Homework for Pre-Algebra & Math Games

2021 Spring Semester Homework & Classwork

May Bonus Session- Week 3 of 3 this is for the current week. Check on Week 2 for homework do Monday

Thursday, May 27, 2021

Homework— I’m not finished posting homework. Looking for some new videos to help with probability…. Friday 5/28 8:45

Review (about 30 problems) (these are optional. I’ll assign them on Thursday for students who didn’t have time to do them as Monday’s homework.)

• WATCH Counting Principle & Tree Diagram AoPs Counting with Multiplication Part 1

• McD 6.8 Counting Principle page Day 3 McD 6.8 page 317 problem 17

• McD 8.5 Slope — Chap 8 Mid-chapter quiz on page 418 problems 1-15 all

• McD 9.3 Pythagorean theorem page 467-468: # 23-33 odds (Hint draw a picture of the word problems), Square also do #44, PENTAGON also do #21, 24, 44

• McD 12.5 Other Rules of Exponents READ pages 674-675 and do the checkpoints 1-16 all

• Optional Geometry quiz game: angle measurements, area, volume. https://www.mathgametime.com/games/geometry-quiz

New Material: Probability Compound Events— are they independent or dependent?

Monday, May 24, 2021

Homework
Study for the Chp 7 Test on Thursday 5/27 Use the quiz we did in class today to study for the Chp 7 test on Thursday. Here are the full solutions to our quiz. To study for this test here’s what I recommend.

1. Look over your test. Which kinds of problems did you miss? Make a list of those.

2. Watch the videos under Percent on our Math Videos page. I added 6 new videos to address areas I think you need work on. As you watch, compare the problems on the test to the problems in the video. Can you pause the video and do the problem before Richard does?

3. Look at the “MOST COMMONLY MISSED PROBLEMS” heading below. If you missed those problems, follow the directions I’ve outlined there to shore up your understanding of those problems.

4. Try the Chp 7 test on page 372. I am posting the answers below so you can check your own work. Try it first open brain (no notes or book), then open notes, then open book. Our test will be open book. But that means I’ll shorten the time you have to do it. Or you can do it open brain and then open notes with longer time. You choose.

MOST COMMONLY MISSED PROBLEMS and how to study for those problems. Based on today’s results from the quiz students should review the following:

• The most frequently missed problems were #19 & 20. These are the simply interest problems in which one needs to use the formula A (account balance) = P + PRT and then solve for one of the variables such as R (interest rate) or A. Reread page 362-363 especially example #2. Do the checkpoints for these and on page 364-365 problems 5, 6, 8-13 (6. 1.25 years or 15 months, 8. interest is $500, account balance = $1750, 10. interest = $72,90, balance of account = $672.90, 12. interest = $4, balance of account = $104) We have videos on this on our math videos page under “Interest Rates & Balance of Account); the second video is similar to our problem where we are solving for one of the variables.

• The next most commonly missed problem was #18— this is a find the original price after a discount has been applied problem. (I thought this was the hardest problem on the test.) This is also a 7th grade common core standard so if you are in 7th grade or want to skip 7th grade math, you need to know this.

  • The formula used here is Retail price = wholesale price multiplied by (100% +Markup percent) or

  • Retail price = wholesale price multiplied by (100% - discount percent)

  • This is just like example 4 in 7.6 on page 359. Do the check point #4 (answer is about $66.67) also do page 360 #19-22 (answers to evens 20. about $11.16, 22. $300)

• The next most commonly missed problem was #11 I highly recommend you watch the collection of percent videos on our Math Videos Page, especially where Richard shows us the three basic percent problems and how to solve them.

  If you learn how to translate the sentence into an equation you don’t need to memorize a formula! As you watch, write the problem down and pause the video to try to solve it BEFORE Richard does. See if you can turn the sentence into an equation. Dr. Dan’s videos also demonstrate how to do this. If you missed problem 11, watch the Dr. Dan videos.

  • We can use this formula a = p% multiplied by b where p is the percent, a is a part of the base, and b is the base OR we write it as a proportion: a/b = p/100

  • See example 4 on page 346 of 7.5. Do checkpoint 5 and page 348 #12, 13, 14 (answers to evens 12. 30,000 14. 75)

  • Read the summary on page 347 b = base, a = a part of a base

• Chp 7 Test on page 372 even answers 1. 33/100, 2. 13/20, 3. 24%, 4. 7/50, 5. 0.68, 6. 0.425, 7. 90%, 8. 147%, 9. 51, 10. 72, 11. 82.5, 12. 5.88, 13. 88 games, 14. 22.8, 15. 288.6, 16. 66.6%, 17. 45%, 18. 500, 20. 32.5% 21. 30%, decrease, 22. 10% increase, 23. 37.5% increase, 24. 15% decrease, 25. about $172 billion, 26. $840, 27. $520, 28. $31.95, 29 $150, 30. $1872.72

After you’ve studied for the Chapter 7 test, if you have time you may do these review problems. Otherwise, I’ll assign them for Thursday’s homework.

Review (about 30 problems) (these are optional. I’ll assign them on Thursday for students who didn’t have time to do them as Monday’s homework.)

• McD 6.8 Counting Principle page Day 3 McD 6.8 page 317 problem 17

• McD 8.5 Slope — Chap 8 Mid-chapter quiz on page 418 problems 1-15 all

• McD 9.3 Pythagorean theorem page 467-468: # 23-33 odds (Hint draw a picture of the word problems), Square also do #44, PENTAGON also do #21, 24, 44

• McD 12.5 Other Rules of Exponents READ pages 674-675 and do the checkpoints 1-16 all

• Optional Geometry quiz game: angle measurements, area, volume. https://www.mathgametime.com/games/geometry-quiz

Classwork- took the quiz on percents, worked on review problems, reviewed the quiz answers— how to do each problem.

May Bonus Session- Week 2 of 3

Thursday, May 20, 2021

Homework

• Study for a test on Chapter 7 (Percent Problems). This is one of two hardest chapters in the book and is a required standard for 7th grade. It is also one of the most commonly used bits of math in everyday life so it’s really good to know well. Use the steps we described in class to study (see notes below in classwork)

Classwork

• Learned what a “degree of term” means when referring to polynomials. How to write a polynomial in standard form (highest degree term first then in descending order). How to divide a polynomial by a monomial. (12.1, 12.2, 12.3)

• How to study for a quiz or test

  • Step 1 Ask “What is going to be on the quiz/test?”

    • As soon as you hear that you are going to have a test, listen for information about WHAT will be covered on the test and HOW you will be tested (multiple choice? short answer? essay? can I get partial credit for partly correct answers? It it timed? Open book? Open note? If your teacher doesn’t tell you these things ASK “Mr. Euclid, what is going to be on the test?” Then TAKE NOTES on what they say.

    • For our test it will be 20 short answer question not multiple choice. Yes you can get partial credit for partly correct answers. Yes it is timed (45 minutes). The first try is closed book (open brain and open calculator.) After you’ve completed the test I’ll quickly tell you which problems if any you got wrong and then you may attempt those missed problems a second time with your notes (open notes, closed book). Your notes should include how to do sample problems and formulas.

  • Step 2 Ask “How do you recommend we prepare for this test?”

    If your teacher doesn’t tell you how they recommend you study for the test, ASK “Ms. Pythagoras, how do you suggest we study for this test?” Then TAKE NOTES on what they say.

    • 1 Read all the example problems in each section of chapter 7 of McD. As you read the examples make a list of all the formulas you might need to memorize. Note: the problems in section 7.2 and the “find the percent of the number” problems in 7.3 can ALSO be solved using the percent formula which is taught in 7.4 a = p% of b

    • 2 Do some checkpoints after each example problem and check your answers.

