of movie
5. This pie chart shows how Cormac spent the €60 he got for his birthday.
(c) How many people chose
(i) Drama? _____
(ii) Western? _____
(iv) Animated? _____ (v) Comedy? _____
(iii) Thriller? _____
(vi) Scary? _____
(d) What percentage of those surveyed chose either comedy or drama? _____________
(e) How might a movie rental library use this information? _____________
Name: _______________________________________
Date: ___________________
177
Page 177: Averages and Pie Charts
Linkage
Number: Operations, fractions
Shape and Space: Lines and angles
Integration
SESE Science: Collecting, organising and interpreting data from surveys, trials and experiments
SESE Geography: Collecting, organising and interpreting data from surveys, trials and experiments
Maths at home/parental involvement
Carry out a survey at home, collect the data and make a pie chart. Think of a suitable survey
question. For example, name something that is wheeled around. Likely answers are pram,
wheelchair, shopping trolley, wheelbarrow, etc. Ask lots of people and carefully record their
answers. Tabulate and graph.
110