Intro to Algebra 1 Fall Semester

Week 9 & 10 HW Nov 14/15/ & Nov 28/29

How do you eat an elephant?

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

Week 9 HW Nov 14/15

There are videos demonstrating every concept. We did examples in class on Tuesday of everything except scientific notation, which we did last week.

Quizzes and Tests Schedule

Week 6 Chp 1 Quiz

Week 7 Chp 2 Quiz

Week 9 - none— moved to next week

Week 10 - Chp 1-3 Cumulative Test and possiblyChp 5 Quiz (Fractions)

Week 11 - Chp 4 (Exponents, Factoring)

Week 12 - Practice Final chp 1-5

WINTER BREAK - 3 WEEKS

Week 13 Review for Final Exam

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

Concepts for Intro to Algebra: McD Chp 4.7, 6.1, Review chp 5

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

Key concepts

Reviewingd ratios (6.1) and a special ratio called a unit rate which enables us to compare items per gallon (such as how many miles per gallon VeAnna gets on her motorcycle vs. Eduardo in his motorhome or price per square foot. Unit rates enable us to quickly see which rate is greater or lesser. Unit rates have a denominator of 1.

Conversion factors such as 1 pound = 2.2 kilograms or 12 inches = 1 foot. (chp 6.1 still) We use these conversion factors to write EQUIVALENT RATES or to simply convert something from one unit to another. This is useful when we’re trying to figure out how much the 600 kg cow weighs in pounds since we think in pounds in the US. The key step is to include the units when calculating so we can cancel out the units we’re converting FROM so we’re just left with the units were converting TO.

Recommended: 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.

HW Week 9

33 Problems

SQUARE & PENTAGON problems are harder problems for students who want a challenge. Doing these problems gives one an extra 10% on this homework assignment.

HW Part 1 of 3

PENTAGON Watch Magic of Math’s 9 minute video on how to write repeating decimals as a fraction and do the three problems at the end of her video. Do you see a short cut? Hint: look at the denominators on the final fractions; do you see a pattern?

Chp 5 - Fractions: Chp 5 Review pg 258-261: #7, 9, 11, 13, 17, 21, 23, 27, 29, 31, 33, 35, 37, 39

If you need to review fractions I have a giant list of fraction videos at the bottom of this week’s HW.

Chp 6.1 Unit Rates and conversions…

Read example 4 on page 271. Then watch and take notes on this video called “Unit Conversion the Easy Way” by ketzbook. Problems 31-35 are conversion problems like those in this video.

Optional videos:

  1. pg 273-4 PP #31, 33, 35, 43, 45, & 39- in part C & D of #39 the problem as written and then also calculate if gasoline costs $4.80.

  2. MR # 49, 51, 55, SQUARE also do 56

Even answers 6.1 #56: first afternoon rate is 24 pg/30 minutes = 0.8 pages per minute. Second afternoon rate is 33 pg/45 minutes = 0.73 pages per minute. First afternoon has a faster rate since 0.8 is greater than 0.73

HW Part 2 of 3

Intro to Geometry: watch and take notes with DRAWINGS Math Antics “Points, Lines and Planes” 7 minutes

Chp 4.7 Scientific Notation… Do page 207-8 PP# 27, 39, 44, 46 SQUARE do 37 & 64 — this is the last part of chp 4 which we need to work on.

Optional videos

Chp 6.1 Unit Rates and conversions… Chp 6.1 pg 272 GP# 1-9 odds

Optional videos from last week

Optional: Math in real life visit this modular-design-your-own-pre-fab small structure website and design two different buildings that have the same square footage. https://shop.studio-shed.com/# (Chp 6.1 Unit Rates…)

  1. Write down what the purpose of each building is (guest house? home office? music room? game room?)

  2. What is the unit rate (or price per square foot) of each building?

  3. Which one do you think is better for the price and why?

Chp 6.2 Writing and Solving Proportions Re-read pg 275-277. Do pg 278-279 PP# 9-19 odds

In this section you may use cross products (butterfly method) to solve the proportion if you understand how to do that. (See video below.)

