High-Impact Math Instructional Routines

High-Impact Math Instructional Routines

Routine 1: Number Talks (10 min, 3x weekly)

Purpose: Build mental math strategies, flexibility, fact fluency

Steps: 1. Pose: Present problem visually (e.g., "9 + 6 = ?") 2. Think: Students mentally solve, show thumb-up when ready 3. Collect: Teacher writes all answers without judgment 4. Explain: Students share strategies 5. Connect: Link strategies to math properties

Sample Strategies Students Share: - "I know 9+1=10, so 9+6 is 10+5 = 15" (Making 10) - "I counted on from 9: 10, 11, 12, 13, 14, 15" (Counting on) - "6+6=12, plus 3 more is 15" (Doubles plus)

Key: Celebrate multiple approaches, build mathematical discourse

Routine 2: Concrete-Representational-Abstract (CRA)

Required by B.E.S.T. Instructional Guide (B1G-M)

Phase 1 - Concrete: - Use physical manipulatives (base-ten blocks, counters) - Students physically construct/manipulate - Build initial concept through touch

Phase 2 - Representational: - Transition to drawings/diagrams - Squares for hundreds, lines for tens, dots for ones - Bridge between physical and symbolic

Phase 3 - Abstract: - Use numbers and symbols only - Write in expanded form, standard algorithms - Apply to word problems

Example (Grade 3 - MA.3.NSO.1.2): - Concrete: Build 2,530 with base-ten blocks - Representational: Draw place value chart - Abstract: 2,530 = 2,000 + 500 + 30

Routine 3: Story Problem Daily Practice (5-10 min)

Steps: 1. Present: Display one word problem, read together 2. Think-Pair-Solve: Students draw/solve, discuss with partner 3. Debrief: Share 2-3 strategies, show multiple approaches 4. Answer in sentence: "She got 4 more stickers."

Vary problem types: - Result unknown (3 + 5 = ?) - Change unknown (3 + ? = 8) - Start unknown (? + 5 = 8) - Comparison problems

Routine 4: Which One Doesn't Belong? (K-8)

Purpose: Critical thinking, vocabulary, argumentation

Steps: 1. Display: Show four numbers, shapes, or expressions 2. Prompt: "Which one doesn't belong? Defend your reasoning." 3. Discuss: Multiple correct answers based on different attributes

Example: 16, 25, 36, 49 - "49 is only odd number" - "36 is only multiple of 6" - "25 is only one that's 5 squared"

Routine 5: Error Analysis (Grades 3-12)

Purpose: Deepen understanding by diagnosing mistakes

Steps: 1. Present: Show worked problem with common error 2. Investigate: Pairs identify the error and explain why wrong 3. Correct & Justify: Solve correctly with justification

Example Error: - Problem: 3(x + 2) = 21 - Wrong work: 3x + 2 = 21 - Students identify: Didn't distribute to both terms

Routine 6: Math Centers Rotation (15-20 min daily)

Sample Centers: - Place Value: Build numbers with blocks, write expanded form - Fact Fluency: Games like "Turn Over 10" or addition war - Measurement: Measure objects with nonstandard units - Teacher Table: Small group targeted instruction

Key: Clear routines so students work independently while teacher focuses on intervention

Routine 7: Counting Circle (K-1, 5-10 min)

Steps: 1. Whole-Class Count: Count together with pointer on chart 2. Count Around: Pass counting from student to student 3. Count by Tens: Choral count 10, 20, 30... to 100

Variations: - Start at unusual number (37) - Count backwards - Skip count by 2s, 5s

Key Principles

• Daily practice: Short, consistent routines beat long sporadic lessons
• Multiple representations: Same concept in different ways
• Student discourse: Talking about math deepens understanding
• Error as learning: Mistakes are opportunities, not failures
• Spiral review: Continuously revisit earlier skills