Solving 1- and 2-step problems using scaled picture graphs
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Basics on the topic Solving 1- and 2-step problems using scaled picture graphs
Solving a Scaled Picture Graph with Questions
Do you like playing video games? At the end of each round in a special racing game, the virtual players are ranked against each other. The rankings are shown on a leaderboard ... that looks just like a scaled picture graph! This text on reading a picture graph helps you answering questions based on the picture graph.
A picture graph or pictogram is a type of graph where the data is displayed using images. On the leaderboard, every one hundred points is shown by one star. We can use and interpret this data to find out how many more points we need to be the champions.
Pictogram – Maths Problems
We can use information in picture graphs to analyse questions about the total number, more/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 word problems using a scaled picture graph.
One Step Scaled Picture Graph Problems
First of all, read the question and find keywords like “how many more”, “how many less”, or “how many fewer”. These words hint at a difference between two things, so we know to write a subtraction equation. Next, locate the first data point on the graph. Then, use the key to determine its value. This is important because the picture graph is scaled, so one image represents more than one in value. Count each picture using the value in the key.
Let’s look at an example: If the key says each picture equals one hundred and there are five and a half pictures, count by one hundred for each full picture and fifty for a half picture. The value of this data point would therefore be five hundred and fifty:
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 picture graph problems, typically the larger number is written first and the smaller number is subtracted from it. Finally, solve for the difference:
Two Step Scaled Picture Graph Problems
Similarly to the one step scaled picture graph problems, read the question and find keywords like “how many more” or “how many fewer”. But this time, a two-step 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 two-step problem. We will need to write and solve the first equation before we can write and solve the second one:
Again, locate the specified data on the graph. Use the key to determine its value. Count each picture using the value in the key. 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 fewer”, 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:
Solving Problems Using Pictograms – Summary
Remember, if you want to solve problems including picture graphs, you can follow these steps:
| Step # | What to do |
|---|---|
| 1 | Find the keywords |
| 2 | Locate the data on the graph |
| 3 | Set up the equation and solve |
Have you practised yet? On this website, you can also find graph questions, “how many more or less” worksheets and exercises to analyse and interpret data.
Transcript Solving 1- and 2-step problems using scaled picture graphs
"Go, go, GO!!" "Yes, I did it! Maybe this will put me at number one on the leaderboard!" Not quite, Nari. You see, he's been racing for hours in hopes of leading the other players. Each time he finishes a race, the player rankings appear in a scaled picture graph. Nari can use this graph to ask himself 'how many more' and 'how many less' questions to help him work out how he can get to number one. Let's help Nari analyse this data by "Solving One- and Two-Step Problems Using Scaled Picture Graphs". Remember, when solving for 'how many more' or 'how many less', we are looking for a DIFFERENCE between values. First, Nari wants to know how many more points Turbo Mouse scored than him. To begin, find the key words 'how many more'. These words hint at a difference, so we will write a subtraction equation. Next, locate Turbo Mouse on the graph. He earned five and a half stars. Now, we must use the key because the picture graph is scaled. One star represents more than one point. Each whole star is worth one hundred points. So, count in steps of one hundred for each whole star and steps of fifty, or half of one hundred, for half stars. One hundred, two hundred, three hundred, four hundred, five hundred, fifty. Turbo Mouse has five hundred and fifty points. Next, find Nimble Nari. Nari earned three and a half stars. Using the scaled key again, count in hundreds for each whole star and in fifties for the half star. One hundred, two hundred, three hundred, fifty. Nari has three hundred and fifty points! Then, setup the subtraction equation. Turbo Mouse's score five hundred and fifty, minus Nimble Nari's score three hundred and fifty equals. Finally, solve! Five hundred and fifty minus three hundred and fifty equals two hundred. Turbo Mouse scored two hundred MORE points than Nimble Nari! Secondly, Nari thinks Flying Squirrel and Speedy-pede may team up, so he wants to know how many fewer points he scored than Flying Squirrel and Speedy-pede combined? To begin, find the key words: 'how many fewer', 'Flying Squirrel and Speedy-pede', and 'combined' . The key word COMBINED tells us we need to find the sum of Flying Squirrel AND Speedy-pede's points before we can subtract Nari's. This makes it a two step problem, BUT we can still follow the same process as before. First, look at the graph. How many stars did Flying Squirrel earn? She earned two and a half stars. What do we do next? We count her score by using the key's scale. One hundred, two hundred, fifty. Flying squirrel earned two hundred and fifty points. Now, how many stars did Speedy-pede earn? We count again. One hundred, two hundred. Speedy-pede earned two hundred points. Remember, Nari wants to know how many fewer points he scored than Flying Squirrel and Speedy-pede combined. The key word, COMBINED, tells us we need to find the total of Flying Squirrel and Speedy-pede's points. Part one will be setting up an addition equation. Flying Squirrel's points plus Speedy-pede's points equals. What is the sum? The sum is four hundred and fifty points. Now that we have completed step one, we can move on to step two. In step two we are looking for HOW MANY LESS, which tells us we are going to setup a subtraction problem. How many points did Nari score? He scored three hundred and fifty points! Starting with our larger number, we write four hundred and fifty minus three hundred and fifty equals. Now solve! Nari scored one hundred fewer points than Flying Squirrel and Speedy-pede combined. Let's review! To solve one and two step problems using a scaled picture graph: First, find the key words. Next, locate the data on the graph. Then, total the value of the data by counting according to the scaled key. Finally, setup up the equation and solve! Repeat all of the steps once more if there is another part. Did Nari improve since the last race? Yes, but he can't seem to reach first place. Turbo Mouse has done it again! Who is this TURBO MOUSE?!
