Download Topic 10 guided notes

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Key Words/Topic
and Assignments
10.1 & 10.2 Understanding
Integers & Comparing and
Ordering Integers
Topic 10 Guided Notes
Integers
Information, Definitions, Solutions
New Terms
Integers are made up of the ______________ _____________, their
opposites, and ________. They can be positive or negative.
Opposites are numbers that are the same ____________ from zero.
Absolute value measures the distance from _________. The distance is
ALWAYS expressed as a positive value.
Today’s Concept
So far we’ve expressed all answers as positive numbers.
Numbers that are to the right of 0 on a number line. When
we include numbers to the left of 0, with 0 and the numbers
to the right of zero, we have the set of integers.
Numbers to the left of 0 on a number line are called negative
numbers. In order to write a negative number you place a
subtraction sign to the left of the number, so -3 is negative
three.
As you move farther to the left the value of the numbers get
smaller, so -12 is smaller than -3. We can measure the
distance away from 0 by using absolute value. The absolute
value symbol is two vertical parallel lines that surround the
number. For example | -3 | is read “the absolute value of
negative three”.
To get the absolute value of any number you simply drop the
absolute value symbol and the sign of the number. So |-3|
=3 and |3|=3. So -3 and 3 are the exact same distance away
from 3.
Any numbers that are the exact same distance from zero
are opposites.
Group Work
1-9 odd on page 222 & 1-11
p. 224
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Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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HOMEWORK: 11-19 P.
222 & 13-31 odd p. 225 in
textbook.
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Key Words/Topic
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10.3 Rational Numbers on
a number line
Information, Definitions, Solutions
New Terms
Rational Numbers Any ____________ that can be shown as a _________ of
two integers are called ____________ _____________.
Review Terms
Whole numbers 0 and the counting numbers (1,2,3…etc.)
Integers are made up of the ______________ _____________, their
opposites, and ________. They can be positive or negative
numbers.
Opposites are numbers that are the same ____________ from zero.
Absolute value measures the distance from _________. The distance is
ALWAYS expressed as a positive value.
Today’s Concept Rational numbers are any numbers that can be written as a
quotient of two integers (as a ratio). We write this
algebraically as:
For any integers a and b (b≠0), a/b=a÷b
Decimals, fractions, and whole numbers are all rational
numbers. You often have to make comparisons of rational
numbers, both positive and negative. Use what you’ve
already learned this year to compare rational numbers.
1-4
Group Work
1-9 on page 227.
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6.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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HOMEWORK: 10-30 even
P. 227 in textbook.
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Group Work
1-9 on page 227.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 10-30 even
P. 227 in textbook.
Key Words/Topic
and Assignments
10.4 Adding integers
Information, Definitions, Solutions
Today’s Concept When adding integers, or subtracting integers, there are
algorithms (plans) that you can use every time to get the
correct answer no matter the size or complexity of the
equation’s numbers.
Addition of Integers Algorithms
Adding Integers with the same sign – Use when adding
positive numbers to other positive numbers or when adding
negative numbers to other negative numbers.
1. Remove the signs (determine the absolute value of the
numbers- remember absolute value represents the
distance away from 0).
2. Add the absolute values of the numbers together.
3. Place the sign back onto your answer if negative.
Group Work
1-9 on page 231.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 11-35 odd
P. 232 in textbook.
Ex +4 + +8 =
Steps 1 & 2. Drop signs & add 4 + 8 = 12
Ex -4 + -8 =
Steps 1 & 2. Drop signs & add 4 + 8 =12
Step 3. Put the sign back -12
Adding Integer with different signs – Use when adding
positive numbers to negative numbers or when adding
negative numbers to positive numbers.
1. Remove the signs (determine the absolute value of the
numbers- remember absolute value represents the
distance away from 0).
2. Subtract the smaller absolute value from larger
absolute value.
3. Put the sign of the number that had the largest
absolute value from the problem on the answer.
