6 tips to help your child have a solid understanding of counting

Counting is an interesting concept that I find many people have a misunderstanding about. Counting may seem simple but it requires a high level of thinking in order to have a strong foundation of number.

Many parents come to me for advise when their child begins to struggle with Mathematics during school. It is important to gather data on what concepts the child is having difficulty with. Usually a child has formed a misunderstanding or has not gained an understanding about a particular Math concept. Counting is one concept that can cause children a lot of grief later in school if they do not have a strong understanding in this foundational concept.

So what should we as parents and educators be helping our children do when it comes to counting? Below is a list of 6 tips that parents and educators can use to ensure that their child is gaining a strong foundation in counting.

Tip 1: Importance Of Rote Counting

imagesRote counting, which means counting without equipment and any help is the first stage of building a strong foundation in learning to count properly. From the age of 2, children should be observing adults counting often through everyday life experiences. I know my 2 year old son hears me count to three many times in a day before he goes to timeout. Children will begin to emulate adults and start to count, even if it is their own version, mixing lots of the numbers up. Encourage your child to count with you while you are doing your fruit and vegetable shopping (count the potatoes as you put them in the bag) or going up or down stairs.

Once children are able to count to 20 by themselves, they have already succeeded in achieving the first stage in counting. It is hoped that by the time the child is 5 - 6 years old, they should achieve this stage. However there are some 3 year olds that would also be able to achieve this step. It is all about modelling and practice.




Tip 2: Number Mispronunciations 

imagesOnce children become confident with counting, they begin to count faster and numbers begin to sound joined together. If a child is not pronouncing their numbers correctly, it may cause misunderstandings in Mathematics later on. The most common mispronunciation is the “teen” and “decade” numbers.

Many younger children will sound like they are using decade numbers for the teen numbers.

eg 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 30, 40, 50, 60, 70, 80, 90, 20, 21, 22

This may seem harmless but it can lead to a lot of misunderstandings. When asked questions like “What number is after 16?”, they will say 70. I try and reinforce the correct pronunciation with the idea of “angry numbers” and “Tea numbers”

I ask the child to show me an angry face and get them to realise what their mouth is doing. (Usually teeth together, mouth slightly apart and stretched). I tell them that this is what the mouth has to do for the angry numbers also known as teen numbers.

I then ask the child to show me how they can pretend to drink tea. (Usually a pincer grip, thumb and pointer finger together, and flicking the wrist). I get them to do this action for the decade numbers “ty” aka tea numbers. 30, 40, 50 etc.

This will help the child distinguish between both the decade and teen numbers. It is also important for us, as adults to pronounce our numbers correctly as children need to hear it, in order to say it.

Tip 3 - Counting forwards and Backwards

For some reason, many children are only exposed to counting forwards and not backwards. Both ways are essential for counting yet as educators and parents, we tend to favour forward counting and give our children little or no experience with counting backwards.

Counting backwards is important for a number of reasons. The most apparent is for the concept of subtraction. Children are more likely to be able to answer the question of what is one more of a particular number, then what is one less of that same number. To work out one less, they usually take one object away and then have to recount all the objects again.

To help your child, start with a particular number of toys on the floor, say 16 and get them to pack them away back in the container. Help them start with the number 16, as they put one away say 15 left, as they put another away say 14 left etc.

Practising to count backwards with make a huge impact on their understanding of how numbers work. Try not to count larger numbers, but instead opt for counting backwards. It will be tricky at first, but once they understand it, they will flourish.




Tip 4 - Use equipment

imgresIt is important for children to see objects in order to help them develop their one to one correspondence. This means that they can point to an object and say a number, then point to the next object and say the next number in sequence.

To develop one to one correspondence, children need to organise their equipment in a logical way. If a child does not know where to start I tend to guide them into putting them in a line or putting them in a pile and they can move the object across while counting.

Using board games is a great way to develop the concept of counting. With my four year old, I play trouble and snakes and ladders a lot. She is now able to move her players piece two and three places without even counting as she has a solid understanding of two and three.

It is essential to focus on small numbers for one to one correspondence for a long time. Once they are really confident with numbers under 10, they should be able to transfer this knowledge to all other numbers.

