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5th Grade · 5.G.A.1 · 5.G.A.2

Graphing points on a coordinate plane in 5th grade

Graphing points on a coordinate plane is how 5th grade math puts numbers on a grid, a little like a map. A coordinate plane is a grid made from two number lines that cross at 0. Your child learns to find a point from a pair of numbers, like (6, 3). Your child also uses points to show real situations, such as money saved each week.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

What it means, in plain words

The coordinate plane and ordered pairs 5.G.A.1

A coordinate plane, also called a coordinate grid, has two number lines called axes. The x-axis goes across and the y-axis goes up. They meet at the origin, the point where both numbers are 0. In 5th grade, children use only the first quadrant, the part of the grid where both numbers are 0 or more.

Each point has an address called an ordered pair, such as (6, 3). The two numbers are its coordinates. The first number, the x-coordinate, says how far to move across from the origin. The second number, the y-coordinate, says how far to move up. The order matters, so (6, 3) and (3, 6) are two different points.

The names match up: the x-coordinate goes with the x-axis and the y-coordinate goes with the y-axis. Many teachers say "walk before you climb" to help children remember to go across first and then up.

Your child should be able to:

  • Name the x-axis, the y-axis and the origin
  • Say which number in an ordered pair is the x-coordinate and which is the y-coordinate
  • Plot a point from its ordered pair, starting at the origin
  • Write the ordered pair for a point shown on a grid

Example

How do you plot the point (6, 3)?

  1. Start at the origin, (0, 0).
  2. The x-coordinate is 6, so move 6 units to the right along the x-axis.
  3. The y-coordinate is 3, so move 3 units up.
  4. Put the dot there. The point (3, 6) is somewhere else: 3 across and 6 up.

Graphing points to show real situations 5.G.A.2

Graphing points becomes useful when each axis stands for something real. On a map of a campsite, the x-axis might show meters east of the gate and the y-axis meters north. On a graph of savings, the x-axis might show weeks and the y-axis dollars.

Graphing points on a coordinate plane in 5th grade often starts from a table: each row of the table becomes one point. Then your child explains what a point means in the situation. On a savings graph, the point (4, 20) means that after 4 weeks there are 20 dollars saved.

Your child should be able to:

  • Turn each row of a table into an ordered pair and plot it
  • Choose sensible steps for an axis, such as counting by 5s
  • Explain what the two coordinates of a point mean in a real situation
  • Read a point from a graph and answer a question about it

Example

A savings jar starts empty and gets 5 dollars every week. Graph the first 4 weeks. What does the point for week 3 mean?

  1. Make a table: week 0 has 0 dollars, week 1 has 5, week 2 has 10, week 3 has 15 and week 4 has 20.
  2. Put weeks on the x-axis and dollars on the y-axis. Count the y-axis by 5s.
  3. Plot (0,0)(0, 0), (1,5)(1, 5), (2,10)(2, 10), (3,15)(3, 15) and (4,20)(4, 20).
  4. The point (3,15)(3, 15) means that after 3 weeks the jar holds 15 dollars.

Where children usually get stuck

  • Your child plots (2, 5) by going 2 up and 5 across.

    The two numbers look alike, and nothing on the page says which one comes first. The child mixes up the order of the moves.

    What helps. Say "across, then up" every time, and point along the x-axis first. After plotting, read the point back: how far across, how far up?

  • Every point your child plots lands one space too far, as if counting started at 1 on the first line.

    When you count objects, you start at 1. On a grid, you count jumps from the origin, and the origin itself is 0.

    What helps. Put a finger on the origin and count each jump out loud as the finger moves to the next line.

  • Your child puts points in the middle of the squares, not where the grid lines cross.

    Board games and some maps put things inside squares. On a coordinate grid, a point sits exactly where two lines meet.

    What helps. Trace the line for the x-coordinate with one finger and the line for the y-coordinate with another. The point goes where the two fingers meet.

Try four practice questions

Real 5th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Select the coordinate that matches each axis.
    The x-axis matches
    . The y-axis matches
    .
    Show the answer and how to solve it

    The x-axis matches the x-coordinate, and the y-axis matches the y-coordinate.

