Finding the Difference by Counting Up
Grade 4 Eureka Math students learn to subtract mixed numbers by counting up on a number line instead of borrowing. To find 4 1/4 minus 2 3/4, start at 2 3/4 and count up in steps: jump 1/4 to reach 3, jump 1 to reach 4, jump 1/4 to reach 4 1/4. Sum the jumps: 1/4 + 1 + 1/4 = 1 2/4 = 1 1/2. This strategy converts a difficult subtraction into manageable addition hops and visually reinforces the relationship between subtraction and the distance between numbers.
Key Concepts
To find the difference $A B$, you can find the number that must be added to $B$ to get $A$. On a number line, this is the total distance from $B$ to $A$. The difference is the sum of the "jumps" made to get from the subtrahend ($B$) to the minuend ($A$).
Common Questions
What is the counting-up strategy for subtraction?
Instead of subtracting directly, you start at the subtrahend and count forward to the minuend. The total distance counted is the difference.
How do you find 4 1/4 minus 2 3/4 by counting up?
Start at 2 3/4. Jump 1/4 to reach 3, then jump 1 to reach 4, then jump 1/4 to reach 4 1/4. The difference is 1/4 + 1 + 1/4 = 1 2/4 = 1 1/2.
Why use counting up instead of standard subtraction for mixed numbers?
When the fractional part of the minuend is smaller than the subtrahend fraction, borrowing adds complexity. Counting up avoids borrowing entirely.
How does a number line support this strategy?
The number line makes each jump visible. You can track each hop and add them to find the total difference without regrouping.
Is counting up the same as using a number line model?
Yes, the number line is the visual model for counting up. Both represent subtraction as the gap between two points.