      1. If you are getting them wrong, reread the examples and do more check points.

      2. What other resources do you have? Could you watch videos about how to do these problems (we have videos on our website) Do you have a family member or class mate that you could study with?

    • 3 Do some word problems (these are usually harder than the checkpoints) 1-2 per section

    • 4 Make a study list of all the formulas you might need to have memorized. Memorize these (flash cards?)

    • 5 Do the chapter review evens (I’ll post the answers to even problems by Friday night). It would be smart to cover up the examples as you do the chapter review so it is more like a test. Then peek at the examples after you’ve attempted them. This simulates a test. Answers to even problems: 2. markup, 4. Principal is $500, Interest earned is $10, balance is $510. 6. 17/20 (note how this fraction is simplified) 8. 7/25 (also simplified from 28/100) 10. 35% you my use your calculator to do this instead of doing long division 12. 96% 14. 30 16. 63 18. 69 20. 85 24. 130% 26. 300%, 28. 56.25% 30. 120% 32. 39.26 34. 5.4 ALSO DO 35. $78.75 36. 10.4 38. 90% ALSO DO 39. 32 40. increase of 80% 42. decrease of 4% 44. 41.8 46. $209 ALSO DO 47. $280.50, 48. $918

  • These definitions may be helpful since percent problems are in some ways as much about vocabulary as they are about percentages.

    • wholesale price = price the store pays to get the item,

    • markup = how much more is added to the wholesale price- usually a percentage of the wholesale price (wholesale price multiplied by 50% or 130% )

    • retail price = price the costumer pays the store (usually after a mark-up has been applied to the wholesale price)

    • sales tax = percentage of the original bill (like the wholesale price) added to the final bill (solve this like a markup problem: the mark up is the food bill multiplied by the sales tax, say 8%).

    • taxi/uber fare= bill or cost of a tax/uber ride.

    • tip = additional amount of money given to a waiter or driver for good service as a percentage of the bill usually between 10-20%

    • commission = just like a tip, an amount of money a worker earns as a percentage of the sale/bill

Monday, May 17, 2021

Homework

New Material (about 30 problems) updated at 8:24 on Tuesday 5/18

• McD 13.3 Polygons & Angles page 725 problems 1 -7 all, 9-25 odds, 37 -47 odds.

• McD 9.3 Pythagorean theorem page 467-468: # 8-18 evens, SQUARE & PENTAGON also do 20-32 evens.

• McD 6.8 Counting Principle page 315 problems 8- 16 evens, Mixed Review 21-29 odds

  • Optional: WATCH either Moo Moo Math Compound Events Tree diagram Moo Moo Math https://www.youtube.com/watch?v=yxJi5vuO_wU OR Kevin Dorey video https://www.youtube.com/watch?v=Iybt-PMPfQ0

• PENTAGON 13.2 Angle chasing with variable expressions in the angles not just numbers.

  • WATCH Richard from AoPs solve problems involving angles and parallel lines Try pausing the video when he starts to do a problem and and see if you can draw it out, write the equation and solve it. Un-pause after you do each step to see if you are on the right track.

  • Watch one of these more complicated angle chasing videos

    • Much more complicated angles when there are parallel lines with a transversal cutting across two parallel lines with Mario

    • Another sample of finding angles when parallel lines are cut by a transversal https://www.youtube.com/watch?v=uOrXWJQ8vWA&list=PLCqwggKH0w8b3J9_iGeax3huTLTBxl-iS&index=2

  • OPTIONAL: After watching this if you’re feeling bold you can attempt problem 2.12 on our geometry hand out from a week ago (it’s from the AoPs Geometry textbook). It’s a very challenging angle-chasing puzzle!

Review (about 35 problems)

• McD 8.5 Slope intercept form Re-READ page 412-414. DO pages 415-417: problems 2-20even, 43, 45 PENTAGON 22, 24, 26

• McD 12 Polynomials— we did these with algebra tiles in October. I’ll go over a bit of 12.1 terminology and 12.3 in class on Thursday so I’m not giving you review problems on those portions as those are new.

  • DO chapter 12 Prerequisite skills quiz on page 650 problems 1-13 odds.

  • READ chapter 12.2 Read example 1 on page 657— this called the vertical format and it’s one way to combine like terms. DO checkpoints 1 & 3. Read examples 2-4 on pages 658-659. Do checkpoints 7-11 odds. DO page 660 problems 13-27 odds (watch your signs when you’re subtracting a quantity within paratheses:

    for example 5x - (3x + 37) is 5x -3x - 37 Do you remember why this is so?

  • READ chapter 12. 4 Multiplying Binomials page 667— get out your algebra tiles and do problems 1-6 all. Choose 2 problems to draw out your answer. Then read pages 668-669 (We did these kinds of problems about a month ago)

  • Chapter 12.4 READ pages 668-669 Examples 1-3. DO page 670 problems 1-25 odds

Classwork

Angles: Looking for patterns for the sum of angles within polygons. How to figure out the measure of degrees in an n-sided polygon? Degrees of an interior angle of a regular polygon? What are exterior angles?

What’s Next?

After this work on angles, we’re going to

1. Review ratios, proportions, and percent. These are the hardest concepts for most students and are also 7th grade common core standards.

2. Review surface area and volume of 3-D figures & statistics/data analysis and if time solving equations with fraction bars in them (also 7th grade common core standards)

3. Explore new material

   • 11.9 probability of independent and dependent events

   • 12.8 sequences puzzles

   • 13.4 Translations and tesselations— MC Escher’s art work involves tesselations! We’ll make our own tessellating art.

By the end of the three June bonus Super Math Days we will have covered almost all of McD and a fair chunk of AoPs too. That’s all of an advanced 7th grade common core curriculum and we’ll have taken a fair bite out of an advanced 8th grade common core curriculum.

(If you’re interested in the break down, there are about 15-16 sections out of 110 sections of McD which we haven’t worked on extensively: 8.6, 8.8, 8.9, 9.5-9.8, 11.6-11.8, 12.6-12.8, 13.5-13.7. These are all either 8th or 9th grade common core concepts such as tangent/cosine/sine, quadratic functions, and systems of equations. I have shown students some of these concepts so they aren’t foreign next year but we won’t have worked on them systematically because it makes more sense to leave these advanced concepts out in the interest of mastering foundational concepts such as fractions, ratios, percent, and solving linear equations. They’ll get those concepts in Algebra 1 or Math 8H or Math 1H. They don’t need them in pre-algebra, frankly. Incidentally, these are the same concepts that my two amazing math department chairs in Cupertino skipped in our 7th Honors Pre-Algebra class and since those math educators are the best in the state, so I’m happy to follow their wiser more experienced lead.)

If you want to buy McD to use to study over the summer or use as a reference next year, let me know. With shipping they were $15. I may post SHORT review assignment once a week with about 10-20 problems from McD and AoPs over the summer for my own kids to work on so they don’t loose all these hard won skills during July & August!

May Bonus Session- Week 1 of 3

Thursday, May 13, 2021

Homework: Make sure you are showing your work. We will be starting quizzes soon and answers without work will only get partial credit.

• McD 13.2 Angle Puzzles page 718-719: # 2-22 evens, 26-32 evens

  • PENTAGON -challenge problem #24. Hints: first extend the transversal lines made by the sides of the triangle. Doing so will make it easier to see the alternate interior angles. Second hint: look for the straight angle B— what does this tell you about angle 2? This is is pretty hard but worth spending some time thinking about.

• Geometry Handout: finish all the problems

• McD 9.3 Pythagorean theorem page 467-468: #1-6 all, 7-19 odds, Mixed review 37-43 odds We’ll check the even guided practice problems in class.

