These 22 problems practice the coordinate plane in the first quadrant (5.G.A.1 and 5.G.A.2). You will name axes and the origin, read and plot ordered pairs, and find distances along grid lines.
The last six problems are real-world situations such as maps, plant growth, and savings. Draw each point carefully and check the order of the numbers.
Problem 1: Axes and origin
Answer each question about the coordinate plane.
- Which axis is horizontal?
- Which axis is vertical?
- Write the ordered pair for the origin.
Problem 2: Which number is which
In the ordered pair \((6, 3)\), which number tells how far to move right? Which number tells how far to move up?
Problem 3: Read the points
Write the ordered pair for each point.
Problem 4: Plot four points
Plot and label these points: E \((3, 2)\), F \((5, 6)\), G \((8, 0)\), H \((0, 4)\).
Problem 5: Points on the axes
Look at these points: \((0, 5)\), \((5, 0)\), \((3, 3)\), \((0, 0)\). Which lie on the x-axis? Which lie on the y-axis?
Problem 6: Right and up
Start at the origin. Move 4 units right and 7 units up. Write the ordered pair for where you land.
Problem 7: Same numbers, different points
Point P is 9 units right and 2 units up from the origin. Point Q is 2 units right and 9 units up. Write both ordered pairs. Are P and Q the same point?
Problem 8: Distance in a row
How many units apart are K \((2, 3)\) and L \((7, 3)\)?
Problem 9: Distance in a column
How many units apart are the points \((4, 1)\) and \((4, 8)\)?
Problem 10: Find the missing number
Write the ordered pair for each point.
- Point K is on the y-axis, 7 units above the origin.
- Point M is on the x-axis, 6 units to the right of the origin.
Problem 11: A rectangle on the grid
Plot these points and connect them in order: \((1, 1)\), \((6, 1)\), \((6, 4)\), \((1, 4)\). Name the shape. Find the length of its longest side.
Problem 12: The fourth corner
The grid shows three corners of a rectangle: \((2, 2)\), \((8, 2)\), and \((8, 5)\). Write the ordered pair of the fourth corner.
Problem 13: Counting by twos
On this grid each square stands for 2 units. Write the ordered pairs of points Q and R.
Problem 14: Blocks on a map
Each square on the map is one block. How many blocks is it from the Library to the Park? From the Park to the School?
Problem 15: Plant growth data
Priya measured her bean plant. Week 1: 2 inches. Week 2: 4 inches. Week 3: 5 inches. Week 4: 7 inches. Write each pair as (week, height) and plot the points.
Problem 16: Meaning of a point
A graph shows gallons of gas used (x) and miles driven (y) on a road trip. Point \((4, 100)\) is on the graph. Explain what the point means. Then find how many miles were driven on 1 gallon.
Problem 17: Muffin batches
Each batch of muffins needs 3 cups of flour. Make a table for 1, 2, 3, and 4 batches. Write ordered pairs (batches, cups) and plot them.
Problem 18: Spot the mistake
Jamal wants to plot a point that is 7 units right and 4 units up. He writes \((4, 7)\). Explain his mistake and write the correct ordered pair.
Problem 19: Ethan's walk
Ethan walks from Home \((1, 2)\) straight north to the Store \((1, 7)\). Then he walks straight east to the Park \((6, 7)\). Each unit is one block. How many blocks does he walk in all?
Problem 20: Farmers market loop
Four stands are at A \((1, 1)\), B \((5, 1)\), C \((5, 6)\), and D \((1, 6)\). Mei walks A to B to C to D and back to A. How many blocks is the whole loop?
Problem 21: Diego's savings
Diego graphs his savings as (week, dollars). Two points on his graph are \((2, 10)\) and \((5, 25)\). How much more money does he have at the later point? How many weeks passed?
Problem 22: Hiking trail
A trail starts at \((0, 0)\), goes east to \((3, 0)\), north to \((3, 4)\), then east to \((8, 4)\). One unit is one mile. How long is the trail? How far north of the start does it end?
See every chapter on the Grade 5 math page.