Tip 5 - Encourage faster ways of counting

images-1Counting by ones is only an efficient strategy for children if there are only a few objects. Help your child understand the idea of counting by twos and why we would count by twos. You could count pairs of socks, people’s legs and people’s eyes by two’s. Let them see a number line so they can visualise the idea of skipping a number.

Once your child has mastered counting by 2’s (both even and odd numbers), get them to count by 5’s and 10’s. Make sure you always start at a different number so they gain the understanding that counting by 5’s is saying every 5 numbers. Eg Counting by 5’s could be :13, 18, 23, 28, 33, 38

Tip 6 - Get rid of the number chart when they are learning to count

imgres-1Using a number chart can really confuse a child. I tell all the educators and parents I work with to get rid of the chart and replace it with a number line. Numbers need to be viewed as linear as they increase over time. A chart can confuse a child as you need to count row by row.

The number charts can make a return however, when the child is in Year 3. By then they understand the concept of how numbers work and will not be confused by how the chart is constructed.

I hope everyone has enjoyed this week’s blog and has learnt something new to take away and try with your child or class. Next Tuesday night we will be having an interactive Q and A on our facebook page for anyone seeking advise or answers about any educational concern they may have. Further information about this will be posted on our facebook page. Make sure you like our page to always receive the latest information from our website and blog.

Until next time …

Kelly Pisani

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10 Ways To Help Your Child With Math

The teaching of Mathematics has changed significantly over the past 20 years. No longer are we focusing on ensuring children learn processes but ensuring that children understand concepts and have a variety of strategies to solve mathematical problems.

FDPpuzzlesIt can be quite difficult for parents during Math homework time as the problem solving methods that they were taught are very different to how their children are being taught.

Below is a list of 10 ideas that parents can use to help teach Mathematics to their child.




1. Always have maths equipment at home that is easily accessible

CountingChildren need to participate in real world mathematics. This means Mathematics is part of every day life and children need to engage with it in order to be a successful person in our society. It is important to have rulers, scales, measuring cups, tape measures and calculators at home to enable children to use them when they need it. Children need to see adults and help adults when using mathematical equipment as well. This could include, helping to cook by measuring ingredients or helping to use a measuring tape to see how long something is in the home.

2. Use Mathematical Language in your everyday conversation. 

imgres-5It is very easy to fall into the trap of using the same words to describe many things. A classic example of this is the word “big”. Using big to describe the height of something or the length of something or the weight of something or the volume of something does not give the child enough exposure to mathematical language. Adults could use words like “tall” or “high” to describe height, “long” or “short” to describe length and “heavy” or “light” to describe weight. It is important that we use to the correct language to help our children form the right understandings about these mathematical concepts.

3. Give your child time to answer a question

searchAs parents and educators, our main role in educating our children is to facilitate learning not to determine what a child will learn and how a child should learn. Children need time to process questions and process what they need to do in order to solve a task. They need to go through a few steps (even though it may not be the most efficient strategy) it is important to give them time. If we always rush in to “help”, the child will always come to expect this and not try to use any strategies that they do have. If your child comes to you with a question, try and think of another question to ask them that will guide them to the answer. For example, if a child asks you what is 33 + 99, you could ask them if they know what 99 is close to. Then encourage them to go back and think about that and see if they can come up with anything.




4. Always ask how they got to an answer

images-1We may be elated to see that a child has solved a question correctly but getting the correct answer does not really give the teacher or parent much information about their mathematical thinking around a particular concept. We must always ask the child to explain how they solved it. If they can explain their strategy and tell you why they did it, it will prove that they have a very solid understanding about that concept. For example if the student solved the above addition task by saying 132 it shows that they have an understanding of addition. But what level of understanding do they have? Asking them to explain how they got to their answer will shed more light onto this. For example if they said “I drew 99 lines and added another 33 lines and then counted them all”, this shows a very low level strategy to solve an addition problem. If they said “I added 9 and 3 and that was 12, then I put the 2 down and put the 1 near the 9 and then added 9, 1 and 3 which was 13. I then wrote 13 next to the 2 which gave me 132.”, it shows that they have learnt the process of pen and paper trading, but they do not have a good understanding of why they are doing this process. If they said “99 is close to 100 so I just added 100 and 32, because I took away 1 from 33 so I could make it 100”, this shows a very high level strategy that is efficient and shows a solid foundation. Yes they all got it correct but their problem solving strategies explain a lot about the child’s level of understanding.