• McD 6.8 Counting Principle page 315-316: # 1-6 all, 7-15 odds We’ll check the even guided practice problems in class.

• Review Chapter 10 on your own. I suggest reading all the examples and doing the check points. Bring me any questions or examples you want help with. UPDATE: This may take some students more time to do. If so, you may work on this next week as well. 5/14/21

Answers to even 13.2 problems 2) they are parallel, 4) corresponding, 6) Alternate interior 8) 1. corresponding, 2. 8x degrees= 32 degrees 3. 4 10) alternate interior, 12) corresponding, 14) angle 2 = 137, angle 3 = 137, angle 4 =43, angle 5 =43, angle 6 =137, angle 7 = 137, angle 8 = 43. 16a) false - they are alternate interior angles, b) true alternate interior angles formed by a transversal intersecting parallel lines have the same measure. c) tur angle 2 = angle 3 = 45degrees, and 45 + 45 = 90 degrees, 18) 20 2/3 20) angle 1= 100, angle 2 = 80, angle 3 = 100, angle 4 = 80 22) identify two corresponding angles formed by one of the transversals (the diagonal lines running across the parallel lines) then measure their angles. They should be the same measurement if the parallel lines are indeed parallel. We’ll do 24 in class. 26) 23/28 28) 44 30) neither, 32) D

Answers to Geometry handout: 13) any pair of vertical angles have equal measurement. 14) 15 and 75 degrees. 15) 36 and 144 degrees, 16) 30 and 60 degrees, 17) 72 and 108 degrees, 18) 18 and 72 degrees, 19) 30 and 150 degrees, 20) 36 and 54 degrees.

Classwork

Bingo term review— emphasis on geometry terms, angle puzzles, Pythagorean theorem problems, probability problems— using the counting principle for independent events. Next week we’ll review percent problems more

Monday, May 10, 2021

Homework: Make sure you are showing your work. We will be starting quizzes soon and answers without work will only get partial credit.

Bring AoPs on Thursday again, and your compass and protractor.

Review: Slope, Percent, Classifying triangles

• McD 8.4 Slope Review DO p. 407-409: 3- 35 odds, Mixed Review 41-53 odds. SQUARE also do problem 39. PENTAGON also do problem 37.

• McD chp 7.1 REREAD pages 329-330 DO checkpoints 1-9 all and chp 7.2 pages 335-336 DO checkpoints 1-6 all and 7.3 pages 340-341 DO checkpoints 1-17 odds

• AoPs 8.1 Percent Read pages 320-321. Do gray problems 8.1-8.6 (we did most of these in class). Then read the solutions on the following pages.

• McD chp 9 Triangles READ Student Reference p 462-463. DO Checkpoints 1-10 all. (These are quick!)

New Material

• Constructions with a compass: RE-READ McD page 714-715 instructions on how to make perpendicular bisectors, copy an angle and angle bisectors using your compass. We started the following activities in class. DO:

  • Make 2 perpendicular bisectors

  • Copy 4 angles

  • Make 4 angle bisectors.

  • Then teach someone in your family how to do each of these things.

• Square roots McD p. 460-461 2-20 evens, 21-25 odds, SQUARE 24 & 26, PENTAGON 27 -33 ALL

• PENTAGON McD Investigating Right Triangles Concept Activity McD p. 464- do the activity and answer the “Draw conclusions” activities. This helps us understand why the Pythagorean theorem is true.

Correct even problems from last week’s homework: McD pages 455-456 problems 2-44 evens

2) 9; 81, 4) + or - 6, 6) + or -15, 8) -9, 10) -14, 12) +or- 5, 14) +or- 20 16) + or - 5 18) +or - 9 20) +or- 32 22) +or -40 24) 7 ft 26) 111 28) 4 30) 16 32) -3 34) -3.2 36) 10.5 38) 36.4 40) 2.6 42) 8, 44) 9

Classwork: we learned how to use our drawing compasses to make perpendicular bisectors, copying angles, and bisecting an angle. We then practiced this new skill over and over. We reviewed how to write percentages as fractions and solve percent problems using either fractions or decimals. We started our homework!

Week 12

Thursday & Friday, May 6-7, 2021

Homework- due Monday. Note— I shortened the homework on Friday at 3:00 p.m. I moved the slope review homework to this coming Monday.

Make sure your bingo board is neat and complete by tomorrow. Have a board that has at least 49 spaces! It should have these terms on it:

1. # of degrees in a triangle = 180

2. number of degrees in a circle and 4 sided polygon = 360

3. BH/2 = Area of a triangle or 1/2 (BH),

4. Circumference = ∏D or 2∏r

5. Area of circle = ∏r-squared

6. Pythagorean theorem = a-square + b-squared = c-squared

7. Radical sign (undoing squaring) Square root of a non-negative number (n) is a non-negative # whose square is n

8. Equilateral triangle = all sides are the same

9. Equiangular triangle = all angles congruent

10. Obtuse Trianlge = one obtuse angle

11. Right Triangle

12. Isosceles triangle= two congruent sides

13. Acute triangle =all angles are acute (less than 90 degrees)

14. Scalene triangle = no equal sides triangle

15. (x,y) = ordered pair or input, output

16. x —> input (in a function)

17. y-> output (in a function)

18. function = a special relationship between input and out - for each input there is exactly only one output

19. Range = all the y outputs

20. Domain = all the x inputs

21. slope intercept form y = mx + b

22. m = slope

23. b = y-intercept

24. Squares of a product property (ab)-squared = (a-squared) (b-squared)

25. ∏ is approximately 3.1416 Ratio of diameter to circumference of a circle

26. Area of parallelogram =BH

27. Irrational number = Decimal that goes on and on w/o repeating or terminating (ending)

28. Slope formula = m = m = Y₂ -Y₁ / X₂ - X₁ or change in y/change in x which we write like this ∆ in y / ∆ in x

29. Negative exponent —>reciprocal

30. Perpendicular sign

31. reflex angle - measuring the “long way around”

32. adjacent angles= share a line or ray

33. supplementary angles = add up to 180

34. complementary angles = add up to 90

35. vertical angles are across the same vertex from each other and are equal

Square Roots & Simplifying Square Roots (review & some new material)

• McD 9.1 Square Roots— READ McD 453-455. DO pages 455-456 problems 2-44 evens, 45-65 odds SQUARE also do 69, PENTAGON 67 & 69

• McD 9.2 Simplifying square roots READ McD 458-459. DO checkpoints 1-4 on page 459. DO page 460: 1-19 odds and Mixed Review 35-45, 47

• If you need help, check out our math videos page for great videos on how to do these problems under the heading “Square Roots”

Angle Relations: Angles and Parallel Lines (review and some new material)

• McD 13. 1 Vertical, supplementary, complementary angles READ McD pages 709-10. DO pages 711-713 problems 1-27. SQUARE also do 29, 31, 33. PENTAGON also do 31, 33, 35

• McD 13.2 Angles and parallel lines READ pages 716-718 all examples. DO pages 718-720 problems 1-19 odds, SQUARE also do 21. PENTAGON also do 23 & 24.

Classwork: Bingo math terminology review. Simplifying square roots & angle problems. Practice simplifying square root problems. Corresponding angles are equal if the lines are parallel. Alternate interior angles are equal if the lines bisected by the transversal are parallel. Alternate exterior angles are equal if the lines bisected by the transversal are parallel. Practice solving angle-chasing problems. Class time to work on homework.Classwork: Bingo math terminology review. Practice simplifying square root problems. Corresponding angles are equal if the lines are parallel. Alternate interior angles are equal if the lines bisected by the transversal are parallel. Alternate exterior angles are equal if the lines bisected by the transversal are parallel. Practice solving angle-chasing problems. Class time to work on homework.

