numberleaf.A little less prep.

BUILD A STRATEGY / BREAK APART

Make a hard fact
from two familiar ones.

Distributive property multiplication worksheets with arrays. See a worked example, follow a split, then choose your own. Four spacious problems per page, with an explanation prompt and worked keys.

A ready-to-print strategy lessonGuided + independent practice · 2 student pages + 2 keys
Letter PDF ↓A4 PDF ↓Customize →

FROM SEEING TO EXPLAINING

Make it yours

Arrays have 2–10 (or 2–12) rows and 6–10 (or 6–12) columns. Guided splits use 5 or 10 columns in the first part. Independent work accepts any valid vertical split.

PRINT PREVIEW

See both parts.

Use the splitNUMBERLEAF / MULTIPLICATION STRATEGIESUse the splitName: ____________________________ Date: ______________Use the bold line to split the columns. Complete the equations.TRY ONE TOGETHER4 rows × 8 columns: split 8 into 5 + 3.4 × 8 = (4 × 5) + (4 × 3)20 + 12 = 32. Both parts still have 4 rows.1. 9 × 109 × 10 = (9 × ___) + (9 × ___)= ______ + ______= ______2. 6 × 66 × 6 = (6 × ___) + (6 × ___)= ______ + ______= ______3. 7 × 67 × 6 = (7 × ___) + (7 × ___)= ______ + ______= ______4. 7 × 107 × 10 = (7 × ___) + (7 × ___)= ______ + ______= ______Explain one: how did your two smaller facts help you find the total?numberleafmath.com · break apartEdition 0A8NPQW
Readable text for this page

TEACHER & FAMILY NOTES

Keep the rows.
Split the columns.

Before this lesson

The learner should be able to explain rows and columns and interpret multiplication as equal groups. If that is not secure yet, start with reading and drawing arrays. A useful split depends on which smaller facts the learner already knows.

Try the worked example together

Draw 4 rows of 8 squares. Put a vertical line after the fifth column. Point to both smaller rectangles: each still has 4 rows. There are 4 × 5 squares on the left and 4 × 3 on the right, so 4 × 8 = 20 + 12 = 32. Every square belongs to one part; none are lost or counted twice.

Move from a given split to a chosen split

The guided page shows a bold boundary after 5 columns, or after 10 when the array is wider than 10. The independent page removes the boundary. Ask the learner to draw one vertical line between columns, record both smaller multiplications and explain why their choice helps. Keep the same number of rows in both parts. A different split can be equally correct: 4 × 8 can also be (4 × 4) + (4 × 4).

Check the reasoning, not just the total

If a learner writes 4 × 5 + 3, point to all four rows of the second part: it contains 4 groups of 3, not just 3 squares. If they multiply the two partial products, ask which operation combines the counts of two separate sets of squares. If they draw a horizontal split, that can also represent valid mathematics, but it changes the row count; discuss it separately because this page asks for a column split. The independent key shows one possible solution, not the only acceptable one.

Scope and next steps

This resource develops one strategy related to Common Core 3.OA.B.5: using the distributive property to derive multiplication facts. It does not cover all operation properties or demonstrate mastery on its own. The default stays within 100; the optional 12 × 12 range extends beyond that. Learners do not need to memorize the formal property name to explain the idea.

Then connect the strategy to focused fact practice or extend it to place-value area models. Report a confusing question or printing issue.