# Core 4 Maths — C4.6 study guide

## Your daily routine

Choose a day and work through its four lesson areas in order. Read each instruction before calculating. Use paper for fraction shading, number lines and written algorithms. Type the full number name for the number-in-words question. Enter each labelled answer separately, then use the local checker. If you need help, study the worked example: it uses different numbers so you can practise the method before returning to your own question.

## Daily focus

| Day | Counting and fraction focus | Other learning |
| --- | --- | --- |
| Monday | Halves and counting in twos | Six-digit place value, decimal order, written addition and subtraction, area models and division |
| Tuesday | Quarters and counting in fours | Read and write large numbers, compare decimals and connect division facts |
| Wednesday | Eighths and counting in eights | Read number lines carefully, regroup in arithmetic and use partial products |
| Thursday | Thirds and counting in threes | Explain complete thousands, track place-value digits and check inverse operations |
| Friday | Fifths and counting in fives | Bring together fraction models, number words, decimal positions and written arithmetic |

## Counting and fraction models

A denominator tells how many equal parts make one whole. Count by adding an equal part each time. Keep fraction bars the same size. Shade the numerator’s number of small parts, continuing into another bar when needed. In the whole/mixed row, an X means there is no whole or mixed number to write. Complete only the requested cells; the first fraction is a given.

For a fraction of a quantity, divide into equal groups first, then take the required number of groups. An improper fraction may require more than a whole quantity.

## Place value and number lines

Split a six-digit number into its thousands group and its remaining group. Read both in order. Use the word-group scaffold to plan the name, then type the full number in English words in the single answer field. The checker directly checks the number name and spelling, not a substitute digit answer. Optional grammatical “and”, commas, capital letters and hyphens are tolerated; digits are not accepted for this question. The read-aloud Yes/No question records your reflection rather than assessing correctness.

Complete thousands means complete groups across the entire number, not just the digit in the thousands column. To describe a digit’s value, use the digit multiplied by the value of its place.

Compare decimals by aligning their decimal points and looking from left to right. A trailing zero does not change a value. Check the direction of each number line: some decrease towards the right. For the online fields, calculate each mark’s distance from the left endpoint in number-line units. These are not physical centimetres on your drawing.

## Written addition and subtraction

Align ones below ones, tens below tens and hundreds below hundreds. Work from right to left. Show carrying or regrouping above the columns. Enter a separate answer digit for each requested column; use zero for an unused leading place. Use inverse operations to check missing-number equations.

## Multiplication and division

List positive multiples in order and stop at the specified endpoint. Complete every division-table fact, then decide which dividend parts make the final product: not every table fact must be used in the missing-factor calculation.

When multiplying or dividing by ten, the decimal point stays fixed while the digits change places. Complete each number column in the bottom row, including zeros where needed.

In an area model, split a two-digit number into tens and ones. Multiply each part by the same factor, put the two areas into the addition line and combine them. In short division, work from the left and carry each remainder into the next place. Check a quotient by multiplication.

## Checking your work

Use `a/b` for a fraction and a space for a mixed number, such as `2 1/3`. Follow the requested answer form. Re-read the field label if a value is rejected. The study website works with static lesson data and a browser-local checker; it has no account or online teacher answer service.