Lessons 1-2: Using Estimation 
Duration: approximately two 60-minute sessions
Pacing Guide: lesson 1, week 1, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2 

Activities
 

1.   You should read Section 1-1 in your text, pp 3-7, and use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.
 

2.   We estimate when we need a good idea of the answer to a problem, but when the exact answer is not necessary. 
 

3.   For example, I want to figure out whether I have enough money to buy 3 CDs and I know I have $54.  The easy thing to do is to round the prices up from $11.99, $14.79, and $17.99 to $12, $15, and $18, then add them.  12 + 18 is 30, and 30 + 15 is 45, so, even with 10% added for tax (remember to move the decimal one place to the left for 10%, so 45 becomes 4.5), 49.50 is less than 54.  I can enjoy my harpsichord compositions!  

4. We also estimate to make sure that our answers to computation problems are realistic.  After I estimated my CD prices, I added up the costs and got $1231.78!  Since my estimation was for $45, I KNOW I made a mistake, so I checked my work.  I found out that I wrote $11.99 as $1199, so when I added the other numbers, I got my ridiculous answer.  Estimating was a good idea!
    

5. When you estimate a sum or difference, round the decimals to the nearest whole number then calculate.
    

6. You can also use front-end estimation, which is especially good when adding money.  To do that, you add the whole numbers first, then estimate the total amount of cents and add that to the whole number answer for your estimation.
    

7. After you read the material, practice your work.  Do problems 3, 13, 17, and 23 on p 7.   Check them in the Selected Answers at the back of the book.  If you missed any of the answers, do # 1 – 25 odd, and #26.  If you got them all correct, do #45-48, 50, and 51.

Assessment: Complete problem #44 on page 8 of your textbook.

Differentiation
Extensions: Using the receipt from your family’s latest trip to the grocery store, estimate the total cost of the items that were purchased.  Check your estimation against the actual total. Play the Estimation game, Glowla’s Estimation Contraption
Support (RtI tiers 2 & 3):  For extra help, read “Rounding Whole Numbers” on p. 697. 

For extra practice, solve problems 1-4 in the  Extra Practice section of the text, p. 684.

Supplementary Resources: http://pbskids.org/cyberchase/games/ballparkestimation/ballparkestimation.html

Lessons 3-4: Adding and Subtracting Decimal Numbers 
Duration: approximately two 60-minute sessions
Pacing Guide: lesson 2, week 1, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2

Activities

1. When you add or subtract decimal numbers, the most important concept to remember is to Line Up the Decimal Points!  Add zeroes where you need them so that each addend has the same number of digits to the right of the decimal point.  If you don’t line up the decimals, your answer will be WRONG.   
   For example, let’s add  3.4 + 11.32 + 6.54.  If we just line up the numbers, we get
         3.4
      11.32
   +   6.54
       1820
   Logic tells us this answer cannot be correct, and we haven’t any idea where to put the decimal point anyway. 

2. If we line up the decimal points and add zeroes where we need them, however, the problem looks like this:
        3.40
        1.32
    +  6.54
       21.26 
   We can just drop the decimal point into the same position in the answer as it is in the problem, and the solution is logical and correct. 

3. Now, read Section 1-2 in your text, pp 11-13, and use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept. 

4. After you read the material, practice your work.  Do problems 11, 15, 25, and 27 on pp 13-14.
   If you missed any of the answers or found them difficult, do # 6-11, 16-18, 31-33, 38 and 39. 
   If you got them all correct and found them easy, do # 48-53.

Assessment: Complete problems 54-57 on page 15 of your textbook.
 

