The Numeracy Project aims to raise the level of student achievement in mathematics. It is based on research about how children learn and is designed to teach children to think mathematically. There is an emphasis on children developing a sense of number that they can apply to a variety of problems rather than learning by memorising rules.
(For more ideas visit: NZ Maths)
You can support your child’s learning in mathematics by:
★ being positive and enthusiastic about mathematics yourself.
★ discussing positive mathematical experiences with your family.
★ recognising the stage of development your child is at and using this
knowledge to help your child (see below).
★ not feeling you have to know everything, be a learner too. Get your child to
show you how, they will love having you ask and will learn from explaining it
to you.
★ never saying “I was no good at maths at school”. This gives children the idea
that maths is not fun or interesting and this could affect their attitude. Even if we as adults have negative memories of maths, we should try to be positive about it. Remember, the way we were taught may have been quite different to the way maths is taught in schools today... and you may be far better at maths than you realise!
The stages of development that learners move through are listed below. There are many real-life experiences that you can have with your child at all of these stages. It is important that your child is confident at the stage they are at before they move on. Each teacher is \able to discuss which stage your child is working at.
Numeracy stages of development:
Emergent (E) - Stage 0
One to One Counting (CA) - Stage 1
Count from one on Materials (CA) - Stage 2
Count from one by Imaging (CA) - Stage 3
Advanced Counting (AC) - Stage 4
Early Additive Part-Whole (EA) - Stage 5
Advanced Additive Part-Whole (AA) - Stage 6
Advanced Multiplicative (AM) - Stage 7
Advanced Proportional (AP) - Stage 8
These stages are explained in detail below with suggested activities given for each stage.
Emergent (E) - Stage 0
At this stage counting is the most important skill to master. Counting is learnt through repetition, so take lots of opportunities to rote count (just saying the numbers) and counting objects. Count with your child, and help them count right up to 100, or demonstrate it to them so that they hear the patterns of the numbers. Children can begin to explore the number of fingers on their hands and show numbers to 5 on them, perhaps more.
✦Practise counting up to 10 eg number rhymes like “Ten Little Indians” or “Once I caught a fish alive” etc.
✦Practise counting down from 10 eg a rocket blasting off or “Ten Fat Sausages” song.
✦Count groups of objects eg how many knives, forks, spoons on the table, buttons on shirts, counting the number of stairs you’re walking, counting how long it takes to do things e.g. to walk to the door, get undressed for a bath, have a drink.
✦Look at the calendar to see the number today. What number was it yesterday? What will it be tomorrow? ✦Look at the numbers on letter boxes.
✦Practise showing numbers on fingers eg “Show me 5 fingers, show me 2 fingers,” etc.
✦Play ‘Snap’ and dominoes – these help the children count in a fun way and see similarities.
One to one counting (CA) - Stage 1
These children can count a small group of objects but have not yet learnt to add two numbers together. At this stage finger patterns to 10 are a very important tool to have (you always carry your fingers with you and don’t need a container of counters). Support your child with these activities. They are not yet ready to do them by themselves.
✦Continue becoming proficient at showing numbers to 10 on fingers. “Show me 5 fingers, show me 7 fingers,” etc.
✦“Show me 3 fingers on one hand and 2 fingers on the other hand. How many altogether?” (Help the child count from one to find out. They will not yet be able to start from 3 and count on).
✦Show the child 5, 3, 7, 8, etc fingers on your hands and see if they can tell you how many there are. As they get more proficient at this they may recognize patterns instantly. Build up to five fingers on one hand first, then some more eg 7 will be one whole hand and 2 more. This helps the children see patterns more quickly and will link to the tens frames, and other representations of numbers, by building to 5 first.
✦Practise counting up to 10 eg number rhymes like “Ten Little Indians” or “Once I caught a fish alive” etc.
✦Practise counting down from 10 eg a rocket blasting off or “Ten Fat Sausages” song. ✦Look at the calendar to see the number today. What number was it yesterday? What will it be tomorrow?
✦Look at the numbers on letter boxes.
✦Use everyday happenings to discuss numbers – counting people, food, cars in the driveway, wheels on the cars, etc.
✦Include subtraction with addition. We have 9 muffins. How many will be left when we have eaten 2? Find out by eating 2 muffins to see if you were right! ✦Halve and quarter oranges and apples and name the pieces. Count how many quarters there are in two apples when cut, etc.
