Transcript 2-5__Reason_Using_Properties_from_Algebra

5 Minute Check
2.5 Reasoning with Properties of
Algebra
• Students will use Algebraic properties in logical
arguments.
• Why? So you can apply a heart rate formula, as seen in
Ex 3.
• Mastery is 80% or better on 5-minute checks and Indy
work
Standards / Objectives:
• Standard 3: Students will learn and apply geometric
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•
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concepts.
Objectives:
Use properties from Algebra
Use properties of length and measure to justify segment
and angle relationships, such as the angles at the turns of
a racetrack.
Mastery is 80% or better on the 5-minute check.
Algebraic Properties
• Addition property
• Subtraction property
• Multiplication property
• Division property
• Reflexive property
• Symmetric property
• Transitive property
• Substitution property
Skill Development Distributive Property
• a (b + c) = ab + ac
• Can be used to solve equations
• Example:
x + 3 = 7 By subtracting 3 from each
side of the equation, you obtain 4.
Skill Development Example 1: Writing
Reasons
Solve 5x – 18 = 3x +2
1. Given
1. 5x – 18 = 3x + 2
2. Subtraction
2. 2x – 18 = 2
property
3. Addition property
3. 2x = 20
4. Division property
4. x = 10
Skill Development Example 2: Writing
Reasons
•
1.
2.
3.
4.
5.
Solve 55z – 3(9z + 12)= 64
55z – 3(9z + 12)= -64
55z – 27z – 36 = -64
28z – 36 = -64
28z = -28
z = -1
1.
2.
3.
4.
5.
Given
Distributive property
Simplify
Addition property
Division property
Example 3: Using properties in Real Life
Performance Task
• Before exercising, you should find your target
heart rate. This is the rate at which you achieve
an effective workout while not placing too much
strain on your heart. Your target heart rate (r) in
beats per minute can be determined from your
age (a) in years using the equation
• R = 50% to 85% (220-a)
• The percentage varies depending on age.
PAIR SHARE
Find the following:
a.
a = 220 – .7r
b.
Solve the equation for r and write a reason for
each step.
Use the result to find the target heart rate for a
16-year old.
Find the target rate for the following ages: 20,
30, 40, 50, and 60. What happens to the
target heart rate as a person gets older?
c.
d.
a. a = 220 – r /.70
1.
2.
3.
a = 220 – r /.70
.70a = 220 - r
r = (220 – a).7
1.
2.
3.
Given
Multiplication
Addition property
b. Using a = 16, the target rate is:
1.
2.
3.
r = .7(220 – a)
r = .7(220 – 16)
r = 142.8
The target rate for a 16 year
old is about 143 beats
per minute
1.
2.
3.
Given
Substitute 16 for a
Simplify
c. Table Info
Age
Rate
20
140
30
133
40
126
50
119
60
112
• From the table, the target
heart rate appears to
decrease as the person
gets older.
What is the Objective?
• Students will use Algebraic properties in logical
arguments.
• Why? So you can apply a heart rate formula, as seen in
Ex 3.
• Mastery is 80% or better on 5-minute checks and Indy
work
Skill Development Example 4: Using
properties of length
In the diagram, AB = CD. Show that AC = BD
1.
2.
3.
4.
5.
AB = CD
AB + BC = BC + CD
AC = AB + BC
BD = BC + CD
AC = BD
1.
2.
3.
4.
5.
Given
Addition property
Segment addition postulate
Segment addition postulate
Substitution property
Example 4 cont
Addition
Property
of
Equality
Skill Development Example 5: Using
properties of measure
Substitution
Property of
Equality
cont
Angle Addition
Postulate
Exit Slips
• Quick write about what you learned
today and what you need more help
with.
HOMEWORK
• Page 108-109
• # 1-25 All