Week 11

Thursday, April 29, 2021— Students need a drawing compass next week by Thursday.

Homework

Linear Equations

• McD 8.5 Slope intercept form READ page 412-413. PENTAGON also read page 414 about parallel lines and perpendicular lines and read example 4. DO pages 415-417: problems 1-19 odds, 23-27 odds, Mixed Review 35-45 odds

  • SQUARE also do #21

  • PENTAGAON also do #29, & 31— remember the slope of a line perpendicular to another line is the negative reciprocal of other line’s slope.

Geometry: Vertical and Supplementary Angles (this is also in McD chp 13)

• WATCH Angle basics from Math Antics

• WATCH Richard from AoPs explain straight angles (a.k.a. a straight line) https://www.youtube.com/watch?v=EjTaOODJTVg

  • After Richard writes the supplementary angles problem on the board, pause the video and try to draw a picture of the problem. Unpause. Then try to write an equation before he does. Then once he’s written the equation, pause the video and YOU solve for “c” and then figure out the measurement of each angle before he does. Then watch him and correct your work.

  • Do the same when he writes the vertical angle problem on the board.

• WATCH Supplementary & complementary angles from Mr. J

• Handout titled “Chapter 2 Angles” from AoPs Geometry textbook. READ page 14 and then DO problems 2.1-2.11

• SQUARE & PENTAGON also…

  • WATCH Richard from AoPs solve problems involving angles and parallel lines Try pausing the video when he starts to do a problem and and see if you can draw it out, write the equation and solve it. Unpause after you do each step to see if you are on the right track.

  • WATCH this video about supplementary angle problems with variables and equations

Square Root Introduction (McD Chp 9.1)

• READ McD 453-455. DO pages 455-456 problems 1-43 odds. (These go fast)

Review: Percent

• If you are running out of time this weekend, do 1/2 of this chp 7 review now and 1/2 on Monday: McD Chp 7 Chp Review (Percent) pages 368-371 problems 1-49 odds

Classwork

Reviewed slope and slope intercept form. Practiced transforming equations into y = mx + b slope intercept form and finding the slop and y-intercept. Introduction to vertical angles. We drew intersecting lines, measured the angles and discovered that the vertical angles are always congruent (equal). Figured out what a straight angle is (a straight line) and why it is 180 degrees. Then used that information to deduce how to figure out supplementary angles (add up to 180 degrees). We applied this to multiple sample problems as well as harder ones with variables. Next we dipped out toes into solving square root problems.

Monday, April 26, 2021

Homework: I’m not assigning any NEW material out of the textbook (BUT we will have review material out of the textbook). Instead for new material practice, watch the videos below and do the small problems presented in the videos when the instructor tells you to pause the video and do the problems. Note— you’ll see all this again in your algebra class/Math 8/Math 1 classes.

New Material: Function Notation— The parentheses after the f(3) = 4x - 2 DOESN’T mean multiply 3. I know, that’s weird. It means “plug in this quantity of 3 wherever you see x.” So you would do this f(3) = 4 (3) - 2 which = 12 - 2 = 10

• WATCH this introductory video on function notation Do the problems with the instructor (Kevin Dorey) and add them to your math notes.

• WATCH this video on function notation from Mario’s Math Tutoring.

Review Material: Slope

• WATCH these videos. I’d like your feed back on how helpful it is to do the problems while watching the videos.

  • TRIANGLE: Introduction to slope: WATCH this video on steepness and direction of a line and slope and DO the problems Kevin tells you to pause the video and do.

  • ALL: Calculating slope from a graph WATCH this video on figuring out slope by looking at the graph of the linear function. DO the problems Kevin tells you to pause the video and do.

  • TRIANGLE & SQUARE: Slope Formula change in y/change in x WATCH THIS VIDEO Calculate slope using any two points on a line and DO the problems Kevin tells you to pause the video and do.

  • PENTAGON: slope of parallel and perpendicular lines WATCH this video This is advanced and you won’t be doing the stuff at the end of next year but it’s cool.

• DO McD 8.4 Slope of a Line p. 407-409 DO problems 4-30 evens.

Review Material: Ratio, Proportion, and Probability & Solving multi-step equations and inequalities

• McD Chp 9 Classifying Triangles READ student reference p. 462-463 then DO Checkpoints on page 463 #2, 6, 8, 10. Answers will be posted Wednesday or discussed in class.

• McD Chp 6 Chp Review (Ratio, Proportion, Probability) pages 318-321 DO odds #1-33 (We haven’t learned section 6.8 students doing PENTAGON works should attempt problem 35 after watching this video on tree diagrams by MooMooMath and reading the example in the review. If you need another video here’s one)

• TRIANGLE ONLY McD Chp 3 Review (Solving Multi-step equations & inequalities) pages 154-157: all odd problems 1 -33 odds

Get Ahead (8.5) OPTIONAL: How to graph a line when you have an equation in y = mx + b or slope-intercept form. WATCH this video.

Classwork

We played perfect square bingo and new vocab bingo. Then we worked on function notation (section 8.7 of McD). Function notation f(x)= 25x +4 looks weird the first time you see it (we looked at it briefly last week). This is partly because we’ve spent a year thinking of parentheses as meaning multiply. But in this situation it means “substitute in this quantity w/in the parenthesis when every you see x” We’ll do more of that on Thursday. Then we’ll probably jump ahead to chapter 9 and slightly more familiar concepts while we let the linear equation/slope/graphing concepts rest in our minds for a bit and the spiral back to it during the June bonus time.

Week 10

Thursday, April 22

Homework -Even answers posted 2 pm Friday 4/23

• McD chp 8.4 Slope = m = rise/run or ∆ in y / ∆ in x

  • Download these three pages:

    • Steps for using x and y intercepts to graph an equation of a line as in #9 in 8.3

    • Square of a product— DO the five problems on this page Solutions are here.

    • Slope formula which isn’t in the book m = Y₂ -Y₁ / X₂ - X₁.

  • Watch a few of the videos on slope on our Math Videos Page if you haven’t yet.

  • READ p. 404-406. DO pages 407-409: problems 9-33 odds and mixed review 45-53 odds. SQUARE - also do 34, 35 and try 39. PENTAGON - also do 37 & 38. Answers: 34. A line with zero slope is a horizontal line and the y value is always the same for every x value and it has a slope of 0. The equation of a horizontal line is y= some number. Whereas a line with an undefined slope is a vertical line. It has the same x value for every y. The equation is x = some number. 38. Slope is rise over run. So the slope of the steepest part of trail A is 15/50=3/10 and the steepest part of trail B has a slope of 30/75 = 2/5= 4/10. 4/10 is a steeper slope than 3/10. The bigger the value of m for the slope, the steeper the slope is. Since 4/10 is bigger than 3/10 the trail with a 4/10 slope is steeper. Or you could convert both fractions to decimals and compare them.

• McD chp 8.3 x & y intercepts

  • DO page 400-402: problems #4-26 evens, and problem 9 (see hint sheet above “Steps for using x and y intercepts” This is like the treats problems we did with chocolate and gummies and apples and cherries). SQUARE also do 27, 29, 30. PENTAGON also do 32, 33. Answers 4. x-intercept = -2 and y-intercept = 4. Answers to 6-24 are here . Answers to problem 26 & 32a are here

• McD parallel, perpendicular and skew lines READ student reference pages 410-411 to refresh your memory

• AoPs Square Roots

  • Read p. 351-352 of AoPs chapter 9.

  • WATCH: If you didn’t watch Richard’s review of square root awesomeness, watch it now: Square Root introduction part 1 by Art of Problem Solving

  • DO Gray Problems 9.1-9.3,

  • Ask a parent to quiz you on the squares of 1 through 20. Identify the ones you don’t know, make flash cards and start memorizing them.

