Pre-Course Summer Review for Honors Algebra 1

Algebra is the bridge between arithmetic and higher math.

Summer Pre-algebra Review

Keep your pre-algebra skills sharp & get your stuff organized

To prepare for Algebra 1 students should complete one of these math reviews in August prior to the start of our math class in September.

Also get your binder ready and gather your supplies. Supplies are listed on the seminar page for this class.

Option #1 - Math 7 Review

The Math 7 review covers typical 7th grade math. It’s easier than the pre-algebra review but has more problems.

Divided into 7 HW sets with a total of 140 problems. Download print out the Math 7 practice problems using the “Math 7 Review” button at top right.

Option #2 - Pre-algebra Review

The Pre-algebra review covers pre-algebra concepts and uses problems from the McDougal Littel Pre-Algebra textbook, edition 2005. Fewer problems but harder concepts than the Math 7 review.

It’s not the end of the world if you don’t remember how to do everything on this review. BUT the coming year will be easier if you work to refresh your memory on these concepts.

Get yourself organized first

  • Get a binder just for math (and a spiral notebook too) and organize it.

    See the supplies listed on the seminar page for this class. Organize your binder the way I explain on the supplies section of that page.

    Notes/Handouts

    Tests/quizzes

    Bingo/IMPS Important Math Principles (definitions, formulas etc)

    Graded HW

    Pocket is for ready-to-turn-in homework pages which aren’t in the HWPW (Homework & Practice Workbook )

  • Print out a table of contents NEW

    I highly recommend you also get a spiral notebook in which to do your homework and write class notes. This way the HW and notes never get out of order. You can tape a table of contents directly into the front page your spiral notebook.

  • Modify your algebra tiles so you have negative tiles.

    This year you need to work with negative variable and constant tiles. One face of each tile needs to be red to represent negative.

    You can make one face red a few ways: nail polish, acrylic or craft paints or spray paint. If you go for the spray paint option, smush all the tiles together so no other faces are exposed and spray paint the top of your tiles without getting overspray on the other faces.

Option #1

Math 7 Review

Choose 20 problems from each week’s HW set to do for a total of 140 problems.

Helpful pages in the McDougal Littell Pre-Algebra textbook (referred to as “McD” for short.)

  • Table of formulas for geometric figures p. 818

  • Other formulas including slope, probability, permutations p. 819

  • Table of properties p. 820-821

    • properties of addition and multiplication e.g. inverse property, commutative property,

    • properties of exponents (aka exponent rules),

    • other properties such as product property of square roots, cross products property

Summer Set/Week 1

Algebraic Reasoning & Integers and Rational Numbers (fractions and terminating or repeating decimals) - 25ish problems (corresponds to chp 1-4 and 5.2-5.5 in McD. See also Skills Review Handbook p. 778-780 in McD)

  1. Page 4 Lesson 4 “Translating Words into Math” - problems do multiples of 3 (3, 6, 9, etc)

  2. Make a note card explaining the commutative property, associative property and the identity property See McD . 820-821

  3. Page 6 Lesson 1 “Integers” - problems 1, 2, 11-21 odds, 23, 24 No calculator

  4. Page 8 Lesson 3 “Subtracting integers” - problems 1, 7-21 odds No calculator

  5. Page 11 Lesson 6 “Equivalent Fractions and decimals” - problem 25 and problems which are multiples of 4 No calculator

  6. Page 12 Lesson 7 “Comparing and ordering Rational Numbers” - multiples of 5 No calculator QUICK SUMMARY SHEET on decimal conversions HERE

  7. Page 14 Lesson 2 “Multiplying Decimals” - multiples of 3 No calculator

SOLUTIONS HERE rates, proportions, integers, fractions & decimals


Summer Set/Week 2

Proportions & Rates - 28 problems (corresponds to chp 6 in McD)

SUMMARY SHEET of Ratios & Proportions HERE

  1. Page 21 Lesson 1 “Rates” - Do problems 1, 4, 8

  2. Page 22 Lesson 2 “Identifying & Writing Proportions” - multiples of 3

  3. Page 23 Lesson 3 “Solving Proportions” using cross products or cross multiplying multiples of 3 and problem 23

  4. Page 24 Lesson 4 “Similar Figures & Proportions” - 1, 3, 5

  5. Page 25 Lesson 5 “Using Similar Figures” - problems 2, 4, 6

  6. Page 26 Lesson 6 “Scale Drawings and Scale Models” - we didn’t do this, but you can figure it out by doing problems 9-11 first and looking at the example pages I’ve linked below. Then do problems 3, 5, 7

SOLUTIONS HERE rates, proportions, integers, fractions & decimals


Summer Set/Week 3

Percents -20 problems (corresponds to chp 7 in McD)

Strategy: write the formulas you think you may be using at the top of the paper to refer back to

  1. Page 34 Lesson 4 “Percent of Change” - problems 1, 3, 9, 11, 17-20

    • Strategies: Write the formulas -for this page, it’s percent of change formula.

