Rich Learning Tasks

168

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Moving Around

Questions to facilitate the learning

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Is there more than one way to get from the square to the circle? Do you move the same total number of

spaces using those different paths?

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If you just picked up the 4 items already on the grid, what different-length paths could you use? What is

the shortest length?

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Could you use the location of two objects, without seeing the grid and figure out how long the path from

one object to the other is?

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How does using a grid system help you locate objects?

Scaffolding the learning

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How many moves does it take to get from A2 to C2 (or (0, 1) to (2, 1))? from A2 to C3 (or (0, 1) to (2, 2))?

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Do you end up in the same place if you move 1 right and then 1 up or 1 up and then 1 right?

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Do you end up in the same place if you move 1 right and 2 up or 2 right and 1 up?

Extending the learning

Students might use a larger grid and place 4 objects so that the total length of the path used to pick up

all 4 objects would be 25 moves.

What’s the point of this task?

Defining location on a coordinate grid is essential background for later grades in math. There are two

kinds of grids provided in this problem—Grid 1, a ‘city grid’ where locations are based on positions in cells

and Grid 2, a Cartesian grid system where locations are based on points. Both grids allow for students to

describe location and movement.

A problem element is added by asking students to move exactly 15 moves to collect all 6 objects. For

example, on Grid 1, students could add objects in cells B2 and D5 and move 1 space up to A2, 1 space

right to B2, 3 spaces up to B5, 1 space right and 1 space down to C4, 2 spaces right and 2 spaces down

to E2 and 3 spaces up and 1 space left to D5. On Grid 2, students could add objects at (2, 2) and (2, 5)

and move 1 space up to (0, 1), 3 spaces up and 1 space right to (1, 4), 2 spaces right and 1 space down to

(3, 3), 1 space right and 1 space down to (4, 2) and 3 spaces up and 2 spaces left to (2, 5).

Students might explore how paths of different lengths might be used depending on the sequence in which

the objects are collected. It is important for students to know that there are generally many paths to get

from one point to another. For example, to get from (2, 2) to (3, 3) you could move right first and then up

or the other way around.

Geometry