block 1 ~ expressions and equations - ms....

2 Block 1 ~ Expressions and Equations ~ Tic-Tac-Toe

BLOCK 1 ~ EXPRESSIONS AND EQUATIONS TIC-TAC-TOE

what’S the proceSS?

Create a poster that explains the process

of solving a multi-step equation.

See page 24 for details.

SMall BuSineSS profitS

Study three different business start-up plans.

Determine how many items the business will need to

sell to break even and make a profit.


order of opS poetry

Write three different poems about the order

of operations.


like terMS gaMe

Create a matching game requiring players to combine like terms

to make pairs.


Math in eVeryday life

Write word problems that can be solved using

equations that require two or more steps to solve.


teMperature SySteMS

Convert temperatures from one system to another.


equation MatS

Produce a “How To...” guide to show others how to use equation mats to solve a

variety of equations.


coMpound inequalitieS

Solve compound inequalities and graph

solutions on a number line.


one doeS not Belong

Make cards with different equations. Ask participants

to find the one that does not belong.


14 Lesson 1.3 ~ The Distributive Property

REVIEW

31. Evaluate each expression when x = 2. a. 5(x + 8) b. 3x − 2 _____ 6

c. (x + 5)² + 2x d. 16 ( 1 _ 2 x + 1 )

32. Frances earns $20 per day for yard work plus $4 more for every pound of yard debris she removes. a. Write an expression that represents the total amount Frances would be paid for a day of yard work when she disposed of x pounds of yard debris. b. How much would Frances get paid on a day when she removed 18 pounds of yard debris? Use words and/or numbers to show how you determined your answer.

tic-tac-toe ~ or de r of opS poe try

Poetry is an art form that is composed of carefully chosen words to express a greater depth of meaning. Poetry can be written about many different subjects, including mathematics. The order of operations is a key element in mathematics so that all students, teachers and mathematicians reach the same answer when calculating the value of the same expression. Write two different poems about the order of operations. One should be an acrostic poem

and the other should be a quatrain. Research and find another style of poetry. Write one more poem about the order of operations using this style.

tic-tac-toe ~ l i k e te r MS ga M e

Write 15 variable expressions containing like terms that have not been combined. Make sure you have a minimum of five expressions containing parentheses. Cut thicker paper (such as cardstock, construction paper, index cards or poster board) into 30 equal-sized pieces. Write each expression on one card. On another card, write the expression in simplest form. Use these cards to play a memory game with a friend, classmate or family member. Record each pair of cards that each participant wins on a sheet of paper by listing the non-simplified and simplified expressions. Turn in the cards and the game sheet to your teacher.

24 Lesson 1.5 ~ Solving Two-Step Equations

REVIEW

Copy each line and insert any combination of the four operations (+, −, ×, ÷) to make each statement true. Use mathematics to show that your answer is correct.

23. 2 3 5 = 17 24. 12 6 10 = −8

25. −1 2 2 = 0 26. 20 5 50 5 = 45

Simplify each expression.

27. 9(x − 2) 28. −7 + 6(x − 5) + 2x 29. 2x + 4x + 7x − 3x 30. 2(x − 1) + 3(x + 1)

31. 4(x + 8) − 12 32. −5(x + 3) + 5x + 13

tic-tac-toe ~ te M pe r atu r e Sy Ste MS

There are three common units of temperatures: Fahrenheit, Kelvin and Celsius.

1. Research the three common units of temperature. Where was each one invented? Where is each one most often used? How are the units related to each other? The following relationships are used to convert one unit of temperature to another:

F = 1.8C + 32 K = C + 273.15 2. Convert the following units from one system to another. a. 20° C to Fahrenheit b. 20° C to Kelvin c. 78° F to Celsius d. 289.5 K to Celsius e. −4° F to Celsius f. 315 K to Fahrenheit

3. Develop an equation that will convert Fahrenheit to Kelvin.

tic-tac-toe ~ wh at’S th e proce S S? Solving a multi-step equation can be a complicated task depending on the difficulty of the equation. Create a poster to help classmates through the process step-by-step. Include at least two examples on your poster. Address what a student should do if the following items show up in their equation:

◆ Multiplication or Division ◆ Addition or Subtraction ◆ Variables on Different Sides of the Equals Sign ◆ Variables on the Same Side of the Equals Sign ◆ Parentheses

Lesson 1.7 ~ Solutions to Linear Equations 33

REVIEW

Simplify each expression.

21. 9 + 2x − 4 + 8x 22. 7(x − 2) + 6(x + 1) 23. 7 + 3(x − 4)

24. −9x + 8x + 7y − 6y 25. 7x + 3y − x + 4y − 2x 26. 12y − 3x + 10x − y

Write a simplified expression for the perimeter of each figure.

27.

x − 7x − 7

x − 7

x − 7 x − 7 28. 2x + 9

5x − 1

tic-tac-toe ~ SM a l l BuSi ne S S prof itS

When someone opens a small business, they often use linear equations to determine profits and losses. Three individuals started up three different businesses which are described below.

