Maths Calculation Support
Maths Calculation Advice from Mr Hodgins, Dobwalls Maths Co-ordinator
As you are all undoubtedly doing all you can to support the maths learning of your child during lock down, I thought it would be useful to share some links to Maths videos that I have found on the Internet. The aim of sharing these videos is to give you an idea of how we teach and model calculation skills to your children at Dobwalls which may be a valuable reference point for you over the coming weeks; particularly when your children are completing their daily arithmetic questions.
The videos cover basic concepts and teaching strategies for the four operations (addition, subtraction, multiplication and division) which build on the skills and strategies in lower KS1 all the way up to higher KS2. We approach the teaching of these skills in three steps:
Concrete is the 'doing' stage. During this stage, students use concrete (physical) objects to model problems. Don't panic if you don't have the same equipment available at home - get creative! Use coins, counters, Lego bricks, straws or even spaghetti to help build strong visual representations of a problem.
Pictorial is the 'seeing' stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical objects they have handled and the abstract pictures, diagrams or models that represent the objects from the problem. Here it is helpful to see the concrete objects next to the pictures before moving solely onto a pictorial approach.
Abstract is the 'symbolic' stage, where children use abstract symbols to model problems. In simple terms this means using formal written methods. Students will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem - this is fundamental! Don't feel you have to rush your child onto this stage. They should only use the more formal methods of calculation when they are 'masters' of using objects and drawing pictures.
We understand that taking on the role of maths teacher could be quite a daunting task for some parents, given the methods we use are usually quite different to how we were all taught Maths at school. However, your child will be so used to the approaches shown in the videos and using equipment to support their learning that the chances are it's already second nature to them!
White Rose Maths:
In addition to this, I would recommend the free White Rose online maths lessons: Home Learning. The White Rose Maths Team have prepared a series of maths lessons for your child’s year group that link to the learning they have been carrying out in school.
- Introduction to addition at KS1 - building knowledge from a 100 square to a numberline and onto an empty numberline
(example questions: 7+5, 12+3, 29+18)
- Introduction to addition at KS2 - empty numberline to formal written column method (example questions: 345+21, 543+159, 6790+5281)
- Using concrete resources - (base 10 apparatus) to build towards column addition (including 'carrying'/ regrouping)
(example question: 345+284 - 'regrouping' needed)
- Using concrete resources - (place value counters) and pictorial methods to build towards column addition (including 'carrying'/ regrouping)
(example question: 550+98 - 'regrouping' needed)
- Empty numberline strategies for addition
(example questions: 32+24 - 'jump in 10s' by jumping forward 10, 10 and then 4; 98+34 - 'hit the tens because 98 is so close to 100; 62+39 - 'over-jump' 40 and take away 1)
- Introduction to subtraction at KS1 - building knowledge from a 100 square to a numberline and onto an empty numberline
(example questions: 10-4, 19-7, 45-23)
- Introduction to subtraction at KS2 - expanded to compact method including 'decomposition'/ exchanging
(example questions: 456-35, 218-173, 4525-2701)
- Using concrete resources - (base 10 apparatus) and pictorial methods to build towards column subtraction (without 'decomposition'/ exchanging)
(example questions: 457-35 - no 'exchanging' needed)
- Using concrete resources - (place value counters) and pictorial methods to build towards column subtraction (with and without 'decomposition'/ exchanging)
(example questions: 334-72 - 'exchanging' needed)
- Empty numberline strategies for subtraction
(example questions: 73-23 - 'jump in 10s' by jumping back 10, 10 and then 3; 52-17- 'hit the tens because 52 is close to 50; 43-19 - 'over-jump' by taking away 20 and adding on 1)
- 'Counting on' empty numberline strategies for subtraction
(example questions: 64-27 - find the difference by counting on from 27 until you get to 64 because 27+?=64 is the same as 64-27=?)
- Introduction to multiplication at KS1
(example questions: 3x4 = 3+3+3+3 and 4+4+4)
- Multiplication at KS1 - rows and columns in arrays to build concept of multiplication
(example questions: 5x6, 10x9, 8x6)
- Multiplication in KS2 - drawing arrays in the grid method to expanded multiplication method
(example questions: 124x6, 345x9, 291x3)
- Multiplication in KS2 - expanded multiplication to compact multiplication method
(example questions: 456x15, 918x23)
- Multiplication in KS2 - compact multiplication method when multiplying by a two-digit number
(example questions: 562x45, 3497x82)
- Difference between 'grouping' and 'sharing' for division
(example questions: 10÷2 - 10 sweets 'shared' between 2 friends is 5 or how many 'groups' of 2 sweets make 10)
- Using an empty numberline for 'grouping'
(example questions: 12÷4 - jumping 'groups' of 4 from 0 until you make 12)
- Using arrays to build concept of division
(example questions: 20÷5 - can be built in an array as 5 groups of 4 or 4 groups of 5 by knowing commutative relationship between 4, 5 and 20)
- Short division bus stop method - using concrete resources
(example questions: 55÷5, 93÷3)
- Short division bus stop method - using concrete resources to build to pictorial methods - up to 3 digit numbers
(example questions: 84÷6, 392÷7 - no remainders)
- Short division bus stop method (abstract)
(example questions: 623÷9, 785÷4 - with remainders)
- Short division bus stop method - turning remainders into decimals (Year 6)
(example questions: 723÷4 - remainder is 3 so can be changed to 3/4 or 0.75)
- 'Chunking' method for division
(example questions: 442÷26, 1728÷16 - normally used when dividing by a 2-digit number or as an additional strategy alongside bus stop method)