Data and Graphing

Sorting Objects by Single Attributes

Sometimes we have a mixed-up group of objects. Sorting means putting objects into groups that belong together.

When we sort by a single attribute, we use one thing only to make the groups. An attribute is a way something looks, like its color, shape, or size.

For example, if we sort by color, we only look at color. We do not sort by shape or size at the same time.

Things we can sort by:

• Color: red, blue, green
• Shape: circle, square, triangle
• Size: big, small

How to sort objects

1. Look at all the objects.
2. Choose one attribute.
3. Make groups for that attribute.
4. Put each object into the right group.
5. Check that you used only one rule.

Let’s learn with examples.

Example 1: Sort by color

You have these crayons: red, blue, red, yellow, blue.

We will sort by color.

• Red group: 2 crayons
• Blue group: 2 crayons
• Yellow group: 1 crayon

We can count them like this:

Red: \(2\), Blue: \(2\), Yellow: \(1\)

This is sorting by one attribute because we only used color.

Example 2: Sort by shape

Look at these shapes: circle, square, triangle, circle, square.

We will sort by shape.

• Circle group: 2 shapes
• Square group: 2 shapes
• Triangle group: 1 shape

Count:

Circle: \(2\), Square: \(2\), Triangle: \(1\)

We did not look at color or size. We only looked at shape.

Example 3: Sort by size

You have these bears: big bear, small bear, big bear, small bear, small bear.

We will sort by size.

• Big group: 2 bears
• Small group: 3 bears

Count:

Big: \(2\), Small: \(3\)

Since \(3 > 2\), there are more small bears than big bears.

Example 4: Be careful to use only one rule

Look at these buttons:

• big red button
• small red button
• big blue button
• small blue button

If the rule is sort by color, the groups are:

• Red group: 2 buttons
• Blue group: 2 buttons

If the rule is sort by size, the groups are:

• Big group: 2 buttons
• Small group: 2 buttons

Both ways are correct, but you must choose one attribute at a time.

Tips for sorting

• Say the rule first: “I am sorting by color.”
• Touch each object one time as you place it in a group.
• Make sure every object goes into a group.
• Check that you did not mix two rules together.

Try thinking about these questions:

• What attribute are we using?
• How many groups do we need?
• Which group has more?
• Which group has fewer?
• Are all the objects sorted?

Why sorting helps

Sorting helps us organize objects so they are easier to count and compare. It also helps us get ready to make tallies and graphs later.

Summary

Sorting means putting objects into groups. When we sort by a single attribute, we use one rule, like color, shape, or size. We place each object into the group that matches that one rule. Then we can count the groups and answer questions about them.

Sorting Objects by Multiple Attributes

Sometimes we sort objects into groups. We can sort by one attribute, like color. We can also sort the same objects in a different way, like shape or size.

An attribute is something we can notice about an object. For example, an object can be red, big, round, or soft. One object can have more than one attribute at the same time.

That means one object might fit in more than one group, depending on how we sort it. A big red button belongs in the red group if we sort by color. The same button belongs in the big group if we sort by size.

Learning to sort in different ways helps us organize information and answer questions about what we see.

What does “multiple attributes” mean?

Multiple means more than one. Attributes are the features of an object.

Here are some attributes we can use to sort objects:

• Color: red, blue, yellow, green
• Shape: circle, square, triangle
• Size: big, small
• Type: toy, block, button, fruit

When we sort by multiple attributes, we may:

• sort the same collection by color first
• then sort the same collection by shape
• notice that some objects belong to overlapping ideas, like red circles

How to sort objects

1. Look at all the objects.
2. Choose one rule for sorting, such as color.
3. Put objects into groups that match the rule.
4. Count how many are in each group.
5. Choose a new rule, such as size or shape.
6. Sort the same objects again.

When you change the sorting rule, the groups can change too. The objects stay the same, but the way we organize them changes.

Worked Example 1: Sort by color, then by shape

Look at these 4 objects:

• 1 red circle
• 1 red square
• 1 blue circle
• 1 blue square

First, sort by color:

• Red: 2 objects
• Blue: 2 objects

We can write that as:

Red: \(2\)
Blue: \(2\)

Now sort the same 4 objects by shape:

• Circles: 2 objects
• Squares: 2 objects

We can write that as:

Circles: \(2\)
Squares: \(2\)

The objects did not change. Only the sorting rule changed.

