Algebra 1 Fall Semester, 2023

Week 3 & 4 HW September 19/20 & 26/27

Week 3 HW— September 19/20, 2023

Additionally— we decided in class that students will self-correct their practice chp 1 quizzes.

Smart Studying: research shows that students who give themselves micro-quizzes retain information more than those who just re-read the same information.

  1. Quiz yourself on perfect squares 1-16:

    • 13² = 169

    • 14² = 196

    • 15² = 225

    • 16² = 256

  2. Quiz yourself on vocabulary from your class notes: reciprocals

  3. Up your math facts fluency: memorize 11-12s. Make flash cards. Turn those weaknesses into strengths by creating flashcards for the so you are wicked fast at those. Timed in-class quiz on Week 6: 40 questions in 60 seconds.

Work from our regular textbook: Prentice Hall Pre-algebra. (Roller coaster with a green border.)

Quiz Notice: Wed Practice Quizzez Chp 1 #1 & 2 — you are correcting this at home. Solutions are on the Algebra Resource page— button above and linked here.

Note: CW means we did some of these problems in class as classwork (on an ideal day at least!) You don’t need to do it as homework. I list it here because it’s helpful to know where to go back to look for examples. HW means Homework so do it as homework.

PH 1-6 Division is Multiplying by reciprocal

CW p. 42-43 #90-92

HW PH p. 43 #93-95, Word problems 96-98

ANSWERS HERE — okay this is weird, folks. Some students have a different problem 97 (even though we all have the 2004 edition). I’m posting a picture below of the teacher’s edition with the question and the answers down below.

  • 96) a 139 ft, b. less than 4 s; for t = 4, h = 155-16t^2 = 101 so h = for some value less than 4 (about 3.1)

  • 97) a) a = 5000-25 t, b) 312.5 ft, c) 4687.5 ft

  • 98) -23 degrees C

Optional video: Why is division is multiplying by a reciprocal? This is why video— a bit like a proof: Why is dividing the same as multiplying by a reciprocal? from Mathispower

Review Opposites and Negation (AoPs 1.4 handout from week 2) review in class. No additional HW.

PH 2-2 Two step equations & multiplying by a negative

CW: Review Ex 3 

CW PH p85 – grouping symbols p. 85 #58-61, triangles p. 85 #67, matrices p 74

HW PH p. 83-84 #17, 20, 21, 62, 64, 69, 71 SQUARE 75, 81

ANSWERS are on the Algebra resource page which is a button above on the bridge photo.

Review Opposites and Negation (AoPs 1.4 handout from week 2)

PH chp 2.3 Distributing Negatives and Running the distributive property in reverse to FACTOR out common terms….

HW Watch this video & take notes: AoPs Introduction to “Distributive Property” Prealgebra Video At minute 3:10, pause the video and do the problem on the screen before Richard, AofP math wiz, does.

Optional distributive property videos

CW SB 67-68 , 70

HW read PH pg 89 and then do #2 (This is a check understanding word problem. Answers are in the back of your book for all “check understanding” problems which immediately follow the example problems. This is why I assign these as one can quickly check one’s answers and refer to the example immediately above.)

HW do handout SB 68 # 5, 9, 14, 16, 18, 20 ANSWERS are on the Algebra resource page

HW do handout SB 70a Examples 1 & 2, 1 & 2 ANSWERS are on the Algebra resource page

HW read PH pg 90 Ex 4, then do check understanding problems 4a & b, Read Ex 5, then do 5 a & b

PH 2-4 EQ w/ variables on both sides of equation & identities and no solutions

HW p. 98 Read Obj 2: Identities and no solution. #21, 23, 32, 38-40 SQUARE 35,

HW PENTAGON Challenge: preview of solving systems of equations with substitution PENTAGON pg. 100 #55 (This is a systems of equations problem. You need to write one equation in terms of the other variable and substitute that in for the other variable. I haven’t taught you this yet so don’t fret if you can’t do this yet. Here are a few videos on how to solve systems of equations: AoP Solving systems of equations with substitution and this optional video on using the substitution method (solving for one variable and then substitute in or plug in that expression whenever you see that one variable: as is g + f = 30, so f= 30- g, —> plug or sub in (30-g) wherever you see f in the other equation.))

ANSWERS are on the Algebra resource page

Bring Math 8 KIN and Greenie to class during Week 4

Study for PRACTICE Chp 1 test next Wednesday (from the PH textbook chp review pg 67-69). Use the resources at the end of the chapter to study. This is be a practice test so you get a sense of what the tests will look like. Note: you’ll need to read the examples in chp 1 to refresh your memory on these concepts as most are review from prealgebra. We’ll spend a tiny bit of time on them in class on Tuesday but not much.

