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Common Core Math5th GradeGeometry

5.G.2: Graph Points to Solve Problems

Also written as 5.G.A.2 and CCSS.MATH.CONTENT.5.G.A.2 · Cluster: Graph points on the coordinate plane to solve real-world and mathematical problems.

Make Graph Paper for 5.G.2All 26 5th Grade Math Standards

The Official Wording

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.

Common Core State Standards, Grade 5, Geometry · Read it at the source · Checked October 14, 2026

What 5.G.2 Means in Plain English

Fifth graders turn a situation into points and read the points back as the situation. A plant measured weekly gives (1, 3), (2, 5) and (3, 7), and the point (3, 7) says the plant was 7 centimeters tall after 3 weeks. Each axis needs a label and a unit.

This is where 5.G.1 pays off: coordinates now carry units, and a 0 can mean “at the start” or “none left.” In 6th grade the same graphs show equations like d = 65t (6.EE.9), and 6.NS.8 opens the other three quadrants.

5.G.2 I Can Statements

  • I can label each axis with what it measures and its unit.
  • I can graph the rows of a table as points.
  • I can explain what a point’s coordinates mean in the story.

5.G.2 Worked Example

A burning candle turned into a table, then a row of points, then an answer read straight off the graph.

Problem

A candle is 12 cm tall and burns down 2 cm every hour. Make a table for the first 3 hours, graph it, and use the graph to find when the candle burns out. What does the point (2, 8) mean?

A candle burning down, hour by hour
  1. Decide what each axis means before plotting anything.x-axis: hours burning. y-axis: height in cm
  2. Fill the table and write each row as a pair, hours first.(0, 12), (1, 10), (2, 8), (3, 6)
  3. Read one pair as a sentence to be sure the order is right.(2, 8): after 2 hours, the candle is 8 cm tall
  4. Plot the points. Each one is 1 square right of and 2 squares below the one before.Four points falling to the right in a straight row
  5. Keep the pattern going until the points reach the x-axis.(4, 4), (5, 2), (6, 0)
  6. A height of 0 means nothing is left to burn.(6, 0): burned out after 6 hours
AnswerThe candle burns out after 6 hours, at the point (6, 0). The point (2, 8) means that after 2 hours of burning, the candle is 8 cm tall.

Check it: Divide instead: 12 cm at 2 cm an hour is 12 ÷ 2 = 6 hours, the same answer the graph gave.

Common Mistakes with 5.G.2

Axes with numbers but no meaning

Points plotted in the right places on axes marked only with numbers, so nobody can say what (3, 6) means

Try this: Write the quantity and the unit on each axis before plotting, then read one point aloud as a full sentence.

The wrong quantity first

(12, 0) plotted for the start of the candle, with the height written first

Try this: Match the order to the axes: the x-axis is hours, so hours come first in every pair, including the start at (0, 12).

Numbering the axis to fit the data

A y-axis numbered 0, 1, 2, 5, 10, 12, so the points bend instead of falling in a straight row

Try this: Choose one step size for each axis, such as 2 cm per square, and count it out evenly from 0 before writing any data.

Where 5.G.2 Fits

Comes Before3.MD.3Draw picture and bar graphs where one square stands for several items.4.OA.5Generate a number pattern that follows a given rule.
Alongside5.G.1Plot and read points from ordered pairs, across first and then up.5.OA.3Form ordered pairs from two number patterns and graph them.
Comes Next6.EE.9Show two quantities that change together in a table, a graph and an equation.6.NS.8Solve real-world problems by graphing points in all four quadrants.

Practice 5.G.2

Graph Paper GeneratorFree ToolRoom for the whole problem on one sheet: the table in the margin, both axes labeled with units, and the points. Large squares leave space to write what each point means.Large squaresLetterPrint
Make Graph Paper

Quick Check

  1. On a graph of hours walked (x) and miles walked (y), what does the point (2, 6) mean?
  2. A tank holds 10 liters and drains 2 liters a minute. Which point shows the tank empty?
  3. The points (1, 4), (2, 8) and (3, 12) show cups of flour for batches of muffins. How much flour do 4 batches need?

5.G.2: Other Names

5.G.25.G.A.2CCSS.MATH.CONTENT.5.G.A.2

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.