Near doubles: find the one-unit adjustment

Keep a known double in view while changing one of its groups by one. This makes the adjustment available to inspect rather than turning near doubles into a separate collection of facts to memorise.

Keep the known double visible and identify the one-unit difference. The strategy depends on a relationship rather than memorising another isolated answer.

What changed from the known fact?

Four plus five can be seen as four plus four plus one, which is nine.

Build the double of four. Add the extra counter. Explain the adjusted total.

Where is the extra one in the model? Leave both groups visible for checking.

Name the adjustment rather than memorising an unexplained shortcut.

Make the adjustment to the known double visible

Build two groups of five counters, establish the double and then add one counter to one group. Ask what has changed and what information from the original arrangement can still help. Five plus six can be connected to five plus five with one additional unit; the reasoning should be visible rather than reduced to a slogan.

Record both expressions and point to the relevant quantities in the model. The added one changes the total by one because that is the actual quantity introduced. Do not let the written adjustment become a disconnected mark whose value the learner cannot explain.

Now compare a different near-double arrangement, such as four and five, using an appropriate known double. Learners may choose the lower double plus one or another valid relationship. Ask for the connection rather than requiring one prescribed verbal formula.

Distinguish a useful relationship from a visual resemblance

A pair of almost-equal-looking rows is not enough if the objects have not been counted or their quantities established. Aligning corresponding items can make the one-unit difference clear, especially when spacing might otherwise mislead.

Offer a fictional incorrect solution that adds two to the known double despite only one extra counter. Ask which part of the model supports or contradicts that adjustment. This gives the learner something specific to inspect without making an error into a personal judgement.

Provide picture pairs, a divided mat or educator handling where appropriate. A child can direct the addition or removal and explain its effect through pointing or dictation. Speed of fact recall should remain separate from understanding the relationship.

Finish by inviting the learner to create a near-double for a partner, keeping the difference small and explicit. The partner should identify the known reference and explain the adjustment. A successful exchange shows how a useful addition strategy grows from a relationship between quantities, rather than from memorising another answer that happens to sit near a familiar fact.

Resources

Maths Puzzle Generator — Choose arithmetic or missing-number questions only when they match the number relationship being explored.

Near doubles: find the one-unit adjustment

What changed from the known fact?

Make the adjustment to the known double visible

Distinguish a useful relationship from a visual resemblance

Resources

Further reading

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