Primary 4 Mathematics Tuition | Li Hwan Walk Weekday vs Weekend Parent Dilemma

Primary 4 Mathematics: fully worked method and parent decision framework

Put four decimals into ascending order without guessing

The original card set is 4.09, 4.099, 4.9 and 4.909. Write each number with three decimal places for comparison: 4.090, 4.099, 4.900 and 4.909.

All have the same whole-number part, four. Compare tenths first: zero for 4.090 and 4.099, nine for 4.900 and 4.909. The zero-tenths pair must come before the nine-tenths pair.

Within the zero-tenths pair, compare hundredths: both have nine hundredths. Compare thousandths: zero is less than nine, so 4.090 < 4.099.

Within the nine-tenths pair, hundredths are both zero. Thousandths differ: zero < nine, so 4.900 < 4.909. The complete ascending order is therefore 4.09, 4.099, 4.9, 4.909.

Written trailing zeroes in 4.090 and 4.900 do not change the original values. They make columns explicit for comparison, not round the amounts.

Decimal digits have values based on their columns

Draw a chart headed Ones, Tenths, Hundredths and Thousandths. Write each of the four values with its digits aligned under those columns.

The number 4.09 has four ones, zero tenths and nine hundredths; it may be written 4.090 with zero thousandths. The number 4.099 includes an additional nine thousandths.

The number 4.9 has nine tenths, equal to ninety hundredths or nine hundred thousandths, and can be written 4.900. The number 4.909 has nine tenths and nine thousandths.

A pupil who compares the strings ‘099’ and ‘9’ as whole numbers will reach the wrong conclusion. Decimal place positions, not the number of displayed digits after the point, determine magnitude.

Compare whole parts before fractional places

First compare the whole-number part. A decimal beginning with 5 is greater than a positive decimal beginning with 4 regardless of how many hundredths or thousandths the latter contains.

When the whole parts tie, proceed to the tenths; when tenths tie, compare hundredths; and finally compare thousandths if necessary.

This is a left-to-right place-value routine. It is more reliable than trying to read all the digits after the decimal point as a new whole number.

A pupil who orders 4.909 below 4.09 because the last digit nine looks the same needs the aligned chart, not another subtraction drill.

Use zero padding as an equality-preserving tool

Writing 4.9 as 4.900 does not change its value because zeros added at the end of a decimal’s fractional part contribute no additional quantity.

Similarly 4.09 = 4.090. These equalities can be checked with a place-value grid: nine hundredths equal ninety thousandths, and nine tenths equal nine hundred thousandths.

Zeroes inserted between nonzero decimal digits are different. The numbers 4.09 and 4.9 are not equal because the nine occupies the hundredths and tenths places respectively.

The tutor should ask where the zero was placed and which amount it represents before accepting a ‘just add zeros’ rule.

Put the decimals on a number line

Place all four values between 4 and 5 on an increasing number line. The values 4.09 and 4.099 lie close to 4.1, while 4.9 and 4.909 lie close to 4.9.

Zoom in on 4.090 and 4.099. Their difference is nine thousandths, so the second lies a little farther to the right.

Zoom in on 4.900 and 4.909. The second again lies nine thousandths farther right. The number line and place-value chart should give the same ordering.

A learner need not draw a perfectly scaled millimetre chart; the purpose is to see that a number is greater when its value lies farther right, not when its printed decimal has more digits.

Distinguish ordering from rounding

Ordering requires comparing the exact original values. Rounding replaces a number by an approximation at a specified precision, which could make two different numbers appear equal.

For example 4.090 and 4.099 both round to 4.1 to one decimal place, but the original numbers are not equal. Their exact order must be decided from hundredths and thousandths.

Similarly 4.900 and 4.909 may round to the same one-decimal-place value even though their exact ordering differs. Do not round away information before a comparison task.

The instruction ‘arrange from smallest to largest’ does not ask the child to calculate a rounded value or an average. State the relationship requested.

Include equality and equivalent decimal notation

The numbers 3.5, 3.50 and 3.500 are equal. They simply show the same five tenths with different numbers of trailing zeros.

