Learn · Illustrative Mathematics · Grade 6 · Unit 7
Short lessons you can play with. Read temperatures below zero, compare and order signed numbers on the number line, measure distance from zero, graph inequalities, find your way around all four quadrants of the coordinate plane, and pack identical kits with common factors, then check yourself. When you’re ready, practice in Expedition Zero.
Nine chapters follow the unit’s lessons in order. Each step shows one idea with something to change, then a quick check. A wrong answer names the likely mistake and gives one more try. Negative answers can be typed with a minus sign: −4, -4, or −2 1/2.
Every comparison, absolute value, and inequality is shown on a number line, flat or standing up (a thermometer, or sea level). Research on how students learn negative numbers points to the number line as the model that holds up best: “less” means farther left, and opposites sit the same distance from 0 on each side.
The most common mix-up is reading −8 as greater than −3, because 8 is greater than 3. The pages keep two questions apart: which number is less (farther left), and which is farther from zero (its absolute value). A debt of $30 is a balance of −30: less than −12, but a bigger debt.
−4 < 1 and 1 > −4 say the same thing, and the pages flip between them. An inequality’s graph shows its boundary with an open circle (< and >, the number itself left out) or a filled one (≤ and ≥), and stories like “at least 48 inches” are turned into symbols with the reason in words. When only whole numbers make sense (people in an elevator), the solutions are dots, not a ray.
Coordinates are always read as a path from the origin: across first (x), then up or down (y). Swapped coordinates and a flipped sign are named when they happen. Distances along a grid line are found from each point’s distance to the axis, adding when the points are on opposite sides, so no subtraction of negative numbers is needed (that comes in Grade 7).
Stories about splitting things into identical groups use a common factor; stories about packs or schedules that need to line up use a common multiple. The last chapter puts them side by side so students choose on purpose.
Each chapter ends with a link to the matching station in Expedition Zero, the practice game for this unit. Progress is saved on this device.
The unit’s partner activities (info gaps and card sorts) and the open-ended drawing in Lesson 19 work better in class.