Intro to Algebra 1 Fall Semester

Week 3 & 4 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 3 HW

September 19/20

McD PreAlgebra Textbook problems: McD Chp 2.1-2.5

44 McD problems

  1. Chp 2.1 Properties and Operations (6 problems)

    • Read section 2.1, then DO pg 66-67 PP #29-39 odds.

    • Watch and take notes on AoPs video by math wiz, Richard R (he wrote the Art of Problem Solving Pre-algebra Textbook) “Sum of numbers from 1 to 100” on how to use the commutative and associative property super-powers of addition to rearrange complicated looking problems so they are easier to solve. Pause the video at minute 1:45 and use your super powers to pair up addends (numbers in an addition problem)

    • SQUARE Use your addition super powers (commutative and associative properties) to compute the following with less work (look for pairs that add up to the same number or a multiple of 10) Show your steps!

      • a) 99+99+99+101+101+101

      • b) (3 + 13 + 23 + 33 + 43) + (7 + 17 + 27 +3 7 + 47)

    • PENTAGON use your addition super powers to cleverly compute (1 + 2 + 3… 49+ 50) + (99 + 98 +97…51 + 50) Show your steps!

  2. Chp 2.2 Distributive Property (11 problems)

    • Optional videos from last week:

    • Re-read p. 71-72 example 4, then DO p. 73-75 Guided Practice 7 & 9, PP#13-17 odds, 21-31 odds, SQUARE also do 33, 35, 45 & 47

    • Mixed Review #51, 55 -

  3. Chp 2.3 Simplifying Variables (8 problems)

    • Read pg 78-79

    • Do pg. 81 PP#15-27 odds, SQUARE 29,33, 35 PENTAGON 37 plus MR/TP 39-53 odds

  4. Chp 2.4 Translating Words to Math “Variables and Equations” (5 problems)

  5. Chp 2.5 Solving (or Transforming) One-Step Linear Equations (8 problems)

    Remember— whatever you do to one side of the equation, you MUST do to the other side to keep the sides balanced or equal.

  6. Chp 1 Review (4 problems)

    • pg 52-55 Do #1, 2, 5, 11 - POST ANSWERS TO EVENS

    • SQUARE also watch AoPs video “Sum of numbers from 1 to 100” on how to use the commutative and associative property super-powers of addition to rearrange complicated looking problems so they are easier to solve. Pause the video at minute 1:45 and use your super powers to pair up addends (numbers in an addition problem)

  7. Review Student Reference on Mean, Median, Mode and Range on pgs. 39-40 (2 problems)

    • Devised your own memory trick to remember what mean, median, mode and range are. Write it down in your IMPS section. Include the real definition there too. Then explain to a family member what mean, median, mode and range are and how an outlier (like my age in our class list of ages) affects the measures of where the center is and the range which is a measure of dispersion.

    • Do pg 40 problem #4 and pg 45 problem #28

    • (Answers: 4. mean 111.5, median 111, no mode, range 43. 28. a) -49 m, b) -48 m, c) mean

  8. Correct your own work and redo missed problems.

(You book marked “selected answers” in week 0. You’re usually looking at the selected answers for Practice Problems.) Remember to:

  • Mark correct problems with a little colored dot so you and I know that you have checked them against the answer.

  • Mark problems you missed with slash in color.

  • 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

  • Then use the HW self-assessment form (see button up top) to self-assess your work.

Preview: Rates and Unit Rates

Concepts Studied

Review of arithmetic operations with positive and negative integers, distributive property, simplifying expressions by combining like terms, G/PEMDAS order of operations and commutative and associative properties of addition and multiplication (we call these our super-powers because they enable us to move terms around to solve problems faster, particularly when combined with the knowledge that subtraction is adding a negative.) Identity properties. Solving one step equations using inverse operations.

Review of rates and unit rates, and the distance formula d=rt.

We practice many of these concepts with our algebra tiles, including solving one step equations, and simplifying expressions. We’ll build on these visual representations later when we learn to factor polynomials and divide polynomials in algebra. We use our negative tiles to show how adding opposites ( +7 + -7 =0) or additive inverse yields zero (we call these opposites a zero pair or additive inverses) and we can us this principle to isolate variables by moving constants all to the other side of the equation so we can solve for variables. We model how subtraction is adding a negative as in: 7 - x = 7 + -x. Showing negative terms using Algebra tiles. Making zero pairs (+3 +-3 = 0 — these are additive inverses or opposites which yield zero. Adding and subtracting positive and negative integers using algebra tiles. Postulating a rule given the modeling on how to add and subtract positive integers. Building expressions such as -7 +5x -8. Modeling subtraction is adding a negative with algebra tiles.

Translating words into mathematical expressions. Using algebra tiles work mat to model solving equations.

Intro to Algebra - Week 4 HW

September 26/27, 2023

Multiplication Tables up to 10: quiz yourself — this link has a test on 1-10. The button at the top is 1-12s. Figure out which, if any, math facts you are rusty on. Turn those weaknesses into strengths by creating flashcards for the so you are wicked fast at those. Timed quiz again Wednesday of this week: 40 questions in 60 seconds.

