Study Guide — 3.OA.B.5
Apply properties of operations as strategies to multiply and divide
Understand multiplication as equal groups and division as sharing or grouping.
What this standard means
- Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.)
- Apply apply properties of operations as strategies to multiply and divide with models and explanation
- Models multiplication as equal groups or arrays
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Draw arrays for multiplication 2. Use repeated addition to explain products 3. Connect division to missing-factor multiplication
_See printable PDF for diagram._
Common mistakes
- Confusing multiplication with addition
- Unequal groups in array models
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for 3.OA.B.5.
- [ ] Models multiplication as equal groups or arrays
- [ ] Solves division as sharing or grouping
- [ ] Relates multiplication and division facts
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors