Have you ever seen a number with two straight lines around it, like this: |4|? Those lines are called absolute value bars, and they have a special meaning. Let’s explore what absolute value is all about!
Absolute value is a way to describe how far a number is from zero on a number line. Here are some key points to remember:
Let’s try an example. To find the absolute value of 4, think about how far 4 is from zero on a number line. The absolute value of 4 is 4 because it’s 4 units away from zero.
Now, what about a negative number? Consider -3. The absolute value of -3 is 3 because -3 is 3 units away from zero. When the negative sign is inside the absolute value bars, the value becomes positive.
But what if the negative sign is outside the bars? Then the value remains negative.
Imagine you’re walking to a friend’s house for a birthday party. Their house is five blocks away. You walk one block, realize you forgot the gift, walk back one block, and then walk five more blocks to reach the house. Even though the distance between your house and your friend’s is five blocks, you walked more than that.
To find out how far you walked, use absolute value. You walked one block forward, one block back, and then five more blocks forward, totaling seven blocks.
Absolute value bars work like parentheses in math. When solving an equation, you handle what’s inside the bars first. For example, the absolute value of -6 + 2 is 4 because -6 + 2 equals -4, and the absolute value of -4 is 4.
Here are some more examples:
Let’s solve an equation: 8 minus the absolute value of 5 – 11 + 3. First, find the absolute value of 5 – 11, which is -6. The absolute value of -6 is 6. Now, solve the equation: 8 – 6 + 3 = 5.
Absolute value is cool because it helps us understand distances and even weather changes. Remember, every number except zero has an absolute value, and the position of a negative sign is crucial.
Now, go ahead and create some amazing equations using absolute value!
Hope you enjoyed learning with us! Visit us at learn.org for more fun resources and learning tools.
Draw a number line on a large piece of paper or use a whiteboard. Place different numbers on the line, both positive and negative. Your task is to find the absolute value of each number by measuring how far it is from zero. Use a ruler to measure the distance and write the absolute value next to each number.
Create a scavenger hunt where you find objects around the classroom or home that represent different numbers. For example, find 4 pencils for the number 4 or 3 erasers for the number -3. Calculate the absolute value of each number and explain why the absolute value is always positive.
Work in pairs to solve a series of equations that involve absolute values. Each correct answer will give you a clue to solve a larger puzzle or riddle. Make sure to handle the numbers inside the absolute value bars first, just like parentheses!
Write a short story about a journey you take, similar to the birthday party example. Include different distances you travel forward and backward. Calculate the total distance using absolute values and share your story with the class.
Research the temperatures of a city over a week. Plot these temperatures on a graph, including both positive and negative values. Calculate the absolute value of each temperature to understand how far each is from zero, and discuss how absolute values help in understanding temperature changes.
Sure! Here’s a sanitized version of the transcript:
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**Absolute Value for Sixth Grade**
Have you ever seen a number written like this before? What do you think those two lines represent? If you said absolute value, you are exactly right! Here are three things to remember about absolute value:
1. Every number except zero has an absolute value.
2. The absolute value of a number is determined by its distance from zero on a number line.
3. The placement of a negative symbol inside or outside of the absolute value bars is very important.
Let’s try an example. If you were to figure out the absolute value of four, you would look at how far away the number four is from the number zero on a number line. The absolute value of 4 equals 4.
What about the absolute value of a negative number? Let’s take a look at what happens when the negative symbol is inside the absolute value bars. If we count the distance from zero again, we can see that the absolute value of -3 equals 3 because -3 is 3 units away from zero. So, if the negative symbol is on the inside of the absolute value bars, the value becomes positive.
What do you think happens if the negative symbol is on the outside of the bars? In that case, the value is negative.
Let’s do an example looking at distance to help us see how absolute value works. Pretend that you are walking to your friend’s house to go to a birthday party and that their house is five blocks away from yours. After you have walked one block, you realize you left your friend’s birthday gift at home, so you walk back one block to grab it and then walk the remaining five blocks to get to your friend’s house.
Even though the distance between your house and your friend’s house is five blocks, you definitely walked a longer distance than that to get there. So how do you find out how far you walked? Well, first you walked forward one block, then you walked back one block, and then you walked five more blocks to your friend’s house.
To find out the total distance, let’s create an equation using absolute value. You walked one block forward, one block back, and then five more forward for a total of seven blocks.
Absolute value bars are a grouping symbol, just like parentheses. When using the order of operations to solve an expression or equation, absolute value is determined before any other operation, which means you always do what is inside the bars first before determining the answer.
So, the absolute value of -6 + 2 would be 4 because -6 + 2 = -4, and the absolute value of -4 is 4.
Here are a few more examples:
– The absolute value of 4 + 3 equals the absolute value of 7, which equals 7.
– The absolute value of -9 + -1 equals the absolute value of -10, which equals 10.
– The absolute value of 7 – 7 equals the absolute value of 0, which equals 0.
Say you have an equation that looks like this: 8 minus the absolute value of 5 – 11 + 3. What do you do first? If you said to figure out the absolute value of 5 – 11, you are correct. 5 – 11 = -6, and since the negative symbol is on the inside of the absolute value bars, we know that the absolute value of -6 equals 6.
With that information all figured out, we are ready to solve the equation: 8 – 6 + 3 = 5.
Nice work, everyone! Absolute value is pretty cool because you can use it to figure out useful things like distance and weather. Remember that every number besides zero has an absolute value, which you determine by measuring a number’s distance from zero, and that the position of a negative symbol is super important.
Now go have fun and create some amazing equations!
Hope you had fun learning with us! Visit us at learn.org for thousands of free resources and turnkey solutions for teachers and homeschoolers.
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Let me know if you need any further modifications!
Absolute – The distance of a number from zero on the number line, without considering direction. – The absolute value of -5 is 5 because it is 5 units away from zero.
Value – The numerical worth or amount of a number or expression. – In the equation 3x + 2 = 11, the value of x is 3.
Number – A mathematical object used to count, measure, and label. – Seven is a number that comes after six and before eight.
Distance – The amount of space between two points, often measured in units. – The distance between 3 and 7 on the number line is 4 units.
Zero – The integer that represents no quantity or amount; it is the neutral element in addition. – When you add zero to any number, the number stays the same.
Negative – A number less than zero, often representing a loss or deficiency. – The temperature was negative five degrees, which means it was below freezing.
Positive – A number greater than zero, often representing a gain or increase. – The positive numbers on the number line are to the right of zero.
Blocks – Units of measurement used to represent quantities in a visual or physical form. – We used blocks to model the equation 2x + 3 = 7 in class.
Equation – A mathematical statement that shows the equality of two expressions. – The equation 4 + x = 9 can be solved to find that x equals 5.
Units – Standard quantities used to specify measurements. – In the problem, we measured the length of the rectangle in units of centimeters.
