This is a collection of work. Click through the chapters to see the full collection or download the attached standards file.

## Percentages

### Teacher's notes

- Given half of a number, finds 100%, 10%, 5%, 50% and 25%.
- Recognises the equivalence of and 25%.

### Next steps

Find other percentages of the given numbers, such as 60% of 80 (by adding his 50% and 10%); 20% of 160.

## Long multiplication

### Teacher's notes

- When modelled in class, he uses the grid method to multiply a two-digit number by a two-digit number.
- Understands place value when multiplying multiples of 10, for example 20 × 30 = 600.

### Next steps

- Investigate other ways to partition 21 and 32, such as (20 and 1) × (20 and 12).
- Use grid method rather than repeated addition when solving problems.

## Decomposition

### Teacher's notes

When modelled in class, he uses a standard written method to subtract a two-digit number from a three-digit number, bridging the hundreds and the tens.

### Next steps

- Use an efficient written method when solving problems.
- Check calculations by using an inverse method.

## Word problems

### Teacher's notes

- Chooses the correct operations to solve problems.
- multiplies a multiple of 10 by a single digit mentally.
- Uses informal methods to subtract and divide.

### Next steps

Solve a wider range of multi-step problems, including those involving measures.

## What the teacher knows about Peter's attainment in Ma2

Peter reads numbers with up to five digits and understands the place value of decimals to two places. He multiplies and divides whole numbers by 10 or 100. He rounds two-digit and three-digit numbers to the nearest 10 and three-digit numbers to the nearest 100, using this to make approximations when calculating. In the context of temperature, Peter reads and explains negative numbers. He recognises approximate proportions of a whole and uses simple fractions and percentages to describe these, for example , 75%, . He is beginning to understand simple equivalence of fractions (with the help of a fraction wall), decimals and percentages, for example = 25%, = 0.1, = , = , and he solves simple ratio problems.

Peter has a quick recall of multiplication facts up to 10 × 10 and uses his knowledge of inverses to derive the associated division facts. He extends this to larger numbers: for example, given 35 × 76 = 2660, he knows 2660 ÷ 76 = 35. He knows whether to round up or down after division in the context of a problem, for example 'There are 53 pages in each chapter and I am on page 127. Which chapter am I reading?' He adds and subtracts two-digit numbers mentally; calculates complements to 1000, for example 1000 - 240; doubles and halves any two-digit number; and uses his tables knowledge and place value to multiply or divide multiples of 10 by a single digit, such as 30 × 7, 180 ÷ 3. Peter knows efficient methods to add and subtract three-digit numbers, including decimals, in the context of money, although he will often revert to an informal method for subtraction when presented with a word problem: for example, he prefers to use a number line. He multiplies and divides three-digit numbers (including decimals in the context of money) by a single digit, using informal methods, although he sometimes lacks security. He is beginning to use a grid method to multiply two-digit numbers together. Peter interprets a calculator display of 4.5 as £4.50.

Peter solves one-step and two-step number problems choosing and using the appropriate operations and knows how to deal with remainders when they occur: for example, given the information that a story starts on page 1 and is 630 pages long, and that Susie is on page 126, Peter works out how many more pages she needs to read to reach the middle of the book. When told that there are 10 equal chapters in the book, he is able to work out which chapter Susie is currently reading. He carries out simple calculations involving negative numbers in context: for example, he knows 18° Celsius is 22° Celsius above -4° Celsius. He uses and interprets coordinates in the first quadrant.

## Summarising Peter's attainment in Ma2

In Ma2 Peter is best described as working at the lower end of level 4. He has a good understanding of place value in whole numbers and decimals to two places, and he multiplies and divides whole numbers by 10 or 100. In solving number problems, he uses a range of mental methods of computation with the four operations, including quick recall of multiplication and related division facts to 10 × 10. Although he knows efficient methods for three-digit addition and subtraction, including decimals in the context of money, he prefers to use informal methods for subtraction. He multiplies and divides three-digit numbers by a single digit using informal methods. He recognises approximate proportions of a whole and uses simple fractions and percentages to describe these, for example 25%, , . He recognises number patterns and multiples. He is beginning to use simple formulae expressed in words and coordinates in the first quadrant.