What this worksheet helps children practise
A common error is multiplying by the tens digit without using its place value. In 47 × 32, 47 × 3 is 141, but the requested row is 47 × 30, which is 1,410. Say “thirty” before calculating. Another mistake is placing 94 in the wrong columns below 1,410. Point to the ones boxes on the right before adding the two rows.
Children practice using the value of each digit in a multiplier. In 24 × 13, the 3 represents three ones and the 1 represents one ten. The two calculations are therefore 24 × 3 and 24 × 10. This guided fourth grade activity assumes familiarity with multiplication facts, tens and ones, and addition with three- or four-digit numbers. The grade label is a guide to readiness. For a related skill, use 3-Digit by 1-Digit Multiplication Without Regrouping: Multiply from right to left. Write one digit in each answer box.
Preparing a short session
Prepare a pencil, eraser and scrap paper for regrouping notes. Read the two factors and identify the four boxes in each row. Ones belong in the rightmost box; unused boxes on the left may stay empty. The labels, such as ×3, ×10 or ×20, identify the required partial product. Keep the worked example visible and put the answer key aside during the first attempt.
A concrete example to get started
The example is 23 × 14: fourteen boxes with twenty-three tiles in each. Split 14 into 4 + 10. Four boxes contain 23 × 4 = 92 tiles; ten boxes contain 23 × 10 = 230 tiles. Add the two amounts to find 92 + 230 = 322. The zero in 230 records zero ones in the product with ten.
Supporting the activity
Work from left to right, one pair of problems at a time. Find the product with the ones, then the product with the tens. For 36 × 24, the rows are ×4 and ×20, not ×4 and ×2. Record any regrouping on scrap paper before placing each completed partial product in its boxes. Add the two aligned rows to find the final total. To vary the practice, try Mixed Multiplication Facts: Times Tables 2–9: Find each product. Write one digit in each answer box.
What to notice and how to check
The totals are 312, 864, 1,504, 1,508, 2,835 and 2,888. The corresponding partial products are 72 + 240, 144 + 720, 94 + 1,410, 348 + 1,160, 315 + 2,520 and 608 + 2,280. The answer key shows all three rows. Check each multiplication before checking the addition, and ask the child to explain what each partial product counts.
Making the task easier
Cover five problems and complete 24 × 13 together. The first partial product is 72 and the second is 240. An adult can record dictated numbers while the child chooses the boxes and explains the groups. If multiplication by a whole ten is unclear, draw ten equal groups on scrap paper. Return to multiplying by 10 before working with the larger multipliers on the page.
Keep the learning aim, but reduce how much the child has to handle at once. Cover part of the page with another sheet and reveal one task at a time. Demonstrate a separate example, then leave a real opportunity to work something out. An answer reached with support is still a useful attempt; it does not yet show that the same task can be completed independently.
Taking the idea beyond the worksheet
Check 36 × 24 using 36 × (20 + 4), giving 720 + 144 = 864. Then reverse the factors and try 24 × (30 + 6): 720 + 144 again gives 864. With other numbers, the partial products may differ even though the final product stays the same. Discuss why switching the factors preserves the total, using equal rows or boxes rather than a speed challenge.
Use the follow-up to meet the same idea in a different setting. Offer it once the first task makes sense, without insisting that the whole page must be perfect. The child might explain a strategy, make an example or set a challenge for an adult. Return to the worksheet only when it helps connect the two situations. A short conversation or a practical activity can be enough to finish the session. To continue exploring, use 3-Digit by 2-Digit Multiplication with Partial Products: Find both partial products, then add them on the Total row.
Downloading and printing the PDF
This free PDF contains one worksheet designed for A4 paper. Download the file using the button on this page and open it in your PDF reader. Choose actual size or a 100% scale, check the orientation in the print preview and turn off any browser headers or footers. The illustrations use vector lines, so their outlines stay sharp when printed. Check the margins on one copy before preparing several sheets for a group. The level shown on the page is a guide, rather than a requirement to complete the activity at a particular age.