Full chapter index

Read 2.40 m as two metres and forty hundredths of a metre. Begin with this original teaching case: Place a two-metre strip beside a forty-centimetre strip and label the combined length 2.40 m. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Because one metre contains one hundred centimetres, one hundredth of a metre equals one centimetre. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Partition the decimal into 2 m plus 0.40 m, then convert only the fractional part. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner states 2 m 40 cm and explains the hundredths relationship. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Find out whether the problem is place value, the unit fact or mixed notation. Begin with this original teaching case: Ask for 1 m in centimetres, 0.01 m in centimetres, 0.10 m in centimetres and 2.40 m in mixed units. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Each answer tests a different link in the conversion chain. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Record the first point at which the explanation becomes uncertain before teaching further. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The repair targets the earliest missing relationship rather than assigning a whole conversion worksheet. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Make 1 m = 100 cm the stable reference. Begin with this original teaching case: Compare a metre rule with ten ten-centimetre segments and one hundred one-centimetre segments. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Changing units does not change the length; it changes how many chosen units are needed to describe it. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Build a ratio table for metres and centimetres with 1, 0.1 and 0.01 metre. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The child predicts whether the number becomes larger or smaller when changing to centimetres. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Connect tenths and hundredths to a named unit. Begin with this original teaching case: Read 0.4 m as four tenths of a metre and 0.40 m as forty hundredths of a metre. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The two decimals have equal value, and forty hundredths of a metre are forty centimetres. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Use a hundred-square or segmented metre strip to show both names for the same portion. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner explains why the trailing zero does not turn forty centimetres into four centimetres. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Carry out the conversion with both decomposition and multiplication. Begin with this original teaching case: Write 2.40 m = 2 m + 0.40 m and also 2.40 × 100 cm. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The mixed form keeps two complete metres separate, while the all-centimetre form is 240 cm. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Convert 0.40 m to 40 cm, then reverse from 240 cm to 2 m 40 cm. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: Both routes agree and the child labels every quantity. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Use the tempting wrong answer as a reverse check. Begin with this original teaching case: Convert the claimed answer 2 m 4 cm back into metres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Four centimetres are four hundredths of a metre, so the decimal is 2.04 m, not 2.40 m. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Write 4/100 m beside 0.04 m and compare it with 40/100 m. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner can disprove the original error without being told the correct answer. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Separate decimal value from display precision. Begin with this original teaching case: Compare 2.4 m, 2.40 m and 2.400 m on the same number line. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Adding zeros to the right of a decimal does not change its value, although context may use the written precision deliberately. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Remove trailing zeros, locate the value, then restore the original notation. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The child recognises equal lengths while respecting a requested answer format. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Protect the zero in the tenths place. Begin with this original teaching case: A learner reads 2.04 m as two metres forty centimetres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The four occupies the hundredths-of-a-metre place, which maps to centimetres one for one. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Use a place-value table labelled metres, tenths of a metre and hundredths of a metre. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner reports 2 m 4 cm and checks that it is only slightly longer than two metres. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Handle a value below one metre without inventing a whole metre. Begin with this original teaching case: A ribbon is labelled 0.40 m and the requested answer is in centimetres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Multiplying by one hundred converts metres to centimetres because centimetres are the smaller unit. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Calculate 0.40 × 100 = 40 and attach cm. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The answer is checked against the benchmark that half a metre is fifty centimetres. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Move from 245 cm to metres and mixed units. Begin with this original teaching case: Divide 245 cm into two groups of one hundred and a remainder of forty-five. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Two hundred centimetres are two metres and forty-five centimetres remain; in decimal metres the result is 2.45 m. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Use quotient and remainder first, then write the decimal form. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner converts back to 245 cm without loss. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Keep 2 m 40 cm distinct from 2.40 m while recognising equivalence. Begin with this original teaching case: Compare the space-separated unit labels with a single decimal number carrying one unit. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Mixed notation uses two unit counts; decimal notation expresses the whole length in metres. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Read each form aloud before calculating. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The child does not write 2.40 m cm or treat the 40 as a decimal without a unit relationship. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Choose a common unit before combining. Begin with this original teaching case: Add 2.40 m and 75 cm. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: A sum is interpretable when both addends are expressed in compatible units. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Convert to centimetres for 240 + 75 = 315 cm, then state 3 m 15 cm or 3.15 m as requested. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The result is estimated as a little more than three metres. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Regroup or use a common unit without losing place value. Begin with this original teaching case: Find 3 m 5 cm minus 1.40 m. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Writing both as centimetres gives 305 cm minus 140 cm, avoiding a false 5 minus 40 step. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Subtract to obtain 165 cm and convert to 1 m 65 cm. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: A reverse addition reproduces the starting length. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Carry the conversion understanding into a multi-step task. Begin with this original teaching case: A rectangle measures 2.40 m by 85 cm. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Perimeter requires compatible units and two pairs of equal sides. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Convert 2.40 m to 240 cm, calculate 2(240 + 85) and express the answer in the required unit. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner checks that the perimeter exceeds twice the longer side. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Read starting length, used length and requested form. Begin with this original teaching case: A 2.40 m ribbon has 65 cm cut away. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The subtraction compares lengths, so both quantities must first use compatible units. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Use 240 cm minus 65 cm, then convert the remainder. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The answer is smaller than 2.40 m and the unit matches the question. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Use physical benchmarks before exact arithmetic. Begin with this original teaching case: Decide whether 2.40 m is closer to two metres or two metres four centimetres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Forty centimetres is a substantial fraction of a metre, while four centimetres is only a small extension. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Visualise a metre rule or compare with 0.5 m = 50 cm. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner rejects an implausible mixed-unit answer before checking detailed working. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Let the calculator execute arithmetic after the conversion decision is made. Begin with this original teaching case: A display shows 2.4 × 100 = 240 but the learner writes 240 m. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The numerical operation does not supply the target unit; the written relationship does. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Write m → cm and the factor 100 before entering numbers. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The final label and magnitude are both correct. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Prevent a useful factor from being carried into square units unchanged. Begin with this original teaching case: A child uses ×100 to change 2.4 m² into cm². Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: One square metre contains 100 × 100 square centimetres because both dimensions change unit. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Draw a square metre as a 100-by-100 centimetre array. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner keeps this article’s length conversion separate from an area conversion. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Understand why a task may preserve 2.40 m even though 2.4 m has the same value. Begin with this original teaching case: A table records lengths to the nearest centimetre in metres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: The second decimal place may communicate the recording resolution, while value equality remains true. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Follow the table heading and required precision without claiming that extra zeros create extra length. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The child states both the value relationship and the presentation requirement. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Move from unit facts to mixed problems. Begin with this original teaching case: Use 0.01 m, 0.1 m, 0.40 m, 2.04 m, 2.40 m, reverse conversions and a final perimeter problem. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Variation exposes whether the learner understands positions rather than copying two digits after the point. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Fade the place-value table after accurate explanations appear. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: Delayed practice remains accurate with new values and changed requested units. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Separate unit memory, decimal place value, operation direction and communication. Begin with this original teaching case: One child knows 1 m = 100 cm but reads 0.04 as four tenths; another converts correctly and omits cm. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: These errors need different next questions even if both final answers are marked wrong. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Use a short cold sequence and listen to the reason for each step. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: Improvement appears in accurate conversions, estimates and reverse checks with fewer prompts. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Match support to the pattern across schoolwork. Begin with this original teaching case: The mistake occurs once after rushing versus across money, mass, length and time conversions. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: A local slip may need one correction; a cross-unit place-value pattern deserves structured repair. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Collect three recent examples and ask the child to identify what one decimal place represents in each context. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The family can name the teaching job before choosing more worksheets or tuition. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.

