Compare and Order Integers - Twinsburg 3 Study Guide...comparing integers. -4 < 3 Negative 15, 4 is...
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Chapter 3 This study sheet provides students and parents with the basic concepts of each chapter. Students still need to apply these skills in context. They need to know when to apply each concept, often after working through a word problem, table, chart, or graph. Some problems may be more challenging than the ones shown here, but students first need to understand these basic concepts. There are usually several ways to solve a math problem, but this guide will show you the easiest way for 6 th graders. The sections are listed in the order that I plan on teaching them, and that is subject to change. We do not use every section of the textbook. Click on the blue links to navigate through the study guide. You can also view videos at Khan Academy and Virtual Nerd. Section 3.1 Topic: Understand Positive and Negative Numbers Common errors to avoid: Try this problem on another sheet of paper: Practice more at these websites: Integers include whole numbers and their opposites. They can be positive or negative. Two numbers are opposites if they are the same distance from 0 on a number line, but on opposite sides of 0. Example: What is the opposite of -3? Step 1 Graph the integer -3 is a negative number so we must graph it 3 steps to the left of zero. Step 2 Now, graph the number’s opposite on a number line. Since -3 is three places to the left of 0, its opposite (3) will be three places to the right of zero. Number lines can also be vertical, like this On a vertical number line, positive numbers are located at the top and negative numbers are located at the bottom. Be sure to use the correct words. The number -2 is read “negative two” not “minus two.” Using words such as minus and plus to describe negative and positive numbers can become confusing when subtracting, adding and comparing negative and positive numbers. Name the integer that represents the following situation. “Sam lost 7 lbs. after two months of dieting. “ Graph this number and its opposite on a number line. Answer Integers and Number Lines IXL.com Section 3.2 Topic: Compare and Order Integers Common errors to avoid: Try this problem on another sheet of paper: Practice more at these websites: To compare integers and order integers, place them on a number line. Integers to the right are greater, and integers to the left are less. Compare the following numbers on a number line. 3, -6, 1, 5, -9, -2 We can see the correct least-to-greatest order is -9 < -6 <-3 < -2 < 1 < 3 < 5 On a vertical number line, the numbers located at the bottom are less and the numbers located at the top are greater. Don’t forget to look at the sign of each number when comparing integers. -4 < 3 Negative 4 is less than 3. Order the following integers from greatest to least. 15, -20, 0, -2, -6 Answer Space Race IXL.com
Transcript of Compare and Order Integers - Twinsburg 3 Study Guide...comparing integers. -4 < 3 Negative 15, 4 is...
Chapter 3
This study sheet provides students and parents with the basic concepts of each chapter. Students still need to apply these skills in
context. They need to know when to apply each concept, often after working through a word problem, table, chart, or graph. Some
problems may be more challenging than the ones shown here, but students first need to understand these basic concepts. There
are usually several ways to solve a math problem, but this guide will show you the easiest way for 6th
graders. The sections are listed
in the order that I plan on teaching them, and that is subject to change. We do not use every section of the textbook.
Click on the blue links to navigate through the study guide. You can also view videos at Khan Academy and Virtual Nerd.
Section
3.1
Topic:
Understand Positive and Negative Numbers
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
Integers include whole numbers and their opposites. They can be positive or negative. Two numbers are opposites if they are the same distance from 0 on a number line, but on opposite sides of 0. Example: What is the opposite of -3? Step 1 Graph the integer
-3 is a negative number so we must graph it 3 steps to the left of zero. Step 2 Now, graph the number’s opposite on a number line.
Since -3 is three places to the left of 0, its opposite (3) will be three places to the right of zero. Number lines can also be vertical, like this On a vertical number line, positive numbers are located at the top and negative numbers are located at the bottom.
Be sure to use the correct words. The number -2 is read “negative two” not “minus two.” Using words such as minus and plus to describe negative and positive numbers can become confusing when subtracting, adding and comparing negative and positive numbers.
Name the integer that represents the following situation. “Sam lost 7 lbs. after two months of dieting. “ Graph this number and its opposite on a number line. Answer
Integers and Number Lines
IXL.com
Section
3.2
Topic:
Compare and Order Integers
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
To compare integers and order integers, place them on a number line. Integers to the right are greater, and integers to the left are less. Compare the following numbers on a number line. 3, -6, 1, 5, -9, -2
We can see the correct least-to-greatest order is -9 < -6 <-3 < -2 < 1 < 3 < 5 On a vertical number line, the numbers located at the bottom are less and the numbers located at the top are greater.
Don’t forget to look at the sign of each number when comparing integers. -4 < 3 Negative 4 is less than 3.
Order the following integers from greatest to least.
15, -20, 0, -2, -6 Answer
Space Race
IXL.com
Section
3.4
Topic:
Compare and Order Rational Numbers
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
In the same way we can compare and order Integers with a number line (Lesson 3.2), you can also use a number line to compare and order rational numbers. Rational numbers include decimals and fractions.
When comparing and ordering rational numbers, don’t forget to look at the signs for each number. Negative numbers will always be less than positive numbers.
