Math 7 Prerequisites

What does my student need to understand and know how to do to enroll in 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.)

    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.

  • Multiply and divide, add and subtract 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. Start with this video.

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

    NOTE: I’ll teach positive and negative addition, subtraction, multiplication and division in the first few weeks.

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

  • Add and subtract fractions with the same denominator. Know how to multiply fractions and how to turn an improper fraction into a mixed number.

    NOTE: In this class we will learn/review how to add, subtract, multiply and divide fractions with different denominators without a calculator.

    RESOURCES: Math Antics has great youtube videos on this.

  • Find area and perimeter of rectangles and triangles.

    RESOURCES: Math Antics has great youtube videos on this.

Recommended courses to take before Math 7 at Farm School

Beast Academy 5 - I highly recommend Beast Academy. It’s the best math curriculum I’ve seen. While I’m not a fan of most online programs, Beast Academy has a terrific one that my own children loved. It helped prepare them for very accelerated math path both because it encourages nimble mathematical thinking and because it covered concepts at a deeper level. Students who have completed Beast Academy level 5 find that their homework doesn’t take them as long as peers who haven’t done Beast Academy.

A common core grade 5 math program like Math Mammon, or Singapore or Math In Focus level 5 or comparable course the bare minimum.

Students who struggle with math should also have completed a grade/level 6 math course. 6th Grade math is primarily a review of 4-5 grade math plus the following concepts. (We review and deepen our understanding of these concepts in Math 7)

  • ratios, unit rates, proportions,

  • common factors and multiples

  • area of triangles, quadrilaterals, volume and surface area of prisms

  • read a number line plot, histogram and find the average (mean) and median

What does this Math 7 course cover?

See monthly outline pdf here.

One can use this outline to coordinate projected state-standards/I can statements with charter schools.

Fall Semester Concepts

  • Chapters 1 & 2, 8

    Order of Operations PEMDAS

    Properties of Numbers, associative and communative properties of addition and multiplication and distributive property of multiplication.

    Variables and Algebraic Expression

    Translating words to math expressions

    Subtraction is adding a negative & negation

    Absolute value, Additive inverse/opposites, Positive and Negative integers

    Adding Positive and Negative Integers

    Multiplying and dividing Positive and Negative Integers

    Simplifying algebraic expressions by combining like terms

    Building blocks of geometry: lines, line segments, rays, angles, points, parallel and perpendicular

    Angles: right, acute, obtuse,

  • Chapters 2 (finish) 3 & 8…

    Multiplying and Dividing Integers

    1 Step Equations

    Equivalent Fractions and Decimals, Rounding

    Intro to exponents

    Ordering Fractions and Decimals

    Adding & Subtracting Decimals

    Multiplying Decimals

    Dividing decimals

    Solving Equations with Decimals

    Fractions with Unlike Denominators

    Angles: complementary and supplementary

    Angles formed by parallel lines and transversals (vertical, alternate interior and alternate exterior)

    Angles in Polygons

  • Chapters 3 (finish), 8 (finish), 4, 5 & 10

    Congruent figures

    Multiplying Fractions and Mixed Numbers

    Dividing fractions and mixed numbers

    1 Step Equations with Fractions

    Intro to probability: likely, unlikely, certain, impossible, as likely as not, complements

    Theoretical Probability

    Unit Rates

    Is it proportional? Equivalent Ratios/fractions

    Are the figures similar ?

    Missing lengths in similar figures

  • End of first semester: Review of chp 1-4, & 8

    Bonus: Pythagoras, square numbers and square roots

    Solving Proportions Using Cross Products (Butterfly Method)

    Square Numbers, Square Roots & a Greek guy named Pythagoras

    Intro to scale factors & drawings

    Review of chp 1-4, & 8

Spring Semester Concepts

  • Chapters 4 (finish), 5 (finish), 6, 11 & 9

    Review of Proportions (chp 4)

    Scale Factors & Drawings

    Interpreting Graphs

    Slope

    Linear Equations – Direct Variation

    Two-step equations intro

    What is a percent? Converting from Fract to Dec to  %

    Mental math estimating percents- odds

    Simple Interest

    Percent of change

    Perimeter of polygons and Circumference of a Circle

    Area of Circles

  • Chapters finish 6, 7, 11

    Percent applications:  commission, sales tax, proportions to find percent of earns and percents to find total revenue

    Simple interest…

    Multi-step equations with clearing fractions & variables on both sides

    Solving Equations with Variables on Both Sides

    Intro to solving Inequalities with addition and subtraction

    Writing Inequalities, Graphing them on a numberline and then graphing compound inequalities

    Solving Inequalities by multiplying or dividing

    Solving multi-step inequalities and equations

    Estimating Area of irregular figures and composite figures

    classifying and naming three-dimensional figures

    Measures of Central Tendency and impact of Outliers

    Populations and Samples

    Box and Whisker Plots

  • Chapters finish 9 & 10

    Volume: Prisms and Cylinders

    Surface Area

    Making Predictions

    Experimental Probability

    Review of experimental and theoretical probability

    Probability of compound events: 2 Independent Events and 2 Dependent Events

    Combinations

    Permutations

  • End of Second Semester: Review!

    Review all chapters, emphasis on 4-11

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?

Parents, administer this short pre-algebra readiness assessment to your student.

If this test is quite easy for a child, then that student is probably ready for Honors Pre-algebra. HOWEVER, our HPA+M8 class covers all of Honors Pre-algebra plus all of Math 8 and we do all that in two fewer months than traditional schools since the Farm School math semester is 14 weeks versus 17-18 weeks. That means our pace is wicked fast. 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 really fast learners/good at math already.

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 really 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.

You can see what we cover in Math 7 here or look at the drop-down menus above.

  • 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.)

    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?

Prior to the start of class in September, 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 math 7 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.