1. An equation representing total profits is shown for Business #1. Write the equations for the total profits for the other two businesses.2. For each business, determine how many items they will need to sell to earn back the amount of money they spent for starting their business.3. Each business has a goal of making a total profit of $10,000 in the first quarter of the year. Determine how many total items they will each need to sell to reach their goal.4. Design your own small business. a. Choose one item to sell. Describe why you would like to sell this item. b. Estimate the total start-up costs. Explain how you came up with this amount. c. Estimate the total profit you hope to make per item sold. Explain how you came up with this amount. d. Repeat #1 - #3 above for your small business idea. e. Do you think there would be enough interest in your product to reach the goal of $10,000 in the first quarter? Explain your reasoning.

Business #1Sarah’s Coffee ShopStart-Up Cost = $275

Profit per Coffee Sold = $2.50Equation:

P = −275 + 2.50C

Business #2Jason’s Skateboarding Store

Start-Up Cost = $400Profit per Board Sold = $14

Business #3Jamal’s Gaming ShopStart-Up Cost = $750

Profit per Game Sold = $9.75

38 Lesson 1.8 ~ Linear Inequalities in One Variable

tic-tac-toe ~ coM poun d inequa l iti e S

Compound inequalities contain two inequality symbols. An example of a compound inequality is 4 < x < 9. This can be read “x is greater than four and less than 9.” A solution to a

compound inequality is a value that makes the statement true. In this case, any number between 4 and 9 makes the statement true. For example, 5.5 is a solution, 4 < 5.5 < 9, because it is greater than 4 but less than 9.

To graph a compound inequality, place open or closed circles (depending on the inequality) on each end value and connect the circles with a line in between.

0 5 10When solving compound inequalities, you must isolate the variable in the middle part of the inequality. In order to maintain the balance of the inequality, you must perform operations on ALL THREE parts of the inequality (left, middle and right)

Example: Solve 2 ≤ x − 1 < 11. Graph the solution. 2 ≤ x − 1 < 11 Add 1 to all three parts of the inequality. +1 +1 +1 3 ≤ x < 12

0 5 10

Solve each inequality below. Graph the solution on a number line. 1. 2 ≤ x + 2 ≤ 6 2. 6 < 2x < 16 3. −5 ≤ x − 2 < −3

4. 5 < 3x + 5 ≤ 17 5. 1 < x _ 3 − 1 < 2 6. 1 _ 2 ≤ 2x − 3 ≤ 1

tic-tac-toe ~ one doe S not Be long

Create ten game cards. Each game card needs three equations on it that require two or more steps to solve. Two of the equations on a card should represent equations that have the same number of solutions (one, none or infinitely many). The other equation should have a different number of solutions. Participants try to locate the equation that does not fit. The cards can be used as a game or as a full class activity like a warm-up. Change the placement of the equations that do not belong so they are not always in the same spot on the cards.

42 Block 1 ~ Review

tic-tac-toe ~ equation MatS

Equation mats are used to see a visual model of the equation-solving process. Write a “How To…” guide about using equation mats for different types of equations. Include the following types of equations in your guide: ◆ One-Step Equations ◆ Two-Step Equations ◆ Equations with Variables on Both Sides of the Equals Sign

tic-tac-toe ~ Math i n eV e ry day l if e

Create a booklet of eight word problems that can be solved using multiple-step equations and inverse operations. On each page, write a word problem. On the corresponding back side of the page in the booklet, show how to solve the problemusing equations. Be sure to end the page by answering the problem in a complete sentence.

Lesson 1.7 ~ Solutions to Linear Equations

Solve each equation. Describe the number of solutions (one, none or infinitely many).

58. 2(x + 3) − 5 = 9 59. 3(x − 5) = 3x − 15 60. 2x − 5x + 7 = −3x + 4

61. 1 _ 2 (4x − 3) = 2x + 5 62. 2x + 7 = x + 7 63. 6x + 10 = 5x + 10 + x

64. 4(x + 1) = 3 + 4x − 1 65. 10x − 3 = 4x + 18 66. x _ 5 − 5 = 1

67. The perimeter of one figure is x _ 2 + 12. The perimeter of another figure is 1 _ 2 (x + 12). Joey says their perimeters are equal. Do you agree or disagree? Explain your answer.

Lesson 1.8 ~ Linear Inequalities in One Variable

Solve each inequality. Graph the solution on a number line.

68. 6x + 8 ≥ 50 69. 2 < −1 + 3x

70. x __ −3 − 1 ≥ −2 71. 11x − 7 > 2x + 2 72. 5 < x _ 5 + 6 73. −3(x + 1) ≥ 9

74. A serving bowl used for fruit has a maximum capacity of 18 cups. Each scoop of fruit is 1 _ 3 cup. a. Write and solve an inequality that represents the maximum number of scoops the bowl holds. b. Two cups of marshmallows were added to the bowl prior to the fruit being added. What inequality represents the number of scoops the bowl can hold after the marshmallows were added?

block 1 ~ expressions and equations - ms....

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