lesson
Updated 6 days ago · 2 views
If a research submarine dives 3 meters every minute, where will it be after 4 minutes?
Instead of guessing, we can use repeated addition on a number line to track each jump down.
Multiplication as Repeated Jumps
On a number line, multiplication means starting at zero and taking equal-sized jumps.
In the problem 3×4, the first number is the number of jumps (3), and the second number is the jump size (+4 to the right).
📊A clean, horizontal number line from 0 to 14 with tick marks at every integer. Show 3 distinct curved blue arrows jumping from 0 to 4, 4 to 8, and 8 to 12. Each jump is labeled '+4'. Below the number line, display the repeated addition equation '4 + 4 + 4 = 12' and the multiplication equation '3 × 4 = 12'. Use a clean modern card layout with #1e2945 text, #22b7ff accents, and a light background.
What happens when your jump size is negative?
Jumping Into the Negatives
When you multiply a positive number by a negative number like 3×(−4), you are adding negative groups: (−4)+(−4)+(−4).
Because each jump is −4, you start at 0 and move left 4 units, 3 times in a row, landing at −12.
📊A horizontal number line centered around negative values, showing tick marks from -14 to 2. A bold marker starts at 0. Three curved red/orange arrows jump to the left: 0 to -4, -4 to -8, and -8 to -12. Each jump is clearly labeled '-4'. Below the line, show '(-4) + (-4) + (-4) = -12' and '3 × (-4) = -12'. Use modern styling with red/orange accent (#ff5757) and bold landing point at -12.
Let's put this into action with another problem to make sure the pattern is clear.