The mathematics is built in order, and the quizzes follow that order: place value first, then the four operations, then fractions, decimals, percents, signed numbers, proportion, measurement, statistics, powers and roots, and scientific notation. Take them in sequence if you can. Each one has a Guide that teaches the topic, three worked examples, ten questions, and a key that explains every answer, including the wrong ones. If a quiz goes badly, the last part of the key says what to revisit. If it goes well, it names the next quiz.
The whole terrain is named, family by family, on the Flyover. These forty-three quizzes cover all fourteen of its families; the Flyover Diagnostic checks all fourteen and says where to start.
Work on paper if you can, and without a calculator. Every quiz prints clean, black on white, from the print button at the top of its page. On a phone, turn it sideways when a chart is wider than the screen.
The Seahorse Series · Quizzes 1 to 13
- 1Place Value
Reading, writing, and naming numbers through the millions
- 2Comparing, Ordering, and Rounding
Which is bigger, what order they stand in, and which landmark is nearest
- 3Addition & Subtraction with Regrouping
Carrying, borrowing, and the art of making change
- 4Multi-Digit Multiplication
Equal groups, the area of a rectangle, and addition that learned to move in bulk
- 5Division
Fair shares, the missing side, and the three fates of a remainder
- 6Order of Operations
Who speaks first when all four operations crowd into one expression
- 7Factors, Multiples & Primes
Which numbers build a number, which numbers it builds, and the tests that tell at a glance
- 8What a Fraction Is
Equal pieces, an address on the line, and the many names of one amount
- 9Comparing & Ordering Fractions
Why bigger numbers can mean smaller amounts, and the three tools that settle it
- 10Adding & Subtracting Fractions
Why pieces must match before they can be joined
- 11Multiplying Fractions
The word of, the rectangle again, and why the answer gets smaller
- 12Dividing Fractions
How many fit inside, and why the answer turns out larger
- 13Decimal Place Value
Fractions with the denominators agreed in advance
The Deep Sea Series · Quizzes 14 to 22
- 14Adding & Subtracting Decimals
One rule, and you have met it twice already
- 15Multiplying & Dividing Decimals
Where the rule bends, and why it is not broken
- 16Converting Fractions & Decimals
The same number, written two ways
- 17What Percent Means
Hundredths, wearing a sign
- 18The Three Percent Questions
The part, the whole, and the rate
- 19Percent in the World
Discount, tax, tip, interest, and change
- 20Below Zero
Opposites, order, and how far from nothing
- 21Adding & Subtracting Signed Numbers
One line, two directions, and no new rules
- 22Multiplying & Dividing Signed Numbers
A short rule, and the reason it is true
Out of All Proportion · Quizzes 23 to 25
- 23Ratios & Unit Rates
What the word per is doing
- 24Setting Up & Solving Proportions
Two ratios, one missing number
- 25Proportional Reasoning in the World
Recipes, maps, mixtures — and when the tool is wrong
The Okapi Series · Quizzes 26 to 28
- 26Units and Conversions
Inches to feet, minutes to hours, and why a square kilometer needs the factor twice
- 27Perimeter and Area
The walk around, the fill inside, and why doubling the sides does not double the floor
- 28Mean, Median, Mode, and Range
One number for many, and how to read fifteen skulls in a row
Creatures in Flight · Quizzes 29 to 33
- 29Exponents
The small raised number, what it counts, and how fast it runs
- 30Square and Cube Roots
Running a power backward, and what that tells you about size
- 31Rules of Exponents
Three moves that keep the count of factors honest, and the ladder down past zero
- 31aFractional Exponents
The bottom of the fraction is a root, the top is a power, and the chart is complete
- 32Scientific Notation
A number between 1 and 10, a power of ten, and one bird that lives at both ends of the line
- 33Words to Symbols
A letter for a number you do not know yet, a sentence turned into an equation, and a bee that turns a place into a dance
Two tools for exponents
These go with Quizzes 29 onward. Neither is a quiz, and neither is scored. Use them whenever the rules will not stay put.
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The Exponent Machine
Every rule worked one step at a time, with the exponents circled as they move, and a second mode where you decide the move yourself before the answer appears. It reads aloud if you want it to. There are only three moves — add, subtract, multiply — and the rest follow from them, which is what the machine is built to show.
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The Rules of Exponents, One Page
All eight rules on a single sheet, with an example under each. Made to print black on white for a wall, a folder, or the back of your notebook.
The Restoration Series · Quizzes 34 to 42
The quizzes that fill in what the first five series left out: probability, volume, angles, similar figures, graphs, polynomials, quadratic equations, functions, and lines and systems. The plate at the top of each is a wall painting from the Jesuit church in Funchal, Madeira, painted between about 1680 and 1850 and photographed in 2006 while restorers were uncovering it from under later layers.
Quiz 42 sets two other kinds of restoring side by side: a body regrowing what it lost, and a country trying to repair a wrong it did to its own people.
- 34Favorable Outcomes
How likely, out of how many — and how to count the ways
- 35What Fits Inside
Volume, surface area, and the sheet that hands you both
- 36Where Two Lines Meet
Angles on a line, at a crossing, and in a triangle
- 37Same Shape, Different Size
Similar figures, scale, and the shape left over when you cut the top off a triangle
- 38What the Graph Says
Five kinds of picture, and one kind of average
- 39Out and Back
Adding polynomials, multiplying two binomials, and running the multiplication backward
- 40Two Answers
Harder equations, quadratics by factoring, and the formula for when factoring will not work
- 41One In, One Out
What makes a relationship a function, and how to match a table or a graph to its rule
- 42Room for Both
Slope as a rate, the equation of a line, and two lines at once
Still to come
Every family on the Flyover now has a quiz of its own. What comes next is more practice where students need it most, and more quizzes will appear here the way they always have: one at a time.