An equality problem is different from ordering strictly distinct values. The pupil should recognise an equal pair and not invent a difference merely because one printed string has more characters.

Contrast 3.05 with 3.5. They are not equal: three and five hundredths is less than three and five tenths. This difference is about the position of the five, not the count of zeroes.

A useful tutor includes both an equal-trailing-zero case and a different-position case so the learner’s rule is not overgeneralised.

What the first wrong ordering reveals

A response placing 4.099 above 4.9 often results from reading 099 as ninety-nine and 9 as nine without considering place values.

A response treating 4.09 and 4.9 as equal may come from ignoring the meaningful zero in the tenths place of 4.09.

If the child writes 4.900 < 4.090, the tenths columns have been compared incorrectly. Return to four ones plus nine tenths versus four ones plus nine hundredths.

A correct order obtained only after the tutor pads every number may still need a delayed task to see whether the child chooses that support independently.

The error report should separate whole-number comparison, tenths, hundredths, thousandths and equality notation.

Weekday tuition and deliberate decimal reading

A weekday Primary 4 class can revisit an uncorrected school ordering problem before the learner forgets which two numbers seemed confusing.

Confirm the actual teaching address rather than assume a class operates within Li Hwan Walk. Include meals, travel, school responsibilities and sleep when evaluating the hour.

A short focused lesson can build a place-value chart, compare a pair differing only in thousandths and then ask for an unfamiliar list without direct guidance.

A delayed new problem is more informative than copying the original four numbers after their full ordering has been shown.

Weekend tutorials and representations

A weekend lesson may allow unhurried work with place-value grids or number-line strips to show why trailing zeroes preserve exact decimal values.

An activity should end with a correctly ordered written list and a spoken explanation, not only coloured columns. The learner should later work without the chart supplied by an adult.

Family sport, outings and other enrichment can make weekends tiring too. Choose the time that permits accurate concentration and adequate recovery.

The best routine respects schoolwork and allows a fresh independent comparison during the following week.

Three-pupil feedback and a four-stage check

One child may compare the tenths correctly but miss a thousandth. Another may incorrectly equate 4.09 and 4.9. A third may know equality of 3.5 and 3.50 but apply that idea to nontrailing zeroes.

These require different prompts: identify the decisive thousandths, align the tenths and hundredths, or distinguish trailing from internal zeroes.

Ask for independent first orders before peer discussion. One confident classmate’s answer should not conceal another learner’s starting decision.

Progress can be checked through place-value reading, equality of trailing-zero forms, ordering mixed-length decimals and a fresh unseen list after a delay. The checkpoints are adaptable, not guaranteed mastery dates.

Confirm the real venue and a new independent question

The MOE Primary Mathematics syllabus updated October 2025 defines the grade’s scope, and the Mathematics learning hub offers connected lessons. URA’s residential street records include Li Hwan Walk. This geography is not a claimed eduKate classroom location. Confirm actual 3-pax placement, fees, lesson venue and full journey through eduKate, then ask what unfamiliar task will demonstrate independent learning after a delay.

Primary 4: twenty-two independently checked worked problems and transfer questions

All tasks in this practice bank use original fictional values. Work the initial problem before reading its solution, state which quantities are known and which are requested, and check by an inverse relationship, a place-value representation or an unfamiliar changed condition. A correct number copied after the answer is shown is not evidence that the method can be used independently.

1. Order four decimals near 4 using thousandths

Unseen Primary 4 number-card problem: arrange 4.09, 4.099, 4.9, 4.909 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 4; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 4.090, 4.099, 4.900, 4.909. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 4.9 and 4.09 place the nine in different columns.

