Honors Pre-Algebra + Math 8 (HPA+M8) Prerequisites

What are the minimum standards for what my student needs to understand and know how to do for this class?

  • Math facts fluency is the number one predictor of student success in pre-algebra. Students should be able to complete 40 problem multiplication text with facts from 1 to 10 in less than 2 minutes. We’ll work up to being able to do this in under 60 seconds.

    WHY DOES THIS MATTER?

    If they don’t know their math facts solidly, it will take them far too long to complete homework and they’ll get discouraged. One can’t be trying to remember what 6 x 7 is and also solving for x in -12x(4x+3) = 7x(6x -2) Struggling to recall basic facts takes up too much bandwidth. We don’t use calculators for whole number calculations.

    TOOLS TO GET UP TO SPEED

    Flash cards. Kid-made flash cards are best! (Write it down, write it in your brain.)

    Practice multiplication quizzes are here. These include 11’s and 12’s

    Xtramath.org Use it every weekday morning for 10 to 15 minutes in summer or starting now! It’s worth the $2 per child for an entire year for additional customization features. I recommend starting with multiplication 1-10s with 6 seconds to answer. Then shift to 3 seconds to answer, then 2 seconds. Then move on to addition, subtraction and division. This is tedious but super effective. At the end of each session a 100’s chart appears to show student and parent which facts the student has mastered, answered correctly but slowly, missed and which were not yet quizzed.

    2 minute car math facts drills— for the first two minutes of every car ride review math facts for the 7s, or 8s, or 11s or which ever set of facts the student needs to practice.

  • Understand positive and negative numbers on a number line. RESOURCES: Math Antics - Negative Numbers - YouTube

    NOTE: We will review positive and negative addition, subtraction, multiplication and division in the first few weeks, but it’s best if students are familiar with those basic operations before the start of class. We go over this quickly.

    Students also need to be able to multiply and divide multiple digit numbers (“column math”) without a calculator.

    Long division by hand resources: If the traditional long division algorithm doesn’t make sense, try the hangman division method.

  • Add, subtract, divide and multiply decimals without a calculator. Round to tenths, hundredths, thousands, compare and order decimals.

    RESOURCES: Use the Skills Review Handbook in our pre-algebra textbook McDougal Littell Pre-Algebra 2005 or 2008 editions pages 770-797.

  • How to add and subtract fractions with the same denominator. How to multiply fractions.

    How to turn an improper fraction into a mixed number.

    NOTE: In this class we will review how to add, subtract, multiply and divide fractions with different denominators without a calculator. But we will NOT spend much time on this skill. I’ll assume students have done this before.

    RESOURCES:

    Use the Skills Review Handbook in our pre-algebra textbook McDougal Littell Pre-Algebra 2005 or 2008 editions pages 770-797.

    Math Antics has great youtube videos on this.

  • Find area and perimeter of rectangles and triangles. Find the volume of cubes.

    Familiarity with surface area and volume of more complicated shapes is helpful (that’s covered in Math 7. We’ll review it.)

    RESOURCES:

    Use the Skills Review Handbook in our pre-algebra textbook McDougal Littell Pre-Algebra 2005 or 2008 editions pages 770-797.

    Math Antics has great youtube videos on this.

  • Read bar, pie, line graphs, histograms.

    Helpful but not required to read and make stem & leaf plots, and box and whisker plots

    RESOURCES: Use the Skills Review Handbook in our pre-algebra textbook McDougal Littell Pre-Algebra 2005 or 2008 editions pages 770-797.

  • Classmates who have taken Math 7 with me or another comparable Math 7 class are going to understand these concepts already and we’ll review these quickly then build upon these topics.

    PROBABILITY

    Familiarity with basic probability (theoretical probability, experimental probability)

    SOLVING MULTI-STEP EQUATIONS AND INEQUALITIES

    Comfortable solving two step equations (2x + 5 = 15)

    Comfortable solving two step equations with distributive property and fractions 3(4x-7) = 79+ 2x

    Able to solve multi-step inequalities

    LINEAR EQUATIONS

    Be able to graph y = 2x + 1 using a chart (substituting in values for x and finding out what y is)

    What is slope? What is a constant rate of change or slope versus a variable rate of change?

Pre-Course Diagnostic Tests

Parents, if you are unsure about whether or not your student is ready, you may administer this two-part pre-algebra readiness diagnostic. No calculators, unlimited time.

Part 1: 26 question  pre-algebra readiness assessment. Parents, give your student this quick test. No calculators. Answers are on the last page.

If this test is quite easy for the child, then that student is probably ready for Honors Pre-algebra. The next diagnostic exam will tell us more. Move on to that.

If this was hard, then students probably need to brush up on their Math 6 and Math 7 concepts AND probably work on their basic arithmetic facts fluency. I have a self-paced Math 7 course that students can take over the summer if they need to refresh basic Math 7 concepts. It has test-out-of-stuff-I-already-know options.

