Download 1-2 Notes

Math 1-2: Warm-up
Use the four-step plan to solve each problem.
1. At the local grocery store, a pound of potatoes cost $0.29, and a pound of
bananas cost $0.39. What combination of potatoes and bananas could you
buy for exactly $1.36?
For exercises 2-4, use the following information.
A basketball player scored 27 points in the first game, 19 points in the second
game, and 32 points in the third game.
2. Estimate the total number of points the basketball player scored.
3. About how many more points did he score in the first two games than in the
third game?
4. About how many more points did he score in the last two games than in the
first game?
5. What is the next figure in the pattern ▲►▼
A. ▲
B. ◄
C. ▼
D. ►
Math 1-2: Variables,
Expressions, and Properties
Objective: Evaluate expressions
and identify properties.
Vocabulary
1.
2.
3.
4.
5.
variable – a symbol, usually a letter, used to represent a
number.
algebraic expression – a combination of variables,
numbers, and a least one operation.
numerical expression – a combination of numbers and at
least one operation.
evaluate – to find the value of an expression by replacing
the variables with numerals.
order or operations – the rules to follow when more than
one operation is used in an expression (PEMDAS)
• P – parentheses, brackets, fraction bars
• E – exponents
• MD – multiply & divide (left to right)
• AS – add & subtract (left to right)
Vocabulary
6. powers – represent repeated multiplication.
7. equation – a mathematical sentence that
contains the equal sign
8. open sentence – an equation that contains a
variable.
9. property – an open sentence that is true for
any numbers
10. counterexample – a statement or example that
shows a conjecture is false.
Evaluate a Numerical Expression
1. Evaluate 3 + 9 – 2 x (8÷2).
Evaluate a Numerical Expression
2. Evaluate 8 + 5 x (12 – 6 ÷ 3).
Evaluate Algebraic Expressions
Evaluate each expression if q=5, r=6, & s=3
1. 3r + 2s – 4
Evaluate Algebraic Expressions
Evaluate each expression if q=5, r=6, & s=3
**fraction bar – acts as grouping tool (rewrite)
2.
6q
3r – 3
Property
Algebra
Arithmetic
Commutative
a+b = b+a
a∙b = b∙a
6+1 = 1+6
7∙3 = 3∙7
Associative
a+(b+c) = (a+b)+c
a∙(b∙c) = (a∙b)∙c
2+(3+8) = (2+3)+8
3∙(4∙5) = (3∙4)∙5
Distributive
a(b+c) = ab+ac
a(b-c) + ab-ac
4(6+2) = 4∙6 + 4∙2
3(7-5) = 3∙7 - 3∙5
Identity
a+0 = a
a∙1 = a
9+0 = 9
5∙1 = 5
Identify Properties
Name the property shown by:
1. 12∙1 = 12
2. 3(2+5) = 3∙2 + 3∙5
3. 5+(8+12) = (8+12)+5
4. 2(bc) = (2b)c
Find a Counterexample
1. The sum of an odd number and an even
number is always odd.
2. The sum of two odd numbers is always odd.
•
•
an example that shows that a conjecture is false
it only takes one counterexample to prove that a
statement is false
Assignment
• Pgs. 14-15 (14-48e)
• 1-2 Word Problems (ec)