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Multiplication · Grade 4

Multiplicative Comparison Word Problems

Compare a reference amount with a second amount that is a whole-number multiple of it. Use equal units for smaller multipliers, or split a two-digit multiplier into tens and ones. Choose the range that matches the child's multiplication goal.

4 problemsAnswer key includedPrintable worksheetA4 & US Letter
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Teaching notes for parents and teachers

How to teach it

Draw one reference amount and repeat it the stated number of times. Use tens and ones to split a larger multiplier when helpful.

Ask your student

Does the story mean this many more, or this many copies?

If your student needs help

If the student adds the multiplier, compare an extra group with repeated copies of the reference amount.

Choosing and using the worksheet

The default activity has four short comparison questions with a reference amount and a whole-number multiplier from one through nine. One question uses a multiplier of one; three use a multiplier greater than one. The compared amount is always the unknown. Zero, fractional multipliers, unknown references, and unknown multipliers are not included in this set.

Each question includes matching bar units, an equation box, an amount box, and space to explain the relationship. The bars share a scale within a question; do not compare their lengths across different questions. The answer key gives a multiplication equation and the second amount. A correct reversed multiplication equation or division check can also show understanding.

Build a two-digit multiplier from tens and ones

Choose Two-digit multiplier when the child understands what times as much means and is ready to multiply two two-digit numbers. The reference amount and multiplier are both known. The unknown is the second amount. Instead of drawing dozens of separate bars, the model groups every ten copies into one labeled box.

For example, an amount is 21 and a second amount is 62 times as much. Sixty-two copies are six groups of ten copies and two single copies. A box labeled 10 stands for ten copies of 21, and a box labeled 1 stands for one copy of 21. These boxes are labeled counters, not bars drawn to scale: the labels tell how many copies they represent. They do not show the product.

Reference amount: 2162 copies = 6 tens + 2 ones1010101010101121 × 60 = 1,26021 × 2 = 421,260 + 42 = 1,302
Six tens of copies and two single copies preserve all 62 copies.

Multiply each part of the multiplier

Split 62 into 60 + 2. Multiply the same reference amount by both parts: 21 × 60 = 1,260 and 21 × 2 = 42. Then combine the partial products: 1,260 + 42 = 1,302. This is the distributive property, 21 × (60 + 2) = (21 × 60) + (21 × 2).

The zero in 60 matters. Calculating 21 × 6 gives 126, which counts six copies rather than sixty copies. Multiplying by 60 makes the value ten times as large: 1,260. Ask the child to name the unit in the first partial product: six tens of copies, or sixty copies altogether.

Use a smaller second example

For 29 × 14, split 14 into 10 + 4. Ten copies of 29 make 290. Four copies make 116. The two partial products total 406.

Reference amount: 2914 copies = 1 ten + 4 ones10111129 × 10 = 29029 × 4 = 116290 + 116 = 406
One ten of copies and four single copies make fourteen copies.

This example also shows regrouping inside a partial product: 29 × 4 = 116. The tens-and-ones split of the multiplier does not mean every partial product will be a two-digit number. Keep the full value of each product before adding.

Check the size and the relationship

Estimate before accepting an answer. Since 21 is close to 20 and 62 is close to 60, the product should be near 1,200. The exact answer 1,302 is reasonable; 168 or 172 is not. For 29 × 14, 30 × 14 = 420, so 406 is a sensible result.

Check the relationship in reverse when division is familiar: 1,302 ÷ 62 = 21 and 406 ÷ 14 = 29. The quotient should recover the reference amount. The check confirms both the calculation and the meaning of times as much.

If the child writes 21 × 6 + 21 × 2: ask whether the first term represents six copies or sixty copies. Replace 6 with 60, or write 21 × 10 × 6, before combining the parts.

What the printable asks

The Two-digit multiplier activity has four short quantity-comparison problems with different pairs of factors. Both factors are from 10 through 99. The picture groups the multiplier into tens and ones without revealing either partial product or the final amount. A sheet contains no more than one multiplier ending in zero, so at least three questions have a nonzero ones partial product. If the multiplier ends in zero, there are no single copies to add: the ones partial product is zero. The answer key shows the full equation and the second amount.

Use the equation box for the complete multiplication statement. In the working area, record the tens partial product, the ones partial product, and their sum. Choose Two-digit reference for a smaller multiplier from one through nine, or One-digit reference when the child is still learning the comparison language.

Make a practice set

Select the worksheet, answer key, or both. When both are selected, the answer key prints after the questions. Keep it separate if you want your student to work independently.

Print materials

After your student finishes

Ask the child what the reference amount represents and what the multiplier counts. For a two-digit multiplier, check the tens and ones partial products and their sum. When division is familiar, use it to check that the second amount gives back the reference amount.

More about multiplication · Grade 4 worksheets

Grade 4 selected skill connection: 4.OA.A.1; 4.OA.A.2 (selected compared-amount-unknown cases). The two-digit reference and two-digit multiplier options support place-value multiplication in 4.NBT.B.5; the latter uses selected 10–99 by 10–99 products. See the Common Core standards for this grade. This worksheet does not cover every requirement in the standard.