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- Know and use mental addition and subtraction strategies for integers
- Know and use mental multiplication and division strategies for integers
- Know and use mental arithmetic strategies for decimals
- Know and use mental arithmetic strategies for fractions
- Use factors to simplify calculations
- Use estimation as a method for checking mental calculations
- Use known number facts to derive other facts
- Use known algebraic facts to derive other facts
- Know when to use a mental strategy, formal written method or a calculator

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Estimating Angles Estimate the size of the given acute angles in degrees.
- Times Tables A collection of activities to help you learn your times tables in only 5 days.
- Mental Strategies Practise your mental arithmetic skills and learn some new strategies with this self marking exercise.
- Rounding Ten Round the numbers to the nearest whole number or the given power of ten.
- Beat The Clock It is a race against the clock to answer 30 mental arithmetic questions. There are nine levels to choose from.
- Arithmagons Find the missing numbers in these triangular, self-checking puzzles and discover the wonders of these fascinating structures.
- Just In Time Every 10 seconds a new calculation appears on the screen: A dynamic visual aid.
- Grid Arithmetic Fill in a multiplication grid with the answers to simple multiplication and division questions.
- Rounding Video A reminder of how to round numbers to significant figures, decimal places and to the nearest power of ten.
- Rounding DP A self marking exercise requiring students to round numbers to a given number of decimal places.
- Rounding SF A self marking exercise requiring students to round numbers to a given number of significant figures.
- Eleven In Your Head Multiply numbers by eleven in your head.
- Estimating Estimation is a very important skill. Use this activity to practise and improve your skills.
- Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
- Rounding Snap If the last card put down equals the previous card to the nearest whole number then all players race to shout SNAP!
- One Minute Maths A challenge to mentally add numbers together without making the classic place value mistakes.
- Partial Pyramids Calculate the missing numbers in these partly completed pyramid puzzles.
- Estimating Percentages Estimate the percentages represented by the diagrams.
- If Then What? Deduce multiplication and division results from a related calculation.
- Pyramid Puzzle Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?
- Quick Can you multiply a number by 1001 in your head? This exercise provides practice in this and other similar challenges.
- Estimation Golf Play a round of golf using your estimation skills rather than golf clubs.

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Estimating The ability to estimate values is an often overlooked part of Mathematics. Estimating lengths, weights, time, angles and solutions to problems should be practised regularly. Pupils should make sensible estimates of a range of measures in relation to everyday situations. A basic ability to estimate quantities without counting, like when choosing a checkout line at the supermarket, can be called a person’s innate ‘number sense’. Practising this kind of estimating may actually improve a pupil’s ability in other areas of mathematics. This is one of the findings of research published in Psychological Science, a journal of the Association for Psychological Science. Practising estimation can be a lot of fun when presented as a game, challenge or group activity and provides the opportunity for the teacher to introduce variety in the mathematics classroom.
- Mental Methods Though using pencil and paper are as useful as having up-to-date technology skills, there is no substitute for strategic mental methods for working out calculations and solving problems. The activities in this topic are designed to improve pupils' abilities to use their brains. Calculating 'in your head' can be a difficult task. If you cannot remember what you have worked out or simply do not know how to solve a problem then it can be very challenging and frustrating. It is important to learn and practise mental arithmetic and using mathematical patterns, you can dramatically improve the speed and accuracy of your mental mathematics. See also the Arithmetic topic and our Number Skills Inventory.
- Rounding The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of pupils. See also the "Approximating" Starters. Once the principles of rounding have been understood, a fun way to practise the skills is to play "Rounding Snap".

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

Arrange the digits 1 to 6 to make a three digit number divided by a two digit number giving a one digit answer.

This activity requires students to memorise fifteen numbers in a three by five grid.

Start with 100. Halve it to get 50. Halve that to get 25. Continue as far as possible.

Move the numbered cards to form five 2 digit numbers which are all multiples of three.

How close can you get to the target by making a calculation from the five numbers given?

This is the Maths version of the traditional memory game. Memorise 10 mathematical facts then recall them as they disappear from view.

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.