Exploring Number Patterns

Grade 4-6 Mathematics (Ontario Curriculum)

Duration: 60 minutes

Class Size: 8 students

---

Curriculum Expectations

Mathematics, Number Sense and Numeration

• Demonstrate an understanding of whole numbers derived from problems involving multiplication and division (Grades 4-6)
• Identify, describe, extend, and create growing and shrinking number patterns, using tables where appropriate
• Solve problems involving addition, subtraction, multiplication, and division of whole numbers
• Read, represent, compare, and order whole numbers using various tools

Specific Expectations (Ontario Curriculum, Grades 4-6):

• Grade 4:
  • Use tables to represent and extend number patterns involving addition and subtraction (4NR1)
  • Solve multiplication and division problems, including those involving multiples of 10 (4NR3)
• Grade 5:
  • Create and extend increasing and decreasing number patterns, involving addition and multiplication, using tables and explicitly describe the pattern rule (5NR1)
  • Solve problems involving multiplication and division, with two-digit numbers (5NR3)
• Grade 6:
  • Identify and extend number patterns involving addition, subtraction, multiplication, and division, using tables and graphs (6NR1)
  • Solve problems involving all four operations on whole numbers (6NR3)

---

Learning Goals

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

• Use tables to represent addition and multiplication number patterns clearly.
• Distinguish between addition and multiplication patterns through hands-on examples.
• Solve word problems involving addition and multiplication using the tables of number patterns.
• Extend number patterns involving all four operations (addition, subtraction, multiplication, division).

---

Materials Needed

• Whiteboard and markers
• Student notebooks or worksheets with pre-made empty tables
• Number cards (1 to 20)
• Counters or small cubes
• Calculators (optional)
• Projector or smartboard (optional) for visual display

---

Lesson Breakdown

Minds On (10 minutes)

Objective: Activate prior knowledge and introduce the difference between addition and multiplication number patterns.

1. Warm-Up Problem:
   Display this addition pattern table on the board:

   Step	Number
   1	2
   2	5
   3	8
   4	11

   • Ask students: "What operation connects the numbers from one step to the next?"
   • Guide them to identify that the number increases by 3 (addition pattern).

2. Comparative Pattern:
   Next, show a multiplication pattern:

   Step	Number
   1	2
   2	4
   3	8
   4	16

   • Ask: "What rule connects these numbers?"
   • Discuss how the number doubles each time (multiplication by 2).

3. Emphasize visibly how the two patterns differ on the board/table.

---

Action (35 minutes)

Activity 1: Table Construction and Pattern Identification (15 minutes)

• Provide students with blank tables with two columns: Step number and Number.
• Task: Create their own simple addition and multiplication patterns starting at 1 or 2.
• Encourage students to describe the rule aloud to their partner (e.g., “add 4” or “multiply by 3”).
• Circulate and provide scaffolding, ensuring that each student understands the mechanics of the operation.

Activity 2: Word Problems Using Number Pattern Tables (20 minutes)

• Present word problems that require filling tables and identifying operation rules.

• Examples (graded by difficulty):

  1. Addition problem:
     “Every day, Sarah reads 3 pages more than the previous day. On Day 1, she reads 5 pages. Use a table to show how many pages she reads each day for four days.”

  2. Multiplication problem:
     “A bacteria culture doubles in size every hour. If it starts with 3 bacteria, how many are there after 4 hours? Fill in the table.”

  3. Subtraction and Division Extension:
     “A runner reduces her time by 2 minutes every week. Starting at 28 minutes, create a table for 5 weeks.”
     “A cake is divided equally among 2, then 4, then 6 people. Show the number of pieces each person receives over the four steps.”

• Students work in pairs to fill the tables and then write the rule that governs each pattern (addition, subtraction, multiplication, or division).

• After completion, facilitate a class discussion comparing strategies and solutions.

---

Consolidation (10 minutes)

• Invite volunteers to display their tables and explain the rules in front of the class.
• Highlight how tables make patterns clearer and help solve word problems.
• Discuss how understanding number patterns ties into real-life situations (growth, decrease, equal sharing).
• Emphasize vocabulary: step, pattern, rule, increase, decrease, multiply, divide.

---

Assessment and Feedback

Formative checks:

• Informal observation during pair work to assess understanding of operations and table construction.
• Listening to students explain rules and their reasoning.

Summative task (exit ticket):

• Give a short table pattern for students to complete individually and write the operation rule.

• Example:

  Step	Number
  1	10
  2	7
  3	4
  4	1

  Question: What operation is used, and what is the rule?

---

Differentiation Strategies

• Provide manipulatives (counters, cubes) to support concrete understanding.
• Pair students strategically to assist peer learning.
• Offer extensions by asking higher-level students to create their own word problems with tables.
• Use visuals and colour coding on tables for ELL or students requiring additional support.

---

Cross-Curricular Connections

• Language: Reading and writing word problems supports literacy skills.
• Science: Growth patterns (doubling bacteria) incorporate concepts from life sciences.
• Technology: Use of calculators or software tools for pattern visualization can be included as an extension.

---

Teacher Reflection Prompts

• Did students show clear differentiation between addition and multiplication patterns?
• Were the tables effective as visual tools for understanding?
• How well did students apply number operations in the context of word problems?
• Which students need additional scaffolding or challenges?

---

This lesson plan adheres closely to the Ontario Mathematics Curriculum expectations on number patterns and operations for Grades 4-6, engaging students in practical application through tables and word problems to deepen conceptual understanding and fluency.