List the steps a teacher would take to guide learners to determine the Greatest Common Divisor (GCD) of numbers 420 and 600.

Guide learners to break down each number into its prime factors.

Point out the prime factors that appear in both factorizations: 2, 3, and 5.

For 2, the lowest power is $2^2$. For 3, it's $3^1$. For 5, it's $5^1$.

The Greatest Common Divisor of 420 and 600 is $\boxed{60}$.

5. A teacher intends to teach her class how to make patterns with different shapes. Describe how she would organize the class to prepare and arrange the shapes for the lesson.

Collect a variety of shapes (e.g., squares, circles, triangles) in different colors and sizes. Ensure there are enough for each group or pair of learners.

Divide the class into small, collaborative groups to encourage peer learning and interaction.

Provide each group with a set of mixed shapes.

Explain what a pattern is (a repeating sequence) and show a simple example, like "circle, square, circle, square."

Instruct groups to create their own patterns using the shapes, encouraging them to describe their patterns to each other. Circulate to observe and provide assistance.

6. Describe how one would lead learners to obtain the next number in the pattern 1, 5, 13, 25, 41, ___.

Guide learners to calculate the difference between each number in the sequence.

• $5 - 1 = 4$
• $13 - 5 = 8$
• $25 - 13 = 12$
• $41 - 25 = 16$

Observe that the differences (4, 8, 12, 16) are increasing by 4 each time. This is a pattern of multiples of 4.

Based on the pattern, the next difference should be $16 + 4 = 20$.

Add 20 to the last number in the sequence (41).

The next number in the pattern is $\boxed{61}$.

7. List the steps you would follow to explain to your class how to find the G.C.D of the numbers 18, 36 and 42.

Guide learners to list all numbers that divide evenly into 18, 36, and 42.

• Factors of 18: $1, 2, 3, \textbf{6}, 9, 18$
• Factors of 36: $1, 2, 3, 4, \textbf{6}, 9, 12, 18, 36$
• Factors of 42: $1, 2, 3, \textbf{6}, 7, 14, 21, 42$

Point out the factors that appear in all three lists: 1, 2, 3, 6.

From the common factors, identify the largest one.
The Greatest Common Divisor (GCD) of 18, 36, and 42 is $\boxed{6}$.