Tally Charts and Picture Graphs

A pile of things is easier to count in groups. Sorting means putting things that are alike together. You choose what makes them alike.

Choose one rule

A sorting rule tells you where each thing belongs. You could sort buttons by color. Red buttons go together. Blue buttons go together. The shape of a button does not change its color group.

Each named group is a category. For a color rule, your labels might be “red,” “blue,” and “green.” Say the rule before you begin. Then pick up one thing at a time and find its group.

Imagine sorting socks by color. A red sock with stripes goes in the red group. Making a separate “striped” group would mix two rules. The sock could then fit in two places.

If a thing does not fit your named groups, add “other.” A yellow button can go there when your groups are red, blue, and other. Every thing must have exactly one place.

Sort and count crayons

You have 12 crayons. You sort them by color:

Touch each crayon once as you count its group. Then add the group counts:

5 + 4 = 9, and 9 + 3 = 12.

That matches the 12 crayons you started with. Now look through the groups. Is each crayon in its color group? Did you count each one once? Checking the crayons catches mistakes that a matching total can miss.

There are 3 groups, but there are 12 crayons. The red group holds 5 crayons. Listen for what a question asks you to count: the groups or the things inside them.

A new rule makes new groups

You could sort the same leaves by color or by size. Color might give you green, yellow, and brown groups. Size might give you small and large groups. Tell your friend which rule you chose so they can follow your sorting.

Data is information you collect to answer a question. You might want to know your class’s favorite pet. The answers you collect help you find out.

Make the choices clear

Ask, “Which pet do you like best: dog, cat, or fish?” Tell everyone the choices before they answer. A question such as “What do you like?” could bring answers about toys, food, or games. Those answers would be hard to put into a few groups.

Use two, three, or four clear choices. Add “other” when someone may need a different answer. In a favorite-choice question, ask each person to pick just one.

A survey means asking people a question and recording their answers. Ask each person once. Write the answer right away, before you ask the next person. You can write it on a list or make a mark beside its group name.

Follow Mia’s survey

Mia asks 15 classmates to choose their favorite pet. When a child says “dog,” she marks dog. When a child says “cat,” she marks cat. She does this for every answer.

At the end, Mia counts:

• Dog: 7 children.
• Cat: 5 children.
• Fish: 3 children.

7 + 5 + 3 = 15.

The total matches the number of children she asked. She also checks that each answer went into the right group once. Waiting until the end to remember everyone’s answers would make that much harder.

If you ask 15 children but record only 14 answers, check back with them. Find the missing answer and put it in its own group.

You can watch and count, too

Some questions need no survey. To find the weather on school days, look each day and record what you see. To count toy cars by color, look at each car and mark its color.

Write a source note beside your data. It tells where the information came from. “Our class, Monday” tells you whose answers you collected and when. Those answers describe your class. To find out another class’s favorites, ask that class.

A tally mark is a short line for one thing you count. Draw a new mark each time you count one more thing. Three things look like “|||.”

Draw the fifth line across

Start with standing lines, side by side. For four things, draw “||||.” When the fifth thing comes, draw a line across those four. The crossing line is the fifth mark. Together, the marks make a bundle of five.

For the sixth thing, start a new standing line beside the bundle. Leave a little gap so you can see the bundle clearly. Keep adding marks. When the new group reaches five, cross its four standing lines, too.

You can use tallies while things happen. Each time a child answers your question, add one mark. You do not need to erase a number and write a new one after every answer.

Count bundles, then single lines

Suppose you see two full bundles and three single lines.

1. Count the bundles: “5, 10.”
2. Keep counting for the singles: “11, 12, 13.”
3. Write 13 as the number you counted.

The bundles hold 10 marks. The singles add 3 more. This is quicker than counting every mark from one.

Show 17 with tallies

To draw 17 marks, make three full bundles first. They hold 5 + 5 + 5 = 15 marks. Add two single lines beside them.