• Check the answers for Monday’s 8.3 even problems on p. 402 I posted the answers using the wrong browser so they didn’t stay posted. Here they are: 34. 3, 36. -5, 38. 30% increase, 40. 50% decrease, 42. yes, 44. no,

Optional Get Ahead video watching

• Refresh your memory of the exponent laws so working with squares and square roots is easier: Summary: Laws of Exponents from Math Antics: https://www.youtube.com/watch?v=LkhPRz7Hocg Write these rules down (again— you should already have them in your notes). There are more exponent videos on our Math Videos Page

• Do you remember the divisibility rules? Quiz yourself: write them down from memory then check your Art of Problem Solving book or our Math Videos page for the divisibility rules.

Classwork

We played perfect square bingo, then added new math terms and equations and symbols to our new bingo sheets (Pythagorean theorem, slope intercept form of an equation). We examined why we define the square root as the NON-NEGATIVE root of a NON-NEGATIVE number and practiced products of squares problems. Solved function problems by graphing a linear equation in two variables by solving for x and y intercepts, then graphing those two points and interpreting the graph. Slope is a ratio. It’s the change in y / change in x = difference in y’s / difference in x’s. Positive and negative slopes, and equation for slope of a line. Preview of function notation ∫(x) = 3x + 1 which will appear in 8.7 (I try to introduce new or tricky concepts or concepts with a lot of new vocabulary a week or two or sometimes months ahead of when we’re going start using it so it has time to sink in. We call this spiraling. We’re doing this with the square root problems as well as function notation and we’ve been doing a little bit of slope stuff for weeks before this week’s actual slope homework. We’ll also take a little break from new chapter 8 materialsoon so students can do several sets of review with this material before we move on to new function material.)

Monday, April 19 - lighter homework due to state testing

Homework

• McD chp 8.3 x-intercept and y=intercepts

  • If you didn’t watch the videos from last week, do that now.

  • RE-READ example 1 on page 398 of McD. then DO checkpoint #1

  • Read example #3

  • DO p. 400-402: 1, 3, 5, 7 and 11-17 odds, 21, 23, 25. Mixed review 34, 36, 38, 40, 42, 44 (answers will be posted on Tuesday evening. Sorry I used the wrong browser when editing the website so the answers I posted didn’t stay saved. Super weird. Here they are again: 34. 3, 36. -5, 38. 30% increase, 40. 50% decrease, 42. yes, 44. no,

    • SQUARE AND PENTAGON also do #9 and 19.

• McD chp 8.4 slope

  • Watch the videos on slope on our math videos page.

  • Read p. 404-406.

    • TRIANGLE and SQUARE: DO check points 1, 3, 5, 7

    • PENTAGON attempt p. 407-409: problems 2-36 evens

• Optional Get ahead video watching

  • We’ll be working on square roots so refreshing your memory of the exponent laws would be prudent. Summary: Laws of Exponents from Math Antics: https://www.youtube.com/watch?v=LkhPRz7Hocg Write these rules down (again— you should already have them in your notes). There are more exponent videos on our Math Videos Page

  • Square Root introduction part 1 by Art of Problem Solving

  • Do you remember the divisibility rules? Quiz yourself: write them down from memory then check your Art of Problem Solving book or our Math Videos page for the divisibility rules.

Week 9

Thursday April 15

Classwork

We worked lots of functions problems focusing on: how to write an equation in function form (y = stuff here)and how to write an equation in slope intercept form (y = mx + b). How to make a table to figure out ordered pairs to graph an equation. Problem solving strategies: how to rewrite a problem in a simple way to see if you know how to solve it, then go back to the original problem and solve it using the same steps/procedures. Why is the equation of a horizontal line always y = some positive or negative number, and the equation of a vertical line x = some positive or negative number?

Homework- we will have light homework this week due to state testing

New Material

• McD chp 8.2 DO p. 395: # 14, 18, 22, 28, 30, 33, 34, 35, 36, 37, 38, SQUARE also do 39c, & 41. PENTAGON also do 39c, 41 & 42

  • Answers to even questions: we’ll look at the graphs of the equations in class 14. yes, it’s a solution 18. yes it’s a function, 22. no it’s not a function (it’s vertical line so it can’t pass the vertical line test. 28. y= 1/3(x) + 3 30. y = 5/2(x) - 3. 34. 146,000 square km 36. a = -2, 38. a = 4, 42a. the y's are in order {9, 4, 1, 0, 1, 4, 9} 42b. we’ll look at the the graph in class (it’s a parabola- U-shaped curve with the y intercept at -2) 42c. No it isn’t a linear equation because linear equations are LINES and this is a curve. But it is a function because it passes the vertical line test.

• WATCH video of Mario’s Math Tutoring on equation of the horizontal and vertical lines

• We have many new videos that I’ve curated for our Pre-Algebra video website. You’re welcome to go watch those if you have more time; press the “Math Videos” button above.

Review Material

• WATCH

  • Solving linear equations with fractions part 1 with Richard from AoPs (includes clearing fractions method): https://www.youtube.com/watch?v=BtWX9kSNWrc&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=7

  • Solving linear equations with fractions part 2 with Richard from AoPs (also includes clearing fractions method to knock out the fractions): https://www.youtube.com/watch?v=aW4fKupD0eQ&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=8

  • Solving linear equations - special cases with NO SOLUTION or INFINITE SOLUTIONS with Richard from AoPs: https://www.youtube.com/watch?v=yPWu02VnGxM&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=9

• AoPs 5.3 Solving linear equations part 2. DO AoPs page 215 problems 5.12-5.15. PENTAGON DO 5.13 - 5.17 )

Monday April 12

Classwork

Solved a challenging daily puzzler in which we had to take an equation in two variables and write it in terms of one variable to plug that into the other equation to solve it. Phew! Reviewed what is a function, made a table of solutions to find ordered pairs to plot on a coordinate plane. Made graphs of horizontal lines & vertical lines (the equation for a horizontal line is always y=some number and the equation for a vertical line is always x = some number). Put equations in “function form” y = mx + b. Introduced slope intercept form. M = the slope of a line which is the change in y over the change in x (sometimes called the rise over run). b = is where the line hits or intercepts the y-axis. Compared similar linear equations with same slope and different y-intercepts.

Because more than half our students have state testing this week, we’ll have light homework.

Homework

New Material

• McD 8.1 Relation & Functions Do p. 388-390: 8-20 evens. Square- also do problem 21. Pentagon also do problems 21, 24, 26.

• McD 8.2 Linear Equations in Two Variables Reread the examples 3-5 on pages 392-393. DO page 394-5: 13-31 odds.

Review

• McD 7.7 Simple and Compound Interest p. 365-6 problems 17-24 all, Square also do #37. Pentagon do #25 & 26

• AoPs 5.3 Solving Linear Equations— This is the same review as from Thursday however some students didn’t find the problems as the page number was wrong— it’s 223 not 233 so if you didn’t do these last week, do them this week.

