ClassX Video Lessons Subjects Algebra Absolute Value for 6th Grade | Learn how to solve absolute value equations
Have you ever seen a number with two straight lines around it, like this: |4|? That’s called the absolute value! Let’s learn some cool things about absolute value:
Let’s try an example. To find the absolute value of 4, think about how far 4 is from zero on a number line. It’s 4 spaces away, so the absolute value of 4 is 4.
What about a negative number? If we look at -3, it’s 3 spaces away from zero. So, the absolute value of -3 is 3. When the negative sign is inside the absolute value bars, the number becomes positive.
But what if the negative sign is outside the bars? Then the number stays negative.
Imagine you’re walking to your friend’s house, which is five blocks away. You walk one block, remember you forgot a gift, go back one block, and then walk five more blocks to your friend’s house. Even though your friend’s house is five blocks away, you walked a total of seven blocks.
Absolute value bars are like parentheses; they group numbers together. When solving math problems, you find the absolute value before doing other operations. For example, the absolute value of -6 + 2 is 4 because -6 + 2 equals -4, and the absolute value of -4 is 4.
Let’s solve this equation: 8 minus the absolute value of 5 – 11 + 3. First, find the absolute value of 5 – 11. That equals -6, and the absolute value of -6 is 6. Now, solve the equation: 8 – 6 + 3 equals 5.
Great job! Absolute value helps us understand distances and solve math problems. Remember, every number except zero has an absolute value, and it’s all about how far the number is from zero. Pay attention to where the negative sign is!
Now go have fun and create some amazing equations!
Draw a number line on a large piece of paper. Place different numbers on the line, including both positive and negative numbers. Then, use a ruler to measure the distance each number is from zero. Write down the absolute value of each number. This will help you visualize how absolute value represents distance from zero.
Create a scavenger hunt where you find items around your house or classroom that represent different numbers. For each item, write down a number and its absolute value. For example, if you find 3 apples, write down 3 and its absolute value, which is also 3. This activity will help you connect absolute value to real-world objects.
Work with a partner to create equations that include absolute values. Challenge each other to solve the equations. For example, you could write an equation like |5 – 8| + 2 and solve it together. This will help you practice using absolute value in mathematical operations.
Write a short story that involves a journey or a trip, similar to the real-life example in the article. Include distances and use absolute values to describe how far characters travel. Share your story with the class and see if they can identify the absolute values in your story.
Create a piece of art that represents absolute value. Use different colors to show positive and negative numbers, and use lines or shapes to represent the distance from zero. Display your artwork and explain how it relates to the concept of absolute value.
Sure! Here’s a sanitized version of the transcript, removing any unnecessary elements while keeping the educational content intact:
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**Absolute Value for Sixth Grade**
Have you ever seen a number written with two vertical lines around it? 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. To find the absolute value of 4, look at how far away the number 4 is from zero on a number line. The absolute value of 4 equals 4.
What about the absolute value of a negative number? If we look at the absolute value of -3, we can see that it is 3 units away from zero. Therefore, the absolute value of -3 equals 3. When the negative symbol is inside the absolute value bars, the value becomes positive.
Now, what happens if the negative symbol is outside the bars? In that case, the value is negative.
Let’s consider a scenario to understand how absolute value works. Imagine you are walking to your friend’s house, which is five blocks away. After walking one block, you realize you left a gift at home, so you walk back one block to retrieve it and then walk the remaining five blocks to your friend’s house.
Even though the distance between your house and your friend’s house is five blocks, you walked a longer distance overall. To find out how far you walked, you walked one block forward, one block back, and then five blocks forward, totaling seven blocks.
Absolute value bars are grouping symbols, just like parentheses. When using the order of operations, absolute value is determined before any other operation. For example, the absolute value of -6 + 2 would be 4 because -6 + 2 equals -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 is 7.
– The absolute value of -9 + -1 equals the absolute value of -10, which is 10.
– The absolute value of 7 – 7 equals the absolute value of 0, which is 0.
Now, consider the equation: 8 minus the absolute value of 5 – 11 + 3. What do you do first? If you said to find the absolute value of 5 – 11, you are correct. 5 – 11 equals -6, and since the negative symbol is inside the absolute value bars, the absolute value of -6 equals 6.
With that information, we can solve the equation: 8 – 6 + 3 equals 5.
Great job, everyone! Absolute value is useful for figuring out things like distance. 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 very important.
Now go have fun and create some amazing equations!
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Feel free to ask if you need any further modifications!
Absolute Value – The distance of a number from zero on a number line, without considering direction. – The absolute value of -5 is 5 because it is 5 units away from zero.
Number – A mathematical object used to count, measure, and label. – The number 7 is an odd number and comes after 6.
Zero – The integer that represents no quantity or amount; it is neither positive nor negative. – When you subtract 5 from 5, the result is zero.
Negative – A number less than zero, often represented with a minus sign. – The temperature was negative 3 degrees Celsius this morning.
Positive – A number greater than zero. – The positive numbers on the number line are to the right of zero.
Distance – The amount of space between two points, often measured in units. – The distance between point A and point B on the graph is 4 units.
Equation – A mathematical statement that shows the equality of two expressions. – In the equation 3 + x = 7, you need to find the value of x.
Math – The study of numbers, quantities, shapes, and patterns. – We use math to solve problems and understand the world around us.
Spaces – Gaps or intervals between objects or points, often used in geometry. – There are equal spaces between each tick mark on the ruler.
Bars – Symbols used in mathematics to denote absolute value or to group terms. – The bars around -8, written as |-8|, indicate that we are finding the absolute value.