Worked Example 2: One object can fit different groups

Look at these 5 buttons:

• big red button
• small red button
• big blue button
• small blue button
• big red button

First, sort by color:

• Red: 3 buttons
• Blue: 2 buttons

Now sort by size:

• Big: 3 buttons
• Small: 2 buttons

Let’s think about one button: a big red button.

• It belongs in the red group when we sort by color.
• It belongs in the big group when we sort by size.

So one object can be described in more than one way.

Worked Example 3: Overlapping categories

Look at these 6 shapes:

• 2 small triangles
• 1 big triangle
• 2 small circles
• 1 big circle

Sort by shape:

• Triangles: 3
• Circles: 3

Sort by size:

• Small: 4
• Big: 2

Now let’s answer a question: How many are small triangles?

There are \(2\) small triangles.

Small is one attribute. Triangle is another attribute. Together, they make a smaller group inside the collection.

So some groups can overlap. A shape can be in the small group and also in the triangle group.

Worked Example 4: Re-sorting the same collection

Look at these 8 classroom objects:

• 2 red crayons
• 2 blue crayons
• 2 red blocks
• 2 blue blocks

First, sort by type:

• Crayons: 4
• Blocks: 4

Next, sort the same objects by color:

• Red: 4
• Blue: 4

Now answer this question: How many blue blocks are there?

There are \(2\) blue blocks.

Those objects are in the blue group when we sort by color, and they are in the block group when we sort by type.

Things to remember

• The same collection can be sorted in different ways.
• An object can have more than one attribute.
• When the sorting rule changes, the groups may change.
• Some categories can overlap, like red squares or small circles.

Try these questions in your head

1. If you have a small green square, which groups could it belong to?

• small
• green
• square

2. If you sort toys by type, will color matter?

No. If the rule is type, then we group by what kind of toy it is.

3. If you sort the same toys by color, will the groups change?

Yes. The toys are the same, but the rule is different, so the groups can change.

Summary

Sorting by multiple attributes means looking at objects in more than one way. You can sort the same objects by color, shape, size, or type. One object can belong to different groups because it has more than one attribute. This helps us organize data and answer questions about what we have.

Recording Data with Tally Charts

Sometimes we count how many things we have. We might count toys, pets, colors, or favorite fruits. A tally chart helps us record our counting in a quick and neat way.

Tally marks are little lines we draw as we count. They help us keep track so we do not lose our place.

In a tally chart, we usually count one thing at a time. For each new thing, we add one more tally mark.

How tally marks work

The first four tally marks are straight lines:

$$ | \quad || \quad ||| \quad |||| $$

The 5th tally mark is special. It goes across the first four marks to make a group of five.

It looks like this:

$$ |||| $$

with the 5th mark crossing through the group. We can think of it as a bundle of 5.

Grouping by five helps us count faster. Instead of counting every single mark one by one, we can count by fives and then add extra ones.

For example, one full group of five is:

$$5$$

One full group of five and two more marks is:

$$5 + 2 = 7$$

Why tally charts are helpful

• They are quick to draw.
• They help us stay organized.
• They make counting easier because we can see groups of five.
• They help us answer questions about our data.

Parts of a tally chart

A tally chart has categories and tally marks.

• A category is what we are counting, like apples, bananas, or cats.
• The tally marks show how many.

Here is a simple tally chart:

Favorite Snack

• Apple: |||
• Crackers: ||||
• Cheese: ||

This chart shows:

• 3 children chose apple.
• 4 children chose crackers.
• 2 children chose cheese.

How to make a tally chart

1. Choose the categories. Decide what kinds of things you are counting.
2. Listen or look carefully. Count one item at a time.
3. Draw one tally mark for each item.
4. Make a group of five. On the 5th mark, cross the first four.
5. Count the tallies. Count groups of 5 first, then extra marks.

Worked Example 1: Counting pets

A class talks about pets. We want to record how many students have each kind of pet.

• Dog, Dog, Cat, Dog, Cat

Let us tally them one at a time.

Dogs:

• 1st dog: |
• 2nd dog: ||
• 3rd dog: |||

Cats:

• 1st cat: |
• 2nd cat: ||

The tally chart is:

• Dog: |||
• Cat: ||

So, there are 3 dogs and 2 cats.

Worked Example 2: Grouping by five

Now let us count red flowers. We see 6 red flowers.

We make tally marks like this:

• 1: |
• 2: ||
• 3: |||
• 4: ||||
• 5: one group of five
• 6: one group of five and 1 more

We can count it as:

$$5 + 1 = 6$$

So 6 tally marks means one bundle of five and one extra.