  • TRIANGLE: AoPs page 223 Exercises 5.3.1 - 5.3.4

  • SQUARE: AoPs page 223 Exercises 5.3.1 - 5.3.5, 5.3.6a

  • PENTAGON AoPs page 223 Exercises 5.3.1 - 5.3.5, 5.3.6 b & c

Week 8

Thursday April 8

Classwork

Discussed what simple annual interest is versus compounding interest. (Compound interest is when you are earning or paying interest on interest that has already accrued (earned). We did side by side comparisons of me borrowing $100 from Holden and paying 2% simple interest annually versus paying interest compounded annually. With the interest compounded annually, each year I was paying interest not just on the $100 (principal) I borrowed but on the interest that was charged from the previous year so the balance was growing faster and I owed him a bit more money at the end. If the interest rate or the principal had been larger amounts I would have owed him much more money in the end!)Reviewed relations and functions. Reviews vocab terms (input, output, domain, range). Learned how to map a relation, graph an ordered pair (x,y). What is a function? It’s a specific kind of relationship between the x’s (inputs) and y’s (outputs). An input can only have one output. Recall the example we did with age and height? At any moment in time (x years old), Carter can’t be both 3 feet tall and 6 feet tall. He can only be one height (y an output) at a given time (x). But he might not have grown at all one year, so at x age (3 years old say) he could have been 3 feet tall and stayed 3 feet tall at 4 years old (another x input).does it pass the vertical line test?

Homework

Homework is mostly the same for everyone. REMEMBER TO CORRECT YOUR WORK!!!!

New Material

• McD 7.7 Interest Compounded Annually

  • READ p. 363 description of compound interest and example #3 on page 364 to refresh your memory

  • DO the one-page handwritten compound interest problem set which I gave out in class PROBLEM 6 SHOULD READ “Why is the interest not HALF what you earned in problem 5” instead of “double: (If you need another copy of the handout it’s available to download  here). Solutions are here. Remember, these problems are just plug in/substitute values for the variables. Don’t let converting to a percentage rate to a decimal or large numbers intimidate you.

  • PENTAGON- Also do the Technology Activity on page 367 “Computing Compound Interest” — Many investment accounts or credit card accounts don’t just compound the interest annually, they compound it more frequently— up to daily! So there is a slightly different formula for figuring that out. Read the page and do the “Draw Conclusions” problems.

• McD 7.7 Simple Interest DO McD page 364-366 problems 2-16 evens (we did 12 & 16 in class), Mixed review 29-37 odds. PENTAGON— also do problems 22, 24.

  • Answers to even problems 2) sample answer: in simple interest, interest is earned only on the original principal, while in compound interest, interest is earned on both the principal and any previously -earned interest. This is why when you are investing, compound interest works in your favor but as a borrower means you end up paying back more money. 4) Interest = $56.25, Account balance = $2556.25. 6) t = 1.25 years or 15 months. 8) Interest = $500, Account balance = $1750. 10) Interest = $72.90 Account balance = $672.90, 12) Interest = $4, Account balance = $104. 14) $306. 16) 6.25

• McD 8.1 Relations and Functions

  • ALL: READ p. 385-387. If you need another explanation of what a function is, re-WATCH this video with Rob of Math Antics.

  • TRIANGLE: DO the checkpoint problems after each example on page 385 & 386.

  • SQUARE & PENTAGON: Do p. 387 guided practice 1, 3, 5 all, page 388: 9-17 odds.

Review Material

• McD Chp 2 Review (Solving 1 step equations) pages 108-111 problems 1-47 odds. Do not use a calculator. Yes, you have to solve the decimal problems on paper.

• AoPs 5.3 Solving Linear Equations.

  • TRIANGLE: AoPs page 223 Exercises 5.3.1 - 5.3.4

  • SQUARE: AoPs page 223 Exercises 5.3.1 - 5.3.5, 5.3.6a

  • PENTAGON AoPs page 223 Exercises 5.3.1 - 5.3.5, 5.3.6 b & c

Classwork Monday April 5:

Linear equations— x’s are inputs, and all the inputs are the domain. y’s are outputs and all the outputs are the range. Functions are a relationship that for each input there is exactly one output. (different x values -inputs- can yield the same output, but for one input x, there can be only one output y, otherwise it is not a function. More on that Thursday). Simple interest = Prt P= principal amount, r = rate, t= time in years. These problems sort of blew student’s minds today so we’re going to do just a few problems today and we’ll do more Thursday. I’ve found two good videos that review this material. This is just about plugging in numbers into an equation and solving for the unknown variable, but the numbers are big and involve decimals so that can be daunting at first. I keep reminding the students part of math is learning the vocabulary. Thursday we’ll play bingo to help solidify these new terms in our minds.

Homework- mostly the same for triangle, square and pentagon- check your work using a different color pen/pencil & redo incorrect problems.

I FIXED PROBLEMS WITH THE HOMEWORK AT 1:56 PM Tuesday: correct review homework is there now and easier interest problems posted. And I eliminated the fraction review. I’m sorry for the mix up!

Review Material (if you need a refresher on how to do these problems look back at example problems in the text book or on our math videos page)

• McD Percent problems Mid-chapter quiz DO page 350 problems 1-22 all

• McD 7.6 Applications— Word Problems READ pages 357-359 examples. DO p. 359 problems 1-23 odds

• AoPs section 5.2 Solving Linear Equations I. DO AoPs pgs. 214 Exercises 5.2.1- 5.2.5. Pentagon Do 5.2.6 also.

New Material

• Simple Interest: WATCH— video by Mario on simple interest and the first 7:30 minutes of this video —> organic chemistry tutor do several simple interest problems including ones where you are solving for the rate (r) or t (time in years to earn a certain amount of interest) (the last 3 minutes is an advertisement for an algebra course)

• McD 7.7 Simple Interest READ McD p. 362-363 (stop at compound interest) Read examples 1 & 2.

  • Triangle & square— Simple Interest Problems by Ms. Lisa set #1 Solutions are here. I recommend you look at the solution for the first one after you do it to make sure you’re on the right track.

  • Pentagon—DO McD page 364-365 problems 1-17 odds

• Get ready for linear equations: McD 8.2 Linear Equations in two variables. Read the examples McD p.391-392. Then WATCH this video with Rob of Math Antics.

Week 7

Classwork Thursday 3/18: Applying our knowledge of percents to word problems. More input-output box puzzles to prepare us for working with functions. Dipping our toes into new concepts: Using x,y coordinates generated by plugging values into a function to graph a line. Function form or slope-intercept form of a line (y = mx + b) where m is the slope or steepness of the line and b is where the line hits or intersects the y-axis.

Recommended videos: If you have a Great Course subscription, I highly recommend you watch episodes 6, 7, 8, 9, and 10 of “Algebra 1” with James A. Seller. These are detailed medium-paced explanations of graphing, graphing lines, slope of a line, slope intercept form and more.

Homework: we did the homework in class! If you didn’t finish it, here’s what you need to finish. McD 7.6 p. 359-361 Guided practice 1, 3-7 all, 8-22 evens. Do it Friday so you have a full two weeks without a math assignment. When doing these problems use the examples. Ask yourself, is this like a markup problem in which I’m adding some percentage of the original amount to the original amount to get the new price? (Problems about tips and sales tax and mark ups are approached the same way.) Which example problem in the book fits this situation?

These problems are in some ways mas much about vocabulary as they are about percentages.

• wholesale price = price the store pays to get the item,

• markup = how much more is added to the wholesale price- usually a percentage of the wholesale price (wholesale price multiplied by 50% or 130% )

• retail price = price the costumer pays the store (usually after a mark-up has been applied to the wholesale price)

• sales tax = percentage of the original bill (like the wholesale price) added to the final bill (solve this like a markup problem: the mark up is the food bill multiplied by the sales tax, say 8%).

• taxi/uber fare= bill or cost of a tax/uber ride.

• tip = additional amount of money given to a waiter or driver for good service as a percentage of the bill usually between 10-20%

Answers to even problems from McD section 7.6: 4. $48, 6. $24.20, 8. $76.50, 10. $27.75, 12. $189 14. $44.10, 16. $30.25 18. $22, 20. about $11.16, 22. $300

Classwork Monday 3/15: Input-output box puzzles— what expression is in the box? If I put in x and get out y, what is happening to x in the box to yield y? (Eg. if when x is 0, y is 0 & when x is 1, y is3 & when x is 2, y is 6? The expression must be y=3x. Preview of function notation f(x) = 3x. Percent of change formula = amount of increase/original amount. This is from McD 7.5.

