# Four Operation Ladders – Guide for Parents

At Highfield, we believe in the importance of equipping children with a variety of methods for carrying out mental and written calculations.  This booklet contains information about the progression of methods we teach children to use when writing down their methods for addition, subtraction, multiplication and division calculations. The methods taught at Highfield have been chosen not only to help your child get the right answers, but also because we believe them to be the best ones to help develop their mathematical understanding.  Children are expected to progress up each of the four ‘ladders’ during their time at school, so that they are able to quickly and confidently answer number questions at the expected level by the end of Year 6.

Children are given regular practice answering questions in all four operations, and are given the chance to move up on the next ‘rung’ of a ladder when they show they are very confident on the rung they are currently on. There is not usually a fixed year group that a certain method is taught; your child will be introduced to a new method when their teacher believes them to be ready.

Your child should be aware of the rung they are on for each of the four operations. When your child is doing any maths work outside of school that would require the use of a written method, we ask that you support them by using the method that they have been taught. Worked examples for every rung are given in this booklet, to show you how the questions should be solved.

## ++ Addition ++

11.  I can add any numbers using the standard column method.
10. I can add a mixture of whole and decimal numbers using the standard column method.
9.  I can add decimal numbers using the standard column method.
8.  I can add HTU + HTU using the standard column method.
7.  I can add HTU + HTU numbers above 500 using the expanded column method.
6.  I can add HTU + HTU numbers below 500 using the expanded column method.
5.  I can add TU + TU using the expanded column method.
4.  I can add TU numbers above 50 on a number line, jumping in tens, then units.
3.  I can add TU numbers under 50 on a number line, jumping in tens, then units.
2.  I can add a teen number to a number under 50 on a number line, jumping in tens, then units.
1.  I can add two single-digit numbers on a number line.

View worked examples of Addition

## — Subtraction —

9.  I can use decomposition to subtract numbers higher than 1000.
8.  I can use decomposition to subtract decimals.
7.  I can use decomposition to subtract HTU numbers.
6.  I can use expanded decomposition to subtract HTU numbers, including borrowing across 0.
5.  I can use expanded decomposition to subtract HTU numbers (borrowing needed, but not across 0).
4.  I can use expanded decomposition to subtract HTU numbers (no borrowing needed).
3.  I can find the difference between HTU numbers, using a number line.
2.  I can find the difference between TU numbers above 50, counting on from the smallest number using a number line
1.  I can find the difference between numbers under 50, counting on from the smallest number using a number line

View worked examples of Subtraction

## xx Multiplication xx

11.  I can use a compact vertical method to multiply.
10.  I can use an expanded vertical method to multiply.
9.  I can use grid method to multiply by numbers with 2 decimal places.
8.  I can use grid method to multiply by numbers with 1 decimal place.
7.  I can use grid method to work out TU x TU.
6.  I can use grid method to work out HTU x U.
5.  I can use grid method to work out TU x U.
4.  I can use grid method to work out teen numbers x U.
3.  I can partition to work out teen numbers x U.
2.  I can use repeated addition on a number line to work out U x U questions.
1.  I can draw pictures to work out U x U questions.

View worked examples of Multiplication

## ÷÷ Division ÷÷

10.  I can use the compact division method to divide.
9.  I can use chunking to divide with decimals.
8.  I can give remainders as fractions.
7.  I can use chunking to work out THTU ÷ TU.
6.  I can use chunking to work out HTU ÷ U.
5.  I can use chunking to work out TU ÷ U.
4.  I can use repeated subtraction to work out TU ÷ U, with remainders.
3.  I can use repeated subtraction to work out TU ÷ U on an empty number line.
2.  I can use repeated subtraction to work out TU ÷ U on a structured number line.
1.  I can share counters into equal groups to divide.

View worked examples of Division