Grade 1 Math: Comparing Things (Length, Capacity, and Area)
Hello! Welcome to your math studies. The "Comparing Things" skills we are about to learn are very important in our daily lives. Let's learn how to use math to correctly answer questions like, "Which pencil is longer?" or "Which cup can hold more juice?"
It might feel a bit tricky at first, but once you master the key points, you'll be fine. Let's work through this together and have fun!
1. How to Compare Lengths
There are a few rules for comparing lengths. By learning the right method rather than just "eyeballing" it, you will be able to compare things accurately.
① Align the Edges (Direct Comparison)
When comparing the length of two items, the most important thing is to "align the edges." If one side is uneven, you can't tell for sure which one is longer.
Example: Stand two pencils up on a desk and align their bottoms perfectly.
② Using Another Object (Indirect Comparison)
When comparing things you can't move (like a desk at school and a desk at home), use a "piece of string" or a "paper tape." You can mark the length of one item on the string and then use that to compare it to the other item.
③ Using "How Many" (Arbitrary Units)
You can use items of the same size, such as erasers or blocks, to compare things by counting, like "3 blocks long" vs. "5 blocks long." This will become the foundation for learning units like centimeters (cm) in the future.
Key Points:
・Keep it straight when comparing (it won't measure accurately if it's bent).
・Always make sure to "align the edges."
【Common Mistake】
Sometimes, people try to judge the length of items placed diagonally just by looking at them. Always remember to lay them "straight" and "align the edges."
2. How to Compare Capacities (Volume/Liquid Comparison)
"Capacity" refers to the amount of liquid or substance a container can hold.
① Transfer to Containers of the Same Shape
When comparing the amount of water in differently shaped plastic bottles, relying only on your eyes can be misleading. In such cases, try transferring the water into "cups of the exact same shape." The one with the higher water level has the larger "capacity."
② Fill Until One Is Full
Try pouring water from Cup A into Cup B:
・If the water overflows from Cup B... A has more
・If Cup B does not become full... B has more
③ Counting "How Many" with a Smaller Container
Just like with length, you can use a small cup to count and express the amount, such as "This bucket is 10 cups" or "That bucket is 8 cups."
Key Point:
・When comparing capacity, be careful not to spill any while pouring!
【Fun Fact】
In Japanese, the word for capacity, "kasa," sounds exactly like the word for "umbrella." In math, however, it refers to "volume" (the amount of space something takes up).
3. How to Compare Areas
Finally, here is how to compare "area," such as the size of a park or a sheet of origami paper.
① Try Overlapping
If you have two pieces of paper, you can "overlap" them; the one that sticks out is the larger one. Here, too, it is important to align the corners properly.
② Count the Grid Squares
Imagine a floor covered in tiles. You can tell which is larger by counting how many squares of the same size fit into each area.
Example: Shape A is 6 squares, and Shape B is 4 squares. Therefore, A is larger!
Key Point:
・Even if the shapes are different, if one has more grid squares, it is "larger."
Summary: The Secrets of Comparing
The basics of "Comparing Things" taught in Grade 1 come down to these three points:
1. Standardize the conditions: Align the edges or use the same containers to ensure a fair comparison.
2. Use tools: It is helpful to use intermediate items like string or small cups.
3. Convert to numbers: By counting how many units something is, you can explain it clearly to anyone.
At first, you might find it hard to tell which is the longest or which holds the most. But as you pick up different objects and check them with your own eyes, you will start to understand intuitively. Try looking for things around you that you can compare and give it a try!