Decimals and Negative Numbers Help: Why Your Child Keeps Getting Stuck (And What Actually Works)

Your child can add 47 and 26 in their head without pausing. Put 4.7 plus 0.26 in front of them and the answer comes back as 7.3, or 0.73, or a number with no obvious source.

I'm Aadam, and I've taught decimals to hundreds of 11+ and GCSE students at SHLC. Hardly any of them had an addition problem. They had a place value problem that looked like one.

The real problem isn't the arithmetic

Watch a child work through a page of decimal questions and their arithmetic is right while the answers are wrong. Three mistakes cause most of it.

Lining up the digits instead of the decimal points. Write 4.7 plus 0.26 with the right hand edges level and you have answered a different question. Line up the points and put a zero in the empty column, and the same child gets it right first time.

Assuming longer means bigger. Ask which is larger, 0.45 or 0.7, and a lot of children say 0.45, because 45 is bigger than 7. They are comparing the digits instead of the columns those digits sit in.

Reading negatives as if the minus sign is decoration. A child who says minus 3 is smaller than minus 7 has understood the numbers and ignored the sign.

All three are gaps in what each column is worth. A worksheet of decimal sums leaves them open, because it never asks your child what the columns mean.

Why worksheets alone don't fix it

A decimals worksheet hands your child twenty questions and an answer sheet. If they line the digits up under each other, they get most of the page wrong, mark it, and take away the message that decimals are hard.

They needed someone to stop them at question one and say: write the decimal points underneath each other before any digit.

Decimals and negatives also look like two separate chapters when they are one idea twice over. Both ask where a number sits on a line. A child who learns them as two unrelated sets of rules ends up with twice as many rules to forget.

The decimal and negative number skills that trip children up, in order

Each one leans on the one before it. A gap near the top shows up as confusion much further down, which is why jumping straight to long multiplication with decimals rarely helps.

1. Reading what each column is worth. Tenths, hundredths and thousandths, said out loud. Everything else in the topic rests on it.

2. Comparing and ordering decimals of different lengths. 0.4, 0.35 and 0.409 put in order, by filling the short ones out with zeros first so every number has the same number of columns.

3. Rounding to a given number of decimal places. Including the case where the digit rounds up to 10 and carries into the column on its left, which is where your child loses most of the marks here.

4. Significant figures and estimating. Rounding each number to one significant figure to get a rough answer before doing the real one.

5. Multiplying and dividing by 10, 100 and 1,000. The decimal point stays exactly where it is and the digits move columns. Children taught to move the point get it right for multiplying and wrong for dividing.

6. Adding and subtracting decimals. Points lined up, empty columns filled with zeros, then it is ordinary column addition.

7. Multiplying decimals. Do the whole number multiplication, then count how many decimal places went in and put the same number back into the answer.

8. Dividing decimals. Make the number you are dividing by whole first by multiplying both numbers by 10 or 100, then divide normally.

9. Negative numbers on a line. Ordering, comparing and finding the difference between two temperatures that sit either side of zero.

10. Adding and subtracting negatives. Including what happens when two signs meet, taught as a movement along the line your child can point at.

What actually closes the gap

Three things, in the order I teach them.

Fix the setting out first. Decimal points underneath each other, every time, even on questions your child finds easy. Fill the gaps with zeros so every number has the same number of columns. Give it a few days and one whole family of mistakes stops appearing.

Make the number line real. Temperature is the easiest way in, because a child already knows that minus 7 is colder than minus 3. Once the line is real, a negative number is a position your child can point to, and the difference between two temperatures is the gap between two points.

Estimate before you calculate. One line of rough working, with every number rounded to one significant figure, catches the answer that is ten times too big. It gains more marks than anything else in this topic, because it catches the mistake your child has already made.

The lessons we built to fix this

Our Decimals, Estimation and Negative Numbers Bundle is built in exactly that order. Seven interactive lessons, 43 units, 722 questions.

Comparing and Ordering Decimals starts with what each column is worth, then ordering decimals of different lengths and placing them on a line.

Rounding Decimals to Decimal Places covers rounding to one, two and three decimal places, including the carrying case.

Significant Figures and Estimation teaches significant figures and then uses them to estimate answers and check them.

Multiplying and Dividing by Powers of 10 shows the digits moving columns while the point stays still, in both directions.

Adding and Subtracting Decimals drills the setting out until it is automatic, then moves to money and measures.

Multiplying and Dividing Decimals covers both methods and the checks that catch a misplaced point.

Negative Numbers runs from ordering and temperature differences through to adding and subtracting negatives.

Each lesson opens with a worked example your child clicks through one line at a time, so the setting out arrives before the practice. Answers stay hidden until they click, so a number has to be committed to before it can be checked. Questions climb from a gentle tier to a hard one, so a shaky child starts where they are.

Decimals and negatives run through every other topic on the paper, so if more than one area needs work, this bundle also sits inside The Complete 11+ Maths Course, all 80 lessons in teaching order.

What to do this week

You can test this at the kitchen table tonight.

Write these three numbers down and ask your child to put them in order, smallest first: 0.4, 0.35, 0.409. If they say 0.35 is smallest, they are comparing digits rather than columns, and that is a week of work to put right.

Then ask them this: what is 4.7 plus 0.26? If they set the sum out with the right hand edges level rather than the points level, start there before anything else.

Our free decimals practice page has more questions you can use tonight at no cost, and each one names the lesson it comes from, so you can see where the work is needed.

If you would rather have the whole sequence taught in order, the Decimals, Estimation and Negative Numbers Bundle covers it end to end, and single lessons are there if only one topic is broken. If you would rather talk it through with a teacher first, book a free consultation.

Aadam, SHLC Tutors