Grade 5 · Go across before moving up · 555 of 750
Go across before moving up: horizontal coordinate x: 2; vertical coordinate y: 8
A map for a classroom activity places a destination at the ordered pair (2, 8). Find the destination and the length of the horizontal-then-vertical route, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A map for a classroom activity places a destination at the ordered pair (2, 8). First find the destination and the length of the horizontal-then-vertical route. Then answer: What point would result if the two coordinates were exchanged?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
An ordered pair gives horizontal movement first and vertical movement second. Swapping the coordinates usually selects a different point because the two numbers refer to different axes.
Work through the reasoning
Step 1
Identify the quantities and the task
A map for a classroom activity places a destination at the ordered pair (2, 8). The first task is to find the destination and the length of the horizontal-then-vertical route. An ordered pair gives horizontal movement first and vertical movement second. Swapping the coordinates usually selects a different point because the two numbers refer to different axes.
Step 2
Calculate the original result
(x, y) = (2, 8). The destination lies 2 units right and 8 units up. This route has length 10, which is not generally the straight-line distance.
Step 3
Complete the follow-up calculation
What point would result if the two coordinates were exchanged? (8, 2). It is a different point because the horizontal and vertical moves change.
The answer
(x, y) = (2, 8). The destination lies 2 units right and 8 units up. This route has length 10, which is not generally the straight-line distance. Follow-up: (8, 2). It is a different point because the horizontal and vertical moves change.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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From experiment to screen.
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The mathematical idea
A map for a classroom activity places a destination at the ordered pair (2, 8). An ordered pair gives horizontal movement first and vertical movement second. Swapping the coordinates usually selects a different point because the two numbers refer to different axes. The destination lies 2 units right and 8 units up. This route has length 10, which is not generally the straight-line distance.
(x, y) = (2, 8)
03 · Reflect and transfer
Explain what changes and why.
Begin at the origin, move right to the x coordinate, then move up to the y coordinate. The timeline separates these two moves. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.