Preview & Review Videos

Classwork Tuesday & Wednesday 9/19-20

Tuesday: using exponents when the base is a fraction, simplifying expressions by combining like terms, distributing a negative, clearing fractions and decimals, distributing negatives through fractions (it’s the same, but just a pain because, well, fractions.) Translating words into mathematical expressions. Showing negative terms using Algebra tiles. Building expressions such as -7 +5x -8. Modeling subtraction is adding a negative with algebra tiles.

Wednesday: two step equations, getting the variable on one side of the equation, division is multiplying by a reciprocal. Practice quiz for PH chp 1. Translating words into mathmatical expressions. Reviewed mean, median, mode and range and impact of outliers on each measure of central tendency or dispersion in the case of range. Using algebra tiles work mat to model solving equations. Reviewed power of a power exponent rules — multiply the exponents (a^m)^n = a ^(mn) (sorry my website tools won’t let me insert superscript which is super annoying so I have to use the ^ symbol to mean raised to a power.

Week 4 HW— September 26/27 —complete

Test solutions have been posted 9/28 5:40 pm

Note-this is a short HW week. Week 5 will be longer. You may get a head start on week 5 by starting the chp 1 test I-missed-these-kind-of-problems. See note next to the chp test solutions post.

Smart Studying: Re-read your class notes and write little summaries or annotations. Look at the highlighted vocabulary words from chapters 1 & 2 and add them plus their definitions to the IMP section of your binder.

Prentice Hall Algebra 1 HW

 Concepts: Equations -motion, two variables, consecutive integer.  Linear equations and basic exponents. Intro to slope.

Redo missed problems from Practice Test - Chp 1

Fix the problems you missed. Attempt it first by looking at the examples in the textbook.

Chp 1 TEST SOLUTIONS ARE HERE Note: next week part of the HW is to do 5 problems for each problem you missed on the test so that you understand those types of problems. You’ll notice that the test solutions pdf has an answer page which lists exactly what section and example matches the test problem and what HW problems are suitable to practice that skill/concept. This is a light homework week. You might want to start working on this bit of next week’s HW if you missed more than two or three problems.

PH 2-5 Equations

with 2 variables by writing/def. one variables in terms of another, Consecutive Integer problems, Motion (d=rt) problems

ANSWERS to HW problems in section 2-5 are here-pg 108 and here- pg 107.

Reread pg 104 Ex 2 on Consecutive integer problems. Optional video on consecutive EVEN integers with Mario’s Math Tutoring

Pg 105 Ex 3 is a Motion in the Same Direction (a.k.a. overtaking problem) These are hard problems initially, so we will do a few of them every week for a while. We’ll do more in class on Wednesday and again next week and the week after that.

Please watch all three videos and take notes before doing the problem.

HW pg 105 check understanding # 3 (D=RT Motion Problems “Dirt” problems)

PENTAGON HW PG. 108 #10-11

HW p. 107 #1 & 4 SQUARE 8

PH 6-1 Calculate Slope

— we did not do this in class, but we did this in pre-algebra last year. I’ll post videos for those who are encountering this concept for the first time or who need a refresher. (There were some SB handouts that I didn’t pass out due to time constraints. We’ll tackle them next week.)

HW Read p. 282-286 Do check understanding #1-5

Videos— watch at least one and take notes to jog your memory from last year (or if this is brand new to get a preview of this concept. I’ll review it in class next week. We have a bunch of slope handouts to work through that used to be here but which we’re postponing until next week)

PH 6-2 Slope Intercept Form & Standard Form

— just read section 6.2 in your textbook.

Video: Equation of a line, slope intercept form, functions, perpendicular lines & horizontal lines Math Antics Basics of Linear Functions

Note— we’ll review standard form either next week or the following week in class; it’s less useful than slope-intercept form though so we don’t use it as often.

PH 8-1 Review Basic Exponents

HW P. 394 Check Skills #1-9 (answers to “check skills you’ll need” are in the back of the book)

PENTAGON WORK from the orange textbook: Algebra Structures and Methods — PDF of 2.5, 2.7, 2.8, 2.9 HERE

  1. The Distributive Property of Multiplication - Factoring to make problems easier

    • Watch AoPs Introduction to “Distributive Property” Prealgebra Video At minute 3:10, pause the video and do the problem on the screen before Richard, Art of Problem Solving math wiz, does.

    • READ p. 65-66. Do pg. 68-69 problems # 13, 15, 17, 43 49, 63, SQUARE skip 13 and instead 67, 71 PENTAGON skip 15 as well and instead try 73

  2. PENTAGON— problems from the orange textbook — PDF Section 2.7 Adding Consecutive Numbers

    • READ pg. 75-76 examples. Do pg. 77-78 choose 5 problems that don’t involve products 1, 7, 11, 13 (Most students did these in class on Tuesday of week 2 so you get Pentagon bonus points on your homework if you have 5 problems done)

    • Note: you don’t know how to solve equations with both squared variable AND variables raise to the first power yet. Those are quadratic equations which we’ll learn how to factor and then solve later this year.

Optional Geeky Math and Science Videos: Unit Rates and Conversion and Significant Figures