Solving 1 and 2step problems using scaled bar graphs
Basics on the topic Solving 1 and 2step problems using scaled bar graphs
Scaled Bar Graph Problems
Analyzing bar graph problems is a task that you are likely to encounter in 3rd grade. You will be asked to answer questions containing keywords like “how many more” and “how many less” to analyze the data. In this text you will learn the necessary information about 3rd grade math problems using scaled bar graphs.
Analyzing Scaled Bar Graphs
We can use information in bar graphs to analyze questions about the total number, questions of “more” or “less”, and “how many” in each category. When solving for “how many more” or “how many less”, we are looking for a difference between values. Let’s learn how to solve these one and two step bar graph problems in 3rd grade math.
Scaled Bar Graphs – Answering One Step Questions
To solve problems using a scaled bar graph, read the question and find keywords like “how many more” or “how many less” or “how many fewer”. These hint at a difference between two things which implies a subtraction equation. Next, locate the first data point on the graph. Carefully use the scale to determine the height of the bar. This is important because the bar graph is scaled, so one interval represents more than one unit in value. Let’s use an example. If the scale goes up by ten and the bar is halfway between thirty and forty, the value of the bar is thirtyfive. Thirtyfive is halfway between thirty and forty.
Next, repeat these steps to find the value of the second data point from the question. Once both values are known, set up the subtraction equation. In bar graph problems in 3rd grade, typically the larger number is written first and the smaller number is subtracted from it. Finally, solve for the difference. Now you have solved a onestep bar graph word problem for 3rd grade.
Scaled Bar Graphs – Answering Two Step Questions
Similarly as for solving one step questions, read the question and find keywords like “how many more” or “how many less” or “how many fewer”. But this time, a twostep problem will include words like “together” or “combined”. These words tell us to find a sum of two items before we can find an overall difference. This makes it a twostep problem. We will need to write and solve the first equation before we can write and solve the second one.
Similarly, locate the specified data on the graph by using the scale to determine the height of the bar. This is important because the bar graph is scaled, so one interval represents more than one unit in value. Next, do the same to find the value of the second data point from the question. Once both values are known, set up an addition equation. Remember, the key words combined or together told us to find a total before finding a difference. Add the value of the first two items to find the sum.
With part one complete, move on to part two. Here we are looking for “how many less”, which tells us to set up a subtraction problem. Locate the third data point and use the key to determine its value. Write an equation with the sum from part one and subtract the value of the third data point from it. The difference is the solution to the two part problem. Now you have solved a twostep bar graph problem for 3rd grade.
Scaled Bar Graphs – Steps for Answering Questions
This video about scaled bar graphs for kids in 3rd grade presented the necessary steps for solving questions about values on scaled bar graphs. Here are all the essential steps listed in a chart:
Step #  What to do 