    1. 1Look for matching letters in the axis name and the coordinate name.
    2. 2The x-axis matches the x-coordinate because both share the letter x.
    3. 3The y-axis matches the y-coordinate because both share the letter y.

    Common mistake. A common mistake is swapping the letters, such as matching the x-axis with y-coordinate. The axis name and coordinate name should use the same letter.

    The idea underneath. The x-coordinate tells a point's position along the x-axis. The y-coordinate tells its position along the y-axis.

  2. 2On level
    Point A is shown on the graph below. The x-axis shows days, and the y-axis shows centimeters. Sofia wrote two statements to explain point A.
    Plant Growth Log
    12345678910123456789100DaysCentimetersA
    Mark each of Sofia's statements True or False.
    Sofia's statementTrueFalse
    "The x-value shows 3 days."
    "The y-value shows 6 centimeters."
    Show the answer and how to solve it

    The statement about 3 days is True, and the statement about 6 centimeters is False because point A is (3, 8).

    1. 1Find the ordered pair for point A. It is 3 units to the right and 8 units up, so point A is (3, 8).
    2. 2The x-axis is labeled days, so the first number, 3, means 3 days.
    3. 3The y-axis is labeled centimeters, so the second number, 8, means 8 centimeters.
    4. 4Now check Sofia's statements. The statement about 3 days is True. The statement about 6 centimeters is False because point A shows 8 centimeters, not 6.

    Common mistake. A common mistake is misreading the y-coordinate of point A as 6 instead of 8. Count carefully up the y-axis from the origin to where point A sits — it lands on 8, not 6.

    The idea underneath. In an ordered pair, the first number matches the x-axis meaning and the second number matches the y-axis meaning.

  3. 3On level
    Each card shows an ordered pair with one number highlighted.
    Select all cards where the highlighted number is the x-coordinate.
    A
    (3,7)\displaystyle \left(\textcolor{#c94c7c}{3}, 7\right)
    B
    (5,2)\displaystyle \left(5, \textcolor{#c94c7c}{2}\right)
    C
    (9,4)\displaystyle \left(\textcolor{#c94c7c}{9}, 4\right)
    D
    (1,13)\displaystyle \left(1, \textcolor{#c94c7c}{13}\right)
    Show the answer and how to solve it

    Select the cards with (3, 7) and (9, 4) because each one highlights the first number in the ordered pair.

    1. 1In an ordered pair, the first number is the x-coordinate and the second number is the y-coordinate.
    2. 2Check each card by position, not by which number is larger.
    3. 3Only the cards with (3, 7) and (9, 4) highlight the first number, so those are the cards to select.

    Common mistake. A common mistake is choosing the highlighted 13 in (1, 13) because it looks important or large. The x-coordinate is always the first number, even when it is smaller than the second.

    The idea underneath. Coordinate names depend on order, not value: the first number is the x-coordinate and the second number is the y-coordinate.

  4. 4Stretch
    The graph below shows hours on the x-axis and miles on the y-axis. The purple point is highlighted.
    123456789123456780HoursMiles
    Select the ordered pair for the highlighted point.
    A
    (2, 7)
    B
    (7, 2)
    C
    (2, 8)
    D
    (1, 7)
    Show the answer and how to solve it

    The ordered pair is (2, 7) because the highlighted point is 2 units across and 7 units up.

    1. 1Find the purple point. There are also gray points on the same column and row, but focus only on the highlighted one.
    2. 2Trace straight down from the purple point to the x-axis. It lines up with 2, so the x-coordinate is 2.
    3. 3Trace straight left from the purple point to the y-axis. It lines up with 7, so the y-coordinate is 7.
    4. 4Write the coordinates in order as (2, 7).

    Common mistake. A common mistake is writing (7, 2) by reading the y-value before the x-value. Also, the gray point at (5, 7) is on the same row — make sure to trace only the purple point.

    The idea underneath. In an ordered pair, the first number tells the horizontal position and the second number tells the vertical position.