Worked Example 3: Recording fruit choices

Eight children choose their favorite fruit:

• Apple, Banana, Apple, Apple, Banana, Apple, Banana, Banana

Let us sort and tally.

Apple

• 1st apple: |
• 2nd apple: ||
• 3rd apple: |||
• 4th apple: ||||

Banana

• 1st banana: |
• 2nd banana: ||
• 3rd banana: |||
• 4th banana: ||||

The tally chart is:

• Apple: ||||
• Banana: ||||

Both fruits have 4 votes. They are the same.

Worked Example 4: A full group of five and more

A teacher counts 7 blue blocks.

First make 5 tally marks as one full group. Then add 2 more.

We count:

$$5 + 2 = 7$$

So 7 is shown with one group of five and two extra tally marks.

If we had 10, that would be two groups of five.

We could count:

$$5 + 5 = 10$$

Tips for using tally charts

• Count slowly. Add one tally for each item.
• Do not skip items.
• Do not add extra tallies.
• Remember the 5th mark makes a group of five.
• Check your work by counting the tallies again.

Common mistakes to watch for

• Making 5 straight lines instead of a group of five.
• Forgetting to tally one of the items.
• Putting a tally in the wrong category.
• Counting tally marks without using the groups of five.

Let us read a tally chart

Suppose a chart shows:

• Cats: one group of five and 1 more
• Dogs: |||

Cats have:

$$5 + 1 = 6$$

Dogs have:

$$3$$

So there are 6 cats and 3 dogs. Cats are more than dogs.

Practice thinking

• If you see a full group of five, start by saying 5.
• Then count the extra marks: 6, 7, 8, and so on.
• This helps you count quickly and correctly.

Summary

A tally chart is a simple way to record data. We use one tally mark for each item we count. The 5th tally mark makes a group of five, which helps us count faster. When we read a tally chart, we count groups of 5 and then add any extra marks.

Constructing Picture Graphs

Today we will learn how to make a picture graph.

A picture graph uses small pictures or symbols to show information. It helps us count and compare things in a quick, easy way.

In this lesson, each picture will stand for 1 thing. That means:

$$1\ \text{picture} = 1\ \text{item}$$

So if there are 4 apples, we draw 4 apple pictures. If there are 2 cats, we draw 2 cat pictures.

What is data?

Data is information we collect. We can collect data about favorite fruit, pets, colors, or toys.

When we make a picture graph, we put the data into groups. These groups are called categories.

For example, if we ask, “What is your favorite fruit?” the categories might be:

• Apples
• Bananas
• Grapes

Steps for making a picture graph

1. Look at the data. Find out what things you are counting.
2. Name the categories. Write the group names.
3. Choose a picture or symbol. You can use stars, circles, smiley faces, or small drawings.
4. Remember the key. The key tells what each picture means. In this lesson, the key is always: $$1\ \text{picture} = 1$$
5. Draw the pictures. Draw the right number of pictures next to each category.
6. Check your work. Count the pictures to make sure they match the data.

Important things to remember

• Each row should be for one category.
• Each picture should stand for the same amount.
• In this lesson, each picture stands for exactly 1.
• Draw pictures in a line so they are easy to count.
• Do not draw too many or too few pictures.

Example 1: Favorite pets

Here is some data:

• Dogs: 3
• Cats: 2
• Fish: 4

We will use ● as our picture.

Key: ● = 1

The picture graph looks like this:

Dogs: ● ● ●

Cats: ● ●

Fish: ● ● ● ●

Let’s check:

• Dogs have 3 circles, so that means 3 dogs.
• Cats have 2 circles, so that means 2 cats.
• Fish have 4 circles, so that means 4 fish.

This picture graph is correct because each picture means 1.

Example 2: Favorite colors

Suppose we ask 6 children about their favorite colors. The data is:

• Red: 1
• Blue: 3
• Green: 2

We will use ★ as our picture.

Key: ★ = 1

The picture graph is:

Red: ★

Blue: ★ ★ ★

Green: ★ ★

Now let’s answer questions from the graph.

• Which color has the most? Blue, because it has 3 stars.
• Which color has the fewest? Red, because it has 1 star.
• How many children chose green? 2, because there are 2 stars.

Example 3: Sorting toys and making a graph

Let’s say we count toys in a room.

• Cars: 4
• Balls: 2
• Dolls: 3

We will use ■ as our picture.