Solving 1- and 2-step problems using scaled picture graphs exercise
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Reading a pictogram.
HintsLook at the scale and work out what each star represents. Then you will be able to count up by that amount.
If there is only half of a star shown, it represents half of the whole star.
Half of 100 is 50, so half of a star is 50 points.
SolutionFirst, look at the scale to see what each image represents. Each star represents 100 points for this pictogram graph. Then, look at the specific animal and count up in 100's for each star. If there is half a star, then you will add 50.
Turbo Mouse has 500 points. Nimble Nari has 250 points.
Flying Squirrel has 450 points. Speedy-pede has 350 points.
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How many more points did Flying Squirrel score than Nimble Nari?
HintsLook at the scale and work out what each star represents. Then you will be able to count up by that amount.
If there is only half of a star shown, it represents half of the whole star.
The question asks how many more points Flying Squirrel scored than Nimble Nari. Think about what equation will help you to solve this.
SolutionBy looking at the graph, we can see Flying Squirrel scored 450 points and Nimble Nari scored 250 points.
We need to work out how many more points Flying Squirrel scored than Nimble Nari.
To work this out you can subtract 450 - 250 = 200, or count up starting at 250 and ending at 450, which is also 200.
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Compare how many points some of the animals scored.
HintsLook at the scale and work out what each star represents so you know what to count by.
If there is only half of a star shown, it represents half of the whole star.
Work 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:
- The first part of the question to work out is: how many points did Turbo Mouse and Flying Squirrel score together? So, 350 + 250 = 600.
- The last part of the question to work out is: how many more points did Turbo Mouse and Flying Squirrel score than Nimble Nari? To do this, you can subtract 600 - 500 = 100 or you can count up starting at 500 and ending at 600, which is also 100.
For the second question:
- We need to work out how many fewer points Flying Squirrel scored than Speedy-pede.
- To do this, you can subtract 450 - 250 = 200 or count up starting at 250 and ending at 450, which is also 200.
- We need to work out how many more points Nimble Nari scored than Turbo Mouse.
- To do this, you can subtract 500 - 350 = 150 or count up starting at 350 and ending at 500, which is also 150.
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Solve the word problems by looking at the picture graph.
HintsLook at the scale and work out what each book represents so you know what to count by.
If the question asks how many more or how many fewer, think about what equation will help you solve this.
SolutionFor the first question:
- We need to work out how many more Year 3 read than Year 5.
- To work this out, we can subtract 12 - 4 = 8 or count up starting at 4 and ending at 12, which is also 8.
- The first part of the question to work out is: how many books did Year 4 read? 16.
- Then we need to work out how many book Year 5 read: 4
For the third question: *First we need to work out how many books Year 6 read: 12 *Next we look to see how many books Year 2 read: 4 *Finally we subtract the total to get our answer: 12 - 4 = 8
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How many more children chose piano than drums?
HintsLook at the scale and work out what each smiley face represents. Then you will be able to count up by that amount.
The question asks how many more chose piano than drums. Think about what equation will help you solve this.
Find the number of students who chose piano and the number of students who chose drums and then subtract.
SolutionBy looking at the graph we can see 5 children chose drums and 20 children chose piano.
We need to work out how many more people chose piano than drums.
To work this out, you can subtract 20 - 5 = 15 or count up starting at 5 and ending at 20, which is also 15.
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Figure out which word problems are solved correctly.
HintsLook at the scale and work out what each ball and part of the ball represents, so you know what to count by.
Work 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.
2 answers are correct.
SolutionFor the first problem:
- we need to work out how many more games Mary played than Sam.
- to do this, you can subtract 90 - 45 = 45 or count up starting at 45 and ending at 90, which is also 45, so this answer was incorrect.
- the first part of the question to work out is: how many games Alex and John played. So, 55 + 40 = 95.
- the last part of the question to work out is: how many more games did Alex and John play than Sam. You can subtract 95 - 45 = 50 or you can count up starting at 45 and ending at 95, which is also 50, so this answer was correct.
- the first part of the question to work out is: how many games John and Mary played. So, 40 + 90 = 130.
- the last part of the question to work out is: how many fewer games did Sam play than John and Mary. You can subtract 130 - 45 = 85 or you can count up starting at 45 and ending at 130, which is also 85, so this answer was incorrect.
- the first part of the question to work out is: how many games Sam and John played. So, 45 + 40 = 85.
- the last part of the question to work out is: how many more games did Mary play than Sam and John. You can subtract 90 - 85 = 5 or you can count up starting at 85 and ending at 90, which is also 5, so this answer was correct.