  2. Page 35 Lesson 5 “Application of Percents” problems 2-8.

    • Strategies: Write the formulas you will be using at the top of the paper

  3. Page 36 Lesson 6 “Simple Interest” - problems 1, 3, 8-10

    • Strategies: Write the formulas down - on this page, it’s the simple interest formula.

SOLUTIONS HERE percents

Graphs - 19 problems (Corresponds to chp 1 and chp 8 in McD

  1. Page 27 Lesson 1 “The Coordinate Plane” - #1-4, 5, 15-18 (corresponds to 1.8 in McD)

  2. Page 28 Lesson 2 “Interpreting Graphs” #1-4

  3. Page 29 Lesson 3 Slope and Rate of Change #1-6

BONUS: What’s direct variation? READ HERE to find out.

  • How to figure out if x & y move together in direct variation? WATCH this video showing two ways to figure that out (11 minutes)

  • Advanced application and real-life examples of direct variation (when x changes, y changes proportionally) WATCH this video 5 minutes

SOLUTIONS HERE converting fractions to decimals and graphs

Summer Set/Week 4

Collecting, Displaying and Analyzing Data -21 problems (Corresponds to chp 11.1-11.5 in McD)

Here’s an excellent review of measures of central tendency (i.e. mean, median, mode, range), how to figure out how outliers affect a data set, how to make a box and whisker plot, and different kids of population samples. I suggest you read these pages, take notes on them and then try these problems.

  1. Page 37 Lesson 1 Mean, Median, Mode & Range: #1-5 Note, Mean, median and mode are all measures of central tendency— i.e. where the center is. OPTIONAL 6 & 7 - we haven’t done this before.

    • Outlier is the piece of data that is extreme or far away from the other data points in the data set.

    • We have instructions of how figure out how the outlier affects the measures of central tendency posted above under “here’s an excellent review….”

    • In general, outliers goof up the mean or average so when there are outliers we tend to use the MEDIAN instead. (We talked about an example of this with house prices once.)

  2. OPTIONAL Page 38 Lesson 2 Box and whisker plots: 1-7 (you’re going to want to look this up 11.2 of McD and watch this simple video on How to make a Box and Whisker Plot without worrying about outliers. This is hard to remember how to do. I have more videos on our math videos page)

  3. Page 39 Lesson 3 Populations and Samples: #1-4

SOLTIONS HERE collecting, displaying and analyzing data

Summer Set/Week 5

Probability — 38 problems. (Corresponds to chp 6.8 - the counting principle and 11.6 permutations, 11.9 independent and dependent events in McD)

SUMMARY SHEET HERE. Check out our videos on our math video page.

  1. Pages 51-58 - even problems

  2. BONUS Page 59 - Probability of compound events

    • Optional: Try problems # 1-4 The heading says to use an organized list, tree diagram or table to solve but that will take forever to list out this many options. It’s easier to solve most of these as dependent events so P(A) multiplied by P(B after or given A). Hint problem 4 is the probability of multiple events given the previous events happened.

    • If you want to attempt problems 5 & 6 you can either

      • a) treat them like like dependent events P(A) x P(B given or after A). This is the easiest way to solve it.

        • so for example problem 6 is 3/15 x 2/14 x 1/13 = 1/455

        • problem 5 is 3/12 x 2/11 x 1/10 = 1/220

      • b) Or use the combinations formula from McD 11.7 page 621 Because problem 6 is impossible to do using a list, tree diagram or table, unless you want to make a list that’s 1320 entries long. It can be solved as a combinations problem using this formula: nCr = nPr/r! (This is the formula Max asked me to show everyone, but I said, “No, it’ll just muddy the water as you’re learning the permutations formula: nPr)

SOLUTIONS TO - probability HERE Note- There is an arithmetic error in my solution to page 53 problem#6. It should read “4 pants multiplied by 2 sweaters = 8” I wrote (4 x 2 = 6 but we know that’s not true!)

