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Improving Mathematics in the Early Years at  Key Stage 1

We know that  some challenges  are here and there when it comes to some disciplines, especially mathematics and science disciplines   These challenges  forming some elements of fear for mathematics and science which consequently results  in poor performance and lower grades  and this in turn  hampers  their dream of success in their studies.

To deal with above ,At Our Hasti School we plan to make the learning of disciplines like mathematics and science stress-free for students. School organizes and conducts  science exhibition, science day , Mathematics day &  and maths  quiz  etc. Daily two questions ,with their answers , on fundamental Mathematics and science  are displayed on the Mathematics subject & science  subject  display Boards respectively . this helps in building confidence among learners

We at our *Hasti school first to know the weaknesses  and strengths of  learners in the subjects,   Diagnostic tests  are conducted based on the fundamental concepts children have learnt in the previous class or grade the  performance of each and every child is then critically analyzed and accordingly remedial measures are implemented. to ensure that the difficulties are solved   and learner enjoy the subject.

The Number concept and maths vocabulary is to strengthen in  Primary classes that is Grade one  the key class 

It is observed and proven fact that there is a gap that exist for children who have rarely played with dice, cards, board games or dominos.

‘Try asking children to show you 7 fingers* – now spot the ones who don’t have 5 as a bench mark to find 7.’ So how then can we avoid these pitfalls and ensure that children gain a greater understanding of the relationships that numbers have with each other?

Teacher one day  did put some coloured chalk sticks  in  biscuit  box  and asked one of our 3 year old boys “What have you got in there?”  asked him.

“Pencils !” he jubilantly told to teacher .

Great  teacher  thought: he knows and recognizes when he has more than one. “Can I take some out?” teacher asked  &  took out two without letting him see what teacher  had taken. Teacher then  placed them on the floor and asked “What can you see?”

“Pencils ,” he again said.

“How did you see them?” teacher asked. He looked a little blank. So teacher  said  “I saw  1 there and  1 there.”

He immediately responded by saying “Yes, 2.” !!!

Experiences like this are invaluable in helping to develop early number sense and the relationships that exist between numbers.

Getting children to be playful with maths and encouraging them to talk about what they see, how they see it and recognizing how they know it, is fundamental to their confidence around maths and their ability to use and apply this knowledge.

‘Well firstly get your child  playing with dice and cards etc. at home  the children that recognize dice pattern 5 has the advantage of seeing 4 dots and 1, 3 dots and 2 dots, 2 dots and 2 dots and 1 dot. That helps when later they want to add 5 to 7 for example.’ using a tens frame can be a great way of exploring numbers to 10, decomposing and recombining, exploring one more one less, looking for patterns and considering how close to ten.’

‘Games can be an engaging way to practice and extend skills.’ A good example of this would be playing a game where the children have to work out where they are on the board, how many they have to count on and be able to recognize if the dice indicates a number which exceeds what they need: “I only need four to win but I’ve thrown a six… that’s two more than what I need.”Getting children familiar with mathematical language initially in an informal way is vital too.

If we integrate  maths into different activities throughout the day –that story and picture books can be a powerful tool for engaging children with basic maths concepts, while board games (such as Snakes and Ladders) are particularly beneficial to developing understanding of numbers.

We need  to Dedicate time for children to learn mathematics and integrate mathematics throughout the day

Dedicate time to focus on mathematics each day.Explore mathematics through different contexts, including storybooks, puzzles, songs, rhymes, puppet play, and games.

Make the most of moments throughout the day to highlight and use mathematics, for example, in daily routines, play activities, and other curriculum areas.

Seize chances to reinforce mathematical vocabulary.

Create opportunities for extended discussion of mathematical ideas with children.

check what children know in a variety of contexts. Carefully listen to children’s responses and consider the right questions to ask to reveal understanding.

The above practices at our school make children confident and they enjoy the learning of mathematics .

How to Teach Your Children to Do Mental Math*

It is important that everybody learn to do some calculations mentally when paper and pencil or a calculator is not handy.

