6年级课程

这些课程为英文，由 Koydo 导师朗读讲解。

Atlas folds a line of symmetry and tiles a tessellation — no gaps, no overlaps, not a reflection map of one point

Math · 导师：Atlas · 15 分钟

A vibrant mosaic wall covered in colorful repeating tile patterns, with the character 'Atlas' pointing to lines of symmetry on some tiles and demonstrating how shapes fit together perfectly.

Lumi names point, line, and plane as geometry’s starting pieces — not angle types and not triangle sorts

Math · 导师：Atlas · 20 分钟

A classroom with a blackboard covered in geometric figures — triangles, squares, and circles with labeled angle measures — while Atlas holds a protractor and points to the shapes, with rulers and compasses arranged on the desk in front.

Atlas lists domain and range from pairs — inputs in the domain, outputs in the range, not the function test

Math · 导师：Atlas · 18 分钟

A nature park scene with Atlas beside a graph showing dots representing a function, with horizontal and vertical arrows labeled 'Domain' and 'Range'.

Atlas multiplies independent chances — P(A and B) = P(A)×P(B), not a single-event 0-to-1 card

Math · 导师：Atlas · 25 分钟

A game board with two dice and two coins, the guiding character 'education/atlas' explaining compound probability with a large interactive chart.

Lumi converts mixed numbers and improper fractions both ways — 2 3/4 is 11/4, not a new value

Math · 导师：Atlas · 15 分钟

A bright classroom with a large blackboard showing colorful fraction bars, a pizza sliced into fractions, and a bookshelf filled with math books. The guiding character, Atlas, a friendly animated globe with glasses, stands next to the board holding a pointer.

Lumi uses special products — (a+b)² = a²+2ab+b² and (a+b)(a−b) = a²−b² — not general distribute and not factoring

Math · 导师：Atlas · 20 分钟

A colorful classroom with a large chalkboard displaying algebraic expressions, geometric shapes illustrating binomial squares, and the guiding character 'education/atlas' pointing to formulas.

Lumi follows PEMDAS left-to-right — parentheses, powers, then ×÷, then +− — so 2+3×4 is 14

Math · 导师：Atlas · 20 分钟

A colorful classroom with a large whiteboard displaying a step-by-step solution of an arithmetic problem. The guiding character, education/atlas, points to the whiteboard while students attentively watch. Various math symbols float in the background.

Atlas maps statistics as collect, organize, analyze, interpret — not computing mean-median-mode

Math · 导师：Atlas · 20 分钟

A classroom setting with 'Atlas' showing a chart on a board filled with numbers and graphs, surrounded by students holding clipboards collecting data from a weather station.

Lumi uses exponent laws — same base: multiply → add, divide → subtract, power → multiply

Math · 导师：Atlas · 20 分钟

An ancient library with scrolls and glowing equations floating midair, where 'education/atlas' is demonstrating exponent laws on a chalkboard with animated examples highlighting the rules.

Atlas finds the GCF — the largest number that divides both, from shared primes, not the LCM

Math · 导师：Atlas · 15 分钟

A colorful classroom with a large chalkboard displaying factor trees and numbers, posters of numbers and factors on the walls, and the guiding character 'education/atlas' holding a magnifying glass examining numbers.

Lumi wraps a cylinder — SA = 2πr² + 2πrh — two bases plus the rectangle wrap — not a box's 2(lw+lh+wh)

Math · 导师：Atlas · 20 分钟

A bright workshop with a large metal cylinder, a tape measure, and the guiding character 'education/atlas' demonstrating how to measure the radius and height. A 3D diagram shows the two circular bases and the side (curved surface) separately.

Lumi graphs a line from a table of x-values — compute y, plot three points, then connect

Math · 导师：Atlas · 25 分钟

Atlas stands at a sunlit desk using a ruler and colored pencils to carefully plot a straight line across a large sheet of graph paper with labeled coordinate axes.

Lumi double-labels a triangle — sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse)

Math · 导师：Atlas · 20 分钟

A classroom blackboard filled with colorful diagrams of triangles labeled as equilateral, isosceles, scalene, acute, right, and obtuse.

Lumi factors a polynomial as reverse multiply — GCF out, then a trinomial into two binomials — not solving = 0

Math · 导师：Atlas · 20 分钟

A cozy study room with Atlas holding a magnifying glass examining polynomials written on a large paper scroll, students gathered around with notebooks, and a chalkboard showing examples of factoring out the greatest common factor.

Atlas substitutes a number into 3x + 4, then follows order of operations — not combining 3x+7x

Math · 导师：Atlas · 20 分钟

A science lab scene with test tubes labeled with variables and numbers, a character wearing a lab coat writing calculations on a tablet.