1  Find the keywords in the problem. 
2  Locate the data on the graph. 
3  Set up the equation and solve the problem. 
How do you solve grade 3 bar graph problems containing keywords like “how many more” or “how many less”? This text provided the necessary steps to solve these problems. On this website, you can also find scaled bar graph worksheets with one and two step word problems. These worksheets with bar graph word problems include activities and exercises.
Transcript Solving 1 and 2step problems using scaled bar graphs
Nari and Gus couldn't be more excited to start the new soccer season! Coach Beaver is reviewing last season's data to build the new starting lineup. Using a scaled bar graph, Nari and Gus will help analyze the team's scoring record by answering Coach's questions. "Solving One and TwoStep Problems using Scaled Bar Graphs." Remember, when solving for 'how many more' or 'how many less', we are looking for a difference between values. First, Coach Beaver wants to know how many more goals did Nari score than Squirrel? Begin by finding the key words 'many more'. These words imply a difference so we will write a subtraction equation. To find the difference, we first need to find out how many goals Nari and Squirrel each scored. Let's start with Nari. His bar is halfway between thirty and forty, so he scored thirtyfive goals. Next, we find Squirrel's bar. Since Squirrel's bar is just below thirty but well above twentyfive, it is reasonable to guess that she scored twentynine goals. Now we set up our subtraction equation. Remember, Coach Beaver wanted to know "how many more goals did Nari score than Squirrel." Nari's score thirtyfive minus Squirrel's score twentynine equals. Then, we solve! Thirtyfive minus twentynine equals six. We can tell Coach Beaver that Nari scored six more goals than Squirrel last season. Second, Coach Beaver wants to know "how many fewer goals did Rabbit and Gus score together compared to Mouse?" To begin, we find the key words in our question: 'many fewer', 'Rabbit, Gus together' and 'Mouse' . The key word together tells us that we will need to find the sum of Rabbit and Gus' goals before we can subtract it from Mouse's goals. This makes it a two step problem but we can still follow the same process as before. First, look at the graph. How many goals did Rabbit score? Rabbit scored eleven goals. How many goals did Gus score? Gus scored zero goals. Remember, Coach Beaver wanted to know how many fewer goals Rabbit and Gus scored together compared to Mouse? The key word, together, tells us we need to find the total of Rabbit and Gus's goals. Step one will be setting up an addition equation. Rabbit's goals eleven plus Gus's goals zero equals. Eleven plus zero equals eleven goals scored together. We have completed step one, so we can move on to step two. How many goals did Mouse score? He scored thirtyfive goals. In step two we are looking for ‘how many fewer’, which tells us we are going to set up a subtraction problem now. Starting with our larger number, we write thirtyfive minus eleven equals. Let's solve how many fewer goals did Rabbit and Gus score than Mouse? They scored twentyfour fewer goals than Mouse. Before we find out the starting line up, let's remember. To solve one and two step problems using a scaled bar graph: First, find the keywords. Second, identify the needed values on the graph. Third, set up the equation. Fourth, solve. It looks like Coach Beaver has his starting line up thanks to Gus and Nari's analysis! "Hey, Gus why so sad?" "I didn't score any goals last year, Nari, there's no way Coach will put me in the starting line up!" "Uhhh, Gus, you're not supposed to score, you're the goalie of course you'll be on the field!" "Oh yeah!!"
Solving 1 and 2step problems using scaled bar graphs exercise

Reading a scaled bar graph.
HintsLook at the scale and figure out what the graph is counting by.
If the bar is halfway between the 2 numbers shown, then you will need to figure out what number is halfway between.
SolutionFirst, figure out the scale. This scale is counting in 10's. Then, look at the category. In this case, look at the specific animal and find the top of the bar. Then, trace your finger over to figure out which number it is at.
If it is halfway between 2 numbers, then the number won't be shown and you will need to figure out what number is halfway between.
Nari scored 25 goals. Rabbit scored 15 goals. Mouse scored 30 goals.
Squirrel scored 20 goals. Gus scored 5 goals.

How many more goals did Mouse score than Rabbit?
HintsLook at the scale and figure out what the graph is counting by.
The question asks how many more goals did Mouse score than Rabbit. Think about what equation will help you solve this.
SolutionBy looking at the graph, we can see Rabbit scored 10 goals and Mouse scored 30 goals.
We need to figure out how many more goals Mouse scored than Rabbit.
To figure this out, you can subtract 30  10 = 20, or you can count up starting at 10 and ending at 30, which is also 20.

Coach Beaver needs your help!
HintsLook at the scale and figure out what the graph is counting by.
Nari's score isn't exactly on a number shown on the graph. Figure out which number is right before 30.
If the bar is between the 2 numbers shown, then you will need to figure out what the number is.
Figure out if you need to set up 1 or 2 equations to solve for the answer.
If the question asks how many more or how many fewer, think about what equation will help you solve this.
SolutionFor the third question:
 Looking at the graph, Rabbit scored 10 goals, Squirrel scored 15 goals and Mouse scored 35 goals.
 The first part of the question to figure out is: how many goals did Rabbit and Squirrel score together? This means that we need to add their scores together. So, 10 + 15 = 25.
 The last part of the question to figure out is: how many fewer goals did Rabbit and Squirrel score than Mouse? To figure this out, you can subtract 35  25 = 10, or you can count up starting at 25 and ending at 35, which is also 10.
For the second question:
 Looking at the graph we can see Rabbit scored 10 goals and Mouse scored 35 goals.
 We need to figure out how many fewer goals Rabbit scored than Mouse.
 To figure this out, you can subtract 35  10 = 25, or count up starting at 10 and ending at 35, which is also 25.
 Looking at the graph we can see Nari scored 29 goals and Squirrel scored 15 goals.
 We need to figure out how many more goals Nari scored than Squirrel.
 To figure this out, you can subtract 29  15 = 14, or count up starting at 15 and ending at 29, which is also 14.

