day 2 of distributive property

Mrs. Lawrence
Algebra 1
Unit One Lesson 3:
Distributive Properties
standards: A-SSE.1A A-REI.1
Apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the
expression 3 (2 + x) to produce the equivalent expression 6 +
3x; apply the distributive property to the expression 24x + 18y
to produce the equivalent expression 6 (4x + 3y); apply
properties of operations to y + y + y to produce the equivalent
expression 3y
Check point:
*additive inverse of -9 is ?
*multiplicative inverse of 6/11 is ?
*give an example of the commutative property
of addition ______________
Warm ups:
1) Find the area of each rectangle :
A
5 in
6 cm
3 in
B
7 cm
2) Write an expression for the area of each rectangle:
4
x
C
D
5
x+3
3) Find the area of rectangles C and D when x = 3; are your answers reasonable?
4) Find the area of rectangles C and D when x = -1; are your answers reasonable?
Assignment ANSWERS:
1) The additive inverse of -8 is 8.
2) The reciprocal of 1/5 is
5.
3) The multiplicative inverse of 1 is
1.
4) Which integer has NO multiplicative inverse? 0
5) Which number is its own additive inverse? 0
6) What two numbers are their own multiplicative inverses? 1 and -1
Exercises 7 - 17: Identify the property illustrated
commutative
additive
7) -6(10)=10(-6) _________ 10) s + 0 = s __________
of multiplication
8) 1(64) = 64
multiplicative
__________
identity
9) r + t = t + r
commutative
__________
of addition
commutative
13) fxg = gxf ____________
of multiplication
identity
associative
additive
11) 6 + (10 + 8 ) = (6 + 10) + 8 ____________ 14) -d + d = _____________
of addition
associative
12) b(axc)=(bxa)xc ___________
of multiplication
inverse
15) p q = 1 multiplicative inverse
_________
q
p
or reciprocal property
Without a calculator evaluate: 3(68).
Explain your work.
We could break this problem down 3(68)
3(60 + 8) = 3(60) + 3(8)
This is an example of the DISTRIBUTIVE PROPERTY
x+2
3
x
2
3
Examples:
3(x+1)
(x-2)7
(2+5x)x
d (2-d)
Your turn...
a) -6(x+3)
b) (t+2)(-3)
c) -1(1-x)
d) (2x-3)(-4x)
Exit slip
#3
Name: ___________ Date: ____
a) simplify -5(x - 6)
b) -x(-y +4)
Exit slip
#3
Name: ___________ Date: ____
a) simplify -5(x - 6)
b) -x(-y +4)
Exit slip
#3
Name: ___________ Date: ____
a) simplify -5(x - 6)
b) -x(-y +4)
Exit slip
#3
Name: ___________ Date: ____
a) simplify -5(x - 6)
b) -x(-y +4)
Assignment:
Decide whether the statement is true or false. If false, rewrite the right-hand side of
the equation so that the statement is true:
1) 3(2+7) = 3(2) + 7
2) 7(15-6) = 7(15) - 7(6)
3) (9-2)(13) = 9 -2(13)
Use the distributive property to rewrite the expression without parentheses:
4) -s(7 + s)
5) -r (r - 9)
6) 2(3x -1)
7) (3y -2) 5y
8) -9(-t-3)
Write an expression modeling the area of the large rectangle as teh product of its length
and width. Then write another expression modeling this area as the sum of the areas of
the two smaller rectangles. Verify that the expressions are equivalent.
2x
11
x
5
4
9
Warmups...
1) Evaluate
(-3)2 = 9
x when x = -3
2
2) Evaluate |7 - 3| - |3 - 7|
|4| - |-4|
4-4=0
3) What does absolute value mean?
the distance from zero on a number line.
4) rewrite 6(x+2) using distributive property6x+12
5) convert -10 degrees celsius to Fahrenheit
1.8(-10) + 32
using F = 1.8(c) + 32
14 degrees
Discuss...
Exit slip
#3
Name: ___________ Date: ____
a) simplify -5(x - 6)
b) -x(-y +4)
5x + 30
xy - 4x
SOLUTIONS
Assignment:
Decide whether the statement is true or false. If false, rewrite the right-hand side of
the equation so that the statement is true:
1) 3(2+7) = 3(2) + 7
no 3(2) + 3(7)
2) 7(15-6) = 7(15) - 7(6)
3) (9-2)(13) = 9 -2(13)
no 9(13) - 2(13)
yes
6 + 21 = 27
7(13) = 91 117 - 26 = 91
Use the distributive property to rewrite the expression without parentheses:
4) -s(7 + s)
-7s -s2
5) -r (r - 9)
6) 2(3x -1)
6x - 2
-r2 + 9
7) (3y -2) 5y
8) -9(-t-3)
9t + 27
15y2 - 10y
Write an expression modeling the area of the large rectangle as teh product of its length
and width. Then write another expression modeling this area as the sum of the areas of
the two smaller rectangles. Verify that the expressions are equivalent.
2x
11
x
5
11(x+5); 11x + 5(11) = 11x + 55
4
9
(2x + 4)9; 2x(9) + 4(9) = 18x +36
DAY 2 of Properties
Formative assessment lesson
http://map.mathshell.org/materials/download.php?fileid=694
With your shoulder partner on a
mini white board show me...
Multiply n by 4, and then add 3 to your answer.
4n + 3
Add 3 to n, then multiply your answer by 4.
(3+n) 4 or 4(3+ n)
Add 5 to n, and then divide your answer by 3.
(5+ n)
3
Multiply n by n, and then multiply your answer by 5.
2
5n
Multiply n by 5, and then square your answer
2
(5n)
Homework
Worksheet -- Due Monday.
MAP Test tomorrow B327

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