Numerical Literacy

WHAT IS MENTAL COMPUTATION? • When people hear the term "mental computation" many think of the mental arithmetic problems they did at school. Mental arithmetic focuses on producing correct answers quickly.

• While not neglecting the correctness of the answer, mental computation emphasizes the mental processes used to achieve the answer.

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To develop mental computation in the classroom, teachers can encourage students to explain how they arrived at their answers and to compare their strategies with those of other students.

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Number sense refers to a personal understanding of number concepts, operations, and applications of numbers and operations.

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It includes the ability and inclination to use this understanding in flexible ways to make mathematical judgements and to develop useful strategies for handling numbers and operations.

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Hence, mental computation is closely linked to the development of number sense. Emphasising mental computation supports effective numeracy since mental computation is commonly used for calculations by adults and is the simplest way of doing many calculations.

FOR YOUR INFORMATION : • • Mental computation helps children understand how numbers work, how to make decisions about procedures, and how to create different strategies to solve math problems

• Anghileri (1999) claimed that mental computation was calculating with the head, rather than merely, • in the head, that is, mental computation is calculating using strategies with understanding. • Thus, proficiency in mental computation was not confined to accuracy, but also included flexibility of strategy choice. • Therefore, the factors that influence mental computation consist of those that affect flexibility as well as accuracy.

What is teacher’s role in teaching MC ? • Teacher should supporting their students in order to solve their math problems • This can help them to determine their own solution method and have confidence to do so

The strategies using in MC • • • • • • • • • • • •

Count : Count on by 1 Count back by 1 Separation : Right to left Left to right Aggregation: Right to left Left to right Holistic : Compensation leveling

• • Jump method • Split method

Why MC are Important? • Everyone is faced with situations in daily life where there is a need for quick calculations, often in the absence of paper and pencil and without a calculator. Being able to calculate mentally, and especially to make quick mental estimations, is essential for everyday life • • Mental computation is vital to check the reasonableness of calculator

• Children do not merely absorb information passively but interpret selectively and construct their own meanings from it. Well-taught children will always use their understanding of place value and their number sense to work mentally with numbers. Hence they will devise variations of the algorithms taught at school and sometimes invent their own methods to suit the question.

• • By understanding the invented methods that children use for mental computation, the teacher is better

MC Techniques 1.Count on and Count Back •What - Count up or down by place value. For example, 352 – 3 would be calculated, “352, 351, 350. •When - Use this technique when the number to be added or subtracted is 1, 2, 3; 10, 20, 30; 100, 200, 300; and so on. •How - Begin by saying the larger

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2. Choose Compatible Numbers

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What - Select pairs of compatible numbers (numbers that are easy to computer mentally) to perform the computation.

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When - Use this technique if one or more pairs of numbers can be easily added, subtracted, multiplied, r divided, or if they can produce multiples of 10, 100, or other numbers that make calculations easy.

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How - First look for pairs of numbers that are easy to calculate. Perform these calculations first. Then look for other number combinations that can be

3. Left to Right •What - Break apart the numbers into their place values and perform you work from right to left. •

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When - Use this technique when one of the numbers is a single or when most digit-by-digit computations are simple.

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How - Think about each number in its expanded form. Do the calculations for the largest place values on down to the smallest place values. Now combine your answers to each of the smaller computations.

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Examples : Problem: 52 – 17 =

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• I took 10 from the 52 to give me 42. Then I took away 2 more gives me 40. I have 5 more to take away gives 35. Lawrence • First I took away the 2. Then I took away the 10. Then I took away the other 5. My answer is 35. Denzel

• I started at 17 and added 3 to make 20 and then 30 more makes 50 and I need 2 more to get to 52. My answer is 33 …, 35.Kate • First I take 10 from 50 to get 40. Then I take 7 from 2 to get 5 down. My answer is 35. Dominique

• I took 10 from the 52 to give me 42. Then I took away 2 more gives me 40. I have 5 more to take away gives 35. Lawrence •

-10

-5

-2

35

40

42

52

• First I took away the 2. Then I took away the 10. Then I took away the other 5. My answer is 35. Denzel • • •

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35

40

42

52