Adding and subtracting (age 10+)

Activities to try

1. 1

   Charity accounts mission planner

   Why it works: A calculator does not free you from thinking: the estimate is what tells you whether to trust the display, and the final answer must answer the question asked, not report a running total.

   1. Read a real multi-step problem, e.g. 'A charity had 3,450,000 pounds. In March it spent 1,280,000 pounds and received donations of 2,000,000 pounds. In April its costs were 675,450.75 pounds. How much does it have at the end of April?'
   2. Before computing, model the whole problem with a running-total bar and mark every event as a signed change on the bar.
   3. Build a running estimate first: estimate each step's expected result as well as the final total (about 3.45m - 1.28m + 2m - 0.68m is roughly 3.5m, with intermediate ballparks of about 2.17m then 4.17m along the way).
   4. For each step, choose mental, written, or calculator, carry out the computation, and write one sentence saying WHY that method fits those numbers.
   5. After any calculator or written step, compare that result's order of magnitude against your estimate for that same quantity before accepting it.
2. 2

   Defend your plan and tool choices

   Why it works: Being able to justify which operations and methods you used - and what the answer should roughly be - is part of competent problem solving, not an optional extra.

   1. After solving a multi-step problem, explain the plan aloud to a partner or character who challenges it.
   2. Answer probing challenges: 'Why calculator there but mental here? Roughly what should this step come to? Does that final answer make sense in the context?'
   3. Justify each method choice by reference to the specific numbers (for example, round or near-round steps often suit mental methods, structured ones written methods, and awkward large or decimal ones a calculator - but the choice is a reasoned judgement, not a fixed rule).
   4. State the ballpark estimate and say how it would have exposed a mis-keyed result about ten times too small or too large, such as 349,454.93 or 34,945,492.50.
3. 3

   Sequence, method, and spot the impossible answer

   Why it works: Checking an answer against an estimate lets you reject results that are impossible by magnitude, and the correct final answer is the one that matches the question asked.

   1. Put the steps of a given multi-step problem into the correct order.
   2. For each step, select the best method (mental / written / calculator) and give a reason.
   3. Given an estimate for a step, identify which of several candidate calculator answers is impossible because it is the wrong order of magnitude.
   4. Flag any answer that reports a running total instead of answering the actual question.