Count from one on Materials (CA) - Stage 2
These children can now solve addition and subtraction problems to 10 using their fingers, by counting from the first finger. eg When they add 4+3 they will start counting from 1. They now need to learn to hold an image of these numbers in their head. They will need patience and support to do this. They can now explore problems with bigger numbers, to 20, and start to group objects into tens to learn about our place value system.
✦Cut up a calendar so that you have the numbers to 31. Help the child to reassemble the numbers into the right order (you could start with smaller sections first eg 1 – 10, 1 – 20, etc). Use a complete page of a month to check whether it’s correct, or use a complete month to use as a guideline. Count the numbers and point to each number in order. Count backwards while pointing to the numbers. Cover up some numbers and see if the child can tell you what they are. eg. cover 15. The child might count from one to find out, or just know. Uncover the number to see if they were right.
✦Use fingers to learn the groupings to 5. eg 2 and _?, 4 and _?, 3 and _? And groupings to 10: “How many more do we need to make ten? We have 6; we have 8; we have 2, etc” ✦Pizza night! “We have 2 pizzas cut into 6 pieces each. How many pieces altogether? How many will the 4 of us have each if we share them evenly?” Do it with your child to find out.
✦“Nana gave us 20 lollies. Two people will get half each. How many is half of 20?” Share the lollies out to find out. ✦Play card games such as “Fish”.
✦Use fingers to solve addition and subtraction problems to 10, then when really good at that, do it on your fingers behind your back. Check if you’re right by looking at your fingers afterwards.
Counting from One by Imaging (CA) - Stage 3
These children can now hold numbers in their heads without having to look at all the objects and need to learn to count on eg 9 + 4 – is 10, 11, 12, 13 (counting from the 9 now and not from one) and back down for subtraction eg 12 – 3 is 11, 10, 9. It is important that the second number added is no bigger than 4 while learning this skill, as it is the optimum number that can be kept track of in their head. Children can keep track of what they’re adding on either by their fingers or in their head.
✦Count with or for your child in 10s to 100, 2s to 20 or more, 5s to 50 or more. Then back again. Write the numbers down so the child can use them as a guide. Keep skip counting in 2’s, 5’s 10’s etc. To work out three 2’s, use fingers to track – 2, 4, 6. Or use pictures cut out and group into twos etc.
✦Board games eg snakes and ladders, help counting on because the child moves the counter from the number they’re on (at earlier stages children want to move right back to one each time they have a turn as they don’t yet understand about 6 more, 4 more, etc).
✦Bundle iceblock sticks with pipe cleaners into 10s, or pebbles into empty film canisters to see how many there are. Count the ‘tens’ in tens and the ones left over in ones. Start with numbers up to 40 or so. start calling the bundles of ten ‘a ten’. “Let’s get 30 sticks. How many bundles of 10 will that be? How many tens have we got here? How many is that altogether?”
✦Play a game with 2 dice and the iceblock sticks or pebbles and film canisters. Roll the dice and work out how many has been thrown. Collect that number of sticks or pebbles. The rule is that every time you have ten they must be bundled up or put in the canister. Keep playing and see who gets the most. (Often interesting talk will be generated by this game as the children work out who has got the most, how many more they need to have the same number, etc. As adults we can generate this talk without dominating the game too much, to keep the game fun). ✦Play card games such as “Memories”.
Advanced counting (AC) - Stage 4
At this stage children are counting on or back from the largest number to solve addition and subtraction problems. They are also using skip counting as an early means of multiplying. They are working with numbers from 0-100. These children are now heading towards the transition to Part-Whole thinking. They may have trouble believing there are strategies beyond ‘counting on’, as counting on is a milestone in itself and the children are often very proud they have reached this stage! We now need to let them know that they’re very clever at counting on, but now they need to use the knowledge they have of numbers to try to use other clever ways to add numbers. This is a very difficult and lengthy transition to make so remain patient and support the child’s efforts. It may take a while.
Part-Whole thinking is the ability to split numbers into parts and rejoin them to solve sums, without having to count on or back in ones, etc. eg working out 9 + 4 by just knowing that 9 + 1 = 10, so we can take one from the four and add it to the 9, making ten, then we’ll have 3 left. Or, 8 + 7 = 15 because if I know that 8 + 8 = 16 off by heart, I can take one off to get the answer, because 7 is one less than 8.
