# 3rd Grade Pie Chart Lesson Plan

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## Discussion/Introduction

Our graphing units in third grade used to be focused primarily on circle graphs (pie charts), but under the Common Core, bar charts are given a new prominence. Bar charts are intuitively easy to understand for second and third graders, and since they build on and are closely connected to the number line, they follow logically from the other math your students are doing.

But just because bar charts are taking center stage , doesn’t mean we can stop teaching pie charts altogether. While bar charts make comparing the relative size of parts a simple visual exercise, pie charts offer intuitively obvious visual comparisons between parts and the whole. Teaching circle graphs also enables our students to practice fractions in a fun, easy-to-grasp way.

This lesson plan focuses on gaining a visual understanding of whole-part relationships through the use of a simple circle graph, and also gives students an opportunity to practice fractions , as required by section 3.NF.3 (Number and Operations—Fractions) in the Common Core. “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

## Objective

To understand a pie chart (circle graph) and to be able to deduce information about the relative size of the parts shown in it. To be able to compare fractions by reasoning about their size (Common Core 3.NF.3)

## Supplies

• A graph printout from http://www.meta-chart.com/pie, a free pie chart maker
• Paper cutouts: a large circle cut out of thick white paper, and ½, ¼, and $$frac{1}{8}$$ sectors of circles cut out of different colors of construction paper.
• Paper and markers/crayons/colored pencils for each student

## Methodology/Procedure

Start with a review of fractions. Show the students your white circle, and ask what they think of when they see it. Give them some time to discuss what a circle means to them, and validate their feelings and opinions as they share them. These opinions can be as simple as ‘pizza!’ or as abstruse as ‘unending’; there is no one answer. When they have all had a chance to share how they feel about it, explain that to you, since it is a whole, entire circle, it can mean a ‘whole’ of anything—a whole class of children, a whole country, a whole family, a whole bag of skittles.

Cover half of your circle up with your ½ circle construction paper cut out, and ask how much of the circle is colored now. After the students have answered, tell them that since the whole circle meant to you a whole of anything – a whole class, a whole country, a whole bag of skittles—the colored sections mean, to you, half of anything. Half a bag of skittles, half a class, half a country.

Ask half the class to hold up their hands; the front half, the back half, or the side half. Then tell them that you could use this circle to show how many children had their hands up; the colored section would be the children with their hands up, and the white section would be the other children.

Take off the half circle of construction paper and replace it by the ¼. Ask your students if they know how much of the circle is shaded now. They will probably be ready with the right answer; if anyone is unsure, show that ¼ is half of a half, and that four quarters cover the whole circle. Ask a quarter of the class to raise their hands; you will probably have to mark off the demarcation lines for the quarter. Tell them that if the whole white circle represents the class, that construction paper quarter is the part of the class with their hands up.

Go on to $$frac{1}{8}$$, introducing it the same way with your $$frac{1}{8}$$ construction paper sector.

Now show the students the graph printout from http://www.meta-chart.com/share/favorite-colors-in-the-classroom and tell them it is a graph which shows the favorite colors in a class of students like yours. Tell them it is called a pie chart, and ask them if they know why.

Ask which color is the biggest favorite. Then ask which of the three explicitly listed colors the least amount of children seem like.

Now tell them the class was made up of twenty students, and ask them how many students liked blue. Ask whether fewer or more than six students have green for their favorite color, and whether or not five students have purple for a favorite color. Ask if four students might have purple for a favorite color, and then whether two might have liked purple best.

Now take a poll of favorite colors in your classroom, and put the data on your blackboard. It may look something like this:

• Blue – Zack, Katie, Markus, Peter–4
• Green – Jamie, Paul, Christian-3
• Red – Jordan-1
• Pink—Mallory, Katie, Jennifer, Desiree, Madeline-5
• Purple – Desiree -1
• Yellow—Sofia, Edwin -2

Tell your students you want them each to make a pie graph for you, using this data. Suggest they group the smaller amounts together under ‘other’; in the example above, this would be red, purple and yellow, totaling four. Then start with the color most children like, and ask what fraction of the total number of children like that color. In the example above this would be $$frac{5}{16}$$. Help the students relate this to the fractions you’ve already discussed; in this case; just a little more than $$frac{4}{16} = frac{1}{4}$$. Have the students color a generous quarter on their circles, and go on to the next color: in this graph, blue, $$frac{4}{16}$$ or exactly $$frac{1}{4}$$ of a circle.

