Reasoning · Grade 2-1 Measuring Length with Units
Problem
Both trains measure the same width, so they are equal in length.
If two strings of pencils reach across the same desk, they have to be the same length — that is just what 'measuring the same thing' means.
1.MD.A.2Analyze The UnitsTake off the shared 3 long and 2 short from both sides and 4 short = 3 long is left.
Taking the same amount off both sides of a balance keeps it balanced — like removing one block from each pan of a scale.
2.OA.A.1Guess And CheckTaking the same pencils off both trains leaves the two shortened trains still exactly equal.
The two trains reach across the very same desk, so they are a statement that two lengths are equal — a balance you can see.
A balance stays level when the same amount is removed from both pans, so an equality survives the same removal on both sides.
Once 3 long pencils are known to match 4 short ones, repeating that same trade four times matches 12 long pencils with 16 short ones.
That is the trade rule — 3 long pencils always swap for 4 short.
A trade rule is a pattern: each time I see 3 long pencils I can swap in 4 short ones and the length does not change.
1.MD.A.2Look For A Pattern12 makes four groups of 3, so 4 × 4 = 16.
Repeating the same fair trade four times turns 12 long pencils into 16 short pencils, the same way 4 batches of 4 cookies makes 16 cookies.
3.OA.A.3Look For A PatternWhen two rulers measure the same length, take away the parts they share — what is left tells you the fair trade between long and short!