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A mathematics resource for parents, teachers, and students
Further investigations:
Rational Reasoning
Help your student record the daily changes in
two or three stocks.
Students will:
•
Play board and card games with positive and
negative numbers such as Monopoly, Integer
War, and Spades.
•
When watching football games, guide your student in recording gains and losses of yardage.
•
Discuss real life applications of positive and
negative numbers such as temperature, checkbook, and height above or below sea level.
Terminology:
Absolute value: The distance between a
number and zero on the number line.
|-8| =|8| = 8
Additive inverse: The value added to a
number to give a sum of 0. A number and
its additive inverse form a zero pair.
Distributive property: The sum of two
addends multiplied by a number will be the
sum of the product of each addend and the
number.
a(b+c) = ab + ac
Integers: The set of whole numbers and
their opposites. {…, -3, -2, -1, 0, 1, 2, 3, …}
Multiplicative inverse: The value multiplied by a number to give a product of 1.
Reciprocals are multiplicative inverses.
Multiplicative inverses always have the
same sign.
Natural numbers: The set of numbers {1,
2, 3, 4, …}
Negative numbers: The set of numbers
less than 0.
Opposite numbers: Two different numbers
that have the same absolute value -5 and 5
Positive numbers: The set of numbers
greater than 0.
Rational numbers: The set of numbers
that can be written a/b where a and b are
integers and b≠0.
Whole numbers: The set of numbers
{0, 1, 2, 3, 4, …}
Zero pair: A number and its opposite. The
sum of a zero pair is 0. -7 + 7 = 0
Seventh Grade 3 of 7
Compare and order positive and negative numbers, plot them on the number line, plot
them in the coordinate plane, and use absolute value to explore the relationship between
a number and its additive inverse
Investigate positive and negative numbers in real contexts and develop models and algorithms for computing with them
Apply properties of real numbers and order of operations to simplify and evaluate algebraic expressions involving positive and negative rational numbers
Solve problems by writing and solving equations and interpreting their solutions.
•
Classroom Cases:
1. Kumar was playing a game. He had 34 points, but then he lost points on three turns and found
that he had only 22 points. Draw a model to represent this problem and use it to find out how many
points, on average, Kumar lost on each turn. Write and solve an equation to determine the number
of points lost per turn.
Case Closed - Evidence:
34 points
Lost points
Lost points
Lost points
Lost points
Lost points
22 points
i t
34 - 22 = 12
Lost points
12 points
12 / 3 = 4 On average, 4 points were lost on each of the last 3 turns.
Let p = the points lost per turn.
Then
34 + 3p =22
- 34
-34
34
3p = -12
3p
12
3
3
p = -4
Kumar lost 4 points per turn.
2
2. Graph these numbers on a number line and answer the questions:
A. Which number has the greater absolute value: 1.5 or -1
3
5
3
, -0.6, -1
1
2
, 1.5, 0, -1
3
5
.
? How do you know?
B. Which of the fractions and mixed numbers represent terminating decimals? How do you kn
Case Closed - Evidence:
-1 1 /2
_
-1 3 /5
_
_- 2
3
Quadrant: One of the four sections into
which the coordinate plane is divided by the
x– and y– axes.
Kathy Cox, State Superintendent of Schools
3
A. -1 5 =1 5 = 1.6
1
- 0 .6
_
_- 1
1.5 = 1.5
0
_
2 /3
_
1 .5
_
_1
_2
3
Since 1.6 is farther to the right on the number line than 1.5, -1
> 1.5 .
5
3
B. -1 2 and -1 5 Since the denominators of these mixed numbers are factors of 100 (or a power of 10),
the mixed numbers represent terminating decimals: -1.5 and –1.6 respectively.
3. Evaluate the following expressions when a = -3, b = 5, and c = -4.
B. 4a2 - 1
A. ac - 2b
C. 2(b - c)-6a
D. 3b + (7- a)2-5b
Case Closed - Evidence:
A. -3
. -4 -2 . 5 = 2
. (-3)2 -1=35
C. 2(5-(-4)) - 6 . -3=36
D. 3 . 5 + (7 - (-3))2 - 5 . 5 = 90
B. 4
Book’em:
Related Files:
www.ceismc.gatech.edu/csi
The Number Devil - A Mathematical Adventure by Hans Magnus Enzensberger
Produced by the Center for Education Integrating Science, Mathematics, and Computing at Georgia Tech in cooperation with the Georgia DOE. ©2008, 2009 Georgia Institute of Technology