Part 2: This next diagnostic is slightly longer and includes one-step equations and positive and negative integers. Parents, administer this test. No calculators. Answers are on the last three pages.

Students who got at least 32 out of 40 (80%) should be fine in Math 8 + Honors Pre-Algebra as long as they always do their homework and attend class.

Note: this diagnostic test does NOT cover a lot of Math 7 material which I will review but will presume that students have already at least seen, including: ratios, scale drawings, solving proportions, percent applications (sales tax, percent of change, simple interest, etc.), slope, direct variation, mean, median, mode, angle relationships, congruent figures, volume and surface area of 3D figures, experimental and theoretical probability, and multi-step equations.

Note, our pace is quick since we are coving ALL of honors pre-algebra plus ALL of Math 8 and we do all that in 30-32 weeks instead of 36 weeks. (Our Farm School math semester is 15/16 weeks versus 18 weeks for longer breaks.) That means our pace is quick. Therefore, even though we review all of Math 7 within our HPA+M8 course, students who didn’t do Math 7 are going to feel like they are drinking out of a firehose unless they are exceptionally fast learners.

Ideally, students will have completed an integrated Math 7 course or similar 7th grade math class prior to taking this class. Otherwise their homework is going to take a long time since everything will be new to them AND it could be quite overwhelming.

One option for students who really want to be in in HPA+M8 but who haven’t had a solid Math 7 experience, is to take both classes simultaneously. Or buckle down and do all of Math 7 over the summer. I offer a self-paced Math 7 course for students who need a refresher.

You can see what we covered last year in Math 7 here

Over summer, students should make sure they are very fast at their multiplication tables. Prior to the start of class in August, students will submit a timed multiplication quiz showing they can answer 40 questions, math facts 1 through 10, without errors in under 2 minutes. During the first semester, students will memorize 11’s and 12’s math facts.

Practice multiplication quizzes are here. These include 11’s and 12’s.

Honors Algebra 1 Prerequisites

Students who have completed either pre-algebra or a rigorous Pre-Algebra course and who are fluent at basic arithmetic are ready for Algebra.

What should my student know how to do to succeed in Algebra?

(Or at least have learned how to do the previous year and remember how to do with a little refresher. We will go over all of this again in class, but this class can’t be the first time students see the following material.)

  • FLUENCY— students should be able to complete one of these multiplication quizzes of 40 problems with multiplication facts from 1 to 12 in less than 2 minutes. If they don’t know their math facts solidly, it will take them far too long to complete homework. We don’t use calculators for whole number calculations. Flash cards and xtramath.org are a simple way to get ones math fluency up to speed. Once class starts, we’ll have multiplication quizzes and they need to get all 40 problems correct in under 60 seconds.

  • Comfortable with postive and negative integers, including multiply, dividing, adding and subtracting (without a calculator).

  • Variables & Expressions: use order of operations to simplify variable expressions and combine like terms

  • Understand exponent rules: solve 7² / 7³, negative exponents, scientific notation

  • Factors: Find greatest common factors, least common multiple, simplify 21a²/49ab

  • Fractions

    • add and subtract mixed numbers both like and unlike denominators

    • multiply and divide fractions

  • Solve equations: Solve 1-variable equations using multiple transformations such as 6x + 2 = 2(3x+1)

  • Rates, Ratios and Proportions:

    • write an equivalent rate if a jet flies 540 miles per hour write its rate in miles per minute by multiplying by a conversion factor

    • solve proportions 5/6 = x/18

    • find the ratio of corresponding side lengths of similar figures, make scale drawings,

  • Percents

    • convert fractions to percents and vice versa

    • Solve the three basic percent problems: what number is 42% of 93? What percent of 110 is 43? 11 is 22% of what number?

  • Volume and Surface area: find volume and surface area of 3-D shapes such as prisms, cylinders, pyramids, cones (volume formulas do not need to memorized though)

  • Polynomials

    • Add and subtract polynomials by combining like terms and using transformations to isolate variables:

    • Multiply monomials and polynomials using the distributive property: 2x(-3x+7)

    • Multiplying binomials (-2x+5)(3x-1)

F.A.Q.s for Algebra 1

  • No, they just need to have completed a solid pre-algebra or math 8 course.

  • No. They will be lost and frustrated and might lose their love of math or worse yet draw the mistaken conclusion that they aren’t cut out for hard math classes.

  • No. Teaching Texts are watered down. However if a student wants to spend the summer brushing up on their pre-algebra skills they can get a copy of McDougal Littel’s pre-algebra text and do chapter reviews 1-7, and sections 8.1-8.5, 9.1-9.4, chapters 10 (skip 10.7) Chapter 12.1-12.3

  • Absolutely. If you’re in 9th grade and taking the class for HS credit, you’ll have ample samples to upload to a program like Schology or submit to your HST/EF to prove mastery.