Double Digit Blueprint Poster
Math Lab Reference Series // Poster No. 01
Double-Digit Blueprint
Mastering the Standard Algorithm step-by-step with color-coded alignments.
Ones Multiplier
Place Guard
Tens Multiplier
Final Sum
The Annotated Master Problem (36 × 24)
H
T
O
Place Value Columns
+2 +1
Regrouped values go on top of the Tens column
3
6
36 Top Factor (Multiplicand)
×
2
4
24 Bottom Factor (Multiplier)
1
4
4
144 First Partial Product (4 × 36)
7
2
0
720 Second Partial Product (20 × 36)
8
6
4
864 Final Answer (144 + 720)
Place Value Guard: The teal 0 is your most critical step! Because the multiplier digit 2 lies in the tens column, its actual value is 20. This zero secures the place value before you multiply!
1
Ones Column Step
Multiply bottom ones digit 4 by top factor 36:
- \(4 \times 6 = 24\) → Write 4, regroup +2.
- \(4 \times 3 = 12\) → Add the +2 to make 14.
- Write first product: 144.
2
The Place Guard
Before multiplying the tens column, place a 0 in the ones column of row 2:
- This holds the place value open.
- Because you are multiplying by 20 (not just \(2\)).
- Guards your math from sliding left!
3
Tens Column Step
Cross out the used 2. Multiply bottom tens 2 by top 36:
- \(2 \times 6 = 12\) → Write 2, regroup +1.
- \(2 \times 3 = 6\) → Add the +1 to make 7.
- Write second product: 720.
4
Combine Products
Add the two color-coded rows together to find your final product:
- Add columns right-to-left.
- \(144 + 720 = \mathbf{864}\).
- Check your work! Perfect standard algorithm complete!
STUDENT BINDER REFERENCE // KEEP IN MATH SECTION
NAME: ___________________________ DATE: _________