Solve the word problems by looking at the bar graph.
HintsHere is what each fruit represents.
Look at the scale and figure out what the graph is counting by.
If the bar is halfway between the 2 numbers shown, then you will need to figure out what number is halfway between.
Figure out if you need to set up 1 or 2 equations to solve for the answer.
If the question asks how many more or how many fewer, think about what equation will help you solve this.
SolutionFor the third question:
 Looking at the graph, 5 players chose grape, 10 players chose banana and 35 chose apple as their favorite fruit.
 The first part to figure out is the total number of players who chose grape and banana. This means that we need to add them together. So, 5 + 10 = 15.
 The last part to figure out is how many fewer players chose grape and banana than apple. To figure this out, you can subtract 35  15 = 20, or you can count up starting at 15 and ending at 35, which is also 20.
For the second question:
 Looking at the graph, 35 players chose apple, 25 players chose kiwi and 40 chose blueberry as their favorite fruit.
 The first part to figure out is the total number of players who chose apple and kiwi. This means that we need to add them together. So, 35 + 25 = 60.
 The last part to figure out is how many more players chose apple and kiwi than blueberry. To figure this out, you can subtract 60  40 = 20, or you can count up starting at 40 and ending at 60, which is also 20.
 Looking at the graph, 10 players chose banana and 30 players chose orange as their favorite fruit.
 We need to figure out how many fewer players chose banana than orange.
 To figure this out, you can subtract 30  10 = 20, or count up starting at 10 and ending at 35, which is also 20.

How many more people voted for blue than yellow?
HintsThe question asks how many more people voted for blue than yellow. Think about what equation will help you solve this.
SolutionBy looking at the graph, we can see 6 people voted for blue and 4 people voted for yellow.
We need to figure out how many more people voted for blue than yellow.
To figure this out, you can subtract 6  4 = 2, or you can count up starting at 4 and ending at 6, which is also 2.

Figure out which word problems are solved incorrectly.
HintsHere is what each topping represents.
Look at the scale and figure out what the graph is counting by.
If the bar is halfway between the 2 numbers shown, then you will need to figure out what number is halfway between.
Figure out if you need to set up 1 or 2 equations to solve.
If the question asks how many more or how many fewer, think about what equation will help you solve this.
SolutionFor the first problem:
 We need to figure out how many more people voted for pepperoni than bacon.
 To figure this out, you can subtract 325  150 = 175, or count up starting at 150 and ending at 325, which is also 175, so this answer was correct.
 The first part of the question to figure out is: how many people voted for onion and pepper. This means that we need to add them together. So, 200 + 150 = 350.
 The last part of the question to figure out is: how many more people voted for onion and pepper than mushroom. You can subtract 350  250 = 100, or you can count up starting at 250 and ending at 350, which is also 100, so this answer was correct.
 The first part of the question to figure out is: how many people voted for tomato and onion. This means that we need to add them together. So, 50 + 200 = 250.
 The last part of the question to figure out is: how many fewer people voted for bacon than tomato and onion. You can subtract 250  150 = 100, or you can count up starting at 150 and ending at 250, which is also 100, so this answer was incorrect.
 The first part of the question to figure out is: how many people voted for tomato and pepper. This means that we need to add them together. So, 50 + 150 = 200.
 The last part of the question to figure out is: how many more people voted for pepperoni than tomato and pepper. You can subtract 325  200 = 125, or you can count up starting at 200 and ending at 325, which is also 125, so this answer was incorrect.
 The first part of the question to figure out is: how many people voted for mushroom and onion. This means that we need to add them together. So, 250 + 200 = 450.
 The last part of the question to figure out is: how many fewer people voted for bacon than mushroom and onion. You can subtract 450  150 = 300, or you can count up starting at 150 and ending at 450, which is also 300, so this answer was incorrect.