The checked ascending order is 4.09 < 4.099 < 4.9 < 4.909. The first two values are 4.090 and 4.099, separated by 9 thousandths, or 0.009. The largest minus the smallest is 0.819 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 4 and 5. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 4.090 before 4.909 because 90 thousandths are less than 909 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 4.909 > 4.9 > 4.099 > 4.09. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 4.09 and 4.090 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 4.090 into 4.091. The updated ascending values become 4.091 < 4.099 < 4.9 < 4.909 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

2. Order four decimals near 3 using thousandths

Unseen Primary 4 number-card problem: arrange 3.005, 3.05, 3.5, 3.505 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 3; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 3.005, 3.050, 3.500, 3.505. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 3.9 and 3.09 place the nine in different columns.

The checked ascending order is 3.005 < 3.05 < 3.5 < 3.505. The first two values are 3.005 and 3.050, separated by 45 thousandths, or 0.045. The largest minus the smallest is 0.500 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 3 and 4. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 3.005 before 3.505 because 5 thousandths are less than 505 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 3.505 > 3.5 > 3.05 > 3.005. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 3.005 and 3.005 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 3.005 into 3.006. The updated ascending values become 3.006 < 3.05 < 3.5 < 3.505 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

3. Order four decimals near 7 using thousandths

Unseen Primary 4 number-card problem: arrange 7.018, 7.081, 7.18, 7.81 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 7; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 7.018, 7.081, 7.180, 7.810. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 7.9 and 7.09 place the nine in different columns.

The checked ascending order is 7.018 < 7.081 < 7.18 < 7.81. The first two values are 7.018 and 7.081, separated by 63 thousandths, or 0.063. The largest minus the smallest is 0.792 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 7 and 8. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 7.018 before 7.810 because 18 thousandths are less than 810 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 7.81 > 7.18 > 7.081 > 7.018. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 7.018 and 7.018 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 7.018 into 7.019. The updated ascending values become 7.019 < 7.081 < 7.18 < 7.81 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

4. Order four decimals near 2 using thousandths

Unseen Primary 4 number-card problem: arrange 2.009, 2.09, 2.099, 2.909 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 2; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 2.009, 2.090, 2.099, 2.909. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 2.9 and 2.09 place the nine in different columns.

The checked ascending order is 2.009 < 2.09 < 2.099 < 2.909. The first two values are 2.009 and 2.090, separated by 81 thousandths, or 0.081. The largest minus the smallest is 0.900 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 2 and 3. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 2.009 before 2.909 because 9 thousandths are less than 909 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 2.909 > 2.099 > 2.09 > 2.009. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 2.009 and 2.009 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 2.009 into 2.010. The updated ascending values become 2.01 < 2.09 < 2.099 < 2.909 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

5. Order four decimals near 5 using thousandths

Unseen Primary 4 number-card problem: arrange 5.105, 5.15, 5.501, 5.51 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 5; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 5.105, 5.150, 5.501, 5.510. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 5.9 and 5.09 place the nine in different columns.

The checked ascending order is 5.105 < 5.15 < 5.501 < 5.51. The first two values are 5.105 and 5.150, separated by 45 thousandths, or 0.045. The largest minus the smallest is 0.405 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 5 and 6. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 5.105 before 5.510 because 105 thousandths are less than 510 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 5.51 > 5.501 > 5.15 > 5.105. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 5.105 and 5.105 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 5.105 into 5.106. The updated ascending values become 5.106 < 5.15 < 5.501 < 5.51 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

6. Order four decimals near 6 using thousandths

Unseen Primary 4 number-card problem: arrange 6.007, 6.07, 6.7, 6.707 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 6; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 6.007, 6.070, 6.700, 6.707. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 6.9 and 6.09 place the nine in different columns.

The checked ascending order is 6.007 < 6.07 < 6.7 < 6.707. The first two values are 6.007 and 6.070, separated by 63 thousandths, or 0.063. The largest minus the smallest is 0.700 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 6 and 7. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 6.007 before 6.707 because 7 thousandths are less than 707 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 6.707 > 6.7 > 6.07 > 6.007. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 6.007 and 6.007 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 6.007 into 6.008. The updated ascending values become 6.008 < 6.07 < 6.7 < 6.707 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

7. Order four decimals near 8 using thousandths

Unseen Primary 4 number-card problem: arrange 8.08, 8.088, 8.808, 8.88 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 8; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 8.080, 8.088, 8.808, 8.880. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 8.9 and 8.09 place the nine in different columns.

