Intro to Algebra 1 Fall Semester

Week 7 & 8 HW October 24/25 & Oct 31/Nov 1

How do you eat an elephant?

One bite at a time. This is how we get better at math (and everything else). We work at it piece by piece, bit by bit, problem by problem, day by day. Your daily effort will yield great results!

Week 7 HW for Oct 31/Nov 1, 2023

Upcoming Quizzes and Tests

Week 6 Chp 1 Quiz —take home

****Week 7 Chp 2 Quiz****— We skipped this test to allow more in-class instruction time. The material is covered in the 1-3 cumulative test.

Week 8 - Chp 1-3 Cumulative Test

Week 10 - Chp 5 Quiz (Fractions)

Week 11 - Chp 4 (Exponents, Factoring)

Week 12 - Practice Final chp 1-5

Week 14 - Final Exam Chp 1-5 (possibly part of chp 6)

Concepts for Intro to Algebra: McD Chp 4.3-4.6 & chp 3 review

Class Summary/Concepts Studied: Equivalent fractions, comparing and converting fractions to decimals and back again. Exponent rules including zero and negative exponents, A bit of a review of LCM, GCF. Review: AoPs 1.5- Subtraction is adding a negative. AoPs 1.7 Division is multiplying by the reciprocal

Recommended but not required: spend 10 minutes this week on the app Dragon Box Algebra 12+. It is an excellent algebra app which gives you a chance to learn the rules of algebra in a video game format without words.

Week 7 Intro to Algebra HW

Starting this week, our homework is broken into a few sections, usually 3 or 4 part, so that you see the same concepts more than one time each week. Students should always spread their work out over the entire week, not procrastinate doing it until the end of the week. This format helps students budget their time. Each part can be thought of as one or two days worth of homework.

Homework: Part 1 of 3

Smart Studying:

  • Attempt to fix your errors your quizzes or tests which were returned to you today. You may use your books, homework, classwork, videos on the website but not another person or google. ;) Then resubmit your test next week as part of your homework and I’ll re-grade it. That new grade will also go in the grade book. After students turn in the tests a second time, we’ll go over the solutions together or I’ll post them but that won’t be until week 9.

  • Review your class notes from this week. Compare them to the corresponding sections in the book. Do your notes make sense? Are your notes missing something important? If so, what can you fill in from the book to help them be more complete?

  • Take another multiplication 1-10 quiz plus a perfect squares quiz up to 16. Learn a new perfect square this week.

Chp 3 Mid-Chp “Quiz” (not actually a quiz) DO Chp 3 pg 137: do #1-3, 5, 13, 16, 17. #2 Answer: 7(4+n)=-14. n=-6

Review: AoPs 1.5- Subtraction is adding a negative. Use that fact and your addition super powers to rewrite these problems. Also used factoring. Do these problems without a calculator

  1. What is the value of 2090 - 1333 - 2090? (modification of AoPs prob 1.25)

  2. Compute 100 - 2 + 101 - 4 + 102 - 6 + 103 - 8 + 104 - 10 (Exer 1.5.2)

Chp 4.3 Equivalent Fractions… Do pg 184-186 PP# 58-60 all, SQUARE 63

Chp 4.5 Rules of Exponents… Do PP on page 197 #19, 23, 31, 42, 44, SQUARE 35, 36, 37 ,46, 48, 49

even answers: 42) a^5, 44) b^7, 46) x^5y^4, 48) 20a^3,b^4

Review AoPs 1.7 Division is multiplying by the reciprocal

Homework: Part 2 of 3

Smart Studying: Smart Studying: Prepare for your chp 1-3 cumulative take home test next week— probably an in class test.

  • Quiz yourself using the end of chapter study/review questions.

  • Book mark homework sections and notes in your binder to use on the test. Test is open binder, closed book. No calculator.

Chp 4.3 Equivalent Fractions… Re-read examples in this section.

Chp 4.5 Rules of Exponents… Re-read examples in this section.

