Reasoning · Grade 2-1 Calculating Cleverly
Problem
(1) Pairing the ends gives five 20s plus the middle 10: 110.
Evenly spaced numbers balance: every step up on one end is matched by a step down on the other, so each pair has the same total.
2.NBT.B.5Look For A PatternPairing the ends inward gives the same total every time, so a long evenly spaced sum becomes a short multiplication.
As one partner steps up the other steps down by the same amount, so every pair lands on the identical total.
The step up and the step down cancel each other exactly, which is why the pair total never drifts as you work inward.
(2) The 14 evens make seven 30s: 210.
Fourteen terms make exactly seven end-to-end pairs, and each pair lands on the same friendly total 30.
2.NBT.B.5Look For A Pattern(3) Each of 1 to 9 appears twice, so double 45: 90.
Reducing 'each number twice' to the single sum 1+...+9 (which you can pair to 45) makes the big list easy, then you just double.
2.NBT.B.5Solve An Easier Related Problem(4) Bundling neighbours leaves six 1s: 6.
Each '−small +slightly-larger' step nets a gain of exactly 1, so the whole chain just counts how many such steps there are.
2.OA.B.2Change Focus Count The Complement(5) Leaving 99 aside, the rest bundles into five 1s: 99 + 5 = 104.
The very first number has no partner, so set it aside; everything after it pairs into easy differences of 1.
2.OA.B.2Change Focus Count The ComplementPair the ends or bundle the +/− steps and a scary-long chain becomes a few easy sums — pure Grade 2 number sense!