The checked ascending order is 8.08 < 8.088 < 8.808 < 8.88. The first two values are 8.080 and 8.088, separated by 8 thousandths, or 0.008. The largest minus the smallest is 0.800 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 8 and 9. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 8.080 before 8.880 because 80 thousandths are less than 880 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 8.88 > 8.808 > 8.088 > 8.08. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 8.08 and 8.080 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 8.080 into 8.081. The updated ascending values become 8.081 < 8.088 < 8.808 < 8.88 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

8. Order four decimals near 1 using thousandths

Unseen Primary 4 number-card problem: arrange 1.015, 1.051, 1.15, 1.51 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 1; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 1.015, 1.051, 1.150, 1.510. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 1.9 and 1.09 place the nine in different columns.

The checked ascending order is 1.015 < 1.051 < 1.15 < 1.51. The first two values are 1.015 and 1.051, separated by 36 thousandths, or 0.036. The largest minus the smallest is 0.495 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 1 and 2. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 1.015 before 1.510 because 15 thousandths are less than 510 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 1.51 > 1.15 > 1.051 > 1.015. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 1.015 and 1.015 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 1.015 into 1.016. The updated ascending values become 1.016 < 1.051 < 1.15 < 1.51 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

9. Order four decimals near 9 using thousandths

Unseen Primary 4 number-card problem: arrange 9.104, 9.14, 9.401, 9.41 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 9; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 9.104, 9.140, 9.401, 9.410. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 9.9 and 9.09 place the nine in different columns.

The checked ascending order is 9.104 < 9.14 < 9.401 < 9.41. The first two values are 9.104 and 9.140, separated by 36 thousandths, or 0.036. The largest minus the smallest is 0.306 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 9 and 10. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 9.104 before 9.410 because 104 thousandths are less than 410 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 9.41 > 9.401 > 9.14 > 9.104. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 9.104 and 9.104 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 9.104 into 9.105. The updated ascending values become 9.105 < 9.14 < 9.401 < 9.41 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

10. Order four decimals near 0 using thousandths

Unseen Primary 4 number-card problem: arrange 0.011, 0.101, 0.11, 0.111 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 0; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 0.011, 0.101, 0.110, 0.111. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 0.9 and 0.09 place the nine in different columns.

The checked ascending order is 0.011 < 0.101 < 0.11 < 0.111. The first two values are 0.011 and 0.101, separated by 90 thousandths, or 0.090. The largest minus the smallest is 0.100 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 0 and 1. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 0.011 before 0.111 because 11 thousandths are less than 111 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 0.111 > 0.11 > 0.101 > 0.011. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 0.011 and 0.011 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 0.011 into 0.012. The updated ascending values become 0.012 < 0.101 < 0.11 < 0.111 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

11. Order four decimals near 4 using thousandths

Unseen Primary 4 number-card problem: arrange 4.005, 4.05, 4.5, 4.55 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 4; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 4.005, 4.050, 4.500, 4.550. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 4.9 and 4.09 place the nine in different columns.

The checked ascending order is 4.005 < 4.05 < 4.5 < 4.55. The first two values are 4.005 and 4.050, separated by 45 thousandths, or 0.045. The largest minus the smallest is 0.545 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 4 and 5. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 4.005 before 4.550 because 5 thousandths are less than 550 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 4.55 > 4.5 > 4.05 > 4.005. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 4.005 and 4.005 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 4.005 into 4.006. The updated ascending values become 4.006 < 4.05 < 4.5 < 4.55 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

12. Order four decimals near 3 using thousandths

Unseen Primary 4 number-card problem: arrange 3.12, 3.201, 3.21, 3.221 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 3; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 3.120, 3.201, 3.210, 3.221. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 3.9 and 3.09 place the nine in different columns.

