# 14.01 Tables

Lesson

## Ideas

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:

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.

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.

### Examples

#### Example 2

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

a

Complete the table.

Worked Solution
Create a strategy

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

Apply the idea
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.

### Examples

#### Example 3

Ms Williams has the following fruit stickers in her drawer:

a

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

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.

b

Which sticker was most common?

A
B
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.

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