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Learning to read and create bar graphs where each unit represents more than one.
Imagine you had to count every single student in your school—hundreds of people! Would you rather draw 500 tiny stick figures, or use a secret math shortcut to show them all with just a few colorful bars?
In earlier grades, one square on a graph usually meant one object. But as numbers get bigger, we use a Scale. A scale is a series of numbers at equal distances that help us measure. Instead of counting by s, we might count by s, s, or s. This is just like skip-counting! The Vertical Axis (the line going up) shows these numbers, while the Horizontal Axis (the line going across) shows the categories we are measuring.
Quick Check
If the scale on a bar graph goes , what is the value of each unit?
Answer
Each unit represents 5.
To read a scaled bar graph, look at the top of a bar and follow it over to the Vertical Axis. If the scale is and the bar reaches the line for , you don't just have blocks; you have items. If a bar ends between two numbers, you have to use your logic. For example, on a scale of , a bar that ends halfway between and represents .
A graph shows how many apples were picked. The scale is . 1. Look at the 'Gala Apple' bar. 2. The top of the bar aligns with the number on the axis. 3. Since the scale is , we know this represents apples total. 4. Calculation: .
Graphs make it easy to see which category has the most or least. To find the difference between two bars, we use subtraction. If the 'Dogs' bar is at and the 'Cats' bar is at , we subtract: . This tells us there are more dogs than cats. Always check the scale before you subtract!
A graph shows books read by two friends. The scale is . 1. Ben's bar reaches . 2. Sarah's bar reaches . 3. To find how many more Sarah read: . 4. Sarah read more books than Ben.
Quick Check
If Bar A is 40 and Bar B is 25, how many more is Bar A?
Answer
15
When you draw a graph, you must choose a scale that fits your data. If your highest number is , counting by s would take too much space! A scale of would be better because you only need marks (). Make sure the space between every number on your axis is the exact same.
You sold cookies, brownies, and muffins. 1. Choose a scale: Since all numbers end in or , a scale of or works. Let's use . 2. Calculate bar heights: - Cookies: units high. - Brownies: units high. - Muffins: units high. 3. Draw: Label your axes and draw the bars to these heights.
If a bar graph has a scale of and a bar is units tall, what is the value?
On a scale of , where would a bar representing end?
The scale on a bar graph can change halfway up the axis (e.g., jumping by 2s then jumping by 5s).
Review Tomorrow
Tomorrow morning, try to remember: If a scale is , how many units would you draw to show the number ?
Practice Activity
Find a handful of colorful items (like cereal or LEGOs). Group them by color, then draw a quick bar graph using a scale of to represent them!