The checked ascending order is 3.12 < 3.201 < 3.21 < 3.221. The first two values are 3.120 and 3.201, separated by 81 thousandths, or 0.081. The largest minus the smallest is 0.101 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 3 and 4. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 3.120 before 3.221 because 120 thousandths are less than 221 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 3.221 > 3.21 > 3.201 > 3.12. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 3.12 and 3.120 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 3.120 into 3.121. The updated ascending values become 3.121 < 3.201 < 3.21 < 3.221 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

13. Order four decimals near 6 using thousandths

Unseen Primary 4 number-card problem: arrange 6.209, 6.29, 6.902, 6.92 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 6; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 6.209, 6.290, 6.902, 6.920. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 6.9 and 6.09 place the nine in different columns.

The checked ascending order is 6.209 < 6.29 < 6.902 < 6.92. The first two values are 6.209 and 6.290, separated by 81 thousandths, or 0.081. The largest minus the smallest is 0.711 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 6 and 7. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 6.209 before 6.920 because 209 thousandths are less than 920 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 6.92 > 6.902 > 6.29 > 6.209. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 6.209 and 6.209 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 6.209 into 6.210. The updated ascending values become 6.21 < 6.29 < 6.902 < 6.92 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

14. Order four decimals near 8 using thousandths

Unseen Primary 4 number-card problem: arrange 8.045, 8.054, 8.45, 8.54 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 8; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 8.045, 8.054, 8.450, 8.540. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 8.9 and 8.09 place the nine in different columns.

The checked ascending order is 8.045 < 8.054 < 8.45 < 8.54. The first two values are 8.045 and 8.054, separated by 9 thousandths, or 0.009. The largest minus the smallest is 0.495 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 8 and 9. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 8.045 before 8.540 because 45 thousandths are less than 540 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 8.54 > 8.45 > 8.054 > 8.045. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 8.045 and 8.045 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 8.045 into 8.046. The updated ascending values become 8.046 < 8.054 < 8.45 < 8.54 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

15. Order four decimals near 2 using thousandths

Unseen Primary 4 number-card problem: arrange 2.306, 2.36, 2.603, 2.63 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 2; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 2.306, 2.360, 2.603, 2.630. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 2.9 and 2.09 place the nine in different columns.

The checked ascending order is 2.306 < 2.36 < 2.603 < 2.63. The first two values are 2.306 and 2.360, separated by 54 thousandths, or 0.054. The largest minus the smallest is 0.324 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 2 and 3. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 2.306 before 2.630 because 306 thousandths are less than 630 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 2.63 > 2.603 > 2.36 > 2.306. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 2.306 and 2.306 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 2.306 into 2.307. The updated ascending values become 2.307 < 2.36 < 2.603 < 2.63 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

16. Order four decimals near 5 using thousandths

Unseen Primary 4 number-card problem: arrange 5.025, 5.052, 5.25, 5.52 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 5; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 5.025, 5.052, 5.250, 5.520. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 5.9 and 5.09 place the nine in different columns.

The checked ascending order is 5.025 < 5.052 < 5.25 < 5.52. The first two values are 5.025 and 5.052, separated by 27 thousandths, or 0.027. The largest minus the smallest is 0.495 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 5 and 6. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 5.025 before 5.520 because 25 thousandths are less than 520 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 5.52 > 5.25 > 5.052 > 5.025. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 5.025 and 5.025 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 5.025 into 5.026. The updated ascending values become 5.026 < 5.052 < 5.25 < 5.52 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

17. Order four decimals near 7 using thousandths

Unseen Primary 4 number-card problem: arrange 7.103, 7.13, 7.301, 7.31 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 7; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 7.103, 7.130, 7.301, 7.310. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 7.9 and 7.09 place the nine in different columns.

The checked ascending order is 7.103 < 7.13 < 7.301 < 7.31. The first two values are 7.103 and 7.130, separated by 27 thousandths, or 0.027. The largest minus the smallest is 0.207 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 7 and 8. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 7.103 before 7.310 because 103 thousandths are less than 310 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 7.31 > 7.301 > 7.13 > 7.103. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 7.103 and 7.103 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 7.103 into 7.104. The updated ascending values become 7.104 < 7.13 < 7.301 < 7.31 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

18. Order four decimals near 1 using thousandths

Unseen Primary 4 number-card problem: arrange 1.408, 1.48, 1.804, 1.84 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 1; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 1.408, 1.480, 1.804, 1.840. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 1.9 and 1.09 place the nine in different columns.

