4th Grade Multiplying Multi-Digit Numbers Test Answer Key and Scoring Guide (PDF)

4th grade multi digit multiplication test answer key – Maths PDF

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This 4th grade multi digit multiplication test answer key covers multiplying multi-digit numbers (Common Core 4.NBT.B.5), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students see how each point on the multiplication test was earned.

Topic: Multiplying Multi-Digit Numbers (4th grade)
Content: Worked solutions and a scoring guide for 9 questions
Standards: 4.NBT.B.5
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students see how each point on the multiplication test was earned. Also, it gives complete solutions to all nine questions, with the partial products listed, the area model completed, and the reasoning for the estimate and the error.

Question 5 shows how a property of multiplication makes a calculation simpler, question 8 explains exactly what Jamal missed, and question 9 combines a multiplication with a subtraction. Add your points out of 20, then spend about 15 minutes redoing every question that lost credit. Then, write each correction with all of its partial products.

Use this answer key to score the test. Each solution lists the partial products, and the scoring note tells how the points are awarded. Total: 20 points.

Grade 4 · Common Core State Standards: 4.NBT.B.5

4th grade multi digit multiplication test answer key: worked solutions

1 – Mental math [2 pts]

\(6 \times 3 = 18\), then attach two zeros. \(1,800\)
\(8 \times 7 = 56\), then attach three zeros. \(56,000\)

Scoring: 1 point for each answer.

2 – Area model [2 pts]

1,500 + 60 + 300 + 12 = 1,872.

\(1{,}500 + 60 + 300 + 12 = 1{,}872\)

\(1,872\)

Also, Scoring: 1 point for the four correct partial products. 1 point for 1,872.

3 – Four digits by one [2 pts]

\(3{,}000 \times 5 = 15{,}000\), \(800 \times 5 = 4{,}000\), \(60 \times 5 = 300\), \(2 \times 5 = 10\).

\(15{,}000 + 4{,}000 + 300 + 10 = 19{,}310\)

\(19,310\)

Scoring: 1 point for correct partial products. 1 point for 19,310.

4 – Two digits by two [2 pts]

Partial products for 67 × 48.

\(2{,}400 + 280 + 480 + 56 = 3{,}216\)

\(3,216\)

Scoring: 1 point for correct partial products. 1 point for 3,216.

5 – Properties [2 pts]

Associative and commutative properties: \(5 \times 18 \times 20 = (5 \times 20) \times 18\).

\(5 \times 20 = 100\), and \(100 \times 18 = 1{,}800\).

\(1,800\)

Scoring: 1 point for a valid regrouping. 1 point for 1,800.

6 – Estimate and solve [2 pts]

Estimate: \(50 \times 30 = 1{,}500\).

Exact: \(48 \times 30 = 1{,}440\) and \(48 \times 1 = 48\), so \(1{,}440 + 48 = 1{,}488\).

about \(1,500\); exactly \(1,488\)

Scoring: 1 point for the estimate. 1 point for the exact product.

Question 7 and after

7 – Muffin boxes [3 pts]

\(24 \times 38 = 24 \times 30 + 24 \times 8 = 720 + 192 = 912\). 912 muffins
\(24 \times 45 = 24 \times 40 + 24 \times 5 = 960 + 120 = 1{,}080\). \(1,080\) muffins
\(912 + 1{,}080 = 1{,}992\). \(1,992\) muffins

Scoring: 1 point for each part.

8 – Find the mistake [3 pts]

The 2 in 23 is 2 tens, so the partial product is \(46 \times 20 = 920\), not \(46 \times 2 = 92\).
\(920 + 138 = 1{,}058\). \(1,058\)
\(50 \times 20 = 1{,}000\). The product should be close to 1,000, so 230 is too small.

Scoring: 1 point for each part.

9 – Stadium sections [2 pts]

All seats: \(9 \times 1{,}250 = 11{,}250\) (\(9 \times 1{,}000 = 9{,}000\), \(9 \times 250 = 2{,}250\)).

Open: \(11{,}250 – 2{,}400 = 8{,}850\).

\(8,850\) seats

Scoring: 1 point for 11,250. 1 point for 8,850.

Total score

Total

20 points

Key facts behind this 4th grade multi digit multiplication test answer key

Key facts

Partial products are the answers to each smaller multiplication; add them for the final product.
Distributive property: 6 × 47 = 6 × 40 + 6 × 7.
A 2-digit by 2-digit problem has four partial products in an area model.
Then, for multiples of 10, multiply the basic facts and attach all the zeros: 30 × 40 = 1,200.
Estimate first by rounding to check that the product makes sense.

Common mistakes with this 4th grade multi digit multiplication test answer key

Students lose points because a partial product is missing. Instead, count the boxes in your area model against the key.
Students skip the estimate in question 6. Also, the estimate is worth a point, and it shows whether the exact answer is reasonable.
Students ignore the second step in question 9. Instead, after finding the total seats, subtract the tickets already sold.
Students copy Jamal’s mistake by multiplying by 2 instead of 20. The tens digit stands for tens, so it needs a zero.

How to learn from your test

Sort lost points into mental math, partial products, and word problems. Practice the weakest group first. Repeat this habit on every problem for the best results.
Redo question 4 with a new pair of numbers. Finally, changing the numbers shows whether you understand the steps.
Teachers can ask students to compare their area models with the key and explain any differences. Repeat this habit on every problem for the best results.

Download the 4th grade multi digit multiplication test answer key as a PDF with the button below and keep it with your notes.

4th grade multi digit multiplication test answer key: frequently asked questions

What is Jamal’s mistake in question 8?

Jamal multiplied 46 by 3 and by 2, but the 2 in 23 stands for 20. He needed 46 times 20, which is 920, not 92. Adding 138 and 920 gives 1,058. His answer of 230 is far too small.

How do I use a property of multiplication in question 5?

Reorder the factors to make a friendly product. For 5 times 18 times 20, multiply 5 times 20 to get 100, then 100 times 18 is 1,800. Using the commutative and associative properties makes the arithmetic easier.

How many seats are still open in question 9?

The stadium has 9 times 1,250, which is 11,250 seats. Subtracting the 2,400 sold seats leaves 8,850 open seats. This question needs a multiplication first and then a subtraction. A quick check like this takes only a few seconds and prevents most errors.

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