At this point you don’t want to focus on the nitty gritty—for instance, it would be counterproductive to divide your circle into sixteen, twenty, or thirty equal portions—as many portions as you have students in your class—and make an exact circle graph by coloring in the appropriate number of sectors. Instead, you want to focus on getting an intuitive sense of the size of different fractions. Your students will  do this by relating the fractions they are unsure of—how much is $$frac{5}{16}$$, anyway? to what they already know. In this case $$frac{4}{16} = frac{1}{4}$$ which is a nice solid quarter, and the $$frac{1}{16}$$ it goes over is less than $$frac{1}{8}$$, which is a fat sliver.

When your students have all created their own graphs have them take turns explaining what they drew and what different sectors mean. Ask them which color is favorite, which is second favorite, which is third favorite. Ask them how the graphs would change if one child changed his favorite color– for instance, if Madeline decided she preferred blue or Jordan switched to green. Then ask them what would happen to the graph if your class was merged with another third grade class of the same size, and all the children in that class liked yellow best.

These exercises should give your students a new familiarity with and perspective on fractions, as well as  opening the doors to understanding data representation with pie charts.

## Common Core Standards

This lesson plan is aligned to Standard 3.NF.3 (Third Grade Numbers and Operations– Fractions, item 3 ) in the Common Core. 3.NF.3 reads: “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

# 3rd Grade Bar Chart Lesson Plan

## Discussion/Introduction

In third grade we get to liven up our bar chart lessons by taking advantage of our students’ new familiarity with multiplication and division. By the end of third grade, the Common Core recommends that students know from memory all products of two one digit numbers. By the time you schedule your bar chart lesson, your students should be comfortable doing skip counting by twos, threes, fives or tens; and that means they shouldn’t have any difficulty interpreting a scaled bar chart.
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# Calves, Baby Camels and a Scaled Bar Chart Lesson

## Objective

In this 3rd grade bar chart lesson, students will learn to analyze and understand data presented on a scaled bar chart. They will learn how to do both simple and multi-step comparing problems using the bar chart.

## Supplies

• Graph printout from www.meta-chart.com/bar/ , or, if your classroom has projector capabilities, a graph prepared and saved on your laptop.
• One sheet of graphing paper for display, with large squares and a height of about ten squares
• Graphing paper and markers for each student

## Methodology/Procedure

Start this lesson with a bit of storytelling. Math and imaginative thinking go well together, and starting a new math topic with an imaginative exercise means you’ll have the attention not only of your technically minded, mathy children but also of those who love their English but usually ‘turn off’ when they come into your classroom.

Once upon a time, far away, in the wild open steppe land of Mongolia, two children lived with their old grandfather and grandmother in a little round tent made of felt. Their little tent was alone on the steppeland; for as far as they could see to the east, west, north and south there was nothing but waving grasses and wooded hills. That, and the camels, yaks, sheep and horses which made up the family wealth.

It was Temuujin’s job to take the horses and yaks to pasture every morning, and Zolzaya, his little sister, took the sheep and goats to the green grass on the other side of the hill. Grandma and Grandpa were getting old, and though they still hobbled around, checked everything, and told the two children what to do, they were past the age for active work.

Then came the spring when Grandpa’s legs were so bad he could not make his rounds of the herds as he had used to. He had to stay in his bed by the fire, and the furthest he could move was to his seat by the fire. He worried about his herds, and though Temuujin and Zolzaya knew everything was going well, he wouldn’t believe them when they told him that. He would ask questions about numbers—how many more kids are there than lambs?—and numbers were not Temuujin’s strong point. When Temuujin was uncertain in answering, he would get angry and say that the boy knew nothing about taking care of animals.

One day Temuujin and Zolzaya decided to do something special to give their grandfather all the information he wanted about the animals. They would count all the lambs, kids, foals, calves and baby camels, and mark down the numbers in a tally chart. Then they would make a bar graph for their grandfather, so he could see exactly how many animals he had without having to go outdoors. They knew that with a bar graph they could solve any comparing problems he asked them just with one glance at the paper.

