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Grade 3 · lesson 1 of 4

Split a Factor and Combine Partial Products

Split the stated factor at five when useful.

About 15 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For 6×8, split eight into five and three.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A factor can be split into parts that are easier to multiply. Multiply every part by the other factor, then add the partial products. The distributive property preserves the original whole because the split parts add to the factor you replaced.

Split the stated factor at five when useful. Compute the two partial products and combine them. Draw separate sections of one array to check that every square is counted once.

The split parts must add back to the original factor. Multiply both parts before combining their products. Split an array into two non-overlapping column sections.

  1. Split an array into two non-overlapping column sections.
  2. Follow the worked example. Point to each number or shape feature and say what it tells you.
  3. Split the stated factor at five when useful.
  4. Try the question and then the three practice questions. Check your answers and explain any change you make.
Worked example

See the method in action

For 6×8, split eight into five and three. Then 6×5=30 and 6×3=18, so 6×8=48. The six-row array has five columns and three more columns. Multiplying only one part would leave columns uncounted. The split parts must add back to the original factor. Multiply both parts before combining their products. Split an array into two non-overlapping column sections.

Your turn

Check your reasoning

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Helpful tips
  • The split parts must add back to the original factor.
  • Multiply both parts before combining their products.
Use a split factor to find 3×8.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

24

Split eight into five and three, multiply both parts, then add. The result is 24.

Take it further

Find 9×7 as 9×5+9×2. Expected: 63.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Use a split factor to find 4×8.
Need a hint?
  • The split parts must add back to the original factor.
  • Multiply both parts before combining their products.
2. Use a split factor to find 5×8.
Need a hint?
  • The split parts must add back to the original factor.
  • Multiply both parts before combining their products.
3. Use a split factor to find 6×8.
Need a hint?
  • The split parts must add back to the original factor.
  • Multiply both parts before combining their products.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.