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

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 ReasonsSolve 5x – 18 = 3x +2

1. 5x – 18 = 3x + 2

2. 2x – 18 = 2

3. 2x = 20

4. x = 10

1. Given

2. Subtraction property

3. Addition property

4. Division property

Skill Development Example 2: Writing Reasons

• Solve 55z – 3(9z + 12)= -64

1. 55z – 3(9z + 12)= -64

2. 55z – 27z – 36 = -64

3. 28z – 36 = -64

4. 28z = -28

5. z = -1

1. Given

2. Distributive property

3. Simplify

4. Addition property

5. 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.

Find the following:a. a = 220 – .7r

b. Solve the equation for r and write a reason for each step.

c. Use the result to find the target heart rate for a 16-year old.

d. 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?

PAIR SHARE

a. a = 220 – r /.70

1. a = 220 – r /.70

2. .70a = 220 - r

3. r = (220 – a).7

1. Given

2. Multiplication

3. Addition property

b. Using a = 16, the target rate is:

1. r = .7(220 – a)

2. r = .7(220 – 16)

3. r = 142.8

The target rate for a 16 year old is about 143 beats per minute

1. Given

2. Substitute 16 for a

3. 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

1. AB = CD

2. AB + BC = BC + CD

3. AC = AB + BC

4. BD = BC + CD

5. AC = BD

1. Given

2. Addition property

3. Segment addition postulate

4. Segment addition postulate

5. Substitution property

In the diagram, AB = CD. Show that AC = BD

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

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