Class 5 Mathematics Chapter 15: Data Through Pictures

A question for the class

Sana wants to know which fruit her class likes best. There are thirty children in her class. She decides to ask every single one of them. Each child may name only one fruit. That keeps the counting fair and simple.

Answers come fast

The answers come faster than she can write them down. Mango, guava, banana, mango again. Writing whole words takes far too long. Sana needs a quicker way to record them before she loses one.

One stroke each

Her teacher shows her tally marks. Each answer becomes one short stroke. Four strokes stand side by side. The fifth stroke lies right across them. That closed bundle is worth five answers.

Why the fifth lies down

The crossed bundle makes counting easy at the end. Each bundle is worth five. Sana counts five, ten, fifteen, and then adds the loose strokes at the end. Counting one stroke at a time would be slow.

The finished tallies

By the end of the break she has five rows of marks. Mango has one bundle and four loose strokes. Banana has one bundle and two. Guava has one bundle and one loose stroke. Chikoo has only three strokes.

Into a table

Now Sana copies the counts into a table. One column holds the name of the fruit. The next column holds the tally marks. The last column holds the number in figures. The table can then be read at a glance.

Reading the table

The table answers questions at a glance. Mango was chosen by nine children, more than any other fruit. Chikoo was chosen by only three, fewer than any other. The rest lie between those two.

Checking the work

Sana adds her five numbers together at the end. Nine and seven and six and five and three come to thirty. That matches the thirty children she asked, so nothing has been lost along the way.

Questions the table answers

How many liked guava? Six children. How many more liked mango than orange? Four more. How many chose either banana or guava? Thirteen between them. Each answer comes straight out of the table.

Remember

• Data means the answers you have collected.
• One stroke for each answer, and the fifth lies across.
• Count the bundles in fives, then add the loose strokes.
• A table shows each choice beside its number.
• The numbers should add up to the number of people asked.

Scenario:

A class counts the birds it sees in the school garden in one week. Nita writes a stroke for each bird in a long line. By Friday her line is too long to count. She keeps losing her place. Their teacher shows the class tally marks in fives, with the fifth stroke crossing the other four. Nita redoes her count in groups of five and totals it in moments. She sees what the grouping bought her. The number of birds has not changed. Counting in fives means she tracks only five at a time.

Analysis:

The data was correct and unreadable. Grouping in fives does not change the count, it changes how much has to be held in the head at once.

Activity:

Count something for a week using tally marks in fives. Total it and say how long the counting took.

Title:

Run your own fruit survey

What You Notice:

If your column adds up to twenty, every answer has been kept. If it does not, one stroke has gone into the wrong row, and the tallies must be counted again.

The government counts every person in India in a census, the biggest data collection there is.

Shopkeepers keep tallies of what sells fastest so that they know what to order.

Counting tally marks — Four upright, the fifth lies down. — Each bundle of five has four standing strokes and one lying across them.

A busy week in the library

The school library lends out books all through the week. On Friday the librarian wants to show the class how busy it has been. She counts the books that went out in each kind and writes the four counts down.

Too many to draw

Story books alone went out twenty-eight times. Drawing twenty-eight little books would fill the whole board. The chart would be very long and nobody could count it quickly. There has to be a shorter way.

One picture for four

So she draws one small book picture for every four books. She writes that rule in a box beside the chart. That box is called the key of the chart. Now twenty-eight books need only seven pictures.

Reading the key first

The key is the first thing to look at on any such chart. It says one picture equals four books. Every picture in every row now means the same thing. Read it before you count anything else.

Counting a row

The story row has seven pictures in it. Seven fours make twenty-eight. So twenty-eight story books were borrowed that week. The counting is done in two short steps.

The poems row

The poems row has five pictures. Five fours make twenty books. That is eight fewer than the story row. The gap of two pictures stands for a gap of eight books.

A half picture

The science row has six full pictures and one half picture. Six fours make twenty-four. The half picture means half of four, which is two books. So the science count comes to twenty-six.

The puzzle row

The puzzle row has three full pictures and a half. Three fours make twelve, and the half adds two more. So fourteen puzzle books went out. That is the shortest row of the four.

