Testinar Grade 5 math

Solving Problems on the Coordinate Plane

Students will solve real-world and mathematical problems on the coordinate plane.

CH10-05 Geometry and Coordinate Plane

Name
Date
Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Nora starts at (1, 2). She adds 2 to the \(x\)-coordinate and 3 to the \(y\)-coordinate to get her next point. If she continues this pattern, what will be her fourth point?
1. (8, 14)
2. (6, 10)
3. (7, 11)
4. (5, 8)
Rule A: Start at 0, add 1 each time. Rule B: Start at 0, add 2 each time. The first five points are shown. Which ordered pair should be plotted next?
1. (5, 9)
2. (6, 10)
3. (5, 10)
4. (10, 5)
Marcus uses two number patterns. One rule adds 3 starting at 1. Another rule adds 4 starting at 2. What is the fifth ordered pair (first rule value, second rule value)?
1. (13, 18)
2. (16, 22)
3. (14, 19)
4. (15, 20)
Use Pattern A values as \(x\)-values and Pattern B values as \(y\)-values. Pattern A adds 5 starting at 0, and Pattern B adds 2 starting at 0. Which list shows the ordered pairs?
1. \((0,0), (5,2), (10,4)\)
2. \((0,0), (2,5), (4,10)\)
3. \((0,0), (3,5), (6,10)\)
4. \((0,0), (5,5), (10,10)\)
Omar plots (2, 3), (4, 6), (6, 9), (8, 12). Looking at his pattern, what should be the next point?
1. (12, 16)
2. (9, 13)
3. (10, 14)
4. (10, 15)
A recipe uses two ingredients. The first ingredient follows: 2, 4, 6, 8. The second follows: 1, 3, 5, 7. Which point is the third pair in the pattern?
1. (10, 9)
2. (8, 7)
3. (4, 2)
4. (6, 5)
Rule A starts at 1 and adds 3. Rule B starts at 0 and adds 4. Which list gives the first four ordered pairs as (Rule A, Rule B)?
1. (1,0), (4,4), (7,8), (10,12)
2. (0,1), (4,4), (8,7), (12,10)
3. (1,1), (4,4), (7,7), (10,10)
4. (3,4), (6,8), (9,12), (12,16)
Lily starts with 2 and adds 1 each time (first sequence). Zoe starts with 3 and adds 2 each time (second sequence). Which point does NOT match the plotted pattern of (Lily, Zoe)?
1. (3, 5)
2. (4, 7)
3. (5, 10)
4. (6, 11)

Teacher and parent reference

Answer key and explanations

C. (7, 11)
Following the pattern: point 1 is (1, 2), point 2 is (3, 5), point 3 is (5, 8), point 4 is (7, 11).
C. (5, 10)
The next Rule A value is 5 and the next Rule B value is 10, so the next ordered pair is \((5,10)\).
A. (13, 18)
Rule 1: 1, 4, 7, 10, 13. Rule 2: 2, 6, 10, 14, 18. Fifth pair is (13, 18).
A. \((0,0), (5,2), (10,4)\)
Pattern A gives the \(x\)-values \(0, 5, 10,\ldots\) and Pattern B gives the \(y\)-values \(0, 2, 4,\ldots\). The ordered pairs are \((0,0)\), \((5,2)\), and \((10,4)\).
D. (10, 15)
Each time \(x\) increases by 2, \(y\) increases by 3. From (8, 12): \(x\) becomes 10, \(y\) becomes 15.
D. (6, 5)
Pairs are (2,1), (4,3), (6,5), (8,7). The third pair is (6, 5).
A. (1,0), (4,4), (7,8), (10,12)
Rule A: 1, 4, 7, 10. Rule B: 0, 4, 8, 12. Pairs (Rule A, Rule B) are listed in choice A.
C. (5, 10)
Lily: 2, 3, 4, 5, 6. Zoe: 3, 5, 7, 9, 11. Point (5, 10) doesn't match—it should be (5, 9).