Check your drawing aloud: “5, 10, 15, 16, 17.” Stop at the last single line.

Count the line across, too

A bundle has four standing lines and one crossing line. Counting only the standing lines gives 4 and misses a mark. Drawing five standing lines and then crossing them gives 6 marks. Draw the crossing line as you say “five.”

You may see a different tally style in another place. Some people draw four sides of a box, then cross it. That bundle still holds five marks.

A tally chart keeps your marks in named groups. Its title tells you what you counted. Each row names a category and holds that group’s marks.

Get ready before you ask

For a pet survey, write the title “Our Favorite Pets.” Make one row each for dog, cat, and fish. Leave room beside each name for tallies. You can add a final column called “Number.”

Point to the right row when someone answers. If they say “fish,” put one mark in the fish row. Keep that answer in just that row. Say the choice quietly as you mark it if that helps.

Read the finished chart

Here are Mia’s answers. The middle column describes her tally marks.

For dog, count “5, 6, 7.” Write 7 in the Number column. For cat, the full bundle gives 5. For fish, count the three single lines.

To answer “How many children chose cat?”, find the cat label. Follow that row to its marks or number. Your answer is 5 children. Keep your finger on the row so you do not read the number next door.

Check the record

Add all the row numbers: 7 + 5 + 3 = 15. Mia asked 15 children, so these totals match. Also check each child’s recorded answer. A mark in the wrong row can leave the total unchanged while changing a group’s count.

If the total does not match, count the marks again. Then check the answers for a missed mark or an extra one.

Keep the counts in a number table

You can show these answers with just the Pet and Number columns. That is a table of counts. It still shows dog 7, cat 5, and fish 3.

Some charts put the categories in columns across the top. Look at the labels to find where each group’s marks belong.

A picture graph shows counts with small pictures. Pictures for the same group sit together in a row across or a column going up.

Read three parts first

The title tells you what the graph is about. “Fruit We Like Best” tells you that this graph shows favorite fruit choices.

The labels name the groups. A row labeled “banana” holds the banana choices. The key tells you what one picture means. In the graph below, each circle stands for one child.

Fruit We Like Best

Key: each circle = 1 child.

Follow one row

How many children chose banana?

1. Find the label “Banana.”
2. Follow that row across.
3. Touch each circle once as you count: “1, 2, 3, 4, 5, 6, 7, 8.”

Eight children chose banana. The orange row has three circles, so three children chose orange.

The circles do not need to look like fruit. The label names the choice. The key says that you are counting children. Stars or smiley faces could show the same answers.

Read columns going up

A picture graph can also have the labels under its columns. Find your label at the bottom. Count the pictures above that label from bottom to top. One picture still stands for one child.

When rows sit close together, it is easy to wander into another row. Start at the label and move your finger along just that row. Touching each picture once also helps you avoid counting a picture twice.

Your counts tell you how many pictures to draw. A clear picture graph also needs a title, group labels, and a key.

Build a pet graph

Start with these favorite-pet counts: dog 7, cat 5, and fish 3. Each child picked one pet.

1. Write the title “Our Favorite Pets.”
2. Write dog, cat, and fish at the start of three rows.
3. Choose a simple picture, such as a circle.
4. Draw one circle for each child’s answer.
5. Write the key: “Each circle = 1 child.”

Draw seven circles on the dog row. Count aloud as you draw them, then stop at seven. Draw five for cat and three for fish.

Make the rows easy to compare

Draw all the circles the same size. Start each row at the same line. Leave the same gap between circles. Grid paper can help: put one circle in each square.

Now the circles line up in places. The first dog circle lines up with the first cat circle. The second lines up with the second, and so on. A longer row will show more answers.

Imagine drawing five huge cat circles with wide gaps. That row could look longer than seven small dog circles. The picture counts are still five and seven, but the sizes could fool your eyes. Use matching sizes and gaps when you draw your graph.