Coordinate decimal value, unit conversion and mixed notation independently. Begin with this original teaching case: A cold task asks for 5.08 m plus 92 cm, with the answer in metres and centimetres. Ask the learner to describe the decision before supplying a rule. A visible first explanation helps a parent or tutor distinguish a missing idea from a rushed execution, an unfamiliar word or a notation slip.

The dependable relationship is precise: Secure work converts through a common unit, preserves the zero in 5.08 and returns to the requested form. Keep the condition beside the conclusion. When the condition disappears, a useful rule can turn into a slogan that seems successful on one familiar question but breaks as soon as the wording, values, apparatus or sentence structure changes.

Use this repair route: Estimate, calculate in centimetres, convert back and reverse-check. Let the learner perform the decisive step and say why it is allowed. If help is needed, give the smallest neutral prompt that restarts thinking. Doing the step for the child can make adult fluency look like student understanding.

Now compare possible causes. One learner may understand the concept but misread the task; another may read accurately but choose the wrong representation; a third may reason correctly and communicate imprecisely. Diagnose reading, concept, representation, execution and final communication instead of reteaching the entire subject.

A useful success check is: The learner obtains 6 m exactly and explains why the decimal digits were not copied as centimetres mechanically. Follow it with one near example and one changed example. The first confirms that the correction was understood. The second tests whether the learner can recognise the same relationship without depending on the wording, numbers or diagram from the model.

For home support, finish by asking, ‘What would you look for first next time?’ A strong reply names evidence, structure, units or a language relationship rather than a memorised command. Praise the check, preserve the child’s explanation and stop before fatigue replaces a sound method with guessing.