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Represent Real-World Problems on a Coordinate Plane

Students graph points in the first quadrant to represent real-world and mathematical situations (e.g., tracking distance over time, mapping locations). They translate between a table of values and points on a coordinate plane.

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Represent Real-World Problems on a Coordinate Plane

Grade 5 · Coordinate Plane · question 1 of 3

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20 rungs. A star at the top.

A graph shows how far a car has driven as the minutes go by. Which variable usually goes on the x-axis?

How it is taught

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A coordinate names a pair of related quantities.

The first number is tickets; the second is cost.

Read it: Points on the coordinate plane

The point (4, 5): start at (0, 0), where the axes cross. Walk 4 across, along the x-axis, then 5 up. The first number is always across, the second always up.

  1. Start at (0, 0), where the x-axis and the y-axis cross.
  2. Walk the first number across, to the right.
  3. Walk the second number up, and mark the point.

Across first, then up, so every pair names exactly one point.

(4, 5) and (5, 4) are different points: the order is part of the pair.

A point on an axis has a 0 in its pair: (4, 0) is on the x-axis.

The first number goes across and the second goes up, always from (0, 0).

Walking 5 across and 4 up, which lands on (5, 4).

The first number goes across: (4, 5) is 4 across, then 5 up.

2 miles an hour, with hours across and miles up. The point for 9 hours is (9, ___). — 18. 9 × 2 = 18: the point is (9, 18).

Lily saves $2 each week — graph her savings

Lily saves two dollars every week. Let's track how much she's saved on a coordinate plane!

Here's a table: at zero weeks, zero dollars. After one week, two dollars. After two weeks, four. After three weeks, six.

Now we draw a coordinate plane. The line across the bottom is the x-axis, and the line going up is the y-axis.

Across the bottom we'll count weeks, and going up we'll count total dollars saved.

Each row in the table becomes one point. The first row, zero and zero, sits right at the origin.

Next row: one week, two dollars. Go right one, then up two — and drop a point!

Two weeks, four dollars: right two, up four.

Three weeks, six dollars: right three, up six.

Look — all four points line up perfectly! That's because Lily saves the same amount every week.

We turned a real-world savings story into points on a coordinate plane. Great work!

Lily saves $2 every weekLet's graph her savings!Lily saves $2 each weekWeekSaved0$01$22$43$601234246Week (x)Saved $ (y)(0,0)(1,2)(2,4)(3,6)All points line up!GRAPHED4 pointsfrom the table
Grade 5 · Turning a savings table into points on a graph

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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