Explains how 3rd grade students can picture multiplication as an array, use turn-around facts, and break a hard fact into easier partial products. Builds from single-digit facts to two-digit by one-digit problems such as 23 × 3, with worked examples and a self-check.
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Curriculum: Texas grade levels (TEKS). We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Multiplication Strategies: Arrays and Partial Products
3rd Grade students (typically ages 8–9) working on multiplication. It is pitched at level 1 · easier.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 15 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try 3rd Grade Doubles and Halves Worksheet — Level 1, then check understanding with the 3rd Grade Multiplication and Division Topic Test.
Success TutoringWorksheets3rd Grade · Mathematics · MultiplicationMultiplication is a fast way of adding equal groups. 4 × 6 means 4 groups of 6, which is 6 + 6 + 6 + 6 = 24. Instead of adding over and over, we learn strategies that get us to the answer quickly and let us check that it is right.
Arrays. An array is a set of objects arranged in equal rows and columns, like eggs in a carton. 3 rows of 5 dots shows 3 × 5 = 15. Turn the array on its side and you see 5 rows of 3, which is 5 × 3 = 15. The answer does not change when you swap the numbers. These are called turn-around facts, and they halve the number of facts you need to learn.
Use an array for 4 × 6
Splitting an array (partial products). If a fact is hard to remember, split one of the numbers into friendlier parts, multiply each part, then add the answers together. The two smaller answers are called partial products. The 5s and 10s are the easiest facts to split around.
7 × 8 by splitting the 7
Bigger numbers. The same idea works for a two-digit number times a one-digit number. Split the two-digit number into its tens and ones, multiply each part, then add.
23 × 3 using partial products
| Fact | Split | Partial products | Answer |
|---|---|---|---|
| 6 × 7 | (5 × 7) + (1 × 7) | 35 + 7 | 42 |
| 8 × 9 | (8 × 10) − (8 × 1) | 80 − 8 | 72 |
| 14 × 5 | (10 × 5) + (4 × 5) | 50 + 20 | 70 |
| 32 × 4 | (30 × 4) + (2 × 4) | 120 + 8 | 128 |
Answers: 1. 3 × 7 = 21 2. 4 × 5 = 20 3. 40 + 8 = 48 4. 36 (30 + 6) 5. 96 (80 + 16) 6. 70 − 7 = 63
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