Chapter 1 Maintaining Mathematical Proficiency

Name_________________________________________________________ Date __________

Chapter

1

Maintaining Mathematical Proficiency

Add or subtract.

1. -1 + (-3)

2. 0 + (-12)

3. 5 - (-2)

4. -4 - 7

5. Find two pairs of integers whose sum is -6.

6. In a city, the record monthly high temperature for March is 56?F. The record monthly low temperature for March is -4?F. What is the range of temperatures for the month of March?

Multiply or divide.

7. - 2(13)

8. -8 ? (-5)

9. -14 ? 2

10. -30 ? (-3)

11. Find two pairs of integers whose product is - 20.

12. A football team loses 3 yards in 3 consecutive plays. What is the total yardage gained?

Copyright ? Big Ideas Learning, LLC All rights reserved.

Algebra 1

1

Student Journal

Name _________________________________________________________ Date _________

1.1

Solving Simple Equations

For use with Exploration 1.1

Essential Question How can you use simple equations to solve real-life

problems?

1 EXPLORATION: Measuring Angles

Go to for an interactive tool to investigate this exploration.

Work with a partner. Use a protractor to measure the angles of each quadrilateral. Complete the table to organize your results. (The notation mA denotes the measure

of angle A.) How precise are your measurements?

a.

A

B

b.

A

B

c.

B A

D

C

D

C

D C

Quadrilateral

m A (degrees)

a.

b.

c.

m B (degrees)

m C (degrees)

m D (degrees)

mA + mB + mC + mD

2 EXPLORATION: Making a Conjecture

Go to for an interactive tool to investigate this exploration.

Work with a partner. Use the completed table in Exploration 1 to write a conjecture about the sum of the angle measures of a quadrilateral. Draw three quadrilaterals that are different from those in Exploration 1 and use them to justify your conjecture.

2 Algebra 1 Student Journal

Copyright ? Big Ideas Learning, LLC All rights reserved.

Name_________________________________________________________ Date __________

1.1 Solving Simple Equations (continued)

3 EXPLORATION: Applying Your Conjecture

Go to for an interactive tool to investigate this exploration.

Work with a partner. Use the conjecture you wrote in Exploration 2 to write an equation for each quadrilateral. Then solve the equation to find the value of x. Use a protractor to check the reasonableness of your answer.

a.

85? 80?

100? x?

b.

x? 72?

78? 60?

c. 30?

90? x? 90?

Communicate Your Answer

4. How can you use simple equations to solve real-life problems?

5. Draw your own quadrilateral and cut it out. Tear off the four corners of the quadrilateral and rearrange them to affirm the conjecture you wrote in Exploration 2. Explain how this affirms the conjecture.

Copyright ? Big Ideas Learning, LLC All rights reserved.

Algebra 1

3

Student Journal

Name _________________________________________________________ Date _________

1.1

Notetaking with Vocabulary

For use after Lesson 1.1

In your own words, write the meaning of each vocabulary term. conjecture

rule

theorem

equation

linear equation in one variable

solution

inverse operations

equivalent equations

Core Concepts

Addition Property of Equality

Words Adding the same number to each side of an equation produces an equivalent equation.

Algebra If a = b, then a + c = b + c.

Notes:

4 Algebra 1 Student Journal

Copyright ? Big Ideas Learning, LLC All rights reserved.

Name_________________________________________________________ Date __________

1.1 Notetaking with Vocabulary (continued)

Subtraction Property of Equality

Words Subtracting the same number from each side of an equation produces an equivalent equation.

Algebra If a = b, then a - c = b - c. Notes:

Multiplication Property of Equality

Words Multiplying each side of an equation by the same nonzero number produces an equivalent equation.

Algebra If a = b, then a ? c = b ? c, c 0. Notes:

Division Property of Equality

Words Dividing each side of an equation by the same nonzero number produces an equivalent equation.

Algebra If a = b, then a ? c = b ? c, c 0. Notes:

Four Step Approach to Problem Solving

1. Understand the Problem What is the unknown? What information is being given? What is being asked?

2. Make a Plan This plan might involve one or more of the problem-solving strategies shown on the following page.

3. Solve the Problem Carry out your plan. Check that each step is correct. 4. Look Back Examine your solution. Check that your solution makes sense in the original

statement of the problem.

Notes:

Copyright ? Big Ideas Learning, LLC All rights reserved.

Algebra 1

5

Student Journal

Name _________________________________________________________ Date _________

1.1 Notetaking with Vocabulary (continued)

Common Problem-Solving Strategies

Use a verbal model. Draw a diagram. Write an equation. Look for a pattern. Work backward.

Guess, check, and revise. Sketch a graph or number line. Make a table. Make a list. Break the problem into parts.

Notes:

Extra Practice

In Exercises 1?9, solve the equation. Justify each step. Check your solution.

1. w + 4 = 16

2. x + 7 = -12

3. -15 + w = 6

4. z - 5 = 8

5. -2 = y - 9

6. 7q = 35

7. 4b = -52

8.

3

=

q 11

9.

n - 2

=

-15

10. A coupon subtracts $17.95 from the price p of a pair of headphones. You pay $71.80 for the headphones after using the coupon. Write and solve an equation to find the original price of the headphones.

11.

After a party, you have

2 5

of

the

brownies

you

made

left

over.

There

are

16

brownies

left.

How many brownies did you make for the party?

6 Algebra 1 Student Journal

Copyright ? Big Ideas Learning, LLC All rights reserved.

Name_________________________________________________________ Date __________

1.2

Solving Multi-Step Equations

For use with Exploration 1.2

Essential Question How can you use multi-step equations to solve

real-life problems?

1 EXPLORATION: Solving for the Angle Measures of a Polygon

Go to for an interactive tool to investigate this exploration.

Work with a partner. The sum S of the angle measures of a polygon with n sides can

be found using the formula S = 180(n - 2). Write and solve an equation to find each

value of x. Justify the steps in your solution. Then find the angle measures of each polygon. How can you check the reasonableness of your answers?

a.

b.

c.

(30 + x)?

50?

(2x + 30)?

(x + 10)?

9x ? 30?

50?

(x + 20)?

(2x + 20)? x?

d.

(x - 17)?

(x + 35)?

(x + 42)? x?

e.

(5x + 2)? (3x + 5)?

(8x + 8)? (5x + 10)?

(4x + 15)?

f.

(2x + 8)?

(3x + 16)?

(4x - 18)? (3x - 7)?

(2x + 25)?

Copyright ? Big Ideas Learning, LLC All rights reserved.

Algebra 1

7

Student Journal

Name _________________________________________________________ Date _________

1.2 Solving Multi-Step Equations (continued)

2 EXPLORATION: Writing a Multi-Step Equation Go to for an interactive tool to investigate this exploration. Work with a partner. a. Draw an irregular polygon.

b. Measure the angles of the polygon. Record the measurements on a separate sheet of paper.

c. Choose a value for x. Then, using this value, work backward to assign a variable expression to each angle measure, as in Exploration 1.

d. Trade polygons with your partner. e. Solve an equation to find the angle measures of the polygon your partner drew.

Do your answers seem reasonable? Explain.

Communicate Your Answer

3. How can you use multi-step equations to solve real-life problems?

4. In Exploration 1, you were given the formula for the sum S of the angle measures of a polygon with n sides. Explain why this formula works.

5. The sum of the angle measures of a polygon is 1080?. How many sides does the polygon have? Explain how you found your answer.

8 Algebra 1 Student Journal

Copyright ? Big Ideas Learning, LLC All rights reserved.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download