Summer Set/Week 6

Multi-step Equations and Inequalities - 31 problems (Corresponds to chp 3 in McD)

  • Page 62 Lesson 3 Solving Multi-step Equations with variables on both sides: #6-13

  • Page 63-66 Lessons 4, 5, 6, 7 Inequalities: #3-13 odds (Don’t forget to switch the direction of the inequality sign with multiplying or dividing by a negative!!)

SOLUTIONS - Multi-step equations and inequalities HERE

Figures & Measurement and Geometry - 31 problems (Corresponds to chp 13.1-13.4 in McD. See also Skills Review Handbook p. 793)

SUMMARY SHEET HERE on angles, 2-D geometric figures, using ratios to find side length of similar figures

  1. Define a point, line, plane, ray, line segment, parallel lines, perpendicular lines, skew lines. Draw a diagram or two with these on it.

  2. Page 41 Lesson 2 Classifying Angles: #1-4 all, 7-12

  3. Page 42 Lesson 3 Line and Angle Relationships: # 5-12

  4. Page 43 Lesson 4 Angles in Polygons: #3-5, 9-13

SOLUTIONS HERE note, on page 47 of solutions, the answer to #3 is wrong: it should be 17 square ft. (I forgot to shorten the right side to match the indentation that’s carved out— a common error!)

Summer Set/Week 7

Measurement and Geometry - 30ish (Corresponds to chp 10 in McD. See also Skills Review Handbook p. 818

SUMMARY SHEET HERE Polyhedra names, volume, surface area (helpful for review #4, 5, 6)

  1. Page 45 Lesson 1 Perimeter and Circumference: #3, 6, 9-11

  2. What is the formula for the area of a circle? Make up your own sample problem.

  3. Page 47 Lesson 3 Area of Irregular Figures: #2, 3, 7, 8, 9— note, on page 47 of solutions, the answer to #3 is wrong: it should be 17 ft. (I forgot to shorten the right side— a common error!)

  4. Page 48 Lesson 4 Intro to 3-D figures: all (see pages 535-536 of McD and the intros to sections 10.5, 10.6, 10.7

  5. Page 49 Lesson 5 Volume: #2, 3, 5, 9,

  6. Page 50 Lesson 6 Surface Area: #1, 4, 5— you can use the fancy surface area formulas in McD but on easier problems like these it is simple to just find the surface area of each face and add them up.

SOLUTIONS TO WEEK 4 HERE note, on page 47 of solutions, the answer to #3 is wrong: it should be 17 square ft. (I forgot to shorten the right side to match the indentation that’s carved out— a common error!)

Option#2

Pre-Algebra Review (McD)

Summer Set/Week 1

  • McD pages 164-166: Do odd problems for the Unit 1 Cumulative Practice for Chapters 1-3

  • McD pages 378-380: Do odd the problems for the Unit 2 Cumulative Practice for Chapters 4-7

SOLUTIONS HERE

Summer Set/Week 2

  • McD page 418 Chapter 8 mid-chapter Quiz

  • McD page 475 Chap 9 mid-chapter Quiz (you’ll need to look up 9.4 as we didn’t review rational and irrational numbers at the end of the year.)

SOLUTIONS HERE

Summer Set/Week 3

  • McD page 569 Chapter 10 Standardized Test— choose half of the problems to do.

  • McD Chp 11.1-11.5 Review the examples then do the Mid-Chapter Quiz on p. 614 (we didn’t go over 11.5 so that section of the review is new material but it mostly vocabulary.)

SOLUTIONS HERE

Summer Set/Week 4

  • OPTIONAL: McD 11.6 Permutations Read the examples, then attempt 5 problems to do in this section.

  • McD 11.9 Independent and Dependent Events: Read the examples, do pages 637-8: #1-13 all

  • McD Chap 11 Review page 640-643: #1-12, 15

  • McD Chp 12 Mid-Chapter Quiz page 673 all

  • McD Chp 12.5 Exponent Rules review: Read examples and do the odd checkpoints on p. 674-676

  • NEW MATERIAL: McD Chp 13 page 714 construct perpendicular bisectors, copy an angle, and bisect an angle. We did not do these in class, so this is NEW.

  • OPTIONAL: McD Chp 13 Mid-Chapter quiz on page 728

    SOLUTIONS HERE

Congratulations for finishing the last week of pre-algebra review questions!