Introduction to Integers
Warm-up
Open with a short task that activates prior knowledge relevant to today’s concept.
Explore
Students investigate the concept using manipulatives, drawings, or partner discussion. Circulate and ask probing questions.
Formalize
Bring ideas together as a class. Record key vocabulary and relationships on the board:
Introduction to Integers
Connect the exploration to the formal representation. Check for understanding before moving to practice.
Practice
Students work the practice set independently. Exit ticket: one targeted question on a slip of paper to check for understanding.
Exit ticket
Students work the practice set independently. Exit ticket: one targeted question on a slip of paper to check for understanding.
Step 1: Extend the number line LEFT of zero on a vertical thermometer: above zero the familiar numbers; below, the negatives: −1, −2, −5, −10 … Each negative is a mirror-address across zero.
Step 2: Read the week's lows: Mon −4°, Tue 2°, Wed −7°, Thu 0°, Fri −1°. Order them coldest to warmest: −7 < −4 < −1 < 0 < 2.
Step 3: Confront the core misread: "−7 is bigger than −4 because 7 beats 4." On the thermometer, −7 sits LOWER — colder — deeper below zero. For negatives, the bigger the bare digits, the SMALLER the number. Say it with the picture, not as a rule: −7 is farther below zero.
Step 4: The comparison sentences to practice both ways: −4 > −7 ("warmer than") and −7 < −4 ("colder than").
Step 5: Zero's special seat: neither positive nor negative — the boundary. "Is 0° warmer than −1°?" Yes, by one degree. Zero being GREATER than a number still surprises them; let the thermometer make it obvious.
Step 1: Set the building: floors above ground are positive, parking levels below are negative, ground is 0.
Step 2: Narrate rides and record them: start at floor 3, ride down 5 → land at −2 (two below ground). Record: 3 − 5 = −2. Start at −4, ride up 6 → floor 2. Record: −4 + 6 = 2.
Step 3: The key noticing: passing zero is nothing special to the elevator — it glides through the lobby. Students expect a jolt at zero; the model shows the number line is seamless.
Step 4: Distance vs. destination: from floor 3 down to −2 — how many floors TRAVELLED? 5 (three to ground, two more down). The destination (−2) and the distance (5) are different questions — this distinction, planted now, is the seed of absolute value.
Step 5: Story problems in reverse: "I rode 7 floors and arrived at −3 — where might I have started?" Two answers: 4 (down 7) or −10 (up 7). Both check ✓ — and the double answer is the interesting part.
Step 1: Sea level: a diver at −12 m, a drone at 25 m, a swimmer at 0. Who's farthest from sea level? |−12| = 12 vs 25 → the drone. "Farthest from zero" ignores sign — distance language again.
Step 2: Money: an account at −40 deposit → −15 + 40 = 25 dollars. The first $15 of the deposit filled the hole; only then did savings begin. The hole-filling image is how negatives-plus-positives compute without rules.
Step 3: Golf: par is 0; scores are strokes relative to it. Rounds of −3, +2, −1, +1 total: (−3) + 2 + (−1) + 1 = −1 — one under par overall. Add by pairing opposites: (−3 + 2) = −1? … or pair (−1 + 1) = 0 first, then −3 + 2 = −1. Opposites cancelling to zero is the deepest integer fact there is.
Step 4: Harvest the pattern across costumes: every context has a natural ZERO (sea level, broke, par), and integers measure both sides of it. Ask students for a fourth costume (elevation, time before/after launch, yards gained/lost) — owning the template means never fearing the sign.