Chp 4.6 Negative and Zero Exponents… pg 201 GP #1-15 odds

SQUARE: Reciprocals: AoPs 1.6 Reciprocals

  • Optional Review video Watch this Art of Problem Solving Video for a review of reciprocals

  • Compute (5 x 6 x 7)(1/5 + 1/6 + 1/7) (Modification of Exer 1.6.5 ) We did a problem like this in class. Remember, we needed to use the distributive property to multiply the (5 x 6 x 7) by 1/5 and then (5 x 6 x 7) by 1/6 and then (5 x 6 x 7) by 1/7 BECAUSE those fractions are being added together. Answer: 107

  • What is the product of any non-zero number and three times it’s reciprocal? Write an expression to justify your answer (Exer 1.6.3 with a modification) Answer: 3. Because n(3 x 1/n) = n(1/n)(3)=(n/n)3= 1(3)=3

Homework: Part 3 of 3

Prepare for Chp 1-3 Test next week:

  • Chp 3.5 Inequalities…. (9 problems) Think: what is special about dividing or multiplying by a negative with inequalities???

    • Watch the review video on translating word problems into inequalities. Pause the video and write the inequality before the teacher does if you can. Translating Words to Inequalities - YouTube 6 minutes by Victoria Miles.

    • Now do pg 146: #12-24 just multiples of 4, then 30-38 evens

    • Even answers here 12) a <-9 16) z < 13 20) t < -108 24) s ≤ 12 30) 5n ≥ 45, n ≥ 9 32) (n/-3) <6, n -18 34) (n/2) ≤5, n≤ 10 36)a) 375c ≤ 7500 38) c ≤ 20 crates

  • Chp 3 Review pages 154-156 #1-7 odds, 19—23, 29-33 odds, 34 (ANSWER 34 IS 10 TIMES OR MORE)

Chp 4.5 Exponent Rules… pg 197 #49, 53, 57

Chp 4.4… Do pg. 190-191 PP#19, 27, 35, 49, 59, 63, read the example on page 191 to refresh your memory, then do 65, 67 SQUARE also do 53, PENTAGON , do 79

Review Chp 1.6 Subtracting Integers

  1. pg 36 PP #12-24 evens: Rewrite these problems as adding an opposite. Example: 8-9 becomes 8+-9. Here’s another example: 8- -11. Change that to 8 + +11 (Remember: keep, change, change)

  2. ANSWERS 12) -1, 14) -16, 16) -15, 18) -24, 20) -17, 22) 177, 24) 23

    Correct your own work as usual

Preview: Chp 4.7 Scientific Notation - NEW Watch Video and take notes- Scientific Notation What is it? Math Magic video

Week 8 HW - Nov 8/9, 2023

Quizzes and Tests Schedule

Week 6 Chp 1 Quiz

Week 7 Chp 2 Quiz - skipped to allow more instruction time

****Week 8 - Chp 1-3 Cumulative Test****

Week 10 - Chp 5 Quiz (Fractions)

Week 11 - Chp 4 (Exponents, Factoring)

Week 12 - Practice Final chp 1-5

WINTER BREAK - 3 WEEKS

Week 13 Review for Final Exam

Week 14 - Final Exam Chp 1-5 (possibly part of chp 6)

Concepts for Intro to Algebra: McD Chp 5.1-5.7 Fractions

Adding and subtracting fractions with like and unlike denominators, multiplying and dividing fractions, including monomials (such as 6a/3a)

Class Summary

****Week 8 - Chp 1-3 Cumulative Test****

Review of dividing fractions (division is multiplying by a reciprocal). Change mixed numbers into improper fractions first (5.5). Solving equations with fractions in them by multiplying by the multiplicative inverse (a.k.a. the reciprocal) to save a step (5.6). Clearing fractions from an equation by multiplying both sides by the lowest common denominator (LCD) and clearing decimals by multiplying by a multiple of 10 (5.7).

Week 8 HW - Nov 8/9, 2023

*****Cummulative Test on Chp 1-3 this week ******

Part 1 of 3 sections

Chp 4.7 Scientific Notation - Review your notes on this video- Scientific Notation What is it? Math Magic video

Chp 6.1 Ratios and Proportions - NEW

CUSTOMIZED FRACTION HOMEWORK. Watch for a email to individual parents letting students know which of the following fraction concepts they need to study.