They were quite sure that this would make their grandfather very, very, happy, and they had exactly one sheet of graph paper to draw their bar graph on.

But when they came in from counting, both Temuujin and Zolzaya had very somber faces. This is what their numbers looked like.

Lambs: 37
Kids: 42
Foals: 11
Calves: 15
Baby Camels: 6

And this is what their graph paper looked like:

Display a simple sheet of large-squared graph paper , with ten squares each way.

How could they put their data on this little sheet? The numbers were too big.

Stop here, and give your students a chance to discuss the problem. After a discussion break, ask for possible solutions.

Temuujin and Zolzaya realized there was only one thing to do: they could scale their bar graph so that each block on the graph paper, instead of meaning 1 animal, meant five. This made some of their numbers very easy to work with. The calves, for instance, being exactly fifteen, would be represented by a bar exactly three squares tall on the bar graph.

What about the baby camels? How could they make a bar that meant ‘six’, if each square stood for five?

Stop again for discussion. Ask any students who have solutions to share them with the class.

Temuujin realized that he would have to divide the square up, in his mind, into five equal slices, and let the camel bar go exactly one $$frac{1}{5}$$  slice over into a second square.

So this is what Temuujin and Zolzaya’s graph looked like.

Display your printout of http://www.meta-chart.com/share/baby-animals-on-the-steppe, or put it on the projector.

They were very pleased when it was done, and carried it proudly in to their grandfather. And after that, they could answer all his questions with just a moment’s hesitation, whenever he asked them about the numbers of animals.

Before you go into these questions, the initial data you put on the blackboard should be erased, so that students are encouraged to base their arithmetic on the graph rather than on the raw numbers.

The first question he asked was, how many more kids are there than lambs?

Let your students decide how to solve this and the following problems, and come in with your ideas only after they have it worked out. If they get stuck, they should be encouraged to see that there is a difference between lambs and kids of just one square, so five animals.

The second question was—how many foals and baby camels are there, altogether?

If your students decide to do this problem as $$5 cdot 2 + 5cdot frac{1}{5} + 5cdot 1 +5 cdot frac{1}{5}$$ , tell them they are right—and then point out that they can also do it as $$(2 frac{1}{5}+1 frac{1}{5})5$$; or, if they prefer dealing with whole numbers and fractions separately, $$5(2+1) + frac{(1+1)}{5} cdot 5.$$

The third question was—how many baby animals are there altogether?

After your students have worked on this problem, show them that one easy way would be to add the whole numbers—7+8+2+3+1=21, add that to the sum of the fractions $$(frac{2}{5}+frac{2}{5}+frac{1}{5} +frac{1}{5}) = frac{6}{5} =1 frac{1}{5}$$, and multiply both by five: $$21 cdot 5 + frac{6}{5}) cdot 5= 105+6=111$$.

Grandpa’s last question—how many fewer foals are there than kids?

This can be done as $$(8-2) cdot 5; + (frac{2}{5}-frac{1}{5}) cdot 5.$$

### Extension Exercise

If there is still time before the end of the lesson, ask the students if they can make a scaled bar graph to let Grandpa know how many horses, cows, and camels there are:
Horses-20
Camels -11
Cows – 18

I’ve found that students respond wonderfully to the use of stories in the math classroom, and sometimes a touch of faraway places and novel situations can make an otherwise ‘booooriing!’ math exercise almost magically fun.

## Common Core Standards

The specific section on bar charts in the 3rd grade Common Core Standards for Mathematics reads: “Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ‘how many more’ and ‘how many less’ problems using information presented in scaled bar graphs” [3.MD.2]. Since our students need to be familiar with reading and interpreting scaled bar charts before they can draw them independently, my scaled bar chart lesson plan, given above, focuses primarily on interpretation and problem solving. Students will also be involved in thinking through the creation of a scaled bar chart and can go on to draw their own charts in an extension exercise if time permits.

# M&M Fun: A Bar Chart Lesson for 2nd Graders

Sample Bar Graph

## Discussion/Introduction

After weeks and weeks of arithmetic and mental math that tax my students’ minds to the utmost, I always enjoy getting to the graph section of our curriculum. It’s a breather, almost, and the change of pace is very welcome.  At the same time, our unit on graphing is a very important one—as students enjoy making colorful charts and graphs they learn how to condense real-world data into a mathematical format that is easy to understand, concise, and easy to analyze.