*Let us see  few beginning mental math strategies that a parent might help a child learn at home*.

*Mental math should not be confused with the memorization* of basic mathematics facts*— such as knowing the times-tables by heart. While memorizing basic facts makes mental math easier, *doing mathematics mentally requires both memorized facts and the manipulation* (strategies) of numbers and operations*  

 The following mental math strategies are arranged in general order *from the easiest* strategies children can learn to perform in their head , *to more difficult and challenging mental math gymnastics*.

*Strategies for Addition*

Doing addition problems in your head is probably the best way to start doing mental math. Even young children—5, 6, and 7 year olds—can do the easiest strategies below. While the first few may seem *trivial to adults* , But they are a *good way for children to begin learning to do mental math*.

When the words “hearing” and “saying” are used in these strategies, they mean “hearing in your head” and “saying in your head.”

Adding One

*Adding one means hearing a number, then saying one number up—or counting up one number*. The best way to introduce this to your children is to *say a number out loud and then, after allowing they time to think, have them tell you the next higher number*. Make it fun by having your children tell you a number and then you tell them the next number. Start with low numbers and, when your children are able to count higher, move to larger numbers.

Adding Two

Adding two means hearing a number, and then saying the number that is two more. To do this, children can either mentally add two or count up by two. *If you first teach your children to count by twos: 2, 4, 6, 8, 10, etc., it will be easier for them to add two mentally. However, remember that they will also have to learn how to count by the* *odd numbers: 1, 3, 5, 7, 9, Also, if children understand that any odd number, plus 2, will always be another odd number, and that any even number, plus two, will always be another even number, these mathematics concepts can help them check their answers mentally*.

Counting-On

*Counting-on is one of the simple but powerful mental math strategies children can learn and is the easiest for most students* —many children figure out this strategy naturally. *Counting-on means a child mentally says the biggest number to add, and then counts-up the second number*, one (or two) at a time. For example, *in the equation 5 + 3, you start with the 5 in your head, and then count up: . . . 6, 7, 8. You might suggest to your children that if they want to add 2 + 6 in their head, they should start with the bigger number, in this case 6, and count up (. . . 7, 8) since, with addition, you can add numbers in any order and get the same answer—order does not matter. *This is called the commutative property of addition*

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When mentally counting-on, children and adults often resort to using their fingers to count up (or down), simultaneously counting on their fingers while they count in their heads. If your children use this handy device, let them. It is not harmful if it helps to make counting-on a useful mental math strategy.

*Making-Ten*(s)

Since ten is the basis of our number system, students who know all the single-digit combinations that equal 10 can make good use of them in doing mental math. The *making ten strategy involves memorizing the number combinations that add to ten*: 7 + 3, 8 + 2, 5 + 5, etc.—they are not as useful if children need to think hard to remember these combinations. *Once students memorize these, counting-on or other strategies become easier. For example, 6 + 4 = 10 may be a trivial problem, but *if you know your combinations of ten, this strategy can then be extended to harder problems, such as 76 + 4, since 76 + 4 = 70 + 6 + 4 = 70 + 10 = 80—easy*!

Rearrange Numbers and Operations

*On paper, we tend to calculate with numbers in the order they are given. Doing mathematics mentally frees us to do calculations in the order we choose and can do more easily*. For example, if we do 6 – 3 + 2 + 4 + 8 in our heads, we can rearrange it as (6 + 4) + (2 + 8) – 3—*two combinations of 10*, then subtract 3 last. However, to do this, a child must be able to remember the numbers and rearrange them mentally. This is hard for some people.

