Algebra 1 HW - Week 1 September 5-6

Due Tuesday, September 12, 2023

I just posted Art of Problem Solving PA (AoPs PA) classwork solutions (orange button, bottom row.) Starting Week 2, students who correct their classwork get bonus classwork points.

Regular Algebra Homework

1. Review Important Properties of Arithmetic

   Required videos to watch below. Take notes. (These videos pertain to Wednesday’s classwork we did from the AoPs handout problems. You do NOT need to work on those Art of Problem Solving handouts at home.)

   The dude in the video is the founder of Beast Academy and Art of Problem Solving math books, Richard Rusczyk.

   • Commutative Property of Addition with Richard of AoPs

     • (Here’s another video -Commutative property of addition — Mr. J

   • Associative property of addition with Richard of AoPs

   • How to use these super powers (associative and commutative properties of addition) to make hard problems easier! Richard of AoPs adds 1 + 2 + 3…. + 98 + 99 + 100 quickly.

2. Do 13 problems from handouts of the McDougal Littell’s Algebra: Structure and Methods Textbook (or refer to the PDFs in red)

   Normally, our homework will be from the Prentice Hall textbook I loaned students in class on Tuesday (roller coaster on the front). But our first week’s homework is from a different textbook.

   Handouts from Algebra Structure and Methods Textbook: I gave students copies of the key pages and here is a PDF of p. 6-22 so you can look at all of that at once. (I also passed out copies of the relevant pages in class)

   Algebra Structure and Methods Textbook PDF HERE pg 6-41, missing pg 15 & PDF of Page 15 is HERE

   ANSWERS POSTED below (Thursday 8:30 pm)

   • Section 1.2 Grouping Symbols READ p. 6-7 examples. DO pg. 8-9 Written Exercises problems # 35, 37, 39, SQUARE PROBLEM 41 A Note about square problems: SQUARE problems are optional but recommended harder problems. When a student completes all the SQUARE problems in homework assignment, they get a bonus 5% on that assignment. Occasionally there are PENTAGON problems and if students do all those even harder problems in addition to the SQUARE problems, they get another 5% for a total of an extra 10% on that assignment.

     If you need a video review here are two videos to help you:

     Video on Grouping Symbols by Math with Mr. J & Video Grouping symbols and order of operations (5 min.) by Math Fortress

     ANSWERS: Section 1.2 Grouping Symbols p.8-9

     • 35) 12 ≠ 6

     • 37) 30 = 30

     • 39) 5(8-6) ÷ 2

   • Section 1.4 Translating Words into Symbols READ p. 14-15 examples. Do pg. 16-18 Written Exercises problems # 11, 13, 15, 19, 21, SQUARE skip 11 & 13 and do 29-39 odds instead.

     ANSWERS: Section 1.4 Translating Words into Symbols pg 16-18

     • 11) 7 + 2

     • 13) (1/2)n -8

     • 15) 5 +n/8

     • 19) g

     • 21) h

     • 29) m-10

     • 31) 17 -x

     • 33a) s -3

     • 33b) d + 3

     • 35a) g-12

     • 35b) b +12

     • 37) formula d = rt. 3r miles

     • 39) 5p cents

   • Section 1.5 Translating Sentences into Equations READ p. 19-20 examples. Do pg. 20-22 Written Exercises problems #3, 7, 11, 13, 19, SQUARE skip #3 & 7, and instead do these harder problems 33, 35

     ANSWERS: Section 1.5 Translating Sentences into Equations

     • 3) a

     • 7) b

     • 11) b

     • 13) d

     • 19) P = side + side + side, 12 = 3 + 4 + x, combine like terms of 3 & 4 —>12 = 7 + x

     • 33) any variable is fine. Let L = actual length of room. (1/100)L = 8.5

     • 35) any variable is fine. This one is quite challenging, so I’ve written out all the steps.

       • Let r = number of red cars.

         • There are 24 cars total.

         • Blue cars = 3 more than twice red ones

         • Blue cars = 3 + 2r

         • Blue cars = total cars - red cars

         • Blue cars = 24 - r (substitute that in where we have “blue cars” in the equation)

         • 24 - r = 3 + 2r

   • Correct your homework using the ANSWER KEY HERE - coming soon— or at the back of the orange loaner textbook. (Using a different color pen or pencil, put a dot by correct problems and a slash through missed problems.) Then redo any problems you missed in a different color or box in a different color. The goal here is to learn from our mistakes.

   • Self-assess: Print out a self-assessment form from the orange button above and cut one out and then attach it to the top of your homework. Then self-assess your homework. Remember, homework is not about getting everything right, it’s about learning and effort because that’s what helps you become an awesome mathematician in the long run. You may go back and fix your heading or anything else on your homework until you get the full 20 points.

3. Watch these preview videos for material we’ll work on in the next two weeks: take notes!

   • Consecutive integer problems Video #1 https://www.youtube.com/watch?v=il0phegSspU

   • What is a matrix and adding in matrices—https://www.youtube.com/watch?v=yRwQ7A6jVLk

   • Exponents review and exponents with negative bases: https://www.youtube.com/watch?v=Yg_bC19aNjY

   • Absolute Value review: absolute value is distance between a number and zero or sometimes distance between two numbers. Watch Math Antics’ 13 minute video here.

4. Memorize the perfect squares 1-12. Week 2 we’ll memorize 13-squared and 14-squared. Week 3 we’ll memorize 15-squared, 16-squared and 20-squared. Then we’ll take a quiz on that. You should also be practicing your multiplication flash cards so you are quick, quick, quick. We will have a pop-quiz on 1-12 sometime in September.

Classwork Summary of Tuesday & Wednesday 9/5-6

• Wednesday— Properties of Arithmetic, plus opposites and reciprocals:

  • Associative (regrouping) & commutative (switching order) properties of addition and multiplication, distributive property of multiplication, identity properties of addition and multiplication. Using algebra tiles to illustrate these properties. Associative and commutative properties combined are our superpowers— they allow us to regroup and reorder problems with all multiplication or all addition to make them easier to solve. We worked on challenging Art of Problem Solving problems to practice this skill as classwork.

  • Opposites (-4 is the opposite of 4. x is the opposite of -x). Opposites are also called multiplicative inverses. How to get the opposite of any number or variable? Multiply it by negative 1.

  • Reciprocals — dividing is the same as multiplying by a reciprocal! Dividing fractions.

• Tuesday— getting to know our Algebra Tiles (a.k.a. Algebra Lab Gear) & Order of Operations— grouping symbols

  • Explored the commutative property of multiplication (terms can commute — switch places and still get the same value 3 x 2 = 2 x 3. Use the corner piece in our algebra tiles to model this geometrically.

  • What’s a variable and a constant? why those names? Multiplying variables by constants such as 6 times x = 6x, how multiplying in the corner piece shows area = length times width.

  • Naming 2D variable blocks such as x times x is x- squared etc. Review of exponents: base, power etc. Naming 3D blocks (volume = length x width x height)

  • Combining like terms in polynomial expressions - which terms are alike?

  • Order of Operations: PEMDAS— fraction bars are a grouping symbol, nested parentheses and brackets (work from the inside out, following PEMDAS within the grouping symbol).

  • CW (Classwork) SB #3 Order of Operations problems.