The whole 6th-grade review in one place — rounding, order of operations, decimals, GCF and LCM, fractions, mixed numbers, and the coordinate plane: study cards, a hints sheet of the classic traps (multiplication chart included), and the review quiz at three levels. Work here, or print it and use a pencil — both count.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🔔 Rounding: underline, then look next door
Underline the digit in the place you are rounding to. Look at the digit right AFTER it: 5 or more → round up; 4 or less → it stays. Then drop the rest. Tenths = 1st decimal digit, hundredths = 2nd.
Five or more, raise the score. Four or less, let it rest.
🚦 Order of operations (PEMDAS)
Parentheses → exponents (5² = 5 × 5 = 25) → multiply and divide left to right → add and subtract left to right. One step per line; bring everything else down.
5² is 5 × 5 = 25 — never 5 × 2.
📐 Decimals: three moves
Add/subtract: LINE UP the decimal points, fill gaps with zeros (48.7 → 48.70), bring the point straight down. Multiply: multiply like normal, then count the decimal places in the problem — the answer gets that many. Divide: move the decimal in BOTH numbers until you divide by a whole number (3.72 ÷ 0.8 → 37.2 ÷ 8).
Points line up to add. Places get counted to multiply. Points travel together to divide.
🧮 GCF and LCM
GCF = Greatest Common FACTOR: list the factors of each number (what divides IN evenly), circle the biggest one on both lists. LCM = Least Common MULTIPLE: skip-count each number, circle the first one both lists share. GCF of 8 and 12 is 4; LCM of 4 and 6 is 12.
Factors divide in. Multiples march out.
🔁 Mixed number ↔ improper fraction
Mixed → improper: (whole × bottom) + top, keep the same bottom. 7 1/8 → (7×8)+1 = 57/8. Improper → mixed: divide top ÷ bottom; the remainder rides over the SAME bottom. 38/5 → 7 R3 → 7 3/5.
The bottom number never changes teams.
🍕 Fractions: add and subtract
Same bottoms? Add or subtract the TOPS, keep the bottom: 3/7 + 2/7 = 5/7. Different bottoms? Find the LCM of the bottoms first, make equivalent fractions, THEN add or subtract. 3/5 + 1/6 → 18/30 + 5/30 = 23/30. Simplify at the end.
You can only add pieces that are the same size.
✖️ Fractions: multiply and divide
Multiply: straight across — top × top, bottom × bottom, then simplify. Divide: KEEP the first fraction, CHANGE ÷ to ×, FLIP the second — then multiply across. Mixed numbers: change them to improper fractions FIRST, every time.
Keep — Change — Flip. Only the SECOND fraction flips.
🗺️ The coordinate plane
A point is (x, y): the x number walks RIGHT (+) or LEFT (−) first; the y number then goes UP (+) or DOWN (−). The x-axis lies flat; the y-axis stands tall. Quadrants use Roman numerals and go COUNTERCLOCKWISE from the top right: I, II, III, IV. Points on an axis — like (0, 4) or (−5, 0) — belong to NO quadrant.
Run before you jump: x first, then y.
⚠️ The error gallery — traps with names
The sleepy neighbor: rounding 18.748 to 18.74? The 8 next door says round UP: 18.75.
Adding the bottoms: 3/7 + 2/7 is 5/7, never 5/14 — the bottom names the piece size, and the pieces didn’t change size.
Dividing without the flip: 3/8 ÷ 7/8 = 3/8 × 8/7 = 3/7. No flip, no dice.
The backwards point: (3, −2) is 3 right and 2 down — never 3 down and 2 right. x runs first.
Clockwise quadrants: I is top right, then COUNTERclockwise — II top left, III bottom left, IV bottom right.
GCF/LCM swap: GCF of 6 and 8 is 2 (a factor, small); LCM is 24 (a multiple, big). If your GCF is bigger than both numbers, you found a multiple.
🎯 How the test will ask
“Simplify if necessary” means the simplify step is PART of the answer — 26/4 isn’t done until it’s 6 1/2.
Rounding names the place in words — underline that place before you look anywhere else.
Plot-the-point questions grade the LABEL too — write the letter next to your dot.
Check division with multiplication: 3.72 ÷ 0.8 = 4.65 because 4.65 × 0.8 = 3.72.
✅ Before the test, can you…
Round 18.748 to the nearest hundredth AND 4.703 to the nearest tenth?
Do 5² before you add?
Line up 48.7 + 6.23 with a zero?
Tell GCF from LCM without peeking?
Turn 7 1/8 into 57/8 and 38/5 into 7 3/5?
Keep–Change–Flip a division of fractions?
Plot (3, −2) — right first, then down?
Term
Meaning in 10 words or less
Numerator
The top number — how many pieces you have.
Denominator
The bottom number — the size of each piece.
GCF
Greatest common factor — biggest number that divides both.
LCM
Least common multiple — first skip-count number both share.
Improper fraction
Top bigger than bottom: 38/5. Worth more than one whole.
Mixed number
A whole number and a fraction together: 7 3/5.
Common denominator
Same bottom for both fractions — same piece size.
Reciprocal
The fraction flipped upside down: 7/8 → 8/7.
Exponent
How many times the base multiplies itself: 5² = 25.
Ordered pair
(x, y) — the address of a point. x runs first.
Origin
(0, 0) — where the two axes cross. Every walk starts here.
x-axis
The flat axis — runs left and right.
y-axis
The tall axis — runs up and down.
Quadrant
One of four rooms the axes cut the plane into: I–IV, counterclockwise.
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Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: take one step per line, pick the decimal rule the problem is actually asking for, read a factor diagram, walk unlike bottoms to a common one, or settle where a point with a zero in it lives.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.