RMA

Box 1 Number Expressions:
- $2 imes 2 - 3 times 1$
- $3 imes 3 - 4 times 2$
- $4 imes 4 - 5 times 3$
- $5 imes 5 - 6 times 4$
Verification Task (Item 1): Show computation for $4 imes 4 - 5 imes 3$ .
- Step 1: Compute $4 times 4 = 16$
- Step 2: Compute $5 times 3 = 15$
- Step 3: Subtract the results: $16 - 15$
- Final Answer: $1$

Task (Item 2): Determine the next number expression for $5 times 5 - 6 times 4$ .
- Answer: Next expression is $6 times 6 - 7 imes 5$ .

Task (Item 3): Identify the algebraic expression representing the number expressions in Box 1.
- Options:
- a. $(n)(n) (n + 3)(n + 1)$
- b. $(n)(n) - [(n + 1)(n - 1)]$
- c. $(n-1)(n - 1) - n(n - 2)$
- d. $n^2 - 3n(1)$
- e. $n^2 - n - 1$
- Observation: Since Box 1 simplifies to 1, the algebraic expression must also simplify to 1.

Task (Item 4): Identify the first and third numbers in the numerical expression.
- 1st number: $-n$ in the numerical expression.
- 3rd number: $-n$ .

Table 1: Powers of 2
- Exponential Form: $2^2$ , $2^3$ , $2^4$ , $2^5$
- Expanded Form: $2 imes 2$ , $2 imes 2 imes 2$ , $2 imes 2 imes 2 imes 2$ , $2 imes 2 imes 2 imes 2 imes 2$
- Values: $4 (2^2)$ , $8 (2^3)$ , $16 (2^4)$ , $32 (2^5)$
Tasks:
- Item 6: Show that $1024$ is a power of $2$ using Table 1.
- Item 7: Write the exponential form of $1024$ .

Item 9: Inquiry on numbers between $0.998$ and $0.999$ .
- Answer: Yes, for example, $0.9995$ is one such number.
Item 10: Show computation for subtracting $0.998$ from $0.999$ :
- $0.999 - 0.998 = 0.001$

Graph Information: Relationship between student absences (x-axis) and overall academic grades (y-axis)
- Point representation: Each point corresponds to an individual student's data.
Tasks:
- Item 12: Count students with a grade below 84 (observed from 5 points below the line).
- Item 13: Justification based on the graph.
- Item 14: Correct interpretations of the data shown:
- a. As absences increase, overall academic grades also increase.
- b. As absences decrease, grades increase.
- c. As absences increase, grades decrease. (Correct Answer)

Range Formula: Range = Highest Value - Lowest Value
Task 16: Should both Purok receive the same amount of financial aid based on average income? Consider the graph information shown.

Table 2 Summary: Participation in music and sports activities for Grade 7 students.
Task 17 - Item 20:
- Count of students participating in music: $18$ .
- Students not participating in any activities: $19$ .
- Probability for both activities:
- Formula: $P= rac{ ext{Number participating in both}}{ ext{Total students}}$

Fig 4 Description: Coordinates with respective points A (-2,4), B (2,0).
Tasks:
- Item 23: Determine coordinates of point C
- Item 24 - 28: Relationships and distances between points; concept of slopes and areas.

Properties: Interior angles in a triangle must sum to $180^ ext{o}$ .
Query (Item 38): Identify angle measures based on integral properties of triangles with sample angles provided.

House Construction Data: Dog house constructed with triangular properties; includes ratios and associated dimensions.
Questions: Length of triangular dog house sides, proportionality of dimensions, and base lengths for toy storage.

Geometry Queries:
- Circumference formula, area computations related to a circular pool and surrounding area.
Query (Items 44 - 48): Solving for area of sidewalk surrounding a pool, volume queries associated with varied depths.

Informational Observation: Calculating rotations in degrees relative to wheel diameter and path length traveled.
Final Query (Item 49): Rotational calculations for the wheel over multiple rolls of travel.