4th Grade Math
Measurement
Unit 7
Lesson One: Units of Measurement- Metric and Customary
The world has two systems that measure length, weight, and volume. These two systems are the Metric System and the Customary System. The only countries in the world that use the customary system are the United States, Liberia, and Myanmar.
Look at the bolded words down below! They tell you the conversions in each unit! You have to use these conversions to answer questions like: how many cups are in three pints?
Here are the units for the metric system! (Most of the world)
Length: (from smallest to largest)
millimeter (tip of a pencil lead)
centimeter (as long as a staple)- (10 mm)
meter (a baseball bat)- (100 cm)
kilometer (more than 1/2 mile)- (1000 m)
Weight: (from smallest to largest)
gram (paperclip)
kilogram (seven apples)- (1000 g)
Volume: (from smallest to largest)
millileter (ten drops from medicine dropper)
liter (bottle of soda)- (1000 mL)
Here are the units for the customary system!(United States)
Length: (from smallest to largest)
inch
foot (12 inches)
yard (3 feet)
mile (5280 ft, 1760 yrd)
Weight: (from smallest to largest)
ounce
pound (16 ounces)
tons (2000 pounds)
Volume: (from smallest to largest)
cup
pint (two cups)
quart (two pints)
gallon (four quarts)
Lesson Two: Prices, Time, and Cooking
Price
When making change, there are many things you have to remember! Remember that there are 100 cents in one dollar.
With a certain amount of money, you can only afford a few things. By adding the things you want to buy and subtracting them from the total amount of money you have, you can see how much money you will have left over.
Example: Say you have $16.50 in your pocket. You want one candy bar and one book. The candy bar is $1.55 and the book is $6.45 If you add the things you want and subtract them from the amount of money you have, you can see how much money you will have left over.
So lets do it. $1.55 + $6.45 = $8. The things you are buying cost $8. If you bought these, you would still have $8.50 left to buy other things.
In the example, you only wanted to buy one of each thing. Say you wanted 3 candy bars instead of 1? How could you use math to help you figure out if you'll have any money left?
Remember, each candy bar is $1.55 and you want to buy 3. Lets learn how to multiply dollars and cents.
First, you multiply the dollars. 3x1= 3. Then, you multiply the change. 0.55x3. Forget about the decimal for now. Do it normally, 55x3.
This gives you 165. This means you owe 165 cents along with 3 dollars. Remember, there are 100 cents in a dollar. This means you owe $1.65 in change. In addition to your $3, it means you owe a total of $4.65 for 3 candy bars.
Don't forget about the book you wanted! It was $6.45. Add $6.45 + $4.65. This means you owe a total of $11.10. You had $16.50, but you just spent $11.10. If you do $16.50 - $11.10, you see that you only have $5.40 left over.
Time
Time can also be added and subtracted. Remember, there is 60 minutes in an hour and 24 hours in a day. By seeing what time something started and ended, you can see how much time has elapsed.
If Jonah starts eating food at 8:35 and he finishes at 9:20, how long was he eating for? To figure this out, you can first figure out how much time passed between 8:35 and 9:00. At 9:00, 25 minutes have passed. After that, 20 minutes passed until 9:20. 25 + 20 minutes have passed. This means that 45 minutes have passed between 8:35 and 9:20.
Recipes
Recipes sometimes involve you adding fractions that have different denominators. In these cases, you have to convert the fractions to have a common denominator.
If you add 3/8 cups of sugar and 3/4 cups of milk, how many total cups are there. You have to convert them so they have a common denominator. You can not simplify 3/8, so you have to raise the denominator of 3/4. You must change the denominator to 8. To do this, you have to multiply the numerator and denominator by 2. This shows you have 3/4 cups can be put into a common denominator and be 6/8 cups.
To figure out the total amount, you have to add 3/8 and 6/8. This is 9/8.
Lesson Three: Area and Perimeter
Finding Perimeter
Perimeter is the measurement of the distance around a shape. This distance is made up by the lengths of all the sides. To find the perimeter, you add all of the lengths.
For example, a rectangle has one side that is 6ft long and another side that is 7ft long. Remember, a rectangle has two pairs of sides that are the same. So if one side is 6ft long, then another side is also 6ft long. Same with 7ft. So you know that there are two sides that are 6ft, and another two sides that are 7ft. This means you have to add 6ft + 6ft + 7ft + 7ft which is 26ft. This means the perimeter is 26ft.
Finding Area
Area is the measurement of the space a flat shape takes up.
The area is all of the space within a shape. To find the area of a shape, all you need is two different side lengths.
Let's use the same rectangle as we used in the example above. One side length is 6ft and the other is 7ft. You can find the area by multiplying 6ft x 7ft. This tells u that the area is 42ft squared. The answer for area is always squared.
Lesson Four: Line Plots
Line plots are made with a number line, with X's placed above each point to show the data. These are a way of showing data, and they help you understand it.
Look at the line plot to the right as an example. This survey asked people how many times they took a trip to the mall last month. The amount of X's above each number show how many people went to the mall that amount of time.
For example, there are two X's above the number 2. This means that two people went two the mall twice last month.
Let's answer the question at the bottom of the picture. How many people went to the mall fewer than two times?
To answer this, we have to count the amount of X's before the number 2 on the number line. This shows the amount of people who went to the mall fewer than two times. If you count the amount of X's, you see that there are 9.
This means there are 9 people who went to the mall less than two times last month.
Lesson Five: Angles and Measuring with a Protractor
Angle Measurements
Sometimes, an angle is at a perfect measurement of 0, 90, 180, or 360 degrees. Look at the picture on the left to see what these angles look like. As you can see, a 90° angle will make a perfect right angle. A 180° angle will look straight. That’s because at a 180° angle, it only goes halfway. However, a 360° angle will have completed its rotation and be a complete angle.
When you do not have an exact angle measurement, you have to estimate the angle measures. This can be done by looking at its relation to the other angles.
When estimating angles, find their relation to the perfect angles like 90, 180, and 360. Are they smaller? Larger?
If an angle is smaller than 90° (a perfect right angle), then it is an acute angle.
If an angle is larger than 90° and smaller than 180°, then it is an obtuse angle.
Adjacent Angles
Adjacent Angles
Angles are adjacent when they combine to make up an angle.
For example, look at the picture on the right. Angles A and B combine to make the whole angle (A+B). There are three measurements- A, B, and A+B. If you are given any two measurements, you can figure out the other by addition and subtraction.
Say that angle A is 30° and angle B is 40°. What's the measurement of the whole angle (A+B)? To find this, all you have to do is add 40 and 30, and you can figure out that the whole angle is 70°.
This can also be done a different way. Say you only have the measurement of angle A, and the whole angle A+B. Angle A is 30° and angle A+B is 70°. From this, you have to figure out the measurement of angle B. You can do this by subtracting 70-30. This gives you 40°.
Given any two measurements in adjacent angles, you can find the missing measurement by addition and subtraction.
There is a tool to find an angle's exact measurement. It's called a protractor! Using it, you can find the exact measurement of any angle.