Key: ■ = 1

Picture graph:

Cars: ■ ■ ■ ■

Balls: ■ ■

Dolls: ■ ■ ■

Let’s think carefully about how we made it.

1. We sorted the toys into groups: cars, balls, dolls.
2. We counted how many were in each group.
3. We drew 1 square for each toy.

If someone drew 5 squares for cars, that would be wrong, because there are only 4 cars.

Example 4: Class snack choices

The class chooses snacks:

• Apple slices: 2
• Crackers: 5
• Cheese: 3

We will use 😊 as our picture.

Key: 😊 = 1

Picture graph:

Apple slices: 😊 😊

Crackers: 😊 😊 😊 😊 😊

Cheese: 😊 😊 😊

Now let’s read the graph.

• How many chose crackers? 5
• How many chose cheese? 3
• Did more children choose apple slices or cheese? Cheese, because 3 is more than 2.

How to check a picture graph

After you draw your graph, ask yourself these questions:

• Did I write each category?
• Did I use a key?
• Does each picture mean 1?
• Did I draw the correct number of pictures for each category?
• Are the pictures easy to count?

Common mistakes

• Forgetting the key: Always show what one picture means.
• Drawing the wrong number of pictures: Count carefully.
• Mixing categories: Keep each group on its own line.
• Using different values: If one picture means 1, it must always mean 1 in that graph.

Let’s practice thinking

If the data says:

• Birds: 2
• Bunnies: 4

And the key is:

❤ = 1

Then the graph should be:

Birds: ❤ ❤

Bunnies: ❤ ❤ ❤ ❤

We draw 2 hearts for birds and 4 hearts for bunnies.

Why picture graphs are helpful

Picture graphs help us see information quickly.

We can use them to answer questions like:

• Which has more?
• Which has less?
• How many are there?
• Are two groups the same?

Summary

A picture graph shows data with pictures or symbols.

To make a picture graph:

1. Sort the data into categories.
2. Count each category.
3. Choose a picture or symbol.
4. Write the key.
5. Draw one picture for each item.

Remember:

$$1\ \text{picture} = 1\ \text{item}$$

If you count carefully and use the key, you can make a correct picture graph.

You are learning how to organize information and show it clearly. Great job!

Constructing Bar Graphs

Today we will learn how to make a bar graph. A bar graph helps us show information with bars.

Each bar stands for a group, like apples, cats, or colors. The taller the bar, the more there are. The shorter the bar, the fewer there are.

A bar graph helps us compare groups quickly. We can look at the bars and answer questions like Which has the most? or Which has the least?

What is in a bar graph?

• Title — tells what the graph is about.
• Categories — the groups we are counting.
• Bars — show how many are in each group.
• Numbers — help us know how tall to make each bar.

How to make a bar graph

1. Collect the data. Count how many are in each group.
2. Write the categories. Put the group names in order.
3. Use numbers. Write counting numbers like \(1, 2, 3, 4\).
4. Draw the bars. Make each bar go up to the right number.
5. Check your work. Make sure taller bars mean bigger counts.

Important idea: The height of each bar must match the count. If a group has \(4\), the bar should go to \(4\). If a group has \(2\), the bar should go to \(2\).

That means the bars must be fair and match the numbers. We do not make a bar too tall or too short.

Example 1: Favorite fruit

A class votes for favorite fruit.

• Apples: \(4\)
• Bananas: \(2\)
• Grapes: \(3\)

We can put this into a bar graph. The apple bar goes to \(4\). The banana bar goes to \(2\). The grape bar goes to \(3\).

Here is the data:

$$\begin{aligned} \text{Apples} &= 4\\ \text{Bananas} &= 2\\ \text{Grapes} &= 3 \end{aligned}$$

So:

• Apples has the tallest bar.
• Bananas has the shortest bar.
• Grapes is in the middle.

Example 2: Pets

Let’s say students have these pets:

• Dogs: \(5\)
• Cats: \(1\)
• Fish: \(3\)

To make the bar graph:

1. Write the title: Our Pets.
2. Write the categories: Dogs, Cats, Fish.
3. Write numbers from \(1\) to \(5\).
4. Draw each bar to the right height.

The dog bar must reach \(5\). The cat bar must reach \(1\). The fish bar must reach \(3\).

Now we can read the graph:

• Dogs are the most.
• Cats are the least.
• Fish are more than cats.

Example 3: Using tallies first

Sometimes we count with tally marks before we draw a bar graph.