Lumi cancels common factors in a rational expression — a polynomial over a polynomial, with holes named

Math · 导师：Atlas · 20 分钟

A modern math classroom with a large screen showing the simplification of the rational expression (x² - 9)/(x + 3). 'education/atlas' stands by the screen holding a tablet, showing factoring steps.

Lumi introduces percent as out of 100 with a 100-grid — not a unit rate per apple

Math · 导师：Atlas · 20 分钟

A bright marketplace with price tags showing discounts, Atlas holding a calculator and a percentage chart, with pie charts illustrating parts of a whole.

Atlas distributes a(b + c) = ab + ac — multiply across the sum, then you may combine

Math · 导师：Atlas · 15 分钟

A colorful classroom with a large blackboard showing algebraic expressions being expanded. Books and geometric shapes decorate the shelves. The guiding character, education/atlas, points to the board with a friendly smile.

Atlas names a principal square root — √25 = 5, never negative on this card — not prime-factor simplifying

Math · 导师：Atlas · 20 分钟

A bright math studio with illustrations of square roots, radical symbols, and 'education/atlas' demonstrating how to simplify radicals using visual models.

Lumi splits a sequence (the list) from a series (the sum) — not writing add-d and not S_n = n/2×(first+last)

Math · 导师：Atlas · 20 分钟

A bright math lab with colorful number lines on the wall, a large screen showing a list of numbers in a sequence, and 'education/atlas' holding a pointer next to a sequence chart.

Lumi simplifies a ratio by dividing both parts — 6:8 = 3:4 — not sharing a total and not cross-multiply

Math · 导师：Atlas · 20 分钟

A vibrant kitchen scene with bowls of fruit and measuring cups, Atlas holding a recipe card showing ingredient ratios, alongside visual ratio bars comparing quantities.

Atlas scales a ratio table — 3:5 to 6:10 to 9:15 — not unit rate per one

Math · 导师：Atlas · 18 分钟

A science lab with a large ratio table displayed on a whiteboard, various measuring tools on a desk, and 'education/atlas' pointing to the table while holding a tablet.

Lumi converts among fraction, decimal, and percent — 3/5=0.6=60% — not mixed-form adding

Math · 导师：Atlas · 20 分钟

A vibrant math lab with three colorful boards labeled 'Fractions,' 'Decimals,' and 'Percentages.' The character 'education/atlas' points to arrows connecting these boards, showing conversions.

Lumi fills a parallelogram with base × height and a trapezoid with ½(b1+b2)×height — height is perpendicular

Math · 导师：Atlas · 22 分钟

A workshop with wooden models of parallelograms and trapezoids on a table, a ruler and protractor nearby, and education/atlas demonstrating how to measure base and height.

Atlas lists integer properties — closed under add and multiply; not a number-line locate-only

Math · 导师：Scribe · 20 分钟

A snowy mountain landscape with a temperature gauge showing positive and negative values, Scribe standing next to a number line illustrating integers from -10 to 10.

Atlas lines up decimal points to add and subtract — tenths with tenths — not ordering decimals and not multiplying them

Math · 导师：Scribe · 20 分钟

A bright kitchen counter holds a mixing bowl with decimal-measured ingredients, a digital scale displaying weights in decimals, and an open recipe book, while Scribe holds a pencil ready to solve addition and subtraction problems in a notebook.

Atlas walks a rectangle’s perimeter as 2(l + w) — distance around, not the fill and not a box wrap

Math · 导师：Scribe · 30 分钟

A workshop with 2D shapes drawn on a large chalkboard and 3D models of cubes and cylinders on tables. 'education/scribe' is holding a ruler and a measuring tape.

Atlas names an angle as two rays sharing a vertex — not the acute-right-obtuse list and not a protractor how-to

Math · 导师：Scribe · 20 分钟

A vibrant classroom with a large protractor mounted on the wall, colorful angle diagrams labeled with degree measurements spread across the desks, and Scribe standing center-right holding a giant protractor and smiling at the class.

Lumi combines like terms to add and subtract polynomials — 3x² with 5x², never 3x² with 3x

Math · 导师：Scribe · 20 分钟

A bright math lab with Scribe standing beside a large digital whiteboard showing two polynomials being added and subtracted step-by-step, students using tablets to follow along, and colorful math symbols floating in the air.

Lumi lists parallelogram properties: opposite sides parallel and equal — not area base × height

Math · 导师：Scribe · 18 分钟

A geometry classroom with a large diagram of a parallelogram on a whiteboard, arrows indicating equal sides and angles, and education/Scribe explaining with a pointer.