Differentiation
Extensions: Read and complete the activities on p. 16  - “Compensation”
Support:  For extra help, read “Rounding Whole Numbers” on p. 697.  For extra practice, solve problems 5-8 in the  Extra Practice section of the text, p. 684. 
For additional work, go to the following websites and work as needed:
Practice worksheets  - http://www.dositey.com/math58.htm
Decimal Numbers – Addition 2, Subtraction
Adding Decimal Numbers
Subtracting Decimal Numbers

Supplementary Resources: http://www.dositey.com/

Lesson 5: Understanding Absolute Value  
Duration: approximately one 60-minute session
Pacing Guide: lesson 3, week 1, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2 

Activities

1. Absolute value is the distance a number is from zero.  We write the absolute value of x as lxl, and the absolute value of –x as l-xl.  The distance is the same whether the number is a positive or a negative number, so the absolute values of numbers which are opposites are the same.
    

2. For instance, 4 and –4 are each 4 spaces away from zero on the number line.  We write the absolute value of 4 as l 4 l and the absolute value of –4 is l –4 l . Since both numbers are 4 away from zero, the absolute value of each is 4.
    

3. The rule says that lxl and l-xl are both x, if x is a positive number.
    

4. You should read Section 1-6 in your text, pp 34-35, and use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.
    

5. After you read the material, practice your work.  Do problems # 36-39 and 41 - 48 on pp 36.
     

6. If you found these problems difficult or you made mistakes, do # 2-20 even, 33-35, 49 – 51, and 56.
    

7. If you got them all correct and found them easy, do # 70-75.
    

Assessment: Complete problems 76-79 on page 38 of your textbook. Email them to Mr. Kercher, kerchadr@d11.org or turn in to Learning Center, Audubon Elementary, Room 4, 2400 E. Van Buren St., Colorado Springs, CO 80909. Label them with your name, the lesson (Lesson 3:title), and your grade (grade 7). He will return them to you with his comments and your grade.

Differentiation
Extensions:  

Research the history of the concept of absolute value using internet and library resources.  Write a paragraph explaining its usefulness.

Support (RtI tiers 2 & 3):  Read p. 696 in the Skills Handbook and do # 1-4 on p. 34 and # 80 – 85 on p. 38.
For extra practice, solve problems 18-21 in the  Extra Practice section of the text, p. 684.
Use this resource to print your own number line:    http://www.helpingwithmath.com/resources/oth_number_lines.htm
Choose this link to print number lines for yourself  Integer Line ( -25 to 25)  
Supplementary Resources: http://www.helpingwithmath.com/resources/oth_number_lines.htm

Lesson 6: Multiplication and Division of Decimal Numbers
Duration: approximately one 60-minute session
Pacing Guide: lesson 4, week 2, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2   

Activities
 

1. Multiplying decimals is just like multiplying whole numbers, with the added step of inserting the decimal point.  After you multiply the digits, count the number of decimal places (numbers AFTER the decimal point) in each factor, add them together, then insert your decimal point that many places FROM THE RIGHT.
   
   For instance, to solve 23.45 * 3.654, first you multiply 2345 times 3654 to get 8568630.  Then you  count the digits to the right of the decimal – 2 in the first factor and 3 in the second, which makes 5 total.  Now, count 5 places to the left from the last digit, 0, and put in the decimal between the 5 and the 6, to find the answer 85.68630.
   
   This is a GREAT place to estimate first to check whether or not your answer is reasonable.  23.45 is a little less than 25, and 3.654 is a little less than 4.  If you round up, you estimate 25 * 4 = 100, and since both factors are less than your estimates, your answer should be a bit less than 100.  Since you calculated that the answer is 85.68630, your answer is reasonable.
    

2. You should read Section 1-3, pp 17 – 20 in your text.  Use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.
    

3. After you read the material, practice your work.  Do problems # 8, 20, 37, and 45 on pp 20-21.
   If you found these problems difficult or you made mistakes, do #  2, 5, 6,17 -19,  38, 43, and 44.
   If you got them all correct and found them easy, do #  43, 46, 57, 59, and 65.

Assessment: Complete problems 66-69 on page 22 of your textbook. 

