CLASS 10 MATHS NCERT CHAPTER 5 EX-5.1 QN2

      Ncert Solutions For Class 10 Maths Chapter 5 Excersice 5.1                                                       Qn2

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Maths phobia is real. Many of us have heard stories about the lengths  students and adults go to avoid mathematical calculations. But does it mean that they are inherently bad at maths? Educators believe that the fear of the subject can be addressed to a large extent if children are taught to relate maths to real-life examples. On the occasion of National Mathematics Day (December 22), we ask a few experts about how the subject can be made more fun for learners.

Using real-life examplesNeha Agrawal, who is a master teacher at Vedantu and manages the learning platform’s maths channel, says: “The reason many children grow up fearing maths is because there is more emphasis on problem solving than understanding the basics. They are not taught to connect textbook maths to real-life situations. For example, while explaining geometric progression in my class, I showed the kids how the coronavirus multiplies in the population.

Similarly, I talk about the experience of riding a giant wheel while teaching trigonometry. When I show that real life objects work according to principles of mathematics, children are no longer afraid of it. The fear of maths is enforced by people who are scared of maths themselves.”Dr TP Sasikumar, a space scientist who has a PhD in mathematics, says: “Maths is the language of nature, science and every subject in the world, be it English, history or geography.

Whatever object (or noun) you choose, you have to describe its attributes like size, physical dimensions etc. In numbers. Similarly, history is a study of timelines which are again numbers. If you want to describe how the earth rotates on its axis and how much time does it take to move one degree, you have to take the help of maths again. The problem is that few educators teach the subject in this way. The stress is more on rote learning in schools. As a result, the foundation for learning the subject remains weak among students.”

VisualiseThrowing some more light on the nature of the subject, Rajeswari Bandaru, who was a teacher in SIP Academy and Hyderabad Public School, says: “The reason why so many struggle to relate to maths is because it is an abstract subject. If I ask you to visualise a tree, you can easily do it by imagining one with a trunk, trees and roots. But if I ask you to visualise a number, you see only the number. You cannot see its other attributes. In SIP Academy, where abacus programme is followed, we used to train students to visualise beads when they were asked to imagine numbers.

That helped them in grasping the subject with more self-confidence.” Dr Sasikumar too feels that visualisation is the biggest tool while teaching mathematics. “A simple example of a person looking at a building through a telescope can help you understand trigonometry. The algebra equations that we learnt in school can make everyday calculations easier. However, we need a good mentor/guru to show us how to do it,” he adds.

Interestingly, Rajeswari was an English teacher who started teaching maths because of her love for numbers. When she was young, her parents discouraged her from taking up the subject as it was not deemed fit for a woman. Is there any truth to the popular notion that women score less in crunching numbers? Says Neha, “It’s nothing but a myth, similar to many other sexist ideas that exist even today. The ability to understand maths has nothing to do with gender. Traditionally, more men received education than women, and as a result, we see fewer women in this field.”

While teaching the basics and active visualisation seem to be good ways to get children enthused in the subject, a few are exploring new ways to make mathematics fun for everyone. Neelakantha Bhanu Prakash, who is known as The World’s Fastest Human Calculator, has embarked on a journey to promote maths as a sport. “Through my company Exploring Infinities, we organise these games which are aimed at children and adults. Just as English has Spelling Bee contests, debates, elocution etc., we make games that will help you understand the subject while having fun. On National Mathematics Day, I hosted an event on my YouTube channel in which I played maths games with four stand-up comedians.”

A tributeNational Mathematics Day is celebrated on December 22 to commemorate the birth anniversary of Indian mathematical genius Srinivasa Ramanujan. It was announced by former Prime Minister Dr Manmohan Singh in 2012.


Jump, Split Or Make To The Next 10: Strategies To Teach Maths Have Changed Since You Were At School

I’m sure most people can remember trying to master a certain maths rule or procedure in primary or secondary school.

My elderly mother has a story about a time her father was helping her with arithmetic homework. She remembers getting upset because her father did not do it “the school way”. I suspect her father was able to do the calculation mentally rather than the school way, which was to use the vertical algorithm.


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Students are expected to add the numbers in the ones (right) column first, before adding the numbers in the tens (left) column. The task becomes more difficult when the total of the ones column is more than 10 — as you then have to “trade” ten ones for one ten.

Students who give the answer as 713 rather than the correct answer of 83 may well have started with the tens column first. Or they may have written 13 in the ones column rather than trading ten ones for one ten.

The formal school algorithms are still used for larger numbers and decimals but we encourage students to use whichever strategy they prefer for two-digit addition.

The trouble with teaching rules is many students then struggle to remember when to apply the rule because they don’t understand how or why the rule works.

Read more: Weapons of maths destruction: are calculators killing our ability to work it out in our head?

The Australian Curriculum: Mathematics states that by the end of year 2, students will “perform simple addition and subtraction calculations using a range of strategies”. By the end of year 4, they will “identify and explain strategies for finding unknown quantities in number sentences”.

We want children to remember how to do these equations in their head, rather than relying on writing down the process. Here are three strategies schools use to teach children how to add and subtract two-digit numbers.

1. Split strategy

This is sometimes called the decomposition, partitioning or partial-sums strategy.

You can add or subtract the tens separately to the ones (or units). For example, using the split strategy to add 46 + 23, you would:

split each number (decompose) into tens and ones: 46 + 23 = 40 + 6 + 20 + 3

rearrange the tens and ones: 40 + 20 + 6 + 3

add the tens and then the ones 60 + 9 = 69

Using the split strategy for addition such as 37 + 65 would be similar, but there would be an extra step:

split or decompose the numbers into tens and ones: 30 + 7 + 60 + 5

rearrange the tens and ones: 30 + 60 + 7 + 5

add the tens and then the ones: 90 + 12

split 12 (10 + 2) to give: 90 + 10 + 2 = 100 + 2 = 102

Many students find the split strategy more difficult for subtraction than addition. This is because there are more steps if performing this strategy mentally.