Ex +4 + -8 =
Steps 1 & 2. Drop signs & subtract 8 – 4 = 4
Step 3. Put the sign back of the number with the largest
absolute value -4
Another example: -4 + +8 = 8 – 4 = +4
Group Work
1-9 on page 231.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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2.
HOMEWORK: 11-35 odd
P. 232 in textbook.
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Key Words/Topic
and Assignments
10.5 Subtracting Integers
Information, Definitions, Solutions
Today’s Concept One algorithm works for Subtracting Integers with the
same sign and Subtracting Integers with different signs.
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Leave the 1st number alone – don’t change anything.
Change the subtraction sign into an addition sign.
Change the 2nd number into its Opposite.
Now use the correct addition algorithm above!
Ex -4 - -8 =
Step 1 & 2. -4 + -8 =
Step 3. -4 + 8 =
Step 4. Use the correct addition algorithm from 10.4
8 – 4 = 4 so -4 - -8 = 4
Ex. -4 - +8 = -4 + -8 = 8 + 4 = -12
Group Work
1-10 on page 235.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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2.
HOMEWORK: 16-28, 34 P.
235 in textbook.
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Group Work
1-10 on page 235.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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HOMEWORK: 16-28, 34 P.
235 in textbook.
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Key Words/Topic
Information, Definitions, Solutions
and Assignments
10.6 & 10.7 Multiplying
Integers & Dividing
Integers
Today’s Concept If you know how to do basic multiplication and division, you
only need to remember a few rules to multiply using
integers.
Multiplication Rules
The product of two integers with the same sign is positive.
So + * + = +, 3*3 = 9
& -*- = +, -3*-3 = 9
The product of two integers with different signs is
negative.
So + * - = -, 3*-3 = -9
& -*+ = -, -3*3 = -9
Group Work
1-7 on page 238 &
1-9 on page 240.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 14-24 p.
238 and 16-30 p. 240 in
textbook.
Division Rules
The quotient of two integers with the same sign is
positive.
So + ÷ + = +, 3÷3 = 1
& -÷- = +, -3÷-3 = 1
The quotient of two integers with different signs is
negative.
So + ÷ - = -, 3÷-3 = -1
& -÷+ = -, -3÷3 = -1
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Group Work
1-7 on page 238 &
1-9 on page 240.
1.
2.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
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HOMEWORK: 14-24 p.
238 and 16-30 p. 240 in
textbook.
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Key Words/Topic
and Assignments
10.8 Solving equations
with integers
Information, Definitions, Solutions
Today’s Concept Use what you’ve learned to solve equations with integers.
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Group Work
1-6 on page 242.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
4.
HOMEWORK: 12- 26 P.
244 in textbook.
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Key Words/Topic
and Assignments
10.9 Graphing points on a
coordinate plane
Information, Definitions, Solutions
New Terms
Coordinate Plane is a _______ containing two __________ _________ that
______________ in a right angle at _______.
x- and y-axes Number lines that ___________ the plane ________ four
_____________.
Quadrants There are four of these in a coordinate plane. They are
numbered I-IV (roman numerals) in a counter clockwise
manner with quadrant 1 in the northeast quadrant.
Ordered pair Gives the _________________ that locate a point
__________ to each axis. This is like an address on the
coordinate plane. Every point has an address that is
identified by the coordinate pair. The x-coordinate is
ALWAYS listed first.1.
Origin The location (0,0) on a coordinate plane.
Today’s Concept Coordinate planes are used all the time in math and the “real
world”. One of the most used applications for using
coordinate points on a coordinate plane is map reading.
Every ordered pair has two bits of data, an x value and a y
value.
Group Work
1-5 on page 246.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 6-22, 24-26
P. 247 in textbook.
The x value is always listed first. If the value is positive,
you move right along the x-axis. If the value is negative,
you move left along the x-axis.
The y value is always listed second. If the value is positive,
you move up along the y-axis. If the value is negative, you
move down along the y-axis.
Group Work
1-5 on page 246.
1-3.
Show work when
appropriate.
Use complete sentences
when appropriate.
Don’t forget your labels.
HOMEWORK: 6-22, 24-26
P. 247 in textbook.
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