Intro to Algebra 1 Fall Semester

Week 1& 2 HW

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!

Intro to Algebra - Week 2 HW

Week 2 Concepts: Absolute value, adding, subtracting, multiplying and dividing positive and negative integers, plotting points on a coordinate plane, distributive property, mean, median, mode and range (measures of central tendency and of dispersion).

McD PreAlgebra Textbook problems: McD Chp 1.5 - 2.2 (32 problems)

Week 1 HW - September 5, 2023

Due next Tuesday - No calculators until second semester unless you are checking your work.

Concepts covered: Week 1 Properties of Arithmetic (commutative, associative prop of addition and subtractions), order of operations, basic exponent rules, absolute value, opposites, variables (substituting in a value for a variable, combining like terms, modeling expressions with algebra tiles)

Homework notes:

  • No calculators until second semester unless you are checking your work.

  • Answers to Pre-Algebra McD textbook ODD problems are in the back of the book.

  • GREENIE ANSWER KEYS are here — find the answers to page 3 and 12 by scrolling through. The page numbers which correspond to each lesson are hand-written. There is also a permanent button on the elephant with a link to the answer keys.

Video help:

HOMEWORK

  1. Smart Studying: Annotating notes and giving your self a micro-quiz

    • Review your notes including in your KIN (Know It Notebook) from class

    • Quiz yourself on perfect squares 1-12, as well as all other multiplication facts 1-12. Three times this week.

  2. Review Important Properties of Arithmetic

    Required videos to watch. Take notes— add them to the notes section of your binder. (These videos help you with the AoPs handout problems we did in class on Wednesday.) The founder of Beast Academy and Art of Problem Solving math books, Richard Rusczyk makes these videos. He’s the dude in the video. They are the best.

  3. McD (This is the McDougal Littell Blue Pre-algebra Textbook) — 15-19 problems . Answers to odd problems are in the back of the book.

    • Variables Chp 1.1:

      • Read p. 5-6. Book mark the table on pg 6 “Common words and Phrases that Indicate Operations”—copy this into your IMP (Important Math Principles)

      • Do p. 7-9, PP# 29

    • Powers and Exponents Chp 1.2

      • Read p. 10-11

      • Optional 10-minute video to review how exponents work: Intro to Exponents by Math Antics

      • Do p. PP# 13, 17, 21, 29, 31, Square problem for bonus points #35, Note: you may use a calculator on very large numbers or decimals with exponents but write out what the problem means (for example n^3 = n x n x n)

    • PEMDAS/GEMDAS Order of Operations Chp 1.3

      • Read p. 16-18

      • Optional Math Antics video on order of operations in case you need a review.

      • Do p. 19 PP# 11, 13, 15, 21, 23, 33, 35, 37,

      • SQUARE also do p. 19 PP# 44 (Answer: a) 148 calories. b) 370 calories if a serving of whole milk contains 20 g or protein, the serving is 20/8 = 2.5 cups and 2.5(148) = 370 Calories)

    • Ordering and Comparing Integers Chp 1.4 (Absolute Value and Opposites)

      • Read p. 22-23 (examples 1-3)

      • Optional review VIDEO: absolute value is distance between a number and zero or sometimes distance between two numbers. Watch Math Antics’ 13 minute video here. Video also addresses order of operations

      • Do p. 25 PP# 19, 23, 26 (answer is 22), 29, 47 SQUARE also do 49

    • Adding Positive and Negative Integers 1.5

  4. Correct your own work using the selected answers at the back of the book (you book marked “selected answers” in week 0) Remember to:

    • Mark problems you missed with slash a pen or colored pencil.

    • Redo the problem in the right-hand column and check your work again.

    • If you still don’t get it, make a note of that problem so we can review these

Greenie HW is optional for our current Intro to Algebra Students. It covers Math 8 (which is 1/3 pre-algebra, 1/3 algebra, and 1/3 geometry) and is important if you plan on going into an Integrated Math 1 class in high school or next. If you want a challenge, tackle these problems.

GREENIE ANSWER KEYS are here — find the answers to page 3 and 12 by scrolling through. The page numbers which correspond to each lesson are hand-written.

Greenie is the Math 8 Homework and Practice Workbook

Greenie #3 – Fractions and Decimals – division is multiplying by reciprocal (1.3)

Geenie #12 – 0 and Neg exponents Intro — First watch these videos

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 additionand 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.

  • Key Concepts:

    • Math 8: Chp 1.3, 3.1 Fractions and Decimals: division is multiplying by a reciprocal. Introduction to exponents. 0 and Negative as exponents intro.

    • PA: Chp 1.2-1.4 Properties of Addition and Multiplication, Order of Operations (PEMDAS/GEMDAS), Negation

SMART STUDYING TIPS

In this class we practice smart studying techniques.

Annotate your class notes means

draw examples, related cartoons, create a mnemonic device, and fill in missing bits

and

quiz yourself means

quiz yourself on key vocabulary terms, formulas, or sample problems.

Table of Contents

  1. 9/5 Algebra Tiles 5-6, 9-10

  2. Notes & handouts on Distributive property, other properties of arithmetic

Week 3 HW

Intro to Algebra

4 problems (This was classwork; most students will have finished in class)

Algebra 1

There are 4, 2, homework problems

  1. Sect 1.9 Absolute Value Do pg. 38-39 problems #5, 7, 9, 19, SQUARE skip 5 & 7 and do 27, 43 instead

  2. Section 2.3 Rules of adding + and - numbers: do pg. 56 Written Exercises #17 & pg 57 Problem 7 and one other odd problem of your choice

  3. Consecutive Integers