A 2nd grade bar chart lesson can be just complex enough to be exciting, but there’s no need to go into the complicated situations that will leave your students scratching their heads in confusion. The free chart-maker at Meta-Chart (http://www.meta-chart.com/) is a wonderfully easy way to make professional,  streamlined charts and graphs; all you do is plug in your data and—eureka!—out comes the graph.

## Objective

Students will learn how to analyze data on a simple single-unit bar chart with four categories. They will learn to solve simple put-together, take-apart, and compare problems using information presented in a bar graph by making use of a free online bar graph maker.

## Supplies

• A mug with around 20-30 colored M&Ms, and ~8 M&Ms for each child in the bag
• 1 sheet of graph paper for each child
• Markers
• Graph printouts from http://www.meta-chart.com/bar (or, if you have projector capabilities, meta-chart graphs prepared and saved on your laptop).

## Methodology/Procedure

When students are investigators what they learn becomes part of them. Bar graphs lend themselves well to a discovery way of teaching because they are, in a way, a special code that can be discovered. Your students will have had some exposure to graphs in grade 1; some will have even done very basic work with bar graphs. They have all the tools they need to figure out what the bar graph is telling them if you give them the time and encouragement to figure it out by themselves.

Teacher: Look, I have a mug here with M&Ms in it. You can’t look inside right now, but here is a graph that tells you what the colors of the M&Ms are.

[Give students a chance to look at it and think about what it is saying.]

Teacher: Can anyone tell me which color I have the most of?

Student: Red!

Teacher: Yes! You are correct. How did you know?

Student: The bar labeled red is the longest.

Teacher: You’re right. Can you tell me how many red M&Ms there are in my cup?

If a student gives the right answer, applaud him and ask for an explanation why. If no-one knows, ask some more leading questions.

Teacher: How long is the red M&M bar? Is there a number which tells how long it is?  What do you think that number might be telling us?

Once the students have figured out how many red M&Ms there are, reinforce that interpretative ability by asking questions about the other colored M&Ms in the mug. Then go on to problems related comparing.

Teacher: How many more red M&Ms do I have than blue?

Lead the students to discover that they can find the difference without doing subtraction by simply noticing how much further the red line sticks out.  Ask questions comparing each of the other lines.

When your students are comfortable comparing, go on to simple put-together and take-apart problems using the data on the graph.

Teacher: If I don’t like red or green M&Ms and decide to throw those ones away, how many will I throw away?

Given the opportunity to discuss and brainstorm, your students should have no trouble solving this. If their thinking was anything less than automatic, follow this up with a similar question. If your dog only can eat yellow or brown M&Ms, how many will he have?  Then ask a take-apart question:

If I actually like green M&Ms and want to have as many green M&Ms as red, how many more green M&Ms do I need to put in the mug?

Once the students are comfortable doing a variety of problems, have them each draw two axis on their own graph paper, and label the vertical axis with numbers 1-6. Distribute around eight M&Ms to each child, and have them draw a bar graph. They can color each bar the bars the same color as the M&Ms for easy labeling. Post the graphs at the front of the room, and discuss which child has the most red, the most green, the most yellow, and so on.

#### Evaluation

You’ll be able to tell how well the students understood the concept of a bar graph by how much help and hand-holding they need when it comes to drawing their own graphs.  Quick comparing and put-together questions on the smaller numbers of their own M&M collections and graphs will give you another way of testing their ability to understand the logic behind bar graphs.

###### A Single Unit Bar Chart Lesson in Your Classroom

If you use my lesson plan I’d love to hear from you regarding your experiences—did you have fun with your students? What is your preferred way of teaching  a 2nd grade bar chart lesson? Please comment!

## Common Core Standards

The Common Core recognizes the importance of learning how to use graphs for data representation and manipulation in the early grades. For second grade, under measurement and data  [ 2.MD.10 ], the Common Core State Standards for Mathematics reads ‘Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems using information presented in a bar graph.’

## Web Resources/Further Exploration

The chart maker at http://www.meta-chart.com is a convenient, easy to use, free way of preparing charts or graphs for any of your classes!