1. Compare. Write < or >
2. Order the numbers from least to greatest.
1.3, -4
, -
Answer
Compare Jeopardy Math Games
IXL.com
Section
3.5
Topic:
Absolute Value
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
Absolute value is a number’s distance from zero on a number line. For example, the absolute value of -2 is 2, since -2 is 2 steps from zero.
The absolute value of +3 is 3, since +3 is 3 steps from zero.
The absolute value of a number is always positive. Do not simply find the opposite of a number when finding the absolute value. Common Error:
|
| ≠ -
Correct Answer:
|
| =
Find the absolute value.
1.|-3
| = ____
2.|8.56|= ____ Answer
Absolute Value Millionaire Absolute Value Balloons
Section
3.6
Topic:
Compare Absolute Value
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
We can use absolute value to compare many situations in the real world. The table below shows the weight changes of three dogs.
If we take the absolute value of each weight change, we can compare the changes and find which dog’s weight changed the most, no matter if it’s a gain or a loss. Duffy |1.3| = 1.3 lbs. Buddy |-1.1| = 1.1 lbs. and Dinah |-1.4| = 1.4 lbs. So, Dinah’s weight changed the most (1.4 lbs.).
Write down the actual value of each number in order to compare them!
A school of fish were swimming at the same depth. Fish #1 dove to a depth of -15 feet. Fish #2 rose 18 feet toward the surface and Fish #3 dove to a depth of -19 feet. Which fish had the greatest change in depth?
Answer
Compare Absolute Values Absolute Value Boxes
-
- - -
-
- -
Section
3.7
Topic:
Rational Numbers and the Coordinate Plane Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
An ordered pair is a pair of numbers such as (5, -2).
To plot the ordered pair (5, -2): First, start at 0 on the x-axis and because 5 is a positive number, we will count 5 units to the right. Second, starting at 5 on the x-axis we will count down 2 units because our y-coordinate is a negative number (-2).
(5, -2) Sometimes we can take a fraction of a step, such as a half
step.
Remember, x-coordinate is graphed first, then the y-coordinate is graphed.
Graph and label the following ordered pairs. A (-3, 6) B (1.5, -2.5) Answer
Coordinate Soccer
Find the Alien
Section
3.8
Topic:
Ordered Pair Relationships Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
There are four regions in a coordinate plane. They are separated by the x-axis and y-axis. These four regions are called quadrants. Quadrants are numbered using Roman numerals I, II, III and IV. (1, 2, 3 and 4).
We say that the point (1, 4) is located in Quadrant I and the point (3, -4) is located in Quadrant IV.
Quadrant I starts in the top right of the coordinate grid and moves counterclockwise until you reach Quadrant IV. Draw a giant C-shape on the grid, and you will pass through the quadrants in order.
Name the quadrants that the following coordinate pairs are in. A (-3, -2) B (2, 5) C (-4, 1) D (3, -5) Answer
Quadrant Basketball IXL.com
Section
3.9
Topic:
Distance on the Coordinate Plane
Common errors to avoid:
Try this problem on another sheet of paper:
Practice more at these websites:
We can use a coordinate plane as a map to find distance between two points. Example: Find the distance between (4, -2) and (4, 3). Step 1: Graph the points. Step 2: Count the distances between the two points along a straight line. Step 3: Double check!
The easiest way to find distance is to draw in each step and count them.
Find the distance between (-3,5) and (4,5). Answer
Distance Game IXL.com
Section Answer Return to Study Guide
3.1
Sam lost 7 lbs. So the integer that would represent the situation is -7. The opposite of -7 is 7.
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Section Answer Return to Study Guide
3.2
Order the following integers from greatest to least.
15 > 0 > -2 > -6 > -20 (Remember it said “greatest to least” not “least to greatest”.)
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Section Answer Return to Study Guide
3.4
1. Compare. Write < or >
because -
is farther to the right on a
number line.
2. Order the numbers from least to greatest.
- 4
< -
< 1.3
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<
Section Answer Return to Study Guide
3.5
Find the absolute value.
1.|-3
| = 3
2.|8.56|= 8.56
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Section Answer Return to Study Guide
3.6
A school of fish were swimming at the same depth. Fish #1 dove to a depth of -15 feet. Fish #2 rose 18 feet toward the surface and Fish #3 dove to a depth of -19 feet. Which fish had the greatest change in depth?
Fish Change in depth (ft.)
Fish #1 -15
Fish #2 18
Fish #3 -19
|-15| = 15 |18| = 18 |-19| = 19 Fish #3 had the greatest change in depth (19 ft.).
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Section Answer Return to Study Guide
3.7
Graph and label the following ordered pairs. A (-3, 6) B (1.5, -2.5) A (-3, 6)
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B (1.5, -2.5)
Section Answer Return to Study Guide
3.8
Name the quadrants that the following coordinate pairs are in. A (-3, -2) – Quadrant III (3) B (2, 5) – Quadrant I (1) C (-4, 1) – Quadrant II (2) D (3, -5) – Quadrant IV (4)
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Section Answer Return to Study Guide
3.9
The distance between (-3, 5) and (4, 5) is 7 units.
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