Topics
14. Data
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AustraliaNSW
Stage 2

14.01 Tables

Lesson
Practice
Lesson

Are you ready?

Can you count up by fives? Let's practice now. Continue this pattern: 5,\,10,\,15,\,20\,...

When you're counting up with this pattern, you are actually looking at multiples of five and saying the answers to your five times tables. Being able to count up by fives or recall your five times tables will help you to quickly add up tally marks.

Examples

Example 1

Find the product of 5\times 6.

Worked Solution
Create a strategy

We can think of 5\times 6 as 5 groups of 6 just like in the image below which has 5 groups of 6 squares:

The image shows 5 rows of 6 squares.
Apply the idea

The image above has 30 squares in total.5\times 6 = 30

Reflect and check

Or we can use the halving strategy by first finding 10 \times 6 and halving the answer.

\displaystyle 10 \times 6\displaystyle =\displaystyle 60Move 6 to the tens and add a 0
\displaystyle 5 \times 6\displaystyle =\displaystyle 30Find half of 60
Idea summary

You can use your knowledge of the 10 times tables and halve the answers to work out your 5 times tables.

You can also reverse this strategy and double the answers to 5 times tables to work out the answers to the 10 times tables.

Create and interpret Tables

This video shows how to turn tally marks into a table.

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Examples

Example 2

A restaurant owner recorded how many employees arrived early, on time or late.

a

Complete the table.

A table with the tally of early, on time and late arrivals. Ask your teacher for more information.
Worked Solution
Create a strategy

Count the number of strokes in each group, then write your answer in the frequency column.

Apply the idea
A table with the tally of early, on time and late arrivals. Ask your teacher for more information.
b

How many employees did the restaurant owner survey in total?

Worked Solution
Create a strategy

Add the numbers in the frequency column.

Apply the idea

To add the frequencies we can use a vertical algorithm and add the numbers down each column: \begin{array}{c} & &1 &0 \\ & &2 &2 \\ &+ &&7 \\ \hline & &3&9 \\ \hline \end{array}

39 employees were surveyed.

Idea summary

Tally marks are in groups of 5. Once there are 4 vertical ones written, the fifth one is drawn horizontally through them.

Frequency Tables

This video shows how to create a table.

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Examples

Example 3

Ms Williams has the following fruit stickers in her drawer:

An image of 2 apples, 4 lemons, 5 oranges and 1 bunch of grapes.
a

Count the number of each type of sticker and fill in the table.

FruitNumber of Stickers
\text{Lemon}4
\text{Apple}
\text{Grapes}
\text{Orange}
Worked Solution
Create a strategy

Count the number of times each fruit appears and put that number in the table next to that fruit.

Apply the idea

There are 2 apples, 1 bunch of grapes and 5 oranges.

FruitNumber of Stickers
\text{Lemon}4
\text{Apple}2
\text{Grapes}1
\text{Orange}5
b

Which sticker was most common?

A
A lemon
B
An orange
Worked Solution
Create a strategy

Look at the numbers in the table and choose the fruit with the highest number.

Apply the idea

Orange is the most common sticker because it had the highest number.

The correct answer is B.

Idea summary

Frequency tables show how many of each item there is.

Outcomes

MA2-18SP

selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs M

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