Let's analyze the problems from both images and solve them step by step.

Image 1 Analysis:

This problem involves arranging learners and a teacher around a table. Here are the sub-questions:

1. 2.1 Six Grade 2 learners sit around one table. The teacher joins the six tables, and eight sit on the two tables. Calculate how many learners would sit at the following tables:

   • 2.1.1 Five tables
   • 2.1.2 Twenty-five tables
   • 2.1.3 Two hundred tables

2. Show the formula and all steps of your calculations.

Solution:

Given:

• Each table can accommodate 6 learners without a teacher.
• With the teacher joining, one additional learner can be accommodated per table.

Let's break it down:

Formula Derivation:

If $x$ is the number of tables, and assuming the teacher joins, the total number of learners at $x$ tables is: $\text{Total learners} = 6x + x = 7x$ Where:

• $6x$ represents the learners.
• $x$ represents the additional space made by the teacher joining each table.

Calculations:

1. 2.1.1 Five tables: $7 \times 5 = 35 \text{ learners}$

2. 2.1.2 Twenty-five tables: $7 \times 25 = 175 \text{ learners}$

3. 2.1.3 Two hundred tables: $7 \times 200 = 1400 \text{ learners}$

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Image 2 Analysis:

This problem involves recognizing patterns and using them to make predictions.

1. 1.1 State how many you will use in Grade 1 to learners when solving patterns.

2. 1.2 Study the pattern below and answer the following questions:

   • 1.2.1 Identify the repeating pattern.
   • 1.2.2 How many elements does the repeating unit contain?

Solution:

1. 1.1:

   • This is a contextual question and likely refers to teaching methods rather than a specific calculation.

2. 1.2:

   • 1.2.1 Identify the repeating pattern:
     • The pattern is: square, triangle, circle, square, triangle, circle.
   • 1.2.2 How many elements does the repeating unit contain?
     • The repeating unit has 3 elements: square, triangle, circle.

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Would you like more detailed explanations on any of these problems or have any questions?

Relative Questions:

1. How would the answer change if the teacher did not join the tables?
2. Can you calculate the number of learners for ten tables using the derived formula?
3. What if the number of learners per table changed to 8 instead of 6?
4. How would you describe the repeating pattern in more complex shapes?
5. How would the pattern change if an additional shape was added?
6. What is the significance of teaching patterns in early grades?
7. How would the seating arrangement change for a different number of learners per table?
8. Can you create a new pattern and identify its repeating elements?

Tip:

When solving problems involving patterns or seating arrangements, always identify the basic unit and understand how it scales with the number of repetitions or tables.