*Visualizing a Mental Number Line*

Number lines, such as those found on the wall in many classrooms, are a visual model of our number system and can be very helpful for children who need to see how numbers are logically arranged. *If children can close their eyes and  visualize a mental number line, this too can be helpful in doing mental math. *The best way to help students picture a number line is to PASTE*  *A PAPER NUMBER LINE IN YOUR HOME WHERE YOUR CHILDREN CAN SEE IT AND USE IT REGULARLY*  ON TV,MIRROR , INFRONT OF DINING TABLE , KITCHEN TABLE ETC. *

*Do you remember in our HASTI PUBLIC SCHOOL*  *we ask children to paste* their aim or objective of future career for ex.*I WANT TO BECOME DOCTOR/ENGINEER/CA/ ARMY OFFICER ETC. or of scoring total % at public exam.for ex.I WILL SCORE 95% MARKS IN MY SSC/HSC EXAM* ..on *mirror, TV*  etc.and *TO WRITE LETTERS TO THEIR 10 RELATIVES AND FRIENDS ABOUT THEIR DETERMINATION TO ACCOMPLISH THE AIM*

Adding Ten

*The number line can teach students that adding ten is easy because ten is an easy “jump” up the number line. No matter what number you start with, the one’s digit stays the same but the ten’s digit increases by one. For example: 5 + 10 = 15, 12 + 10 = 22, 23 + 10 = 33, etc*.

Adding Nine

*Once adding ten is easy to do, adding nine is the next strategy to learn. To add nine, a student just adds ten, and then counts down by one. A child would mentally say 5 + 9 = 5 + 10 – 1 = 15 – 1. Once understood, this mental math strategy is almost as simple as adding ten*.

Double Numbers

*Making use of doubles—5 + 5, 7 + 7, etc.—is a bit harder, but can be very useful for mental math*. Doubles come up often in calculations, so if all the single-digit doubles are memorized, students can combine these known facts with the mental math strategies already mentioned. *For example, when faced with the problem 76 + 6, students can think of it as 70 + 6 + 6. If they remember that 6 + 6 = 12, then they can rearrange the problem as 70 + 12, and then again rearrange the problem as 70 + 10 + 2 = 82*—making it an easy mental math problem.

Near-Doubles

*Once students have memorized their doubles; the use of near-doubles in mental math*  follows easily. *For example, in the expression 5 + 6, if students first remember the double, 5 + 5 = 10, then it is easy to add one more, getting an answer of 11*. Children actually do not have to memorize the near-doubles if they know their doubles. For example, in the equation 37 + 8, when children use the near doubles strategy, it follows that 30 + 7 + 7 + 1 = 30 + 14 + 1 = 44 + 1 = 45.

Front-end Addition

*We frequently do mathematics differently in our heads than we do with paper and pencil. The typical way to add a pair of two-digit numbers is to add the digits in the ones place first, carry ten if necessary, add the digits in the tens place next, and finish by combining the tens and ones results*. *For example*, in the problem 65 + 26, if students first mentally calculate 60 + 20 = 80, the number 80 is pretty easy to remember—to store away mentally for a few moments. If they then add the ones, 5 + 6 = 11, they can recall the easily remembered number, and compute 80 + 11 = 91. Not everyone prefers front-end addition, but those who do often use this strategy without thinking about it.

“Friendly Numbers” Strategy

*certain number pairs go together nicely and are easy to work within our heads; we call these friendly numbers*. For example, 75 + 25 totals 100—we know this well from using money. Although we do not often get many problems as simple as 75 + 25, we can combine this friendly number strategy with other mental math strategies. *For example, to add 78 + 25 students would instead think 75 + 25 + 3, changing it into two friendly numbers* and one easily added number instead.

A Bit of Mental Math Advice

For some students these mental math strategies will be interesting and fun—and may even make them feel mathematically powerful. However, what appeals to one child may be uninteresting and hard to another. If there is one important bit of advice before you share any of these strategies with your children, it is: go slow and proceed only IF your children enjoy learning how to do mathematics in their head. *A few minutes of playing with mental math are plenty—do not make it tedious. If learning mental math tricks is not fun for your children, it is best if you stop and look for other areas of mathematics, such as geometry or puzzles that will appeal to your children more than mental math*

In our Hasti school this is planned and *This is what we do and expect teachers and learners to do and more importantly the parents to play with their wards a  mental mathematics.