Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Find and describe number patterns using addition and subtraction.
• Continue geometric patterns using shape, size, and orientation.
• Find and describe number patterns using multiplication and division.
• Figure out the rule for a pattern and use it to find the next terms.
• Create your own simple patterns.

Lesson summary

Patterns are all around us! From the repeating patterns on a Shweshwe cloth to the arrangement of desks in our classroom, recognizing and understanding patterns is a fundamental skill. It helps us predict what comes next, solve problems, and make sense of the world. In South Africa, recognizing patterns is crucial for understanding things like stockvel contribution cycles, the sequencing of indigenous craft designs, and even predicting peak traffic times. This week, we will focus on identifying, describing, and extending number and geometric patterns. We will specifically look at patterns created by addition, subtraction, multiplication, and division.

Lesson notes

2.1 Number Patterns (Addition and Subtraction) A number pattern is a sequence of numbers that follow a specific rule. This rule tells us how to get from one number to the next. We need to carefully observe the sequence to find this rule.

Increasing Patterns: The numbers get bigger. This often involves addition (adding the same number each time).

Decreasing Patterns: The numbers get smaller. This often involves subtraction (subtracting the same number each time).

Example 1: Increasing Pattern Consider the pattern: 3, 6, 9, 12, ____, ____ To find the rule, we look at how we get from one number to the next. From 3 to 6, we add 3 (3 + 3 = 6) From 6 to 9, we add 3 (6 + 3 = 9) From 9 to 12, we add 3 (9 + 3 = 12) Therefore, the rule is: "Add 3 to the previous number." To find the next two terms: 12 + 3 = 15 15 + 3 = 18 The completed pattern is: 3, 6, 9, 12, 15, 18 Example 2: Decreasing Pattern Consider the pattern: 50, 45, 40, 35, ____, ____ To find the rule: From 50 to 45, we subtract 5 (50 - 5 = 45) From 45 to 40, we subtract 5 (45 - 5 = 40) From 40 to 35, we subtract 5 (40 - 5 = 35) Therefore, the rule is: "Subtract 5 from the previous number." To find the next two terms: 35 - 5 = 30 30 - 5 = 25 The completed pattern is: 50, 45, 40, 35, 30, 25 2.2 Geometric Patterns Geometric patterns involve shapes that repeat or change according to a specific rule. This could involve changing the shape, size, colour, or orientation (the way it's facing).

Example 3: Geometric Pattern Imagine the following sequence: Triangle, Square, Circle, Triangle, Square, ____ The pattern repeats every three shapes: Triangle, Square, Circle. So, the next shape is a Circle.

Therefore, the pattern is: Triangle, Square, Circle, Triangle, Square, Circle.

Example 4: Geometric Pattern with Increasing Elements Pattern 1: One dot (.)

Pattern 2: Three dots arranged as a small triangle (∴)

Pattern 3: Six dots arranged as a larger triangle Pattern 4: ? Learners must visualize or draw Pattern

4. It should have 10 dots arranged in a triangle shape. Notice that the number of dots are increasing according to the pattern 1, 3, 6,

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0. The rule is adding an increasing number to each step. +2, +3, +4, etc. 2.3 Number Patterns (Multiplication and Division) Multiplication and division can also create number patterns. These patterns are based on multiples (results of multiplying a number by different whole numbers) and factors (numbers that divide evenly into another number).

Example 5: Multiplication Pattern Consider the pattern: 2, 4, 8, 16, ____, ____ To find the rule: From 2 to 4, we multiply by 2 (2 x 2 = 4) From 4 to 8, we multiply by 2 (4 x 2 = 8) From 8 to 16, we multiply by 2 (8 x 2 = 16) Therefore, the rule is: "Multiply the previous number by 2." To find the next two terms: 16 x 2 = 32 32 x 2 = 64 The completed pattern is: 2, 4, 8, 16, 32, 64 Example 6: Division Pattern Consider the pattern: 100, 50, 25, ____, ____ To find the rule: From 100 to 50, we divide by 2 (100 / 2 = 50) From 50 to 25, we divide by 2 (50 / 2 = 25) Therefore, the rule is: "Divide the previous number by 2." To find the next two terms: 25 / 2 = 12.5 12.5 / 2 = 6.25 The completed pattern is: 100, 50, 25, 12.5, 6.25 (

Note: While this introduces decimals which may be beyond some learners' current skill level, the emphasis is on identifying the division rule. Whole number answers are preferred at this level). An alternate pattern could involve division with remainders.

Example 7: Division Pattern (With Remainders)

Consider the pattern: 22, 11, 5, _____ To find the rule: From 22 to 11, we divide by

2. From 11 to 5, we divide by 2 and round down. 11/2 = 5.5. round down to

5. Therefore the rule is "Divide by 2 and round down to the nearest whole number." To find the next term: 5 / 2 = 2.

5. Round down to

2. The completed pattern is: 22, 11, 5,

2. Guided Practice (With Solutions)

Question 1: Identify the rule and find the next two numbers in the pattern: 7, 14, 21, 28, ____, ____ Solution: Look at the difference between consecutive numbers: 14 - 7 = 7, 21 - 14 = 7, 28 - 21 =

7. The rule is: "Add 7 to the previous number." Next two numbers: 28 + 7 = 35, 35 + 7 = 42 The pattern is: 7, 14, 21, 28, 35,

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2. Question 2: Identify the rule and find the next two numbers in the pattern: 90, 80, 70, 60, ____, ____ Solution: Look at the difference between consecutive numbers: 80 - 90 = -10, 70 - 80 = -10, 60 - 70 = -

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0. The rule is: "Subtract 10 from the previous number." Next two numbers: 60 - 10 = 50, 50 - 10 = 40 The pattern is: 90, 80, 70, 60, 50, 40 Question 3: Draw the next shape in the geometric pattern: Square, Circle, Triangle, Square, Circle, ____ Solution: The pattern repeats every three shapes: Square, Circle, Triangle. The next shape is a Triangle.