Math // Mathematical Thinking

Choosing the right strategy

Select and use appropriate tools and representations strategically, including choosing between mental methods, jottings, formal algorithms, and calculators for arithmetic with multi-digit numbers, decimals, and fractions

Ages
7 to 8
Type
Thinking skill
Builds on
3 topics
Leads to
1 topic

Quick check

When the learner faces a maths problem, do they think about which method suits it best — like doing easy ones in their head, using a written method for bigger calculations, or sketching a diagram for geometry?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Choose a mental method for 345 + 200 but a written method for 345 + 278
  • Select a ruler vs a metre stick based on the object being measured
  • Decide when a number line is more useful than base-ten blocks for a given problem

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics

You are here

Choosing the right strategy

Ages 7 to 8 // Thinking skill

Leads to

1 topic

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For 7-8 year olds, the target skill is choosing a calculation method (mental, jottings, formal written algorithm, or calculator) and measuring tools by first READING the numbers or the object, rather than defaulting to the column algorithm for everything. 345+200 is a mental case (add two hundreds, tens and ones unchanged), while 345+278 involves regrouping and is where a written method earns its effort. The assessable skill is the justification for the choice, not just the answer — since two methods can both reach 545. Learners also decide which representation fits (for example when an empty number line helps more than base-ten blocks), integrate a calculator as a checking tool with a reasonableness judgement, and match measuring tools to an object's size and precision.

Common misconceptions

  • Applies the formal written method to everything, even 345+200 or 300+300, because it is the 'proper' way — missing the faster mental route (EEF: not self-regulating)
  • Attempts a regrouping calculation like 345+278 in the head and drops a carry, misjudging when a written method is needed
  • Trusts a calculator answer without a reasonableness check
  • Chooses a measuring tool that doesn't fit the object — a 30 cm ruler for a room — ignoring range and cumulative error

Useful representations

  • Mental methods (partitioning, known facts)
  • Jottings / empty number line
  • Formal columnar algorithm
  • Calculator (for checking and awkward numbers)
  • Measuring tools: ruler, metre stick, tape

Teaching practices

  • Teach pupils to look at the numbers before choosing — sort calculations into 'do in your head', 'jot', 'write out', 'use a calculator' — so method follows the numbers (EEF Rec 4)
  • Present a range of methods and ask 'when is each appropriate and efficient?', building considered decision-making rather than a single default
  • Integrate the calculator as a checking tool and teach reasonableness checks, so pupils self-regulate ('less but better') rather than reaching for it or the algorithm reflexively (EEF)
  • Match measuring tools to the object's size and precision — ruler for a pencil, metre stick/tape for a room — and name why the wrong-scale tool fails
  • Prize the justification: two methods may both reach 545, so the assessable skill is the reason for the choice, not the answer

Activities to try

  1. 1

    Method chooser: route each calculation

    Why it works: Reading the numbers first and spotting their features (round hundreds vs messy regrouping) lets you pick the method or representation that costs least effort; the column algorithm is worth its effort precisely for the messy cases, not for every calculation.

    1. Work through a stream of mixed calculations (e.g. 345+200, 300+300, 345+278), and for each one first decide out loud which method fits: do it in your head, jot it down, write it out as columns, or use a calculator.
    2. For each, state WHY that method fits before solving — e.g. 'I can see +200, so the tens and ones don't change, so I'll do it in my head.'
    3. Compare the effort: deliberately set out columns for 345+200 and notice how many steps that takes versus saying 545 straight away.
    4. Deliberately choose the written column method for 345+278 and name why (there is regrouping / a carry to track) it is worth the extra effort.
    5. For a given problem, also decide which representation would help most — for example when an empty number line is clearer than base-ten blocks — and say what about the problem makes that representation fit.
  2. 2

    Calculator check: is that sensible?

    Why it works: A calculator answer should be checked for reasonableness rather than trusted blindly; estimating the rough size and the expected last digit is a quick way to show an answer is sensible or catch a wrong one, though passing these checks does not prove the answer is exactly right (for example, 633 would also pass both).

    1. A calculator returns 623 for 345+278. Decide whether that answer is sensible WITHOUT redoing the exact calculation.
    2. Estimate instead: 345 is about 350, 278 is about 280, so the total should be around 630 — use that to judge the calculator's answer.
    3. Say aloud a quick reasonableness check for the result: rounding to size (≈630), and the last-digit check (5+8=13, so the ones digit should be 3 — 623 ends in 3). Confirm these checks ratify 623 rather than flag an error.
    4. Practise choosing when a calculator is the sensible tool (awkward numbers, checking) versus when a mental or written method is faster.
  3. 3

    Fit the measuring tool to the object

    Why it works: The same 'read the job, then choose the tool' habit used for arithmetic applies to measuring: match the tool's range and precision to the object, and recognise that repeated placement of a short ruler can accumulate error.

    1. Decide which tool to use to measure a pencil versus a room: a 30 cm ruler, or a metre stick / tape measure.
    2. Explain why a 30 cm ruler is a poor choice for a room — it needs many placements, and each placement can add a little error that accumulates.
    3. Match a few objects (book, desk, corridor, pencil) to the tool whose range and precision suits them, and name the reason each time.

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