McD PreAlgebra Textbook problems: McD Chp 2.5-3.2 & 9.1

40 McD problems

  1. Everyweek, make a homework checklist and print it out. Cross off each problem as you do it then highlight on that checklist which problems you need to review in class. Staple HW checklist to HW set.

  2. Chp 2.6 Solving 1-step equations with inverse operations of multiplication and division (6 problems)

    • Read pg 97-99.

    • Optional 9 minutes video “Solve Equations - Multiplication Principle”

    • DO pg.99 PP# 11-17 odds, 29, 31, SQUARE also do #19, 25, 27, 39 , PENTAGON also do 35 and watch AoPs “Distributive Property and Subtraction” Prealgebra Video At minute 2:16, pause the video and do the problem on the screen before Richard, AofP math wiz, does. Add again pause the problem at minute 3:22 and attempt the problem before Richard does. Hint: can you write the big number as 1,000,000 minus something?

  3. Chp 2.6 Mixed Review & Test Prep (3 problems)

    • Do pg. 101 #49, 51, 55,

    • SQUARE also do 53, 57, 58, PENTAGON skip 49 and skip the square work in this section. Instead look up in the glossary what a reciprocal is. Then take notes as you watch “Solving linear equations -saving steps by multiplying by reciprocal” with Richard from AoPs (solving linear equations part 2).

  4. Chp 2.7 Decimals and Equations— (3 problems)

    (You may use a calculator on three problems in this section. Then check all your work with a calculator. )

    • Read pg 102-104 examples 1 -4.

    • Do the checkpoints #3-9 odds, and 15 & 17 after examples 1-4 on pages 102-104. Check your answers with a calculator. SQUARE also do 13

    • Next watch this 9 minute 2 step equation video with negative coefficents then read Example 5 on pg 104. then do Guide Practice #11, and on pg 105 PP# 13 & 19 (no calculator) then use a calculator but show your steps on either 25, 31 or 35 (choose 1 problem)

    • SQUARE also do pg 106-7: 37, 42, 44, 53, 55 & PENTAGON skip the square work and do #45 & 56 instead.

  5. Chp 3.1 Solving 2-step Equations -calculator okay (7 problems)

  6. Chp 3.2 Solving 2-step Equations with like terms that need to be combined and parentheses. (8 problems)

  7. Rates & Unit Rates: (3 problems)

  8. PENTAGON - Chp 9.1 Approximating Square Roots and Evaluating Radical Expressions. (10 problems)

    Occasionally I’ll give you sections of the book that I want you to work on without us having gone over similar problems in class. Why? Learning how to read a math textbook is critical. This section is fairly clear. Give it a shot but don’t panic if you don’t understand it yet. We’ll go over it again later in the year.

    • Read page 453-456

    • Do pg 456 PP#17, 25, 29, 33, 37, 41, 45, 49, 63-69 odds

    • A different method for evaluating radical expressions by breaking down the radican into it’s prime factors Simplifying Radicals Easy Method by Mario’s Math Tutoring

Correct your own work using the selected answers at the back of the book

You book marked “selected answers” in week 0. You’re usually looking at the selected answers for Practice Problems. Remember to:

  • Mark correct problems with a little colored dot so you and I know that you have checked them against the answer.

  • Mark problems you missed with slash in color.

  • 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

  • Then use the HW self-assessment form (see button up top) to self-assess your work.

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.

Concepts Studied

  • Using inverse operations to solve equations with multiplication and division such as 7x = 21. How to handle negative signs in these problems. We also modeled these problems first using algebra tiles and then used symbols.

  • Solving two-step equations. Model first with algebra tiles. Examine how in a problem such as 8y - 3 = 21 it is more efficient to move the constant -3 over by adding 3 to each side of the equation (8y - 3 + 3 = 21 + 3) which simplifies to 8y = 24, which can then divide both sides by 8 to get 7 = 3. The less efficient and messier method is to divide all the terms on both side by 8 first (that would leave us with nasty fractions 8y/8 -3/8 = 21/8 and we’re more likely to make errors that way.) How to solve two step equations when there are parenthesis 8y = 5(y -1) and when we need to combine like terms after distributing a factor.

  • Perfect square bingo and then perfect square quiz. Students may retake the quiz on week 5 if they want to improve their score. The old quiz score will remain but an optional second quiz score will be entered

  • Discussed some of the reasons why we show our steps (see notes below) and why we do several of the same type of problem (neurons that fire together wire together. We’re building fluency and automaticity.)

  • Discussed how to prepare for the Chp 1 quiz and Chp 2 mid-chapter quiz in week 5.

    • Review problems in the "Chp 1 Review” section. Attempt some chp 1 or mid-chapter quiz questions.

    • Make sure your homework is organized so if I let you use HW or CW on the test you can find your work quickly.