Differentiation
Extensions:  Practice multiplying numbers with 3 decimals.  The answers will have six digits to the right of the decimal point.  Why?  Write an explanation so a 6^th grade student can understand where to place the decimal point in a multiplication or division problem.
Support (RtI tiers 2 & 3):  Review Lesson 1-1 and do # 1 – 4 on p. 17, as well as # 70 –77on p. 22. 
Do additional problems on pp. 20 – 22 as needed.
For extra help, read the sections in the Skills Handbook on multiplying and dividing decimals, pp. 703 – 707 and do the exercises in the sections where you are having difficulty. 
For extra practice, solve problems 9-12 on p. 684 in the Extra Practice section of the text.
For additional worksheets with accompanying answers, go to http://mathfactcafe.com/build/ and build worksheets to your specifications. 

Supplementary Resources: http://mathfactcafe.com/build/
 

Lessons 7- 8: Addition and Subtraction of Integers; Multiplication and Division of Integers  
Duration: approximately two 60-minute session
Pacing Guide: lesson 5, week 2, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2 

Activities

1.   Here are the “rules” for multiplying integers with different signs:
(+)(+) = +
(+)(-) = -
(-)(+) = -
(-) (-) = + 

2. Since multiplication and division are inverse operations, the reverse is also true:
   +/+ = +
   +/-  = -
   - / + = -
   - / - = +
    

3. An easy way to remember the rules is that if there are an even number of positive numbers in the problems, the answer will be positive.  Remember that zero is an even number!
    

4. Play the All Arithmetic Operations Mystery Picture game http://www.dositey.com/addsub/Mystery11.htm
    

5. Read Sections 1-7, pp 39 -41 and 1-8, pp 45 – 47 in your text.  Use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.
    

6. After you read the material, practice your work.  Do problems #13, 29, 41, 53, and 57 on pp. 42 - 43.
   If you missed any of these, or found them difficult, do # 11,12, 21 – 24, 50 – 52, 58 – 60.
   If you found these problems easy and got them all correct, do problems #60, 68, 70, 73 – 78.
   Then, solve the problems on pp. 47 – 48, do problems 10, 12, 22, 24, and 43.
   If you missed any of these, or found them difficult, do #  3 – 9 odd, 17 – 21 odd, 25, 33, and 34.
   If you found these problems easy and got them all correct, do problems # 34, 42, 51 – 56.

Assessment: Complete problems 79-82 on page 44 of your textbook.

Differentiation
Extensions:  Write 3 word problems using decimal numbers and at least two different operations in each.  Solve your problems and be able to explain how you solved them.
Support (RtI tiers 2 & 3):  Review Lesson 1-6 and do # 1-9 on p. 39.
Practice by playing LineJump - http://www.funbrain.com/linejump/index.html  at FUNBRAIN  http://www.funbrain.com/index.html  For extra practice, use these worksheets and check your answers from Dositey.com (http://www.dositey.com/math58.htm): 
Example     Addition     Subtraction     Multiplication     Division  

Supplementary Resources: Dositey.com - http://www.dositey.com/math58.htm

Lesson 9: Compare and Order Decimals and Equivalent Numbers
Duration: approximately one 60-minute session
Pacing Guide: lesson 6, week 2, unit 1
Materials Needed: Prentice Hall Mathematics 7 , Course 2 , Explore Learning Gizmo - Comparing and Ordering Decimal  

Activities

1. Fractions, decimals, and percents are all different ways of indicating value.  Therefore, we can write the same number in different ways:  For instance,  ½ = 0.5 = 50%. 

2. Here is a handy chart to help you remember some of the most common conversions:

3. Fraction	1/10	1/8	1/5	¼	1/3	½	2/3	3/4
   Decimal	0.10	0.125	0.2	0.25	0.33	0.5	0.67	0.75
   Percent	10%	12.5%	20%	25%	33%	50%	66 2/3%	75%

4. A fraction is a part of a whole, the decimal is the fraction after the division is completed, and the percent is the decimal number multiplied by 100 ( since with a decimal we are looking at the part of ONE and with a percentage we are looking at the part of ONE HUNDRED).

