SPRING TERM 2

Decimals & Percentages

Decimals up to 3 decimal places - In Year 4, children represented tenths and hundredths as decimals and fractions. By the end of this small step, children will be more familiar with numbers with up to 3 decimal places, with thousandths being introduced later in the unit.

Children make decimal numbers using place value counters in a place value chart and read and write the numbers, as well as working out the value of each digit in the number. They also explore partitioning decimal numbers in a variety of ways.

Percentages - In this small step, children are introduced to percentages for the first time. Children learn that “per cent” relates to “number of parts per 100”. If the whole is split into 100 equal parts, then each part is worth 1%.

Hundred squares and 100-piece bead strings or Rekenreks are useful representations for exploring this concept. This idea can also be linked to previous learning by comparing to hundredths being 1 part out of a whole that is split into 100 equal parts; this will be covered in greater detail in the following steps.

Using bar models, the learning extends to 1 whole being split into 10 equal parts, allowing children to explore multiples of 10%. Children then estimate 5% on a bar model split into 10 equal parts by splitting a section in half, for example 35% is three full sections and half of the next section.

SPRING TERM 1

Multiplication & Division

Multiplying up to 4 digits by 1 digit -  This small step builds on this learning and extends the formal written method for short multiplication to multiplying 4-digit numbers by a 1-digit number. Place value counters in place value charts are used to model the structure of the formal method, enabling children to gain a greater understanding of the abstract procedure. Children continue to use counters to exchange groups of 10 ones for 1 ten and this is extended to include exchanging 10 tens for 1 hundred, 10 hundreds for 1 thousand and 10 thousands for 1 ten-thousand. Children can use their knowledge of rounding and multiplying by multiples of 10 to find estimates to the answers, as a check that their calculated answers are sensible.

Multiplying 2 digits by 2 digits - In this small step, children build on their learning of multiplying by a 1-digit number and begin to multiply by a 2-digit number. Children use the area model to multiply a 2-digit number by another 2-digit number before moving on to the formal written method in the next step. Linking the use of the area model to children’s prior knowledge of arrays helps children to understand the model. 

Multiplying 3 & 4 digits by 2 digits - In this small step, children build on their understanding from the previous two steps to multiply a 4-digit number by a 2-digit number. Children need to be confident with multiplying 2-digit numbers by both 2- and 3-digit numbers before moving on to this step. An area model using place value counters could potentially be useful to support children who need it, but the emphasis should be on using the formal written method. As with the previous steps, children need to understand the role of zero in the ones column when multiplying by the tens. The main focus of this small step is for children to practise completing multiplications of this sort before moving on to solve problems in the next step.

Short Division - Building on informal methods used in Years 3 and 4, this small step introduces children to the formal written method of short division. The formal calculation is shown alongside familiar models, in particular part-whole models, place value counters and place value charts. In this way, the structure of short division becomes clear, enabling children to see the relationship between the model and the formal written method. First, children use the formal method to divide a 2-digit number by a 1-digit number, initially without an exchange and then with an exchange. They then divide a 3-digit number by a 1-digit number, again without and then with an exchange.

Division with remainders - In previous years, children have looked at division with remainders informally. In this small step, they move on to formal calculations that result in a remainder. The formal written method for short division continues to be used alongside familiar models. Children use place value charts and counters so that they associate the remainder with the amount “left over”. The progression of examples is carefully chosen to focus children’s attention on the link between the remainder and the number being divided by. They should generalise that a remainder must be less than the number being divided by. Remainders are represented in the calculation as r1, r2 and so on.

AUTUMN TERM 2

Fractions

Finding equivalent fractions - Children continue to use a variety of representations, including fractions of shapes, number lines and parts of a fraction wall as well as the abstract form, to understand the relationships learnt in from Year 4. They complement this conceptual understanding by using multiplication and division facts to find missing numerators or denominators when working in the abstract.

Converting Fractions (mixed number/improper) - Children use objects and diagrams to make wholes to support converting improper fractions into mixed numbers. Once they are confident with this as a concept, they move on to a more abstract approach using division and remainders.

Adding and subtracting fractions - In this small step, children add and subtract fractions with the same denominator. For adding, this will include adding three or more fractions as well as pairs of fractions.

AUTUMN TERM 1

Place Value

Roman Numerals - Children explore further the similarities and differences between the Roman number system and our number system, learning that the Roman system does not have a zero and does not use placeholders.

Numbers to 10,000, 100,000 & 1,000,000 - A variety of pictorial and concrete representations are used, including base 10, place value counters, place value charts and part-whole models. In particular, the ability to use place value charts needs to be secure, as this is the main representation used in the coming steps where children learn about 5- and 6-digit numbers.

Addition & Subtraction

Addition - Children recap and build on their learning from previous years to mentally calculate sums and differences using partitioning. They use their knowledge of number bonds and place value to add and subtract multiples of powers of 10. Children unitise to help them complete a calculation. For example, if they know that 3 + 5 = 8, then 3 thousand + 5 thousand = 8 thousand and 3,000 + 5,000 = 8,000.

Subtraction - Children revisit the use of the column method for subtraction and learn to apply this method to numbers with more than four digits.children revisit the use of the column method for subtraction and learn to apply this method to numbers with more than four digits.

Multiplication & Division

Multiplication & Division - Children will look to identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers. Children are able to solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes