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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Coordinates become most useful when they stand for something real. A point (3, 15) on a graph might mean 3 hours of babysitting earned 15 dollars, or day 3 of an experiment when a plant was 15 centimeters tall. Fifth graders represent situations like these by graphing points in the first quadrant and then explain what the coordinates mean in the context of the problem.
Doing this well requires labeling. Each axis needs a name and a unit, and the scale must suit the data, perhaps counting by 5s or 10s instead of 1s. Students read graphs to answer questions such as how much the plant grew between day 2 and day 5, or which point shows the greatest cost, and they find distances on the grid by subtracting coordinates. A graph of a simple pattern, such as the cost of tickets at 4 dollars each, also shows the points lining up, which previews proportional relationships in sixth and seventh grade.
A point (4, 20) means nothing without labels. Students should be able to say '4 hours, 20 dollars' or similar for every point they plot.
If the y-axis counts by 5s, a point two grid lines up is at 10, not 2. Students should check the scale before reading or plotting.
Putting time on the vertical axis and distance on the horizontal changes the meaning of each point. The problem usually signals which quantity goes on the x-axis.
Points for whole tickets sold should not always be connected with a line, since half a ticket makes no sense. Context decides.
A plant is 4 cm tall on day 1 and grows 3 cm each day. Write the ordered pairs (day, height) for days 1 to 4 and find how much it grew from day 1 to day 4.
Answer: The points are (1, 4), (2, 7), (3, 10) and (4, 13); the plant grew 9 cm.
Collect simple class data, such as the temperature at each hour or the number of laps run per minute, and graph it together. Ask students to write a sentence for one point, then pose questions that require reading two points and subtracting.
Assessment items show a labeled graph and ask what a point means, which point answers a question, or what the difference is between two coordinates in context.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 5 hours earned 40 dollars
The x-coordinate is hours and the y-coordinate is dollars, so 5 hours of work earned 40 dollars.
Answer: 42
7 tickets cost 7 × 6 = 42 dollars, so the point is (7, 42).
Answer: 12 (also accepted: 12 pounds)
Subtract the y-coordinates: 21 - 9 = 12 pounds.
Answer: A) 40
Each grid line is worth 10, so the 4th line up is 4 × 10 = 40.
Answer: 15 (also accepted: 15 miles)
The hiker covers 3 miles each hour, so 5 hours gives 5 × 3 = 15 miles.
A full lesson with slides, activities and an exit ticket on graphing real-world points, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.G.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn graphing real-world points into a quiz students answer online that marks itself, with a class summary for you.
Build a test →5.G.A.1 is about how the coordinate plane works. 5.G.A.2 uses it to represent real situations and interpret what the coordinates mean.
Only when values between the points make sense, such as time and distance. For counts like tickets sold, separate points are more accurate.