Sea level, 0 °C and the ground floor of a building are all zeros that somebody chose. An integer says how far a thing is from its zero and which way, so a single sign carries direction as well as size. This unit starts there and builds every rule from a picture you can move: why subtracting a negative number adds, why two negatives multiply to a positive, why (−3)² and −3² are different numbers.
No lesson needs a graphic display calculator. Lesson 5 uses a scientific calculator once, to show that it squares before it applies the minus sign.
The lessons, in order
- Lesson 1 · Numbers on both sides of zero What an integer is, opposites, and comparing and ordering with < and >. Move the zero point up a cliff and every height changes sign; the places never move. No calculator
- Lesson 2 · Absolute value and distance Absolute value as distance from zero, and the distance between two integers. Move two points along a number line and watch both distances to zero and the gap between them. No calculator
- Lesson 3 · Adding and subtracting integers Adding and subtracting integers with zero pairs and number lines; subtracting is adding the opposite. Step through zero-pair counters and watch the value stay the same while the pairs go in. No calculator
- Lesson 4 · Multiplying and dividing integers Multiplying and dividing integers, the sign rules and why they hold, and several negative factors. Follow a times table past zero and watch the products keep the same step. No calculator
- Lesson 5 · Powers of negative numbers Powers of negative integers, even and odd powers, and longer calculations in the right order. Compare (−k)ⁿ with −kⁿ row by row: they agree for odd powers and split for even ones. Scientific calculator
- Lesson 6 · Coordinates in four quadrants Plotting and reading points in all four quadrants, and distances along grid lines. Move a point around a grid and watch its coordinates, its quadrant and its distance to another point. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.