Grade 05 Mathematics - EC: M05.C-G.1.1.1
Grade 05 Mathematics - EC: M05.C-G.1.1.1
Continuum of Activities
The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.
This continuum of activities offers:
- Instructional activities designed to be integrated into planned lessons
- Questions/activities that grow in complexity
- Opportunities for differentiation for each student’s level of performance
Grade Levels
5th Grade
Course, Subject
Mathematics
Related Academic Standards / Eligible Content
Activities
- Is the x-axis horizontal or vertical?
- Is the y-axis horizontal or vertical?
- What are the coordinates of the origin?
- Circle the x- axis.
- Circle the y- axis.
- Plot (2, 4) on the coordinate grid.
- Plot (5, 1) on the coordinate grid. Label the point A.
- How many units over is the point (4, 9) from the origin?
- How many units up is the point (6, 1) from the origin?
- List the steps for plotting the point (0, 11) on the coordinate grid.
- What are the coordinates of the point plotted on the coordinate grid?
- What are the coordinates of the point plotted on the coordinate grid?
- (3, 2)
- (2, 3)
- (0, 3)
- (3, 0)
- The point (6,2) is ______ units over and ____ units up from the origin.
- What point is located 3 units up and 7 units over from the origin?
- What is the difference in the number of units up from the origin between the points ( 9,3) and (3,9)?
- Point B is located 6 units north and 4 east of point A. What are the coordinates of point B if point A is on the x axis three units from the origin? Explain your reasoning.
- Explain the difference between points (a, b) and (b, a).
- What is the relationship between Point M (a, b) and Point H (2a, 2b) on the coordinate grid?
- Explain the relationship between the origin and the point (a, b), which is located in Quadrant I.
- Explain the relationship between the points (a, b) and (a + 4, b + 4) within quadrant I of the coordinate grid.
- If (a, b) and (a – 3, b – 3) are points within Quadrant I of a coordinate grid, explain the restrictions on the value of a and b.
- What restrictions must be placed on the value of “a” and “b” for the points (a, b) and (a, b - 6) to be within quadrant I of the coordinate grid? Explain.
- How many points could be plotted in quadrant I of the coordinate grid pictured below? Explain.
- If (2, b) and (2, b – 3) are points within Quadrant I of a coordinate grid, explain the restrictions on the value of “b”.
- What restrictions must be placed on the value of “a” for the points (a, 7) and (a – 5, 7) to be within quadrant I of the coordinate grid? Explain.
Answer Key/Rubric
- horizontal
- vertical
- (0,0)
- Student circles the x-axis (all or partial)
- Student circles the y-axis (all or partial)
- 4
- 1
- From the origin, move up 11 and plot the point.
- (3,4)
- C
- 6 over and 2 up
- (7,3)
- 6 units
- (7, 6). Explanations will vary. Start by determine the location of point A. Since it is on the x-axis three units from the origin, point A is at (3, 0). Start at (3, 0) and move 6 up and 4 right (total of 7 right and 6 up). This is (7, 6) or point B.
- Explanations will vary. The points are reflected or opposites over the x = y line. Student can draw this to help the explanation.
- Explanations will vary. Point H is twice the distance over (along the x-axis) and twice the distance up (along the y-axis) as Point M. Drawings can be used to assist with the explanation.
- Explanations will vary. The point (a, b) is located a units to the right of the x-axis and b units up (north of) the y-axis from the origin.
- Explanations will vary. The point (a + 4, b + 4) is located 4 additional units to the right of the x-axis and 4 additional units up (north on) the y-axis from point (a, b).
- The value of “a” and “b” must be greater than 3. Explanations will vary. Any values greater than 3 will result in a number greater than zero when the subtraction is performed (a – 3 or b – 3) which means these coordinates will be within quadrant I. If the value of “a” or “b” is less than three the result will be a negative number and not fall within the first quadrant of the coordinate grid. If the value of a or b equals 3, the result will be zero and it will land on one of the axis, and not “in” quadrant 1.
- Explanations will vary. The value of “a” must be greater than 0 so the x-coordinate falls within quadrant I. The value of “b” must be greater than 6. Any values greater than 6 will result in a number greater than zero when the subtraction is performed (b – 6) which means the y-coordinate will be within quadrant I. If the value of “b” is six or less than six the result will be a zero or negative number and not fall within the first quadrant of the coordinate grid.
- An infinite number of points. Explanations will vary. Since the x- and y-axis are comprised of lines not segments, they extend infinitely north and east thus producing an infinite number of coordinate points.
- Explanations will vary. The value of “b” must be greater than 3. Any values greater than 3 will result in a number greater than zero when the subtraction is performed (b – 3) which means the y-coordinate will be within quadrant I. If the value of “b” is less than three the result will be a negative number and not fall within the first quadrant of the coordinate grid. If the “b” value is 3, the point will land on the x-axis, not “in” quadrant 1.
- Explanations will vary. The value of “a” must be greater than 5. Any values greater than 5 will result in a number greater than zero when the subtraction is performed (a – 5) which means the x-coordinate will be within quadrant I. If the value of “a” is less than five the result will be a negative number and not fall within the first quadrant of the coordinate grid. If the “a” value is 5, the point will land on the y-axis, not “in” quadrant 1.