Chp 6.3 Using Cross Products to Solve Proportions Re-read pg 280-282. Do pg 282 GP 3-11 odds

Optional Video: Introduction to solving proportions with cross products Watch this Math Antics Proportions video (10 minutes)

Optional Video: Word Problems with proportions. 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.) He calls method 1 finding an equivalent ratio “scaling it up by a factor of _____”

HW Part 3 of 3

Geometry Basics: Read page 285-6 “Basic Geometry Concepts” and

Watch these videos then DO all the checkpoints on page 286 (#1-10) (even answers are below)

Correct work, redo missed problems as usual. Highlight problems on your HW sheet which you want to review in class

McD Chp 5

Fractions

  1. Introduction to fractions - Art of Problem Solving (AoPs) Prealgebra Chapter 4.1

  2. Multiplying Fractions

  3. Dividing by a Fraction

  4. Simplifying fractions

  5. Equivalent fractions

  6. Comparing Fractions using number lines

  7. Easiest Common Denominator - Math Antics https://www.youtube.com/watch?v=N-Y0Kvcnw8g&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=4

  8. Lowest Common Denominator - Math Antics https://www.youtube.com/watch?v=pZEmFSP3Z0I&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=3

  9. Adding & Subtracting Like Fractions - with same denominator

    • Same Denominator or “Like Fractions”: This is a proof from AoPs explains why you can just add the numerators (tops) when the denominators are the same (bottom) Same Denominator

  10. Adding & Subtracting Unlike Fractions - with Different Denominator —Adding fractions with different denominators from AoPs

  11. Adding Mixed numbers

  12. Subtracting Mixed numbers

    • Simple way—> turn everything into IMPROPER NUMBERS Math Antics https://www.youtube.com/watch?v=RqUPSZLwHH0

    • Clever way (FASTER) if you can handle the distributive property to deal with subtraction and negative numbers and mixed numbers, a.k.a how to separate out the integers and fraction separately. There’s a trick to this— use the distributive property to distribute the negative when subtracting. If you master this it’s a faster way to subtract mixed numbers! Mixed number Subtraction with Richard of AoPs

  13. Using Multiplicative Inverses (aka reciprocals) to solve equations with fractions faster

  14. Clearing Fractions from an equation by multiplying by a common denominator or by the reciprocal

  15. Using cross products aka cross multiplication (looks like a butterfly) to solve proportions Start at minute 10 of the video with Prof. Rob Bob https://www.youtube.com/watch?v=De5ghpLlkUQ&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=32

Week 10 HW Nov 28/29

this posting is now complete — HW is due Tuesday December 5

Quizzes and Tests Schedule

Week 6 Chp 1 Quiz

Week 7 Chp 2 Quiz

Week 8 -moved to week 10

***Week 10 - Chp 1-3 Test & Chp 5 take home quiz on fractions)***

Week 11 - Chp 4 (Exponents, Factoring)

Week 12 - Practice Final chp 1-5

WINTER BREAK - 3 WEEKS

Week 13 Review for Final Exam

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

Concepts for Intro to Algebra: McD Chp 6.1-6.3: Ratios & Proportions

Class Summary: theoretical probability, unit rates, ratios, using cross products (butterfly method) to solve proportion problems and test to determine if two ratios are proportional.

Advanced topics: diamond puzzles which are preparation for factoring quadratic expressions masquerading as a puzzle, function notation, figuring out function rules from input-output tables (via a puzzle we call Mr. Function Fox f(x)= some rule)

Recommended: 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.

HW Week 10

SQUARE problems are bonus problems that earn you an extra 2 points on your homework when you do all the square problems in a homework set. PENTAGON problems are harder bonus problems which earn you another 2 bonus points on your homework. If you complete both the SQUARE and PENTAGON problems you can get 22/20 points which is 110% on that homework set.

HW Part 1 of 4

Chp 6.2 Writing and Solving Proportions (new)

Chp 6.3 Using Cross Products to Solve Proportions (new) This is the butterfly method

Geometry Preview Videos to watch (if I’ve already assigned one of these, you can choose to skip it or watch it again. Take notes so you remember the material.)