Lumi reads decimal places — tenths, hundredths, thousandths to the right of the point — not tens to the left

Math · 导师：Scribe · 15 分钟

A bright math corner with a giant place value chart on the wall, showing columns for ones, tenths, hundredths, and thousandths. Scribe points to a large decimal number 4.372 on the board with arrows indicating each place value.

Lumi names a polynomial as terms glued by + and − — never division by a variable

Math · 导师：Scribe · 15 分钟

A colorful classroom with a large chalkboard displaying various polynomial expressions, a friendly robot guide named Scribe pointing to the board, and students watching attentively. The background includes math posters and a bookshelf.

Lumi sorts bar, line, and pie as three ways to show collected data — not mean-median-mode

Math · 导师：Scribe · 25 分钟

A science lab classroom with colorful bar graph and pie chart posters covering the walls, a whiteboard displaying a filled data table, Scribe standing at center pointing thoughtfully at the bar graph, and students viewing charts on computer screens nearby.

Atlas slides a point by a vector — translation is (x, y) → (x+a, y+b), no flip and no turn

Math · 导师：Scribe · 15 分钟

Scribe stands beside a large grid floor with a colorful triangle shape. Arrows show the triangle moving right and up. The background is a lively park with geometric path patterns.

Atlas solves a system by graphing — the shared point is the pair (x, y) that fits both lines

Math · 导师：Scribe · 35 分钟

A math classroom with a large coordinate plane on the whiteboard showing two colored lines crossing at a single marked point, colored markers and graph paper resting on the desk, a magnifying glass placed nearby, and Scribe carefully studying the intersection.

Lumi fills a triangle with ½ × base × perpendicular height — not parallelogram bh and not a box wrap

Math · 导师：Scribe · 15 分钟

A bright classroom with a large chalkboard showing different triangles labeled with bases and heights, a ruler and protractor on the desk, and the guiding character education/Scribe pointing at the board.

Lumi reads absolute value as distance from zero — |−8| is 8, not “delete the minus and add”

Math · 导师：Scribe · 12 分钟

A sunny park scene with a number line drawn on the ground, children standing at different points representing positive and negative integers, and 'education/scribe' pointing at the number line with a measuring tape.

Atlas writes a factor tree to prime-factorize — 12=2×2×3 — not only sorting prime vs composite

Math · 导师：Scribe · 20 分钟

A colorful classroom with a large chalkboard showing numbers and factor trees, an animated character 'Scribe' pointing to a prime number chart and a factor tree diagram.

Lumi splits tens as stems and ones as leaves — not histogram bins and not a mean

Math · 导师：Scribe · 20 分钟

A colorful classroom with a large chalkboard displaying a stem-and-leaf plot, a student desk with data cards, and the guiding character 'Scribe' pointing at the plot.

Atlas isolates x in an inequality and flips the mark when multiplying or dividing by a negative

Math · 导师：Scribe · 20 分钟

A bright classroom with a large whiteboard showing inequality symbols (<, >, ≤, ≥), a student raising their hand, and a guiding character 'Scribe' holding a giant pencil.

Atlas reads a finished bar, pie, or line chart — which bar is tallest, what a slice means — not drawing bins

Math · 导师：Scribe · 20 分钟

A bright science fair room with large posters of bar graphs and pie charts showing survey results. Scribe stands next to a digital touchscreen displaying a colorful bar graph about favorite fruits.

Lumi flips a point over the x-axis to (x, −y) — a reflection, not a slide and not a turn

Math · 导师：Scribe · 15 分钟

Scribe stands beside a mirror-like vertical line on a grid, reflecting a red square to the other side. The background features a futuristic hall of mirrors with geometric patterns.

Atlas names parallel as same slope and perpendicular as negative-reciprocal slopes — not midpoint

Math · 导师：Scribe · 20 分钟

A city street scene with two parallel railroad tracks and a perpendicular street crossing, Scribe pointing to the lines with angle markers highlighting right angles.

Atlas computes a percent change — 20% more than 50 is 60, 20% less is 40 — not 20% of 50 as a bare part

Math · 导师：Scribe · 20 分钟

A colorful marketplace with shoppers comparing price tags on crowded shelves, digital boards flashing changing prices overhead, and bright discount signs reading '20% OFF' hanging above a busy checkout counter.

Lumi shares a total in a ratio — 3:5 of 24 is 9 and 15 — not naming writings and not cross-multiply

Math · 导师：Scribe · 20 分钟

A vibrant marketplace with stalls displaying fruits and vegetables, each with price tags and quantities. Bright banners show ratios like 3:5 and 4:7. The character education/Scribe stands near a fruit stall holding a clipboard.

