Multiplication Chart

How to Use the Multiplication Chart

1. 1. Choose the size. 10 × 10 and 12 × 12 are the usual classroom charts; 15 × 15 and 20 × 20 stretch past the times tables for extension work. Tick Include a row and column for 0 if you want the zero facts.
2. 2. Choose what to show. Print a complete chart for reference, hide a quarter, half or three quarters of the products for fill-in practice, or hide them all for a blank chart students complete themselves.
3. 3. Add emphasis. Highlight one number's row and column — a good way to focus a week on the 7 times table — and shade the square numbers along the diagonal.
4. 4. Print. Fill-in charts print a second page with the completed chart as an answer key. Everything fits one Letter or A4 page in portrait.

Patterns Worth Pointing Out

A multiplication chart is as much a pattern puzzle as a lookup table, and noticing the patterns is how many students stop memorising 144 separate facts and start seeing structure. These are all visible on a printed chart:

• Symmetry. The chart is a mirror image across the diagonal, because 3 × 7 and 7 × 3 are equal. A 12 × 12 chart holds 144 cells but only 78 different facts.
• Squares on the diagonal. The products 1, 4, 9, 16, 25 … run corner to corner. Shade them to see them.
• The 10s and 5s. Every product in the 10 times table ends in 0, and every product in the 5 times table ends in 0 or 5.
• The 9s. From 9 × 1 to 9 × 10, the digits of each product add to 9 (9, 18, 27 … 90), and the tens digit climbs by one as the ones digit falls by one.
• Even and odd. A product is odd only where both the row and the column are odd, which leaves a regular lattice of odd numbers.

The last column counts distinct products, because many facts share an answer: 24 appears for 3 × 8, 4 × 6, 2 × 12 and their reverses. Those counts were computed directly from each table.

Complete, Fill-In and Blank Charts

A complete chart is a reference sheet. A chart with hidden products becomes practice: students fill each gap from the row and column headings, using what they know or counting on. Because the cells are hidden at random, two students with different worksheet numbers fill different gaps; the number in the corner brings the same sheet and its answer key back. A fully blank chart suits students who are ready to build the table from scratch, skip-counting down each row.

Teachers differ on whether students should have a chart in front of them during practice. A reasonable middle path is to use a complete chart while a table is new, a partly hidden one as it becomes familiar, and a blank one as a self-check — and to pair the chart with timed or untimed fact sheets from the Multiplication Worksheet Generator. In the Common Core State Standards, grade 3 asks students to "identify arithmetic patterns (including patterns in the addition table or multiplication table)" (3.OA.D.9) and to know all products of two one-digit numbers from memory by the end of the year (3.OA.C.7). Check your own standards for placement.

Frequently Asked Questions

How do I print a multiplication chart on one page?

Choose the size, then print. Each chart is drawn to fill the width of the page, with the type size reduced for larger charts so a 20 × 20 chart still fits Letter or A4 in portrait. Use 100% scale in the print dialog and turn off headers and footers.

How do I make a blank multiplication chart?

Set Products shown to Hide every product — a blank chart. The numbers along the top and left stay in place; every cell inside is empty. The answer key page prints the completed chart so you can check students' work.

How do I make a fill-in version with only some products missing?

Choose to hide a quarter, half or three quarters of the products. The hidden cells are chosen at random from the whole chart, and the worksheet number in the corner lets you reprint the same gaps and answer key later.

What does highlighting a row and column do?

It shades the row and the column of one number and darkens its headings, so every fact involving that number stands out. It is useful when you are teaching one times table, and because of the symmetry the row and column show the same products.

Why is there a 0 option?

The zero facts are all 0, so most printed charts leave them out. Including a 0 row and column makes the table complete for students who need to see that anything times 0 is 0.

Is there a 12 × 12 chart?

Yes — it is the default. It covers the times tables up to 12, which many curricula teach, and it is one of the four sizes alongside 10 × 10, 15 × 15 and 20 × 20.