# Core 4 Maths — C4.8 study guide

## Your daily routine

Read the instructions, try each question on paper, then enter your own answers and use the local checker. If you are stuck, read the hint or study the separate worked example. Its numbers are different: copy the method, not its answers. Keep written algorithms on paper so you can see your regrouping.

## Daily focus

| Day | Fraction focus | Daily skills |
| --- | --- | --- |
| Monday | Halves and their decimal representations | Eight-digit place value, rounding, expanded form, column algorithms and partitioned operations |
| Tuesday | Quarters and their decimal representations | Equal groups, percentage connections, decimal scaling and an area model |
| Wednesday | Eighths and their decimal representations | Exact counting, fraction conversion, written addition/subtraction and division |
| Thursday | Thirds and recurring decimals | Repeating digits, place-value reasoning, useful division parts and positive multiples |
| Friday | Fifths and their decimal representations | Connect representations and check written operations using inverse operations |

## Counting and fraction conversion

Make equal jumps without changing the denominator or step size. Keep the same position aligned across fraction, whole/mixed and decimal rows. A whole/mixed row may have X cells that are deliberately unused; answer only the listed blanks. The starting value is already supplied in decimal-count questions, so enter the following values through the stated endpoint.

To convert a decimal to a fraction, think about how many equal parts make a whole. Keep the denominator requested in the lesson. Write a single fraction using `a/b`; use a space between the whole-number and fraction parts of a mixed number. Repeating digits must stay exact: the checker uses parentheses around the repeating block. Do not replace a recurring decimal with a rounded estimate.

## Place value

Read large numbers in groups: millions, thousands and ones. A Yes/No read-aloud answer records your reflection; it does not assess how you pronounced the number. When counting complete hundred-thousand groups, consider the entire number rather than just the digit in that place.

For rounding, identify the two neighbouring multiples and compare with their halfway point. For digit value, enter the digit and its place value in separate fields. For expanded form, enter one term per place, from ten millions to ones, including zero for an empty place. Multiplying or dividing by a power of ten changes each digit's place; the decimal point stays fixed in the chart.

## Addition and subtraction

Align ones under ones, tens under tens and so on. Work from right to left. Regroup complete tens when adding, and exchange from the next place when subtracting. Enter one answer digit for each labelled column, including a leading zero if the answer row has more columns than the result needs. Use inverse operations to check missing-number questions.

## Multiplication and division

Calculate every labelled division fact separately. A starting fact helps you calculate a larger part; it is not an additional part of the final total. In an area model, split each factor into tens and ones, calculate all four cells, then add those four products.

Positive-multiple lists begin with the stated positive number, not zero. For division, try partitioning and a written algorithm. Account for any leftover amount exactly, using a fraction, mixed number or exact decimal; check by multiplying back. Enter an exact result for each method.

## Checking and progress

The checker accepts mathematically equivalent numeric values while respecting the requested fraction, mixed or decimal form. Work is stored locally in your browser, so it is not automatically shared across devices. The lessons and checker are static client-side data, not a private answer-key service.