HW Part 2 of 4

Take-home chp 5 quiz on fractions. I decided to email this to parents rather than post it. I emailed it to parents at 1 pm on Friday. Please let your parents know when you are ready to take the test and they can print it for you.

Open NOTES/HW/anything handwritten in your binder, but no calculator and no book (except Lorenzo and Ade— who may use a book since they are jumping into the middle of this). Unlimited time. Each problem is worth 6 points.

Add these formulas to your IMPS page. (see McD 10.4 pge 528-229 for more info):

  • Circumference of a circle = ∏D

  • Area of a circle = ∏r^2

  • Area of a rectangle = b x h or l x w (use a dot for multiply instead of x)

  • Area of a triangle = 1/2 bh

  • Interest = PRT

  • Definitions of solids from pg. 535 (prism, cylinder, pyramid and cone

  • Percent equation a = p% x b (use a dot for multiply instead of x)

  • Percent proportion a/b = p/100

HW Part 3 of 4

Chp 6.3 Using Cross Products to Solve Proportions Re-read pg 280-282. Do pg 283 PP # 23-31 odds

McD 7.1 Percents NEW

  • Required Video- watch and take notes: Converting fractions to percents and vice versa Introduction to percent with Richard from AoPs converting fractions into percents and percents into fractions without a calculator (you can do this easily with a calculator of course. 4/5 means 4 divided by 5 which yields a decimal. Do you know how to convert from a decimal to a percent? A percent is per-100….

  • Re-read pg. 329-330. Do pg 331-333 PP #1, 19, 26, 63, 65, 11, 19, 26 (76%) SQUARE # 55 & 57

Intro to Linear Equations (chp 8 McD) NEW

PENTAGON Hands on Activity #2- Deducing the formula for area of a circle

  • Trace a circle on paper with a radius of 2 inches. Use a fat red marker or crayon to outline the circumference of the circle. Give your circle a radius of about 2 inches. If you have a drawing compass handy use it or put a dot in the middle of a paper and tie a string 2 inches long around your pencil and hold the string down on that dot and extend the string to draw your circle or use a computer to draw a circle a radius of 2 inches.

  • Find the center of the circle. Put a dot there.

  • Then draw an even number of equal “pie slices” radiating out from the center of the circle. The radiating lines are the radius. Label each little radius on your pie slices with an “r” for radius. (Radius is Latin for spoke of a wheel.) Try 20 slices. Color every other pie slice blue. Color the others green.

  • Cut out the pie slices— but cut just outside the red circumference line so you can still see it after the slices are cut.

  • Now rearrange the pie slices into different shapes. Try to find a shape for which you know the formula. Hint: think square and rectangle. What shape are your pie slices almost? What is the formula for the area of that new shape? Can you estimate the area of this circle which is now in a new shape? Could you use a ruler to get lengths and widths to estimate the area?

  • Consider and answer:

    • Could you use what you know about the radius of the circle and the circumference of a circle to find the area of this new shape?

    • Remember: the formula for finding the circumference of a circle = ∏D

    • How could you express the area of that new shape you made in terms of radius and circumference? Hints: What is the length and width of the new shape in terms of radius and circumference of the circle? Look where the red line is— that’s part of the circumference. What fraction of the circumference are two of the sides? Look at the radiating lines that made the pie slices. What part of a circle are they? They radiate from the center and you labeled them “r”. Think about the relationship between the radius of the circle —which is the length of one side of a pie slice— and the circumference of the circle.

HW Part 4 of 4

McD 6.4 Similar and Congruent Figures (new)

  • Required Video - watch and take notes: What does similar mean? How is that different from congruent? Video Similar v. congruent (Math 8 chp 4.3)

  • Do McD pg 290 GP#1, 3, 5, PP#11, 17, 19 review 28 & 29 (28. 14 mi/hr)

Preview: McD 6.5 Similarity and Measurement

Watch this video on how to use proportions to find measurements in similar figures: a longer one (11 minutes) if you need more examples from Organic Chemistry Tutor (This is also in integrated math 8 chp 4.3) You’re doing 8th grade math.