Fractions & Decimals

What this covers

• Reading a fraction as a number: what the denominator counts, what the numerator counts, and where 3/4 or 5/3 sits between whole numbers on a number line
• Building equivalent fractions by multiplying or dividing numerator and denominator by the same number, and simplifying to lowest terms
• Comparing and ordering fractions using common denominators, benchmarks like 1/2 and 1, and same-numerator reasoning
• Adding and subtracting fractions and mixed numbers with like denominators, then unlike denominators using a common denominator
• Multiplying a fraction by a whole number and interpreting it as repeated addition (4 x 2/3 as eight thirds)
• Writing tenths, hundredths, and thousandths as decimals and fractions, comparing decimals by place value, and adding and subtracting decimals with aligned points

Where learners get stuck

Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4

Three years of whole-number work has taught that bigger digits mean bigger amounts. The denominator does the opposite: it tells how many pieces one whole was split into, so more pieces means each one is smaller. The tutor makes the learner say the sentence "eight pieces means smaller pieces" out loud until it stops feeling backwards.

Adding across: 1/2 + 1/3 = 2/5

Adding numerators and denominators separately mirrors how whole-number addition works and gives an answer fast. Learners usually cannot say what the denominator means at that moment; once they can name it as the size of the piece, adding halves to thirds obviously needs same-size pieces first.

Believing 0.45 is greater than 0.5 because it has more digits

Longer numbers are bigger for whole numbers, and "point four five" sounds like forty-five. Reading it as "forty-five hundredths" against "fifty hundredths" fixes it, which is why the tutor insists on place-value names when reading decimals aloud.

What a session looks like

A session usually opens with two or three quick spoken checks ("which is bigger, 2/3 or 3/4, and how do you know?") to find where the learner's reasoning breaks. The tutor then works one idea at a time, asking the learner to explain each step rather than just give an answer, and using shared written problems for the arithmetic. Common tools are number lines, splitting the same whole two different ways to show equivalence, and money or measurement contexts for decimals. Sessions end with the learner restating the rule in their own words and a couple of problems to try independently.

Helpful to know first

• Fluent addition and subtraction within 100 and comfort with multiplication facts up to 10 x 10
• Understanding place value for whole numbers, including what the tens and hundreds columns mean
• Ability to divide a shape or a set of objects into equal groups and recognise when the parts are not equal

Questions

Why does my 4th grader keep adding the denominators?

Because it copies the whole-number rule that works everywhere else. The fix is not more drill on the procedure but getting the learner to say what the bottom number means before every problem. Once they describe 1/2 and 1/3 as different-sized pieces, they see why the pieces must be made the same size first.

When should a child learn decimals versus fractions?

They overlap. Most curricula introduce fractions in grade 3, tenths and hundredths as decimals in grade 4, and decimal arithmetic through thousandths in grade 5. It helps to treat 0.7 and 7/10 as two spellings of the same number from the start rather than as separate topics.

My child can do the steps but has no idea what the answer means. Is that a problem?

It becomes one in grade 5 and 6, when fraction multiplication and division stop matching intuition. Sessions push the learner to estimate first ("is 7/8 + 3/4 more or less than 2?") so an answer like 10/12 gets caught as wrong before the working is even checked.

Can voice tutoring work for something this visual?

Fraction work depends heavily on diagrams, so written problems and number lines are shared during the session. The spoken part carries the explaining: the learner has to justify comparisons and describe what each number represents, which is exactly the part that silent worksheet practice skips.