5. Worksheets

imgres-3Thinking about the information above, it is obvious why worksheets (drill and practice) do not help a child understand a concept. Worksheets and mathematical text books are all about practising processes over and over again until it becomes second nature. Worksheets do not allow conversation about how they solved a problem as it is very limiting and its whole purpose is to teach a process strategy not the concept. It is far better asking a child to record as many number problems that would equal to 20 as they can. This open ended task invites the child to show what they know and areas that they need further development. This question could be asked at children of all ages as the depth of answers should increase with the age of a child. For example it would be expected that children in Year 6 could use fractions, decimals, basic algebra, multiplication, division, addition, subtraction and squared numbers in their answers.

6. The Number Triad

searchIt is important for children to have a strong number sense as this is essential for all areas of Mathematics. Children need to be able to understand the three parts of a number, also known as the number triad. They need to know what the number looks like (symbol), how to read the number (words) and be able to make that number (quantity). As parents and educators, we can expose them to lots of numbers in the environment eg number plates, house numbers and speed limit signs, we can ask them to read numbers that we come across eg read a telephone number that you need to type into a phone and we can constantly ask them to make a number with a collection eg ask them to get you 14 potatoes for a potato salad you are making. All three areas of a number need to be developed to have a strong number sense.

7. Ask the teacher

teacher-meeting-467x267[1]If you are struggling to work out the best way to help your child in a particular area for Mathematics just ask their teacher. Most teachers are more than happy to help by running mini maths lessons for parents to help them understand the way Mathematics is taught in the 21st century classroom.

8. The relationship between Literacy and Numeracy

imgresMost children struggle in Mathematics due to the language of Mathematics. They may not be familiar with particular terms so it necessary to ensure that a child is comprehending the words in a maths task just as much as the mathematical concept behind it. If a Mathematics question is asking a student to find the second least favourite food in a survey, they need to have a good understanding of the words “second” and “least” before they can even attempt to answer the problem.

9. Compare things

imgres-1Encourage your child to compare the size, shape or orientation of objects. Get them to order items from largest to smallest or lightest to heaviest. This should be done during their play. For example, if they are playing with containers in water get them to try and order the containers from the container that holds the most water (largest volume) to the container that holds the least (smallest volume)




10. Develop all areas of Mathematics

imgres-2It is easy to just develop the Number concepts such as Place Value, Fractions, Addition, Subtraction, Multiplication and Division. Equal time needs to be placed on other areas of Mathematics like Measurement (length, area, volume/capacity, mass, time), Data (surveys, graphs, charts) and Space and Geometry (3D, 2D, Position). All these areas need to be developed in context. It needs to mean something to the child in order for them to learn and understand it.

I hope these 10 ideas have given you something to think about.

Until next time …

Kelly Pisani

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15 Ways To Learn Fractions, Decimals and Percentages

Welcome to the final blog in the series “How to help your older child”. In this blog we look at the world of fractions, decimals and percentages.

As children get older, it seems like it is a habit to remove equipment and games from teaching Mathematics. I strongly believe that as children get older it is more important to have resources and meaningful learning experiences to keep students engaged in more complex thinking and more difficult concepts. How do we achieve this? The answer needs to be by making the learning fun, interesting and important to the world of the child.

Unfortunately the teaching of fractions, decimals and percentages usually goes hand in hand with the use of worksheets and text books. Does this constitute as fun, interesting and meaningful to the child? Create a love of mathematics not a learning experience that is dreaded, with a child who is full of anxiety and an area they have no success at. (Think about your experience of Mathematics at school. Do you have a love for the subject? What engaging methods did your teachers use to help you understand mathematical concepts? - if any)

Some Facts About Teaching Fractions, Decimals and Percentages

  • Try to teach them together so the child realises the relationship between all of them
  • When reading a fraction always use the correct terminology eg 6/8 should be read as six eighths, not six over eight
  • When reading decimals always use the correct terminology eg 0.43 should be read as 43 hundredths, not zero point four three
  • Use equipment to show parts of a whole
  • Fractions, decimals and percentages need to be taught as part of a whole and part of many. (eg Part of a whole - cutting up one orange and Part of many - how many of one colour lolly in a packet of colourful lollies)

Please find below a list of 15 games that children can play to develop their concepts about Fractions, Decimals and Percentages.