Homework Monday 3/15

Homework is the same for all.

New Material - Percent of Change

• WATCH this Math Antics Percent Change video

• WATCH this Art of Problem Solving Percent Change or Increase or Decrease video part 1

• Pentagon WATCH this Art of Problem Solving Percent Change video part 2 These are harder problems and shows commons mistakes that students make.

• McD 7.5 REREAD McD 352-354 Examples 1-4 then DO pages 354-355 Guided practice 1-6 all, 7-17 odds

Review material - If you need a refresher, watch the videos on these topics which are on our math videos page

1. AoPs 4.5 Simplifying Fractions. DO AoPs pg. 177 Exercises 4.5.1 c & d, 4.5.2 c & d, 4.5.3 b

2. McD Solving One-Step Equations 2.6 & 2.7 pages 99-100 problems 8-34 evens, page 207 problems 48-55 all, pentagon do 56 too

3. AoPs 5.2 Solving Linear Equations. DO AoPs pgs. 210-211 Problems 5.8-5.11 (square and pentagon skip 5.8)

A look ahead - Linear Equations in two variables:

• WATCH this Math Antics Video about functions inputs & output table

  McD 8.2 & 8.7 READ McD p.391-392 Reread Examples 1 & 2 Show your work. Answers: Example 1 check points 1. no, 3. no.

• WATCH this Math Antics Video about Graphing on a Coordinate Plane

• READ McD p.391-392 Reread Example 3 then try to DO checkpoint 6 & 7 on graph paper. (It’s okay if you don’t know how to do this. This is our first exposure to this concept.)

• Optional for Pentagon: This next video is a bit like drinking out of a fire hydrant— it’s a LOT of information all at once. So don’t sweat understanding it all, instead watch for an overview. It will go over the equation of a line (y=mx +b), functions, perpendicular lines and horizontal lines Math Antics Basics of Linear Functions

• If you like these concepts dealing with lines but want to learn more at a slower pace, there is a Great Courses lecture series called Algebra 1 available with a Great Courses subscription from Amazon that teaches these concepts very slowly. These concepts are in chapter 8 of McD which we will cover thoroughly in weeks 8, 9 and 10 (after spring break). I’ll keep introducing pieces of them before then.

Week 6

Classwork Thursday 3/11: 24 game. Reviewed vocab: coefficent, constant, power, base, exponent. Reviewed simplifying fractions (simplify by factoring out common divisors first, or by factoring the numerator & denominator and canceling out the common factors) then compute. Be a math wizard: don’t multiply huge numbers unless you have to! Review of negative exponents and some exponent rules. New info 7.4- the percent equation.

Classwork Monday 3/8: Chp 6: Reviewed difficult proportion problems using cross multiplication property of proportions. Chp 7.1, 7.2, 7.3 solving percent problems.

MONDAY, MARCH 8, 2021

Homework is the same for Triangle, Square & Pentagon today.

Play this equivalent ratios game for a few minutes: https://www.mathgametime.com/games/ratio-stadium-math-game

NEW MATERIAL- PERCENTS

Chp 7 Prerequisite Skills Quiz DO pg. 328 problems 1-9 all hint for problems 4 & 5— write this decimal as a fraction over 100 or 1000 as appropriate then simplify.

Answers: 1. 4/12, 4:12. 2. 0.625, 3. 0.12, 4. 7/20 5. 7/40, 6. 12, 7. 16, 8. 12 9. 7

Percents & Fractions 7.1 READ 329-330. DO pg 331: 9-29 odds

Percents & Proportions 7.2 READ P. 335-336. DO pg. 337: 1-9 odds, 15, 17

Percents & Decimals 7.3 READ 340-341 DO pg. 342: 1-15 odds, 29-39 odds

REVIEW

Solving equations 3.3 DO pages 805 problems 18-23, 27-30, 51-56 (all)

Answers to even problems: 18. 13, 20.-2, 22. 5, 28. 11 - 4x =6 + x, 30. x>2 (can’t show graph here), 52. x/5 greater than or equal to 20 therefore x is greater than or equal to 100, 54. n less than or equal to 2, 56. d greater than or equal to 7

Similar and Congruent Figures 6.4 DO: pages 290-292: problems 13, 14, 15,

Answers to even problems: 14. 110 degrees

Week 5

Thursday 3/4 Classwork: simplifying or reducing ratios (8/16 can be reduced to 1/2 without changing its value. 8/16 and 1/2 are equivalent ratios. ) Review conversion factors for finding equivalent rates (when changing from words per minute to words per hour or from feet to miles). Cross products property of proportions—why can we do this? How to solve proportions when one numerator or denominator is like this (x + 7). Similar figures.

Monday 3/1 Classwork: Experimental probability with dice. Review of how to use clearing fractions by multiplying by the LCD or using multiplicative inverse or using normal algebra steps to solve problems.

MAKE UP DAY - FEBRUARY 22

No homework. Just finish up your chapter 10 learning. Students are expected to learn the second half of chapter 10 (10.5-10.8) which covers surface area and volumes of 3-D shapes during the February break. They can learn the material however they want to do so. Students should be able to do the chapter 10 review questions and get most of them correct.

Classwork: using proportions to figure out the height of a tree. Building a pyramid net to label parts, including slant height. How to approach surface area problems: write the basic formula down first, then fill out the details, then plug in the numbers. Double check this step! Don’t round answers until the very end— keep the answer in your calculator. To show your steps, write down 2 or 3 decimal places.

WEEK 4

Prealgebra Announcements

• We have no FS classes next week (February 15—19). Make-up Monday class is on February 22. No Thursday classes the week of February 22.

• Supplies:

  • Calculator: Students will want to bring a calculator to class from now on. (A good calculator option that they can use for years is the Texas Instruments TI-30X IIS 2-Line Scientific Calculator. This is between $15-18 and it does everything except graph functions, which means one can use it on tests which don’t allow graphing calculators. There are other good calculators out there and if you already have one that does exponents by all means use it and don’t buy a new one. But if not, a TI calculator will last forever because they are made like tanks and come with a cover. My freshman in high school is currently using my TI-84 graphing calculator that I got for my high school trig/calculus class in 1989. Yep, 32 years old, still relevant and functioning.)

  • Protractor: Eventually they’ll also want to have a protractor at home too.

  • See cardboard box or cylinder note below under homework.

• Students are expected to learn the second half of chapter 10 (10.5-10.8) which covers surface area and volumes of 3-D shapes during the February break. They can learn the material however they want to do so. With your parents’ input make a plan to learn this material, decide which problems you want to tackle to solidify your understanding. (We’ll go over surface area and nets on Thursday February 11th & Monday February 22.)

2/11 THURSDAY

HOMEWORK

Learn the material in chapter 10.5- end of the chapter. You decide what problems to do.

CLASSWORK

• Surface area: We dismantled a cylinder (hot chocolate container) to make a net to figure out it’s surface area. We were able to derive the formula using what we know about the area of circles and area of rectangles. We also dismantled a box to make a net of a rectangular prism to figure out it’s surface area.

• Experimental Probability: we made free throws to figure out the experimental probability of making a basket. Then we used our personal P(making a free throw) to determine the how many shots we’d probably make tomorrow if we took 94 attempts.