The checked ascending order is 1.408 < 1.48 < 1.804 < 1.84. The first two values are 1.408 and 1.480, separated by 72 thousandths, or 0.072. The largest minus the smallest is 0.432 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 1 and 2. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 1.408 before 1.840 because 408 thousandths are less than 840 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 1.84 > 1.804 > 1.48 > 1.408. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 1.408 and 1.408 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 1.408 into 1.409. The updated ascending values become 1.409 < 1.48 < 1.804 < 1.84 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

19. Order four decimals near 9 using thousandths

Unseen Primary 4 number-card problem: arrange 9.029, 9.092, 9.29, 9.92 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 9; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 9.029, 9.092, 9.290, 9.920. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 9.9 and 9.09 place the nine in different columns.

The checked ascending order is 9.029 < 9.092 < 9.29 < 9.92. The first two values are 9.029 and 9.092, separated by 63 thousandths, or 0.063. The largest minus the smallest is 0.891 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 9 and 10. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 9.029 before 9.920 because 29 thousandths are less than 920 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 9.92 > 9.29 > 9.092 > 9.029. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 9.029 and 9.029 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 9.029 into 9.030. The updated ascending values become 9.03 < 9.092 < 9.29 < 9.92 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

20. Order four decimals near 4 using thousandths

Unseen Primary 4 number-card problem: arrange 4.123, 4.132, 4.213, 4.231 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 4; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 4.123, 4.132, 4.213, 4.231. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 4.9 and 4.09 place the nine in different columns.

The checked ascending order is 4.123 < 4.132 < 4.213 < 4.231. The first two values are 4.123 and 4.132, separated by 9 thousandths, or 0.009. The largest minus the smallest is 0.108 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 4 and 5. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 4.123 before 4.231 because 123 thousandths are less than 231 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 4.231 > 4.213 > 4.132 > 4.123. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 4.123 and 4.123 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 4.123 into 4.124. The updated ascending values become 4.124 < 4.132 < 4.213 < 4.231 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

21. Order four decimals near 3 using thousandths

Unseen Primary 4 number-card problem: arrange 3.106, 3.16, 3.601, 3.61 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 3; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 3.106, 3.160, 3.601, 3.610. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 3.9 and 3.09 place the nine in different columns.

The checked ascending order is 3.106 < 3.16 < 3.601 < 3.61. The first two values are 3.106 and 3.160, separated by 54 thousandths, or 0.054. The largest minus the smallest is 0.504 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 3 and 4. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 3.106 before 3.610 because 106 thousandths are less than 610 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 3.61 > 3.601 > 3.16 > 3.106. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 3.106 and 3.106 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 3.106 into 3.107. The updated ascending values become 3.107 < 3.16 < 3.601 < 3.61 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

22. Order four decimals near 6 using thousandths

Unseen Primary 4 number-card problem: arrange 6.039, 6.093, 6.39, 6.93 from smallest to largest. These are decimal numbers, not currency amounts, heights of local houses or dates. The four values all have whole-number part 6; therefore the decision must come from their tenths, hundredths and thousandths. Ask the learner to give an independent first order before showing a place-value chart or announcing which printed decimal has more digits.

Make each card display exactly three decimal places without changing its value: 6.039, 6.093, 6.390, 6.930. For example a trailing zero contributes zero thousandths; adding it after a decimal’s existing digits preserves value. Compare the tenths columns first, then the hundredths for any tie, then the thousandths for any remaining tie. Do not read the printed fractional digits as separate whole numbers, because 6.9 and 6.09 place the nine in different columns.