1. Chalk pictures

chalk fractionsChildren draw a variety of shapes and divide them up into equal sections. Once they have divided up a shape equally they can colour some parts and say the fraction, decimal and percentage relating to their drawing.




2. Play-dough

PlaydoughfractionsChildren make shapes with play-dough and use a plastic knife to divide the shape into equal parts. Once they have divided it up equally they can remove some parts and explain using fractions, decimals and percentages terminology how much they have taken and how much they have left.

3. Fraction Bingo

fraction bingoMake up a bingo card with different representations of fractions. All players have a different bingo card. All the fraction cards are placed in a bag and the caller picks one at a time out. The caller reads the fraction out and players cover up the relevant fraction if it appears on their board. First player with all their fraction pictures covers calls out bingo and becomes the winner.

4. Fraction picture

fraction pictureChildren can make a picture (eg ice-cream bowl) with a variety of colours/flavours. After they complete it, they must describe the amount of colours using the fractions, decimals and percentage terminology. EG 20% of my ice-cream is chocolate or two fifths of my ice-cream is chocolate. (start with objects out of 10 to make it easier)

5. Colour fractions

colourfulfractionsGet your child to cut five equal paper strips using a different colour for each. They can then cut each one up in different ways ensuring that each section of the strip is equal. They can cut one strip in half, one in thirds, one in quarters, one in fifths etc. Let them experiment with more strips. They can paste them all next to each other to help them understand equivalent fractions. EG, A half is the same as two quarters.

6. Clothesline

fractionslineCut up some cardboard and write a variety of fractions, decimals and percentages on them. Give them to your child and see if they can peg them up on string from lowest to highest. They may need to peg some underneath each other to show that they are the same. This will help them with transferring their knowledge to a number line.

7. Puzzles

FDPpuzzlesHave children create their own puzzles that match the same fraction, decimal or percentage together. They may even make up a few and give it to somebody else to put back together.

 

 

8. Bottle caps

FDPmatchingcapsWrite a variety of fractions, decimals and percentage on the back of bottle caps. Hide all the caps around the room or house. Your child must find all caps (make sure you tell your child how many there are) and then pair up caps that mean the same thing. EG two quarters and 50%.

9. Dominoes

fdpdominoesCreate fractions, decimals and percentages dominoes out of cardboard. Children need to put the dominoes next to each other that mean the same.

 

10. Deck of cards

FDPdeckofcardsMake your own set of playing cards but use fractions, decimals or percentages. Get children to play go fish or memory or pairs with these cards. This will help children to read the fraction, decimal or percentage properly.

 

11. Expanded decimals

decimalexpanderMake up a variety of decimals using tenths, hundredths and thousandths. Pick a colour for each place value, EG Tenths are green. Get your child to select 2 or 3 cards - they must be different colours. Put them together and read the decimal. Take them apart and start again.

12. Decimal cups

DecimalcupsUsing styrofoam cups, write numbers 0-10 around the rim. One cup will need to have a decimal point. One person calls out a decimal eg 3 and 23 hundredths. The child must make this using the cups.

13. Ordering decimals

orderingdecimalsHave a variety of decimal numbers written. Children can work independently or in pairs to order the numbers from smallest to largest. They could work out where each number would go on a number line and use equipment to represent the decimal.

14. Food bag

foodpercentPut a variety of coloured lollies in a mystery bag. The child tips out the contents of the bag and groups matching colours together. They could then describe the bag using fractions, decimals and percentages.

15. Plastic eggs

FDPeggmatchUse a plastic egg that can be separated in half. Write a fraction, decimal or percentage on one half and a matching one on the other. Do this for as many eggs that you have. Take all the eggs apart, mix them up and get your child to match the correct ones together.

Hopefully these 15 games will help your children to be engaged and enthusiastic towards learning fractions, decimals and percentages. Knowing the relationship between them all, will help children solve mathematical problems.

Please share this blog if you have found it insightful and if you believe it offers practical information that your can implement at home or in the classroom. Remember to email a copy of it to yourself for reference later on.

Until next time …

Kelly Pisani

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