Operations and Algebraic Thinking
Operations and Algebraic Thinking is a major Grade 3 math domain on the OST. It tests whether you can interpret products and quotients, solve one- and two-step word problems with all four operations, and explain patterns in multiplication and addition tables.
Core rules
- Multiplication means equal groups: 4 × 6 is 4 groups of 6 (3.OA.A.1).
- Division undoes multiplication and has two meanings: sharing and measuring how many groups.
- The commutative property: a × b = b × a. The associative property: (a × b) × c = a × (b × c).
- The distributive property lets you break apart a factor: 6 × 7 = 6 × (5 + 2) = 30 + 12 (3.OA.B.5).
- An unknown in an equation can be found with the inverse operation: 8 × ? = 56, so 56 ÷ 8 = 7.
Worked example
A class has 7 tables with 6 students at each table. How many students? 7 × 6 = 6 × 7 = 42. Using the distributive property: 7 × 6 = (5 + 2) × 6 = 30 + 12 = 42. If the 42 students are split into groups of 6, the number of groups is 42 ÷ 6 = 7 because 6 × 7 = 42.
Traps that cost marks
- Mixing up “3 times as many” with “3 more than.” Three times as many as 4 is 12, not 7.
- In two-step problems, doing operations in the order they appear instead of the order the story requires (3.OA.D.8). Underline the question first.
- Treating division as only sharing. “How many groups of 5 fit in 35?” is 35 ÷ 5.
- Forgetting that a square number such as 36 has the factor pair (6, 6), not two different factors.