Atlas uses a² + b² = c² on a right triangle only — c is the side across the right angle

Math · 导师：Scribe · 22 分钟

A math lab with a large right triangle drawn on a whiteboard, squares built on each side to represent the areas of a², b², and c².

Atlas uses a triangle's angle sum of 180° — if two angles are 40° and 60°, the third is 80° — not side-class names

Math · 导师：Scribe · 15 分钟

A sunny park with various triangular shapes formed by trees, benches, and pathways, showing different triangles in nature.

Lumi picks a center — mean is the fair share, median the ordered middle, mode the most often

Math · 导师：Scribe · 25 分钟

A cozy study room where Scribe stands at a chalkboard covered in neatly written formulas for mean, median, and mode, pointing to a list of test scores arranged in order on a nearby desk.

Lumi walks PEMDAS — parentheses, then exponents, then ×÷ left to right, then +− left to right

Math · 导师：Scribe · 15 分钟

A colorful classroom with a large chalkboard displaying the acronym PEMDAS, surrounded by math symbols and a friendly teacher character 'Scribe' holding a pointer stick.

Lumi splits factors from multiples — factors multiply-to, multiples skip-count, LCM is the smallest shared multiple

Math · 导师：Scribe · 20 分钟

A math garden with numbered stepping stones arranged in rows and columns. The guiding character, education/Scribe, points to stones labeled with factors and multiples. A large chart shows factor trees and lists of multiples. Students examine number cards to find common factors.

Atlas sorts a linear graph — a straight y = mx + b — from a nonlinear curve

Math · 导师：Scribe · 20 分钟

A cityscape with Scribe pointing to two big graphs: one shows a straight line labeled 'Linear', the other a curve labeled 'Nonlinear'.

Atlas mixes fraction and decimal in one sum — 1/2 + 0.25 = 0.75 — not convert-only and not equivalent scale-up

Math · 导师：Scribe · 30 分钟

A bright kitchen scene with measuring cups and a recipe book open to a cake recipe. The guiding character, education/Scribe, holds a measuring cup showing 3/4 cup of sugar. A number line on the wall shows fractions and decimals from 0 to 1. Students use tablets to convert fractions to decimals.

Atlas peels 3x + 5 = 20 with inverse operations until x stands alone — not naming the form

Math · 导师：Scribe · 25 分钟

A modern classroom with a large touchscreen board showing an equation being solved step-by-step. The guiding character, education/Scribe, gestures towards the board with a stylus. Students have notebooks open and are following along.

Lumi fills prisms and cylinders with V = B × h — for a cylinder B = πr² — not surface wrap and not counting cubes as the whole job

Math · 导师：Scribe · 30 分钟

A science lab setting with transparent models of a rectangular prism and a cylinder filled with colored water. 'education/scribe' is holding a graduated cylinder and a ruler.

Lumi undoes a one-step equation — x + 5 = 12 so x = 7 — not two-step peel and not naming ax+b=c

Math · 导师：Scribe · 15 分钟

A math adventure scene with 'Scribe' holding a magnifying glass over a balance scale representing an equation, with numbers and variables on each side.

Lumi splits independent events from dependent events — with-replacement vs without

Math · 导师：Scribe · 25 分钟

A bright classroom where Scribe holds a deck of playing cards beside two rolled dice and a probability tree diagram posted on the board, ready to explore whether events influence each other's likelihood.

Lumi combines like terms — 3x + 5x = 8x — not distributing a(b+c) as the whole job

Math · 导师：Scribe · 15 分钟

A lively math lab filled with colorful algebra tiles and posters showing variables and coefficients. Education/Scribe is holding a tablet displaying an expression being simplified step-by-step.

Lumi fills a circle with A = πr² — the inside, not the around-distance

Math · 导师：Scribe · 20 分钟

A bright classroom with a chalkboard showing a large circle divided into colorful slices, a guiding character 'Scribe' pointing to the slices, and students drawing circles on paper with compasses.

Lumi names square root as a side of a square and cube root as an edge of a cube — not exponent laws

Math · 导师：Scribe · 15 分钟

A nature-inspired classroom with plants and geometric patterns on the walls, 'education/scribe' is holding a glowing cube and square, with root symbols hovering above them.

Lumi evaluates f(4) from f(x) = 2x + 3 — function notation, not the one-output test and not 3x+4 without f

Math · 导师：Scribe · 15 分钟

A colorful classroom with a large blackboard displaying the function f(x) = 2x + 3, a student desk with a calculator, and the guiding character Scribe pointing at the board.