Unit Plan 29 (Grade 3 Math): Mixed Operations & Unknowns in All Positions
Represent and solve 1–2 step math stories using equations with a letter for the unknown, bar models, and estimation to check reasonableness and build flexible problem-solving skills.
Focus: Represent and solve one- and two-step problems with addition, subtraction, multiplication, and division; write equations with a letter for the unknown and check reasonableness.
Grade Level: 3
Subject Area: Mathematics (Problem Solving & Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build flexible problem-solving habits by translating real-world situations into equations with unknowns in any position (e.g., n + 27 = 63, 6 × n = 42, 54 − n = 19). They choose representations (tape/bar models, number lines, arrays) to plan and solve one- and two-step problems, then estimate to check whether answers make sense.
Essential Questions
- How do I decide which operations and representations fit a problem?
- Where can the unknown appear, and how do I solve when it’s not at the end?
- How do estimation and reasonableness checks help me catch mistakes?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Represent one- and two-step word problems with equations using a letter for the unknown.
- Solve problems with unknowns in all positions using bar models, arrays, and number lines.
- Interpret results (including simple remainders) and check reasonableness by mental math and rounding.
- Explain and justify solution paths with clear units, labels, and operations.
Standards Alignment — CCSS Grade 3
- 3.OA.8: Solve two-step word problems using the four operations; represent with equations using a letter for the unknown; assess reasonableness using mental computation and estimation (including rounding).
- 3.OA.3: Use multiplication/division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities; represent with drawings and equations with a symbol for the unknown.
- Mathematical Practices (threaded): MP.1 (Make sense & persevere), MP.4 (Model with mathematics).
Success Criteria — Student Language
- I can write an equation with a letter for the unknown that matches the story.
- I can choose a representation (bar model, array, number line) and explain why it helps.
- I can estimate and use mental math to check if my answer is reasonable.