Favorite colors:

• Red: |||
• Blue: ||||
• Green: ||

Let’s change the tallies into numbers:

• Red: \(3\)
• Blue: \(4\)
• Green: \(2\)

Now we make the bar graph:

• The red bar goes to \(3\).
• The blue bar goes to \(4\).
• The green bar goes to \(2\).

This shows how we can transfer counts into a bar graph. We take the number from the tally chart and draw a bar to match it.

Example 4: Check if the graph is correct

Suppose the counts are:

• Cars: \(2\)
• Bikes: \(4\)
• Buses: \(1\)

If someone draws:

• Cars bar to \(3\)
• Bikes bar to \(4\)
• Buses bar to \(1\)

Is the graph correct?

No. The cars bar is wrong. Cars has \(2\), so the bar should go to \(2\), not \(3\).

This is why we always check that each bar matches its count.

Tips for making a good bar graph

• Give your graph a title.
• Write each category clearly.
• Count carefully.
• Make bars the right height.
• Leave space so the bars are easy to see.
• Check that the tallest bar shows the greatest number.

Questions we can answer from a bar graph

• Which category has the most?
• Which category has the least?
• How many are in each category?
• Are two categories the same or different?

Let’s practice thinking

If ice cream choices are:

• Chocolate: \(2\)
• Vanilla: \(5\)
• Strawberry: \(3\)

Then:

• The vanilla bar is tallest.
• The chocolate bar is shortest.
• The strawberry bar goes to \(3\).

Brief Summary

A bar graph shows information with bars. Each bar stands for a category. The height of each bar must match the number counted.

To make a bar graph, we:

1. Count the data.
2. Write the categories.
3. Use numbers.
4. Draw bars to the correct height.
5. Check that every bar matches its count.

When we make bars carefully, the graph is easy to read and helps us compare groups.

Interpreting Graphs means looking at a graph to understand what the graph is telling us.

A graph helps us see information quickly. We can use a graph to find:

• which group has the most
• which group has the least
• how many there are altogether

In 1st grade, graphs often show categories like favorite fruit, pets, colors, or toys.

Let’s learn how to read a graph step by step.

Parts of a graph

A graph has categories and pictures, bars, or marks that show how many.

• Categories are the groups, like apples, bananas, and grapes.
• Count means how many are in each group.

When we interpret a graph, we look carefully at each category and its count.

Words to know

• Most = the greatest number
• Least = the smallest number
• Total = all the groups added together

If one group has 5 and another has 2, then 5 is more than 2. So the group with 5 has the most.

If the groups are 3, 1, and 4, then 1 is the least.

To find the total, we add all the counts together.

For example, if a graph shows 2 cats and 3 dogs, the total is:

$$2 + 3 = 5$$

How to interpret a graph

1. Look at the title to see what the graph is about.
2. Look at each category.
3. Count how many are in each category.
4. Compare the counts to find the most and least.
5. Add all the counts to find the total.

Worked Example 1: Find the most

Here is a simple picture graph about favorite fruit.

Apples: 🍎🍎🍎

Bananas: 🍌🍌

Grapes: 🍇🍇🍇🍇

Let’s count each category:

• Apples = 3
• Bananas = 2
• Grapes = 4

Which category has the most?

We compare 3, 2, and 4. The greatest number is 4.

So, grapes have the most.

Worked Example 2: Find the least

Now let’s look at a graph about pets.

Cats: 🐱🐱🐱

Dogs: 🐶🐶🐶🐶

Fish: 🐟

Let’s count:

• Cats = 3
• Dogs = 4
• Fish = 1

Which category has the least?

We compare 3, 4, and 1. The smallest number is 1.

So, fish have the least.

Worked Example 3: Find the total

Here is a graph about favorite colors.

Red: ❤️❤️

Blue: 💙💙💙

Green: 💚💚

Count each one:

• Red = 2
• Blue = 3
• Green = 2

To find the total, add all the counts:

$$2 + 3 + 2 = 7$$

So, the total is 7.

Worked Example 4: Find most, least, and total

Now let’s do everything together.

Toys:

Cars: 🚗🚗🚗🚗

Dolls: 🧸🧸

Balls: ⚽⚽⚽

Blocks: 🧱

Count each category:

• Cars = 4
• Dolls = 2
• Balls = 3
• Blocks = 1

Most: The greatest number is 4, so cars have the most.

Least: The smallest number is 1, so blocks have the least.

Total: Add all the counts:

$$4 + 2 + 3 + 1 = 10$$

So, the total is 10.

