Lesson Notes By Weeks and Term v5 - Grade 2

Lesson Video

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Performance objectives

• Find and continue number patterns.
• Describe the rule for a pattern.
• Find missing numbers in a pattern.
• Solve word problems with patterns.

Lesson summary

Patterns are all around us, from the stripes on a zebra to the tiles on the floor. Understanding patterns helps us predict what comes next, which is a useful skill in many situations. In South Africa, recognizing patterns can help us understand things like the repetition in traditional beadwork designs or the way houses are often built in similar rows in townships. This week, we will focus on number patterns and simple rules that govern them. Learning about number patterns will help us with counting, addition, subtraction, and problem-solving. This also lays the foundation for more complex mathematical concepts later on.

Lesson notes

A number pattern is a sequence of numbers that follows a specific rule. This rule tells us how to get from one number in the pattern to the next. The rule could involve adding, subtracting, multiplying (though we'll mainly focus on addition and subtraction in Grade 2), or even dividing.

However, our focus is on addition and subtraction patterns. A rule is a statement that explains how the pattern works. For instance, the rule might be "add 3 to each number" or "subtract 5 from each number." Let's look at some examples: Example 1: Increasing Pattern (Addition)

Pattern: 3, 6, 9, 12, __, __ Step 1: Find the difference between the first two numbers. 6 - 3 =

3. Step 2: Check if this difference holds for the next pair of numbers. 9 - 6 =

3. Step 3: If the difference is consistent, that's likely the rule! The rule is "add 3." Step 4: Apply the rule to find the missing numbers. 12 + 3 = 15, 15 + 3 =

1

8. Completed Pattern: 3, 6, 9, 12, 15, 18 Example 2: Decreasing Pattern (Subtraction)

Pattern: 20, 18, 16, 14, __, __ Step 1: Find the difference between the first two numbers. 18 - 20 = -2 (This means we are subtracting)

Step 2: Check if this difference holds for the next pair of numbers. 16 - 18 = -

2. Step 3: If the difference is consistent, that's likely the rule! The rule is "subtract 2." Step 4: Apply the rule to find the missing numbers. 14 - 2 = 12, 12 - 2 =

1

0. Completed Pattern: 20, 18, 16, 14, 12, 10 Example 3: Missing Number in the Middle Pattern: 5, __, 15, 20, 25 Step 1: Find the difference between two numbers that are next to each other. Let's use 20 and 25. 25 - 20 =

5. Step 2: Assume this is the rule and check if it works. If we add 5 to 5, we get

1

0. Step 3: Check if adding 5 to 10 gives us the next number (15). 10 + 5 =

1

5. It works!

Step 4: The missing number is

1

0. Completed Pattern: 5, 10, 15, 20,

2

5. The rule is "add 5".

Example 4: Word Problem Thando is collecting seashells on the beach. On the first day, she finds 2 shells. On the second day, she finds 4 shells. On the third day, she finds 6 shells. If this pattern continues, how many shells will she find on the fourth and fifth days?

Step 1: Identify the pattern. 2, 4, 6, __, __ Step 2: Find the rule. 4 - 2 = 2, 6 - 4 =

2. The rule is "add 2." Step 3: Apply the rule to find the missing numbers. 6 + 2 = 8, 8 + 2 =

1

0. Answer: Thando will find 8 shells on the fourth day and 10 shells on the fifth day. Guided Practice (With Solutions)

Question 1: Complete the pattern: 1, 3, 5, __, __. What is the rule?

Solution: Step 1: Find the difference. 3 - 1 =

2. Step 2: Check if the difference holds. 5 - 3 =

2. Step 3: Apply the rule (add 2). 5 + 2 = 7, 7 + 2 =

9. Answer: 1, 3, 5, 7,

9. The rule is "add 2".

Commentary: This is a simple increasing pattern. We find the constant difference and apply it.

Question 2: Complete the pattern: 15, 12, 9, __, __. What is the rule?

Solution: Step 1: Find the difference. 12 - 15 = -

3. Step 2: Check if the difference holds. 9 - 12 = -

3. Step 3: Apply the rule (subtract 3). 9 - 3 = 6, 6 - 3 =

3. Answer: 15, 12, 9, 6,

3. The rule is "subtract 3".

Commentary: This pattern is decreasing. Make sure the learners understand subtraction results in a smaller number.

Question 3: What number is missing? 10, __, 30,

4

0. What is the rule?

Solution: Step 1: Find the difference between the known adjacent numbers. 40 - 30 = 10 Step 2: Check if the difference can work between 10 and the missing number. We can add 10 to 10 to get the missing number. 10 + 10 = 20 Step 3: Check if the difference works between the missing number and 30. 20 + 10 =

3

0. It Works!

Answer: 10, 20, 30,

4

0. The missing number is

2

0. The rule is "add 10".

Commentary: This helps learners practice filling in the gaps within a pattern.

Question 4: Sipho plants 3 rows of mielies on Monday, 6 rows on Tuesday, and 9 rows on Wednesday. If he continues this pattern, how many rows will he plant on Thursday?

Solution: Step 1: Identify the pattern. 3, 6, 9, __ Step 2: Find the rule. 6 - 3 = 3, 9 - 6 =

3. The rule is "add 3".

Step 3: Apply the rule. 9 + 3 =

1

2. Answer: Sipho will plant 12 rows of mielies on Thursday.

Commentary: This introduces a practical word problem context, linking patterns to a real-life situation. Independent Practice (Questions Only)

Complete the pattern: 4, 8, 12, __, __. What is the rule?

Complete the pattern: 25, 20, 15, __, __. What is the rule? What number is missing? 2, 4, __, 8,

1

0. What is the rule? What number is missing? 18, 15, __, 9,

6. What is the rule?

Complete the pattern: __, 7, 9, 11,

1

3. What is the rule? Lindiwe saves R5 on Monday, R10 on Tuesday, and R15 on Wednesday. If she continues this pattern, how much will she save on Thursday? A baker makes 7 koeksisters on the first day, 10 on the second day, and 13 on the third day. If the pattern continues, how many will he make on the fourth day?

What is the next number in this sequence: 12, 14, 16, __?

What is the missing number: 30, 25, __, 15, 10?