david raju woodstock school 11 november 2013
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David RajuWoodstock School
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2.5 Reasoning with Properties of Algebra
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Standards/Objectives:Standard 3: Students will learn and apply geometric
concepts.
Objectives:Use properties from AlgebraUse properties of length and measure to justify
segment and angle relationships, such as the angles at the turns of a racetrack.
Use algebraic properties in logical arguments .
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Algebraic propertiesPage 105
Addition propertySubtraction propertyMultiplication propertyDivision propertyReflexive propertySymmetric propertyTransitive propertySubstitution property
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Distributive Propertya (b + c) = ab + acCan be used to solve equationsExample:
x + 3 = 7 By subtracting 3 from each side of the equation, you obtain 4.
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Q 1: Writing ReasonsSolve 5x – 18 = 3x +21. 5x – 18 = 3x + 22. 2x – 18 = 23. 2x = 204. x = 10
1. Given2. Subtraction property3. Addition property4. Division property
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Q 2: Writing Reasons
1. 55z – 3(9z + 12)= -64
2. 55z – 27z – 36 = -64
3. 28z – 36 = -64
4. 28z = -28
5. z = -1
1. Given
2. Distributiveproperty
3. Simplify
4. Addition property
5. Division property
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Solve: 55z – 3(9z + 12)= – 64
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Q 3: Using properties in Real Life
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Find the following:a. Solve the equation for r and write a reason
for each step.b. Use the result to find the target heart rate
for a 16-year old.c. 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?
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1. a = 220 – 10/7r
2. a + 10/7 r = 220
3. 10/7r = 220 – a
4. r = 7/10(220 – a)
1. Given
2. Addition property
3. Subtraction property
4. Multiplication property
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a) Solving for r
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b. Using a = 16, the target rate is:1. r = 7/10(220 – a)
2. r = 7/10(220 – 16)
3. r = 142.8
1. Given
2. Substitute 16 for a
3. Simplify
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The target rate for a 16 year old is about 143 beats per minute
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c. 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.
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In the fig AB =CDShow that AC = BD
1. AB = CD2. AB + BC = BC + CD3. AC = AB + BC
4. BD = BC + CD
5. AC = BD
1. Given2. Addition property3. Segment addition
postulate4. Segment addition
postulate5. Substitution
property
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Assignment
Page 1091.Q 3,42.Q 6,93.Q 15,184.Q 21-255.Q 33
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