Check each group

Compare the drawing with the counts you started with:

• Dog needs 7 circles.
• Cat needs 5 circles.
• Fish needs 3 circles.

There should be 15 circles altogether, because 7 + 5 + 3 = 15. Also check that each row has its own correct count. One extra dog circle and one missing cat circle would leave the total at 15.

You can draw your graph going up instead. Write the labels under the columns. Start every column at the same bottom line and keep the pictures evenly spaced.

You can show the same answers with objects, a list, tallies, numbers, or pictures. When you change the way you show them, each group keeps its count.

Begin with real things

An object graph uses real things to show answers. Each child might put one cube beside their favorite fruit’s label. Line up equal-sized cubes from the same starting line.

To turn that into a picture graph, draw one picture for each cube. Six cubes become six pictures. Keep the group names so the choices stay clear.

Turn a list into tallies

A list records answers one after another. Suppose it says, “Ana: dog; Ben: cat; Sam: dog.”

Read Ana’s answer and add a mark beside dog. Check off Ana’s name. Read Ben’s answer and add a mark beside cat. Check off Ben’s name. Read Sam’s answer and add the next dog mark. The counts are dog 2 and cat 1.

Checking off each entry shows where you have reached. It helps you keep your place and count each answer once.

Show ten days of weather

A class records 10 school days: sunny 5, cloudy 3, and rainy 2.

• In a tally chart, sunny has one full bundle. Cloudy has three single lines, and rainy has two.
• In a number table, the counts are 5, 3, and 2.
• In a picture graph, draw five suns, three clouds, and two raindrops.

The graph needs the key “Each picture = 1 day.” Its title could be “Weather on Ten School Days.”

One full tally bundle becomes five pictures. A bundle saves five counts even though the lines sit close together.

Compare group by group

Check the sunny group in both displays, then cloudy, then rainy. Both must show 5, 3, and 2. The total is 5 + 3 + 2 = 10 days.

Tallies are quick while you collect answers. Number tables make counts easy to read and add. Lined-up objects and pictures help you see which groups have more.

Read the question before you start adding. It tells you which groups you need.

One group

In “Our Favorite Pets,” dog has 7 answers, cat has 5, and fish has 3. “How many chose cat?” asks for just the cat group. Find its row and read 5, or count its marks or pictures. Five children chose cat.

All the groups

“How many children answered?” asks for the total. Each child chose one pet, so add every group:

7 + 5 + 3 = 15 children.

You can add two numbers first: 7 + 5 = 12. Then add the last group: 12 + 3 = 15.

Another way is to look for a ten. Put dog and fish together first: 7 + 3 = 10. Then 10 + 5 = 15. Both ways include all three groups once.

There are three pet categories. That tells you how many kinds of answers there are. The 15 answers tell you how many children took part.

Two groups together

“How many chose dog or cat?” needs only those two groups. Add 7 + 5 = 12. Twelve children chose dog or cat. Leave fish out because the question names dog and cat.

Everyone outside one group

“How many did not choose dog?” asks for the children in the cat and fish groups. Add 5 + 3 = 8.

You can also start with everyone and take away the dog group: 15 − 7 = 8. Eight children did not choose dog. This works because every child gave one answer.

Add four fruit groups

A fruit survey has apple 5, banana 8, grapes 4, and orange 3. To find everyone who answered, include all four:

5 + 8 = 13, then 13 + 4 = 17, then 17 + 3 = 20.

Point to each row as you add its count. The smallest group still belongs in the total. Match your answer to what you counted: children in a survey, cars in a car count, or days in a weather record.

Compare the group counts to find the most and the fewest. Most means the greatest count. Fewest means the smallest count.

Compare pet choices

The favorite-pet counts are dog 7, cat 5, and fish 3. Seven is the greatest number, so dog has the most choices. Three is the smallest, so fish has the fewest.

You can put the groups in order:

• Most to fewest: dog 7, cat 5, fish 3.
• Fewest to most: fish 3, cat 5, dog 7.