5. Open the Explore Learning Gizmo - Comparing and Ordering Decimals and complete the gizmo selection, practicing this skill.

Assessment:  Write each fraction as a decimal and percent: 2/5, 9/10, 1/8, 3/5, and 3/8. 

Differentiation
Extensions:  Extend the conversion chart above by at least 5 more cells, inserting items where needed.  Explain how to convert from fraction directly into percent.
Support (RtI tiers 2 & 3):  For extra help, read the sections on place values and decimals, as well as reading and writing decimals in the Skills Handbook section of your book, pp 700-701.
Supplementary Resources: Conversion chart – Stacy Brisben 7^th Grade (1^st Quarter) 2005-06 

Lessons 10-11: Order of Operations  
Duration: approximately two 60-minute sessions
Pacing Guide: lesson 7, weeks 2 and 3, unit 1.
Materials Needed: Prentice Hall Mathematics 7 , Course 2 , Scientific calculator for extension, p. 55 

Activities

1. First watch the video on Order of Operations. 

2. Remember the mnemonic:  Please Excuse My Dear Aunt Sally to help with the order of operations:  parenthesis, exponents, multiplication and division from left to right, addition and subtraction from left to right.  Remember to do everything inside the parenthesis in the correct order as well!

3. You should read Section 1-9, pp 50-52 in your text.  Use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.

4. After you read the material, practice your work.  Do problems 7,8, 11, and 28.

5. If you missed any of these problems or found them difficult, then do problems 1-6, 10,24,25,31,34-38.

6. If you worked them all correctly and easily, instead do problems 30 – 38, 43- 48.

7. Do the Chapter 1 Review, pp. 62 - 63

Assessment: On page. 54 of your textbook, complete problems 49 – 52.  Then complete the Chapter 1 test pp. 64 - 65.

Differentiation
Extensions:  Create 3 problems which have variables.  Insert parentheses in various places of each problem to change the answers.  Provide the solutions to your multiple problems on a separate sheet.  Read and complete the section:  Technology:  Using a Scientific Calculator – p.55.
Support (RtI tiers 2 & 3):  For extra help, review lesson 1-2 and work through problems 1-5 on p. 50.  

For extra practice, work additional problems on pp. 58-60. 

Solve problems 34 - 41 in the  Extra Practice section of the text, p. 684.
Before taking the test, read the Chapter Review, pp. 62 – 63.   

Supplementary Resources: http://www.sqooltools.com/edvideos/mathfacts/bodmas.html

Lessons 12-13: Exponents and Order of Operations-Part 1 
Duration: approximately two 60-minute sessions
Pacing Guide: lesson 8, week 3, unit 1
Materials Needed: Prentice Hall Mathematics 7 , Course 2, One Grain of Rice:  A Mathematical Folktale - Demi  

Activities 

1. Start with the Investigation on p. 131.  Compete the table and solve the reasoning problem.

2. Read One Grain of Rice:  A Mathematical Folktale by Demi (Scholastic: 1997).  Think about the different ways you could write down how many grains of rice she received each day. 

3. When we have very large numbers that are multiples of a small number, it is often easier to use exponents than it is to write the equation.  An exponent tells us how many times a number – the base – is multiplied by itself – the exponent. 

4. So 5⁴ = 5 x 5 x 5 x 5 = 625.  5 is the base and 4 is the exponent.

5. Now read Section 3-1 in your text, pp. 131 – 133.  Don’t forget the order of operations on the bottom of p. 132!

6. After you read the material, practice your work.  On pp 133-134, do problems 4-6, 8-10, 11a, 13 – 25 odd.

Assessment:  Complete p. 134 #14-36 even problems.