For a subtraction such as 69 – 46, you would:

split or decompose each number into tens and ones: 60 + 9 – (40 + 6)

remove bracket: 60 + 9 – 40 – 6

rearrange tens and ones: (60 – 40) + (9 – 6)

subtract the tens, then the ones: 20 + 3 = 23

Students often make mistakes in the third step. Successful students may say: “I take 40 from 60, then 6 from 9”. Unsuccessful students will say “I take 40 from 60 then add 6 and 9”.

Students who use this strategy successfully are showing they understand place value (the value of each digit in a number) and their knowledge of maths rules needed for algebra.

2. Jump strategy

This is sometimes called the sequencing or cumulative sums strategy. The actual steps taken depend on the confidence and ability of the students.

Some students add increments of tens or ones, while others add or subtract multiples of tens then ones.

For example, adding 46 + 23 using the jump strategy might look like this:


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add two lots of ten to 46: 46 + 10 = 56, then 56 + 10 = 66

add the remaining 3: 66 + 3 = 69

or

add 20 to 46 which becomes 66

add the remaining 3: 66 + 3 = 69

The two versions of this strategy can be shown using an empty number line. Using a blank or empty number line allows student to record their thinking and for teachers to analyse their thinking and determine the strategy they have attempted to use.

Subtracting 69 – 46 with the jump strategy could be done by:


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subtracting four lots of ten (40) from 69: 69 – 10 = 59; 59 – 10 = 49; 49 – 10 = 39; 39 – 10 = 29

then finally subtracting the remaining 6: 29 – 6 = 23

or

subtract 40: 69 – 40 = 29

then subtract 6: 29 – 6 = 23

3. ‘Make to the next ten’ strategy

This is sometimes called the compensation or shortcut strategy. It involves adjusting one number to make the task easier to solve.

The “make to the next ten” strategy builds on the “friends of ten” strategy.

Many students in the first years of primary school create all the combinations of two single digit numbers that give a total of ten.

9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5 …

These are sometimes called the rainbow facts as the children create rainbows as they connect two numbers together. For instance, 9 may be on one end of a rainbow colour and 1 on the other.

By combining the numbers in this way teachers hope students will realise the answer for 9 + 1 is the same as 1 + 9.

In the “make to the next ten” strategy, you add or subtract a number larger than the number given (such as the next multiple of ten) and then readjust the number by subtracting what was added or adding what was subtracted.

In the diagrams the relationships are indicated by the use of arrows.


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So, to add 37 + 65, you would

add 3 to 37 to give 40.

subtract 3 from 65 to get 62

this becomes: 40 + 62 = 102.

If subtracting 102 – 65, you would:

subtract 2 from 102 to make 100

subtract 2 from 65 to maintain the balance

this becomes 100 – 63 = 37.

Many students using this strategy incorrectly add 2 to 65 instead of subtracting 2.

Why these strategies?

Students would have been using all these strategies, or some forms of them, in their head for generations. But for many years, the expectation was that students use the formal written algorithm rather than their own mental strategies.

The introduction of the empty or blank number line allowed students to record their mental strategies, which allowed teachers and parents to see them. Naming these strategies has allowed teachers and students to discuss possible strategies using a common vocabulary.

Read more: Kids prefer maths when you let them figure out the answer for themselves

Rather than teach rules and procedures, we now need to encourage students to explain their strategies using both concrete materials and diagrams to demonstrate their knowledge of addition and subtraction.


‘Maths Lab At Home’ Shows The Way In The New Normal

The pandemic crisis has prompted the Education Department to come up with the ‘Maths lab at home’ initiative to encourage students to perform simple experiments using materials available at homes.

The move is expected to make up for the loss of practical sessions in classrooms and labs. Students of classes 1 to 7 will be part of the Maths lab at home project. “We have started training sessions for teachers. Block resource centres under the Samagra Shiksha Kerala [SSK] will coordinate the implementation,” said Usha Manatt, District Project Coordinator, SSK.

Besides using materials and tools available at home to conduct experiments, the SSK district unit will procure cost-effective learning models and distribute them among students. The department has earmarked ₹30 for each student as aid to meet the requirements. “The resource persons in association with Maths teachers will finalise the experiments to be done by children. Teachers will share videos of experiments through WhatsApp and other platforms with students,” said Ms. Manatt.

In addition, learners will be encouraged to shoot videos of their experiments. They will be documented by block resource centres and shared through YouTube. The objective of the initiative is to kindle interest in Maths among students. It also aims at encouraging parents to join hands with their wards in making Maths learning an interesting and innovative experience.

Teachers handling work experience modules will be roped in for the project. The Education Department hopes that the Maths lab at home project will help in realising that simple learning models can be made at home at reasonable expense.

Making a model of the solar system or a pictorial representation of life in the pandemic times will now be part of the ‘Social Science lab at home’ project of the Education Department.

Similar to the Maths lab at home initiative, the Social Science lab at home programme is meant for students of classes 5, 6 and 7. According to officials, both the projects were conceived based on the inference that students were missing the feel and fun of doing experiments while confined to their homes in the pandemic times. “There were some gaps in the online learning process, and the absence of practical sessions figured top among them. Students used to have experimental sessions in the lab in the regular classroom learning mode,” they said.

For the Social Science lab at home project, the department has devised simple experiments for each class. Accordingly, learners can use chart paper or similar material for making models. SSK block resource centres will support them by providing additional materials. Teachers will guide students and encourage parents to join in assisting their children in creating models.














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