A) MIXED NUMBERS & IMPROPER FRACTIONS

  • McD pg xxx “Pre-Course Practice”— this is right after the pre-course assessment students took for week 0). Do problems 50-57 (Instructions on how to do these concepts are in the student handbook section of McD which is on page 777-780.) ANSWERS 50) 14/9, 51) 19/4, 52) 115/12, 53) 47/3, 54) 3 5/6, 55) 10 3/8, 56) 9 5/6, 57) 26 1/2

  • We also have videos on these concepts on the our math video’s page: see button at top of this page.

B) ADDING FRACTIONS WITH UNLIKE DENOMINATORS

  • Watch videos on how to find the lowest common denominator (LCD) or an easiest common denomination—

  • Chp 5.3

    • reread examples on pages 231-23

    • Do pg. 234-5 PP 12-18 evens ANSWERS 12) 13/48, 14) -7/20, 16) -41/75, 18) -1 13/21

C) DIVIDING FRACTIONS We’ll do more of this for those who need it next week too.

  • Watch videos on dividing fractions. Remember, division is multiplying by the reciprocal of the divisor.

  • Chp 5.5

    • Re-read examples on pg 243

    • Do pg 245 GP & PP 3, 5, 9, 11, 15

Part 2 of the Homework

Chp 4.7 Scientific Notation - read the examples on pg 204-206

Chp 6.1 Ratios and Proportions…

  • Re-read 269-270

  • GP #1-9 odds

Chp 5.1 NEW What are Rational Numbers?

  • Re-read pg 219-221

  • Do pg 222 GP# 1-9 odds. Pentagon skip 1 & 3, do 11 & 13 odd

Chp 5.5… Dividing Fractions = multiplying by the reciprocal of the divisor

  • Do pg 245 PP #17, 18, 24 (answer -42 1/2),

  • SQUARE Do pg 245 MR 39-49

Chp 5.6 Using multiplicative inverse (a.k.a. the reciprocal) to isolate a variable to solve them faster NEW

  • Re-read pg 247-248 example 1 & 2

  • Optional review videos

  • Do pg. 249 GP 1-7 odds, PP# 11 & 13

Chp 5.7 Clearing Fractions & Decimals NEW

Part 3 of the Homework

Equivalent Ratios - Play this game: Equivalent ratios - space invaders equivalent ratio game from MathGameTime.com

Unit Rates: At some point during the next two weeks, go window shopping (online or in a grocery store) and compare the UNIT RATE for different brands of food or another item. In other words, how much do the two brands of ketchup cost per ounce or paper towels cost per roll. Do that for 3 to 5 items.

Chp 4.7 Scientific Notation — this is the last piece of chp 4 we have left to master from that chapter (although we’ll revisit LCM & GCF…)

Chp 5.3 Do pg. 234-5 PP #35, 41, 43, 58 , 60, 63

  • SQUARE do 51 PENTAGON magic square on page 236 Brain Game

Chp 5 Mid-Chp Quiz pg. 236 #3, 5, 9, 11, 15, 17, 25 odds.

  • SQUARE do 11-25 odds instead

  • PENTAGON do #1 & 3— look back at the examples on how to do this. I don’t expect you to memorize how to do this.

Chp 5.6… Multiplying by Reciprocal/Multiplicative Inverse to save a step in solving equations

  • Re-read pg 248 example 3- writing an equation for a two-step problem

  • Do pg. 249-50 GP #9, 15-21 odds, 31

  • SQUARE PP#23, 25 odds, 33 (hint: change it into an improper fraction), 37, 41, PENTAGON 44

Chp 5.7… Clearing Fractions & Decimals Do page 256 PP #29, 31, 33, 35, 39, 43, 47, SQUARE 41

Optional Review on Prime Factorization, Greatest Common Factor (GCF), and Least Common Multiple (LCM)

Here are excellent videos if you missed class on Week 6 or just need a refresher on any of these topics:

Prime Factorization

Least Common Multiples (LCM) — using prime factorizations to find least common multiple

Bonus: Divisors- using prime factorizations to find greatest common divisor

Recommended - Kahoots DragonBox App

  • Recommended but not required: spend 10 minutes this week on the app Dragon Box Algebra 12+. It is an excellent algebra app which gives you a chance to learn the rules of algebra in a video game format without words.