• Algebra 1 (Hexagon work)— what’s the domain mean? {set of numbers}. How to translate word problems into expressions and equations (1.4 in Algebra textbook). Which phrases signal addition (increased by, sum, more than, plus)? Which words signal subtraction (difference between, less than, minus). Which words signal multiplication (of, times, product of). Which words signal division (quotient of, divided by)? Students are ready to tackle Sections 1.1-1.4 if they want to do so. There are just 3 to 5 questions per section that I recommend.

2/8 MONDAY

HOMEWORK— all the same, no separate triangle, square, or pentagon options this week

• GAME: Play this space invaders equivalent ratio game from MathGameTime.com. Play for 5 minutes.

  Chapter 6.2 Proportions Method #1 (find an equivalent ratio) or Method #2 (use algebra) page 278-279: problems 17-25 odds, mixed review 37-49

• Chapter 6.3 Proportions READ the summary on page 282. DO pages 282-83 problem 11, 21-35 odds.

  • OPTIONAL WATCH: Do you need a refresher on how to solve proportions with cross products? Watch this Math Antics Proportions video (10 minutes)

  • WATCH: How to set up a proportions when reading word problems Watch Richard from AoPs set up proportion (equal ratios are called proportions) (Note at minute 6 he “clears” the fraction by multiplying by 2 so he doesn’t have to have a fraction in the numerator. Remember we learned how to do this in the last chapter. It’s an optional step that eliminates fractions from an equation.) He calls method 1 finding an equivalent ratio “scaling it up by a factor of _____”

• Basic Geometry Concepts: READ pages 285-286 about points, lines, rays, segments, rays and angles and congruent parts. This is mostly getting the vocabulary down.

• Bring an old small box (such as cereal box) or a cardboard cylinder we can cut up (such as an oats container or hot chocolate container) if you have one to explore surface area for Thursday. Not required but helpful to get a visual on how to find the surface area of solid shapes.

There will be no homework assigned this Thursday 2/11. You are figuring out the second half of chapter 10 during our February break. Assign yourself the reading and problems you need to master that material and don’t procrastinate or you will be pretty annoyed with yourself at the end of February. We’ll discuss possible approaches/learning plans in class on Thursday if you want.

CLASSWORK SUMMARY

Proportions: three methods of solving proportions (#1 find an equivalent ratio, #2 use algebra, #3 cross products— most people like the cross products method). Bingo review of new math vocabulary, especially area and perimeter formulas, some negative exponents.

WEEK 3

2/4 Thursday Classwork Summary

We’re working on conversion factors so we can convert from pounds to ounces and write equivalent rates. Ratios and rates are probably the hardest material we’ll do all year (with chapter 7 on percents taking a close second.) This is tricky stuff. I’ve included a few videos to help with it. But for some students it takes a few weeks for it to sink in and that’s okay. I’m going to spread this out over a few weeks so we have time for it to gel. We also dipped out toes in theoretical probability (what’s the probability of rolling a 3 with a 6 sided dice? Answer 1/6). We reviewed dividing fractions too.

MONDAY 2/1

HOMEWORK- same for everyone today. Now that we are half way through the year, we’ll be incorporating more review work to keep your skills sharp. This is really important because our new math concepts build on the old ones so you have to remember how to do the old problems so you can do the new ones! These review problems are concepts we’ve already covered. If you have forgotten how to do them you can a) look at the example problems in your text book and b) look at the Math Videos Page for videos on how to do these.

Review

• DO AoPs Section 4.6 Comparing Fractions by finding equivalent fractions with a common denominator: Do pages 180-181 Exercises 4.6.1-4.6.6

• DO McD Chp 6 Prerequisite skills quiz page. 268 odds and problem 8

• DO: McD Section 5.6 Multiplying fractions by the reciprocal p. 249: 17-33 odds, Mixed review 35-41 odds

New Concepts: Clearing Fractions & Ratios

• DO: page 255-257 problems #5-17, 27-45 odds, Mixed Review 47-55 odd, 57.

• Optional —If you need a refresher on how to clear fractions by multiplying by a common denominator or by a reciprocal watch visit our Math Videos page under Fractions #14

• WATCH: Get a preview of rates and ratios with this Math Antics video: https://www.youtube.com/watch?v=RQ2nYUBVvqI

• OPTIONAL: Get ahead by reading McD p. 76 “Rates”

CLASSWORK SUMMARY: Reviewed rational & irrational numbers and converting fractions to decimals (5.1); reviewed simplifying monomial fractions (14xyz/7xy), reviewed comparing fractions by finding equivalent fractions with a common denominator. New material: clearing fractions and decimals by multiplying and intro to ratios.

WEEK 2

Thursday, January 28, 2021

Fractions are hard for just about everyone. So don’t sweat it if fraction homework is hard. It’ll come to you eventually. Just keep trying.

It’s also extra hard that I didn’t get to model how to do problems on Monday. We’ll keep working on fractions throughout the coming months so they have time to click into your brain. We’ll keep playing games like our “Robin Hood” game with them until finding lowest common denominators or easiest common denominators is super easy for you. I’m also reducing the number of fraction problems we do each night so you don’t get too frustrated. We’ll simply keep doing them throughout the next month.

Math concepts for today: using reciprocals (multiplicative inverses) as a short cut to eliminating the fractional coefficent (fraction in front of a variable) when solving equations. Finding easiest and lowest common denominators. Review of rational (can be written as a fraction which either ends or repeats) and irrational numbers (which can not be written as a fraction). Memorizing common fractions and their equivalent decimal notation: 1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 1/3 = 0.3333 repeating (I don’t have a repeat symbol!), 2/3 = 0.66666 (repeating).

Announcing HEXAGON Challenge Work.

Did you know that there are 12 chapters in the standard algebra textbook? Did you know that you can already do most of the problems in chapters 1, 2, 3, and 4? Yep. I’ve already taught you the 4/12 (which is equivalent to one-third) of a standard algebra course. Pat yourself on the back right now for doing such advanced math so well.

So, if you want to start working on algebra while you finish up pre-algebra, you can do that by working on the problems posted on the Algebra 1-Hexagon page! You’ll need a new textbook called Algebra 1: Structure and Method by McDougal Littel (edition 1990 or 2000). I’ll post a picture of it soon. So far I have selected a few review problems from the first few chapters and posted them on the HEXAGON page. I’ll keep adding chapters as we go along. I’m happy to go over HEXAGON algebra problems on Thursdays and I can introduce some of these topics on Thursdays too. There are only a few truly new concepts in Algebra 1 that we won’t touch on in pre-algebra but I’m happy to introduce those to you on Thursdays for those who like the idea of working ahead. And I’ll reduce the Thursday PENTAGON homework so you have time to work on HEXAGON challenge problems.

We’re going to spread our fraction work over a few weeks so that it has time to sink in. So don’t be surprised when we keep coming back to fractions

Monday, January 25, 2021

NO CLASS on Monday due to possible lightening. Easier homework posted below so we don’t fall behind. See you Thursday!

WEEK 1

Thursday, January 21, 2021

Classwork - Review of key geometry terminology and formulas (circles, triangles, parallelograms) from Chap 10 for bingo game. New common denominator game. Scientific notation, adding & subtracting fractions (including mixed numbers & improper fractions) with same denominator. Adding and subtracting with different denominator. Intro to multiplying fractions. Homework is posted below in the three columns.

Monday, January 18, 2021

Classwork—Negative exponents and zero as an exponent (McD 4.6), Rational numbers & irrational numbers, Repeating decimals, terminal decimals (McD 5.1), Review of adding and subtracting negative numbers.

(Note if your student wants extra practice with negative exponents and scientific notation and you have a Beast Academy online subscription, there are additional excellent practice problems in level 5.12. The videos there are great too, but I can’t link to them as BA doesn’t publish their videos online like the other AoPs videos.)