Patterns, Expressions & Data

Grade 5 – 60 Minute Mathematics Session

Common Core State Standards (CCSS) Addressed:

• 5.OA.3: Generate two numerical patterns using two given rules. Identify relationships between corresponding terms.
• 5.OA.2: Write simple expressions recording calculations with numbers and interpret numerical expressions without evaluating them.
• 5.NBT.5: Fluent multiplication of multi-digit whole numbers using the standard algorithm.
• 5.MD.4: Make a line plot to display data in fractions of a unit and solve addition and subtraction problems based on the plot.

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Learning Objectives

By the end of this lesson, students will be able to:

1. Generate and analyze two numerical patterns from given rules, identifying relationships between terms. (5.OA.3)
2. Write and interpret simple numerical expressions without evaluating them. (5.OA.2)
3. Multiply multi-digit whole numbers fluently using the standard algorithm. (5.NBT.5)
4. Create a fraction-based line plot from measurement data and solve related fraction addition and subtraction problems. (5.MD.4)

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Materials Needed

• Whiteboard and markers
• Student notebooks and pencils
• Printed number pattern cards (with different rules)
• Graph paper for line plots
• Fraction strips or visual fraction models
• Multiplication problem handouts
• Exit ticket with multiple choice questions
• Rulers (for measurement activity)
• Projector or chart paper for visual aids

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Lesson Breakdown

1. Introduction & Warm-up (10 minutes)

• Begin with a quick mental math activity: Multiply 23 × 4 and 56 × 7 on the whiteboard.
• Discuss strategies used, reinforcing fluency with multi-digit multiplication. (5.NBT.5)
• Transition: Explain that today students will explore patterns, expressions, multiplication, and work with fraction data.

2. Numerical Patterns Activity (12 minutes)

• CCSS Focus: 5.OA.3
• Present 2 different rule cards as a class:
  • Rule A: Start at 2, add 5 each time (2, 7, 12, ...)
  • Rule B: Start at 3, multiply by 2 each time (3, 6, 12, ...)
• On the board, generate the first 5 terms of each pattern.
• Students work in pairs to:
  • Write down the generated sequences.
  • Identify the relationship between terms at corresponding positions. (e.g., term 1 in A is 2, term 1 in B is 3)
• Discussion: What do you notice? Are terms in one pattern always bigger? When do terms match?
• Emphasize identifying relationships between terms from different patterns as stated in 5.OA.3.

3. Writing and Interpreting Expressions (10 minutes)

• CCSS Focus: 5.OA.2
• Teacher models writing expressions for simple word problems:
  • "Sarah has 4 packs of stickers with 7 stickers each" – expression: 4 × 7
  • Interpreting: Without solving, explain what 4 × 7 means.
• Students write expressions for other verbal prompts, such as:
  • "Five friends collect 8 shells each."
  • "Tom’s book collection grew by adding 10 new books twice."
• Then, students interpret given expressions without calculating, e.g., 6 + 4 × 3.
• Reinforce understanding of order of operations without evaluating.

4. Fluency in Multi-Digit Multiplication (12 minutes)

• CCSS Focus: 5.NBT.5
• Practice multiplying multi-digit whole numbers using the standard algorithm.
• Provide scaffolded problems, increasing in difficulty:
  • 34 × 6
  • 125 × 12
  • 432 × 25
• Students complete these individually or in pairs.
• Circulate and provide support, emphasizing place value and algorithm steps.

5. Fraction Measurement & Line Plot (12 minutes)

• CCSS Focus: 5.MD.4
• Provide each student with rulers marked in halves, fourths, and eighths.
• Students measure classroom objects (e.g., pencil length in fractions).
• Record measurements and create a line plot on graph paper:
  • X-axis marked with fractional units (e.g., 0, ½, 1, 1 ½, etc.)
  • Plot tally marks above each measurement.
• Pose two problem-solving questions using the plot:
  • "What is the total length of the pencil and eraser combined?" (adding fractions)
  • "If you remove an object measuring 1/4 inch from the plot, how does it change the total?" (subtracting fractions)
• Students work out answers using fraction addition and subtraction.

6. Closing & Assessment (4 minutes)

• Review key concepts quickly with whole class:
  • Numerical patterns and relationships
  • Writing/interpreting expressions
  • Multiplying multi-digit numbers
  • Creating and using line plots with fractions
• Hand out a short multiple-choice exit ticket with 4 questions targeting the day’s standards.
• Collect answers and preview next lesson (deeper work on fractions or algebraic expressions).

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Assessment Questions (Multiple Choice)

1. Generate Patterns (5.OA.3):
If Pattern A starts at 1 and adds 3 each time (1, 4, 7, 10…), and Pattern B starts at 2 and adds 5 each time (2, 7, 12, 17…), what is the relationship between the 4th terms?
A) They are the same number
B) Pattern A’s term is larger
C) Pattern B’s term is larger
D) Pattern A’s term is double Pattern B’s

Correct answer: C

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2. Expressions (5.OA.2):
What expression shows “Seven groups of four apples”?
A) 7 + 4
B) 7 × 4
C) 4 × 7 + 1
D) 7 ÷ 4

Correct answer: B

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3. Multiplication (5.NBT.5):
What is 214 × 6?
A) 1,284
B) 1,224
C) 1,344
D) 1,254

Correct answer: A

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4. Line Plot & Fractions (5.MD.4):
A line plot shows the lengths of pencils in inches:
½, ¾, 1, 1¼, 1½
What is the sum of a pencil that is ¾ inch and one that is 1¼ inches long?
A) 2 inches
B) 1½ inches
C) 2½ inches
D) 3 inches

Correct answer: A

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Differentiation & Extensions

• For students needing more support: Use visual fraction strips; work through multiplication problems step-by-step with scaffolding.
• For advanced learners: Challenge them to create their own pattern rules and write expressions to describe them; solve multi-step fraction problems or multiply 3-digit by 2-digit numbers.

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Teacher Notes

• Encourage mathematical discussions and reasoning, especially when finding relationships in numerical patterns and interpreting expressions.
• Use visual aids (charts, fraction strips, number lines) to solidify abstract concepts.
• Monitor student progress during multiplication and fraction tasks, re-teach concepts as needed.

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This lesson supports holistic math understanding relevant for 5th grade while aligning tightly with CCSS. It balances conceptual learning, procedural fluency, and problem solving with formative assessment to inform instruction.