Long Multiplication Grid
Aligned long-multiplication frame.
The Long Multiplication Grid is a structured blank frame that guides students through every sub-step of the formal long-multiplication algorithm. It features clearly spaced rows for each partial product, a dedicated carrying row above the multiplicand, and column dividers wide enough for two or three-digit multipliers. Students in Grades 4–7 use it when moving beyond single-digit multiplication into the standard written method taught before calculators are introduced. The grid removes the need for students to rule their own working space, which is a surprisingly common source of error. Teachers can pre-fill the multiplicand or leave everything blank for full practice. The frame scales from 3 × 2 problems up to 5 × 3 digit challenges by choosing a larger column count.
Learning objectives
- Master the formal long-multiplication written method step by step
- Correctly record partial products for each digit of the multiplier
- Understand why zeros are placed as placeholders in later rows
- Build accuracy when carrying values between place-value columns
- Develop speed and confidence ahead of timed multiplication tests
- Transition from informal arrays to the efficient standard algorithm
How to use this template
- Print the grid and write the larger number (multiplicand) in the top row, one digit per column.
- Write the multiplier on the left side, one digit per row below the multiplication line.
- Multiply by the units digit first, recording each partial product left to right with carrying marks above.
- Move to the tens digit row, add the placeholder zero in the ones column, then repeat the multiplication.
- Add all partial-product rows using the built-in addition section at the bottom to reach the final answer.
Classroom & home ideas
- Introduce the algorithm with a class demonstration on a projected grid before students work independently on printed copies.
- Use colour-coded pencils so each partial-product row is a different colour, making it easy to see which digit generated which row.
- Set a 'mystery number' challenge: give the partial products and ask students to work backwards to find the original factors.
- Homework extension: provide grids pre-labelled with the column count only, letting students choose their own multiplication problems.
- Cross-check with area models: draw a rectangle model alongside the grid to show why partial products equal sub-areas.
Skills & curriculum links
Frequently asked questions
What digit sizes does this template support?
The default layout supports up to a 4-digit number multiplied by a 3-digit number. For larger calculations, use multiple grids side by side.
Why are there small boxes above the top row?
Those are carrying boxes. When the product of two digits exceeds 9, students write the tens digit there as a reminder to add it to the next column.
Can this template be used on a tablet or whiteboard?
Yes — open the PDF on a tablet with a stylus app, or display it on an interactive whiteboard and have students take turns filling in rows as a class.
Is there a version for lattice multiplication instead?
This template is specifically for the formal column method. For lattice multiplication, look for the dedicated lattice grid template in the catalogue.
Make it your own in the Worksheet Studio
Combine this with other worksheets, duplicate it, or generate a fresh version for any grade and language — free, no sign-up.
Open the Worksheet Studio