The checked ascending order is 6.039 < 6.093 < 6.39 < 6.93. The first two values are 6.039 and 6.093, separated by 54 thousandths, or 0.054. The largest minus the smallest is 0.891 in decimal units. These differences provide secondary arithmetic checks, not new answers to an instruction that only asks for ordering.

Independent number-line interpretation: place the four cards between 6 and 7. The smallest must sit farthest left and the greatest farthest right. A chart with thousandth intervals would position 6.039 before 6.930 because 39 thousandths are less than 930 thousandths. A rough sketch should preserve that order even if it cannot draw every one-thousandth interval accurately. Turning the paper or changing the card order does not change the mathematical inequality.

Reverse-order check: the descending list is 6.93 > 6.39 > 6.093 > 6.039. It must contain precisely the same four original quantities. A pupil who produces a fifth distinct value while padding zeroes has changed a number rather than rewritten it. The expressions 6.039 and 6.039 are exactly equal where their only difference is omitted trailing zeroes, but an interior zero cannot simply be removed without changing place value.

Changed-condition transfer: increase only the first card by one thousandth, turning 6.039 into 6.040. The updated ascending values become 6.04 < 6.093 < 6.39 < 6.93 (unless equality arises, in which case an equal sign should replace any strict comparison). The child should decide independently whether the changed card moves relative to the other three rather than assuming its position must change after every tiny increase. Record the first attempt, decisive column, smallest hint and a delayed new ordering exercise.

Parent questions about Primary 4 Mathematics tuition near Li Hwan Walk

What is the correct order of 4.09, 4.099, 4.9 and 4.909?

Ascending order is 4.09, 4.099, 4.9, 4.909. Write them as 4.090, 4.099, 4.900 and 4.909 to compare place values.

Is 4.9 the same value as 4.900?

Yes. Adding trailing zeros after the final nonzero fractional digit does not change a decimal’s value.

Is 4.09 equal to 4.9?

No. Nine hundredths are smaller than nine tenths; the position of the digit nine matters.

Are three-decimal-place comparisons included in Primary 4 Mathematics?

Yes. The updated MOE Primary 4 syllabus covers decimal notation, place values and ordering decimals up to three decimal places.

Why shouldn’t we round the cards before ordering?

Rounding can make different exact values appear equal, so first compare the original digits at the stated place values.

What proves a pupil has learnt the comparison method?

An independent order of new cards, a left-to-right place-value explanation and recognition of equal trailing-zero forms.

Check the actual teaching venue before choosing a weekday or weekend

The Urban Redevelopment Authority lists Li Hwan Walk among the residential streets in the Serangoon planning area. The street name gives local context for families; it does not establish an eduKate classroom at any house, the street itself, or Lorong Chuan MRT. A parent–student consultation should confirm the current class location, fees, suitable three-pupil group, actual available day and full door-to-door travel.

The 2021 MOE Primary Mathematics syllabus, updated October 2025, provides the official level scope. The eduKate Mathematics learning hub connects this lesson with other topics. The Clementi small-group tuition reference illustrates the existing three-pupil approach and a teaching site near Sixth Avenue MRT; it should not be mistaken for proof of a Li Hwan Walk branch.

For another worked Mathematics topic at this same level, read Primary 4 Mathematics Tuition | Li Hwan Close. Select a weekly session that preserves schoolwork, meals, sleep, ordinary family responsibilities and a short independent review after a delay. The goal is to explain a corrected mathematical decision, not merely add worksheet volume.

Continue through Li Hwan Walk Primary Mathematics guides

Each companion level presents a separate MOE-aligned Mathematics skill, original worked examples, first-error diagnostics and new independent review questions. These learning guides serve families in the neighbourhood without implying separate tuition premises at a Li Hwan Walk address.

• Primary 1: Read one-to-one picture graphs
• Primary 2: Compare lengths measured in metres
• Primary 3: Two-step money budgets

For a different worked concept at the same level, read Primary 4 Mathematics Tuition | Li Hwan Close. Continue to the eduKate Mathematics learning hub for related pathways. Verify actual three-pupil group availability, teaching venue, fees and class timing directly.