Choosing the scale

A key of one book would have made the rows far too long to draw. A key of twenty would have squashed them all into one picture each. Then the differences between the kinds would have vanished. Four was a good middle choice.

Remember

• A pictograph shows data as rows of pictures.
• The key says what one picture stands for.
• Multiply the pictures by the key number.
• A half picture means half of the key number.
• Choose a key that keeps the longest row short.

Scenario:

Two children draw pictographs of the same fruit sold in a week. Ravi uses one picture for every 2 fruits and his chart is long. Meena uses one for every 10 and hers is short. Ravi says Meena has hidden some sales. Their teacher asks the class to read the numbers off both. They agree exactly. The class sees that the key did the work, not the pictures. Ravi writes the warning down. Two pictographs cannot be compared by their length until the key of each one has been read, because one picture can mean 2 or 10.

Analysis:

Two charts of one week, both honest, one three times longer. The key is what turns a picture into a quantity.

Activity:

Draw one week of data as a pictograph twice, with different keys. Ask a friend to read both and check they match.

Title:

Make a pictograph of your week

What You Notice:

A friend can read your chart correctly only if the key is there. Cover the key and ask them to try, and you will see how much work that little box does.

Newspapers often draw pictographs, because a row of little pictures is read in a glance.

A pictograph without a key can be read in any way at all, so it means nothing.

Turning pictures into a count — Count the pictures, then times the key. — Seven pictures with a key of four give seven fours, which is twenty-eight.

Saplings on the school ground

Five classes plant saplings on the school ground for a green week. Each class keeps its own count in a notebook. On Monday Ravi collects the notebooks. He puts all five counts together on one chart.

Bars instead of pictures

This time he does not draw little trees. He draws one upright bar for each class instead. A taller bar means a larger count. The bars are all of the same width, so only their heights matter.

The scale up the side

Numbers run up the left side of the chart. They go nought, two, four, six and so on. One step up the side is worth two saplings. That is called the scale of the graph. Every bar is measured against it.

Reading the tallest

Class 5 has the tallest bar of the five. Its top reaches the line marked sixteen. So Class 5 planted sixteen saplings, more than any other class that week.

Reading the shortest

Class 3 has the shortest bar. Its top rests neatly on the line marked six. So Class 3 planted only six saplings, fewer than anybody else.

A bar between two lines

Class 4 is the tricky one to read. Its bar stops halfway between the lines marked ten and twelve. Halfway between those two numbers is eleven. So Class 4 planted eleven saplings.

Never count the lines

Some children count the ruled lines instead of reading the printed numbers. That gives a wrong answer at once. Always put a finger on the top of the bar and slide it across to the scale.

Comparing two bars

Class 2 planted fourteen and Class 1 planted eight. Taking eight from fourteen leaves six. So Class 2 planted six more saplings than Class 1. The words how many more always mean take away.

The whole school

Ravi adds all five counts together at the end. Eight and fourteen and six and eleven and sixteen come to fifty-five. So fifty-five saplings now stand on the school ground. The graph gave him every number he needed.

Remember

• One bar is drawn for each group, all of the same width.
• The scale says how much one step is worth.
• Slide across from the top of a bar to read it.
• A bar between two lines shows the number between them.
• Bars can be added for a total or compared for a difference.

Scenario:

A school in Uttarakhand holds a green week every July. Five classes plant saplings on the hill slope behind the school. Class 1 plants 8 and Class 2 plants 14. Class 3 manages only 6, because its pupils are the youngest. Class 4 plants 11 and Class 5 plants 16. Ravi draws the counts as bars, with the side scale climbing in twos. The Class 4 bar worries him. It stops between two of the ruled lines. His teacher shows him how to read it. She then asks the class a harder question. Each sapling will drink about two litres of water a week. How much water will the whole slope need?

Analysis:

A bar graph with a scale in twos, read for counts, totals and a water estimate for the slope.

Activity:

Count something at home for five days and draw it as a bar graph with a scale of two.

A bar graph with no scale can be drawn to make any bar look big or small.

Rainfall, cricket scores and class attendance are all shown as bar graphs.

Reading a bar — Top of the bar, across to the scale. — Put a finger on the top of the bar and slide it straight across to the numbers.