Keep the names beside their counts as you move them. Otherwise, you might put the numbers in order but attach them to the wrong pets.

In a survey about favorites, the choice with the most answers is the most popular. Dog is the most popular pet choice among these children. The choice with the fewest answers is the least popular.

Order four groups

For fruit, the counts are apple 5, banana 8, grapes 4, and orange 3. Start with 8, the greatest count. Then use 5, 4, and 3. From most to fewest, the fruit order is banana, apple, grapes, orange.

The first row in a chart does not have to be the biggest. In this fruit list, apple comes first but banana has more choices.

Notice equal counts

Now imagine a different survey with grapes 4 and orange 4. Both groups have the same number. They are equal, or tied. Neither group has more. You can keep the tied groups beside each other when you order the categories.

In a neatly drawn picture graph, the longest row shows the most. That works when all pictures have the same size and gaps, and the rows start together. Equal counts then make equal row lengths. If pictures have different sizes or gaps, count them to compare the groups.

“How many more?” asks for the extra part in the bigger group. That gap is called the difference. You can find it by matching, counting on, or subtracting.

Match the pictures

Seven children chose dog and three chose fish. Imagine the two rows starting together. Pair each fish picture with a dog picture.

Three fish pictures make three pairs. Four dog pictures are left without partners. Four more children chose dog than fish.

Count on from the smaller number

Start at the fish count, 3. Count up to the dog count, 7: “4, 5, 6, 7.” Hold up a finger for each step. You take four steps, so the difference is 4.

Start counting steps after 3. Saying “3, 4, 5, 6, 7” and counting all five numbers includes your starting place as an extra step.

Subtract and check

Take the smaller count away from the bigger one:

7 − 3 = 4.

Check by adding the gap to the smaller count:

3 + 4 = 7.

If you answer 7, you have given the whole dog group. The question asks for its extra part. If you add 7 + 3 = 10, you find how many chose dog or fish together. That answers a different question.

More and fewer share the same gap

Fish has 4 fewer choices than dog. Dog has 4 more choices than fish. Some questions say “how many less” for “how many fewer.”

“How many more would need to choose fish to match dog?” also asks for that gap. Fish needs 4 more, because 3 + 4 = 7.

Try fruit choices

Eight children chose banana and three chose orange. Find the extra banana choices: 8 − 3 = 5. So 5 more children chose banana than orange. Check with 3 + 5 = 8. On a lined-up graph, these five are the pictures that stick out past the shorter row.

Your data helps you answer the question you started with. Use the group names and numbers to tell someone what you found.

Give a reason from the counts

A pet survey has dog 7, cat 5, and fish 3. You can say, “Dog is our class’s favorite pet choice. Seven children chose it, more than cat or fish.”

For fruit, banana has 8 choices, apple 5, grapes 4, and orange 3. If your class wants the snack with the most votes, banana is a good choice. Explain, “Banana got 8 votes. That is more than any other fruit.”

Check a statement

A statement says something you can check. “More children chose cat than fish” is true for the pet survey: 5 is more than 3. “Cat got the most votes” is false, because dog got 7.

Find the groups named in the statement. Read their counts before deciding. This helps you catch a mix-up between nearby labels.

A class records 10 school days: sunny 5, cloudy 3, and rainy 2. Someone says, “There were as many sunny days as cloudy and rainy days together.” Add 3 + 2 = 5. The statement is true.

“It rained on most days” is false. Only 2 of the 10 recorded days were rainy.

Look at what you asked

The pet survey asked which pet children liked best. It did not ask which pets they owned. A child can like a dog best without having a dog at home. To find pet ownership, ask a new question.

Your class’s answers also leave another class’s favorites unknown. You can say, “We can’t tell from this data.” Then ask that class if you want to find out.

New questions can grow from your results. Perhaps you wonder whether another class would choose the same favorite fruit. Ask them, record their answers, and make groups for their choices.