Differentiation
Extensions:  Write a story similar to the one Demi describes in her book, using a different number as a base.  Word process it and illustrate it, so that a student a few years younger than you are can understand the concept of exponents.
Support (RtI tiers 2 & 3):  Review Lesson 1-9 if you have trouble doing problems 1-6 on p. 131.
For extra practice, work additional problems on pp. 133-134. 
Solve problems 34 - 41 in the  Extra Practice section of the text, p. 684. 
Supplementary Resources: One Grain of Rice:  A Mathematical Folktale by Demi (Scholastic: 1997). 

Lessons 14-15: Exponents and Order of Operations-Part 2 
Duration: approximately two 60-minute sessions
Pacing Guide: lesson 9, week 3, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2  and SliderMath Game

Activities 

1. You should reread Section 3-1, pp. 131-133 in your text.  Use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.

2. To review:  exponents are the little superscript numbers to the right of a number or variable, the base.  They give you a short way to know how many times to multiply the base by itself. 
   Let’s look at a number:  6³ 
   6 is the base, 3 is the exponent.  Since 3 is the exponent, it tells you to multiply 6 by itself 3 times, or (6) (6) (6) = 216.
   If you want to indicate (9) (9) (9) (9) (9), it is easy to write 9⁵, which equals 59,049. 
   We can do the same thing with a negative number as a base:  (-3)⁴ = (-3) (-3) (-3) (-3) =  81
   By definition, any number to the 0^th power equals 1:  x⁰ = 1 

3. Now play the SliderMath Game. You need to click on the answer before the star finds it!  

4. After you read the material and play the game, practice your work.  Do problems # 20, 32, 36, and 38 on p. 134-135. 
   If you found these problems difficult or you made mistakes, do # 27 – 37 odd, 39 – 44, and 48 -51. 
   If you got them all correct and found them easy, do # 45 – 59. 

Assessment: Complete problems 60-63 on page 135 of your textbook. 

Differentiation
Extensions: 

Review problem 63 on p. 135.  Create your own code using exponents and write a letter to a parent or friend using the code.  Be sure to have a copy of the key available so that your correspondent can translate your letter if he or she gets stumped! 

Support (RtI tiers 2 & 3):  For extra help, review lesson 1-9 and work through problems 1- 6 on p. 131 and problems 68 – 71 on p. 135. 

For extra practice, work additional problems on pp. 133 - 135. 

Solve problems 1 - 5 in the  Extra Practice section of the text, p. 686. 

Supplementary Resources: SliderMath Game

Lesson 16: Exponents and Scientific Notation – very large and very small numbers
Duration: approximately one 60-minute session
Pacing Guide: lesson 10, week 3, unit 1
Materials Needed: Prentice Hall Mathematics 7, Course 2, Scientific calculator 

Activities
 

1.   If you want to measure the distance between the Earth and Pluto, you need to use very large numbers with lots of digits to the left of the decimal point. If you want to measure the size of one atom of sodium, you would use a very small number, with many digits to the right of the decimal point. When using either of these numbers, it would be easy to miss a digit, so your calculations could be hundreds of times too big or too small.  The way scientists deal with very large and very small numbers is by using scientific notation.
First, do the Investigation on p. 136 of your text.  Look for a pattern in the exponents and the numbers used.

2. You should read Section 3-2 in your text, pp. 136 - 137.  Use the Instant Check system to be sure you understand the material you read.  To do this, solve the problems beside the Check Understanding marks in each section, then check your answer with the key at the back of the book, beginning on p. 755.  If you miss a problem, reread the example to clarify the concept.
    

3. Now go to the AAA-Math Website. First, read the section about scientific notation, then click on the practice tab to practice converting numbers into scientific notation (http://www.aaamath.com/dec71i-dec2sci.html#section2.  When you are ready, practice your skill on the Play section of this site:  http://www.aaamath.com/dec71i-dec2sci.html#section3.
    

4. After you read the material, practice your work.  On pp. 136 – 138, do problems 2, 6, 18, and 20.
   If you found these problems difficult or you made mistakes, do # 3 – 19 odd, 23 – 27, 32, and 33.
   If you got them all correct and found them easy, do # 23 – 27, 32, 33, and 35 - 43.