How Far Is 3 Blocks

Walking the Block

Alignments to Content Standards: half-dozen.G.A.3

Task

Here is a map of part of Downtown Salt Lake City. You lot are starting at the corner of 11th Ave. and D St. (on the star).

If you walk Due east to I St., South to 7th Ave., W to D St. and then North to your starting point, how many blocks volition you have walked in total? Describe the shape of your path.
Describe and describe in words at least 2 different ways that you can walk exactly 8 blocks and cease up where you started.
Jessica said the path she took on her walk enclosed a polygon that had an area of half-dozen square blocks. Draw some possible shapes that her walk could take taken. Was her path necessarily rectangular?

IM Commentary

The purpose of this task is for students to apply the calculation of distances on a coordinate airplane to a real life context (6.1000.three). Though explicit coordinates are not given in the problem, the reasoning behind finding the side lengths of the rectangles in the plane is nowadays and this activity could set up for formalizing of this with the Cartesian coordinate plane afterwards. The teacher could besides have students put a Cartesian coordinate system on the map. The could, for example, choose (0,0) for the starting indicate of the walk and so draw the path using coordinates, putting advisable integer coordinates at each street intersection.

The job affords students the opportunity to reason abstractly and quantitatively (MP2) as they map out routes and so describe in words (and maybe coordinates) their location. Students could also make apply of construction (MP7) to find shortcuts to part (b) and so reason about function (c). For office (c), students could also share out unlike solutions and critique each other's reasoning on whether their path forms a polygon that has the right surface area in square blocks (MP3).

To support students working on this chore, it could exist useful to provide colored pencils for the routes in parts (a), (b), & (c). Alternatively, the map could be printed and slid into plastic sleeves and students could describe various routes with expo or vis a vis markers.

An initial conversation may need to happen around directions (due north being "up" every bit indicated in the drawing). The students may annotation that the "blocks" are not perfect squares just the term "cake" is used to define how far a person can walk on i side of the street without crossing any other streets and how it applies to the n-s and east-west directions even though they aren't perfect squares. Some students may recall to walk down one side of the street and and so cantankerous, then walk back on the other side of the street. This scenario should still exist considered an out and dorsum path considering they are are on the same block as described above.

Solution

You lot volition have walked 5 blocks West, 4 blocks S, 5 blocks E and 4 blocks North for a total of 18 blocks. This is shown below. You commencement at the star then go around the boundary of the rectangle in the clockwise management.
Solutions volition vary, but here are a few options:
1. Walk east ii blocks to F St, south 2 blocks to 9th Ave., westward 2 blocks to D st. and and then 2 blocks north to the starting signal: this path follows the square in the picture higher up.
2. Walk i block west to C St., iii blocks south to eighth ave., i blocks east to D st. and so three blocks North to the starting point: this path follows the rectangle in the moving-picture show above.
3. Walk around i square block twice.
4. Walk 4 blocks due east on 11th avenue and so plow around and walk 4 blocks back to the w.
Below is an example of a rectangular route that meets the criteria. In that location are many non-rectangular paths that enclose an expanse of six foursquare blocks: 50-shaped regions, cross-shaped regions, etc.