Tips for reading graphs

• Count carefully.
• Check each category one at a time.
• Look for the greatest number to find the most.
• Look for the smallest number to find the least.
• Add all the numbers to find the total.

Be careful!

• Do not guess. Always count.
• Do not stop after finding one category. Look at all of them.
• When finding the total, add every category.

Let’s practice thinking

If a graph shows:

• Pizza = 5
• Tacos = 2
• Salad = 3

Then:

• Most = Pizza
• Least = Tacos
• Total = $$5 + 2 + 3 = 10$$

Summary

A graph helps us read information fast.

When you interpret a graph, ask yourself:

• Which category has the most?
• Which category has the least?
• What is the total?

Remember:

• Most means greatest number.
• Least means smallest number.
• Total means all added together.

If you count carefully, compare the numbers, and add them all, you can understand any simple graph.

Solving Comparison Questions Using Graphs

Graphs help us look at information quickly. A graph can show how many children like apples, how many like bananas, or how many chose a favorite toy.

Sometimes we look at a graph and answer comparison questions. Comparison questions ask things like:

• How many more?
• How many fewer?

When we compare, we look at two groups and find the difference between them.

What does “how many more” mean?

“How many more” means one group has a bigger number than another group. We want to know how much bigger it is.

What does “how many fewer” mean?

“How many fewer” means one group has a smaller number than another group. We want to know how much smaller it is.

Important idea: “How many more” and “how many fewer” both ask for the difference.

We can find the difference by counting what is extra, or by subtracting.

$$7 - 4 = 3$$

This means 7 is 3 more than 4, and 4 is 3 fewer than 7.

How to answer comparison questions from a graph

1. Look at the two groups in the graph.
2. Find how many are in each group.
3. Decide which group has more and which has fewer.
4. Count the extra pictures, bars, or marks.
5. You can also subtract to find the difference.

Let’s practice with picture graphs.

In these examples, each picture stands for 1 item.

Example 1

A class made a graph of favorite pets.

Dogs: 🐶🐶🐶🐶🐶

Cats: 🐱🐱🐱

How many more children chose dogs than cats?

Step 1: Count each group.

Dogs = 5

Cats = 3

Step 2: Find the difference.

We can count the extra pets: 2 extra dogs.

We can also subtract:

$$5 - 3 = 2$$

Answer: 2 more children chose dogs than cats.

Example 2

A snack graph shows this:

Apples: 🍎🍎🍎🍎

Bananas: 🍌🍌🍌🍌🍌🍌

How many fewer children chose apples than bananas?

Step 1: Count each group.

Apples = 4

Bananas = 6

Step 2: Find the difference.

Bananas have 2 more than apples, so apples have 2 fewer than bananas.

$$6 - 4 = 2$$

Answer: 2 fewer children chose apples than bananas.

Example 3

A toy graph shows this:

Balls: ⚽⚽⚽⚽⚽⚽⚽

Blocks: 🧱🧱🧱🧱🧱

How many more balls are there than blocks?

Step 1: Count each group.

Balls = 7

Blocks = 5

Step 2: Subtract.

$$7 - 5 = 2$$

Answer: There are 2 more balls than blocks.

Example 4

Look at this graph of favorite colors.

Red: ❤️❤️❤️❤️❤️❤️

Blue: 💙💙💙💙💙💙

How many more children chose red than blue?

Step 1: Count each group.

Red = 6

Blue = 6

Step 2: Compare the numbers.

They are the same.

$$6 - 6 = 0$$

Answer: 0 more children chose red than blue.

When both groups are the same, the difference is 0.

Helpful tips

• Read the question carefully. Does it ask “how many more” or “how many fewer”?
• Compare only the two groups named in the question.
• Count carefully. Make sure each picture stands for 1 unless the graph says something different.
• If the groups are equal, the answer is 0.

Words to remember

• Graph: a picture that shows information
• Compare: to look at two groups to see how they are different
• More: a bigger number
• Fewer: a smaller number
• Difference: how many more or fewer

Let’s think about one more way.

If one group has 8 and another group has 5, we can match them one by one.

After matching 5 with 5, there are 3 left over.

So the difference is 3.

$$8 - 5 = 3$$

This means:

• 8 is 3 more than 5
• 5 is 3 fewer than 8

Summary

When you solve comparison questions using graphs, you:

1. Look at the two groups.
2. Count how many are in each group.
3. Find which group has more and which has fewer.
4. Count the extra ones or subtract.

Remember: “how many more” and “how many fewer” both ask for the difference.

You can do it!