Reasoning · Grade 2-2 Working with Short Lengths
Problem
The Shop is compulsory, so count each half and multiply.
Pairing each way to reach the Shop with each way to continue to the School is exactly what multiplication counts.
3.OA.A.1Make A Systematic ListHome to Shop loses two to the missing street: 4 of 6.
Write out every right/up order, then cross out the ones that need a street that is not drawn — four orders survive.
2.NBT.B.5Make A Systematic ListShop to School keeps 2 of 3.
Listing each right/up order and crossing out the one that needs a road that is not there leaves exactly the routes you can really walk.
2.NBT.B.5Make A Systematic ListJoining them gives 4 × 2 = 8.
Choices made in two stages multiply: 4 first choices times 2 second choices give 8 whole routes.
3.OA.A.1Make A Systematic ListEvery route to the school is one way of reaching the shop followed by one way of leaving it, so the two counts multiply.
Which way you took to the shop puts no limit on which way you leave it, so every first half can be joined to every second half.
Because every route passes through the shop exactly once, splitting there names each route by exactly one pair of halves.
Count each half of the trip by listing the streets you can really walk, then multiply — 4 times 2 makes 8, and the page even gives you 8 grids to draw them on!