Subtraction Drawings Guide
Bridges Grade 2 Math • Visual Strategy Guide
3-Digit Subtraction Math Drawings
Bridges Models Page 1 of 2
In the Bridges Grade 2 curriculum, students use visual models to represent subtraction as both taking away (removal) and finding the distance between (difference). Below are the key drawings taught with step-by-step worked examples.
1
Quick Sketches (Sketches of Base Ten Pieces)
Concept: Place Value & Regrouping
Students sketch the minuend (starting number) using shorthand symbols: squares for hundreds (flats), lines for tens (strips), and dots for ones (units). When there aren't enough tens or ones, students decompose (trade) a larger unit.
Quick Key
Square = 100
Line = 10
Dot = 1
Worked Problem: 342 − 165 = ? Regrouping Hundred & Ten
Hundreds (3) take 100 trade → 10 tens Tens (4 + 10 traded = 14) trade take 60 7 tens left Ones (2 + 10 traded = 12) take 5 7 ones left Result Count: 1 Hundred (100) + 7 Tens (70) + 7 Ones (7) = 177
Step 1: Sketch Draw 3 squares, 4 lines, and 2 dots for 342.
Step 2: Check Ones Cannot take 5 from 2. Trade 1 ten for 10 ones (now 12).
Step 3: Check Tens Need 6 tens from 3. Trade 1 hundred for 10 tens (now 13).
Step 4: Cross & Count Cross off 100, 60, and 5. Count remaining pieces: 177.
2
Open Number Line: Jumping Back (Removal)
Concept: Subtraction as "Taking Away"
Students start at the minuend on the right side of the open line and jump backward in friendly place-value parts (hundreds, tens, ones). The landing point is the final difference.
Worked Problem: 425 − 168 = ? Decomposing 168 into: 100 + 20 + 40 + 5 + 3
−100 −20 −40 −5 −3 425 START 325 305 265 260 257 LANDING POINT
Why Bridges splits tens & ones: Jumping to landmark decades (like 305 → 265 and 265 → 260) prevents computational errors when subtracting over hundreds and tens.
Total Jumped: 100 + 60 + 8 = 168 ✓
Bridges in Mathematics Curriculum Guide • Grade 2 Turn over for Adding Up (Distance) & Splitting Models →
Bridges Grade 2 Math • Visual Strategy Guide
3-Digit Subtraction Math Drawings
Bridges Models Page 2 of 2
3
Open Number Line: Jumping Up (Finding the Difference)
Concept: Subtraction as "Distance Between"
Bridges strongly highlights this "shopkeeper's method." Instead of taking away, start at the subtrahend (smaller number) on the left and make friendly forward jumps to reach the minuend on the right. The answer is the sum of all jumps.
Worked Problem: 403 − 287 = ? Ideal for subtracting across zeros!
+3 +10 +100 +3 287 START 290 300 400 403 TARGET
Add up all the friendly jumps: 100 + 10 + 3 + 3 = 116
No regrouping needed when jumping forward to landmark numbers!
4
Splitting by Place Value (Tree / Branch Drawing)
Concept: Expanded Form & Partial Differences
Students draw decomposition branches from each number to subtract hundreds from hundreds, tens from tens, and ones from ones. When negative differences occur, students adjust before subtracting.
Worked Problem: 568 − 234 = 334 (Friendly Split) Place-Value Branch Diagram
5 6 8 − 2 3 4 Hundreds 500 − 200 = 300 Tens 60 − 30 = 30 Ones 8 − 4 = 4 COMBINE PARTS 300 + 30 + 4 = 334
Bridges Grade 2 Strategy Selection: Which Drawing Should I Choose?
Quick Base-Ten Sketches Best when: Learning place value regrouping for the first time, or when concrete visualization of trading 100 for 10 tens is required.
Number Line: Jumping Back Best when: The subtrahend has small digits (e.g., $354 - 112$), making friendly backward jumps of hundreds and tens fast and natural.
Number Line: Jumping Up Best when: The numbers are close together (e.g., $512 - 489$) or subtracting across zeros (e.g., $402 - 188$) to eliminate trading errors.
Bridges in Mathematics Curriculum Guide • Grade 2 Instructional Anchor Chart & Reference Guide