So in order to use these strategies the child needs to have certain knowledge eg Know their doubles to 20 off by heart (6+ 6, 7 + 7, 4 + 4, etc) Know combinations to 10 off by heart (7 + 3, 2 + 8, 9 + 1, etc)
Know 10 + some more off by heart (10 + 2 = 12, 10 + 6 = 16, etc)
✦When playing board games see if the child can work out which number they’re going to land on without having to move space by space. eg I’m on 26 and I’ve thrown a 5. Where will I land? Games such as Ludo and backgammon can involve split moves. eg instead of moving one counter 6, they could move one counter 4 and another 2.
✦Continue playing grouping to 10 games with iceblock sticks or pebbles etc (mentioned in ‘Counting From One By Imaging’ section). Try using 3 dice to make adding the totals a little more challenging.
✦Board games could be played using two multi-sided dice so that the children are adding bigger numbers together eg Monopoly
✦Practise basic facts – doubles (4 + 4, 9 + 9, etc), facts to 20 (eg 16 + 4, 2 + 12, 6 + 11) ✦Practise counting forwards to 100 and back to 0 again (or lower!), counting in 2s 5s 10s. ✦Use the odometer reading of the car to practise reading large numbers. See how many kilometers were travelled on a long trip.
Early Additive Part-whole (EA) - Stage 5
Early Additive children have now become capable of part-whole thinking. Part-Whole thinking is the ability to split numbers into parts and rejoin them to solve sums, without having to count on or back in ones, etc. eg working out 9 + 4 by just knowing that 9 + 1 = 10, so we can take one from the four and add it to the 9, making ten, then we’ll have 3 left. Or, 8 + 7 = 15 because if I know that 8 + 8 = 16 off by heart, I can take one off to get the answer, because 7 is one less than 8. They will recognise and begin to use symbols for common fractions. Children at this stage can work with numbers from 0 – 1000.
✦Car journeys – we’ve travelled 25 km today. If we travel that far tomorrow, how far will we have gone? If we’d stopped 8 km back, what would the odometer reading be? (Children at this stage might mentally solve the problem by using 25 – 5 –3 = 17. Taking away 5 first takes us to a ‘tidy’ number of 20, then their basic fact knowledge should help them know that 20 – 3 = 17. Because they are part-whole thinkers they know that the 8 can be split into 5 and 3 to make working out the problem easier).
✦Use car licence plates - add the numbers on a plate, look for patterns eg. add tidy tens together first.
✦Use car licence plates - add the first two digits to the second two digits. ✦Use car licence plates - read the numbers aloud as a 3 or 4 digit number ✦Explain to your child the strategies you are using to work things out as they occur. You may be surprised by the number of mental strategies you have. See if your child can use your strategy and you use theirs. See if they can think of other ways it could be worked out. eg. when shopping, you may have bought something for $12 and something for $9. How would you work out the total in your head? You may know that $12 and $8 is $20, then one more is $21.
Or that $9 + $9 = $18, and $3 more is $21.
✦Children at this stage need to learn a lot about the Base Ten nature of our number system. Continue playing grouping to 10 games with iceblock sticks or pebbles etc (mentioned in ‘Counting From One By Imaging’ section.) Try using 3 dice to make adding the totals a little more challenging.
✦Continue checking doubles to 20 (4 + 4, 9 + 9, 14 - 7 etc) have been remembered and facts to 20 (eg 16 + 4, 2 + 12, 9 + 11, 17 - 4)
✦Practise automatically knowing facts from the 2, 5 and 10 times tables (multiplication and division) and begin to learn counting patterns and groupings for the others eg 3’s, 4’s etc, forwards and backwards. ✦Take opportunities to share your maths strategies with your child and encourage them to share their own. Play board games and card games together. eg. crib, 500, etc.
Advanced Additive Part-whole (AA) - Stage 6
Advanced additive children use a variety of ways to solve and estimate the answers to addition and subtraction problems and are beginning to solve multiplication and division problems in a variety of ways too. They see numbers as whole units in themselves but are also able to split numbers up and see lots of possibilities for subdivision and recombining. Children working at this stage need lots of reinforcement of their basic facts both in addition & subtraction and multiplication & division. Children can work with numbers up to one million.
✦Make small flash cards of all the basic facts and then put them into piles of those you know and those you don’t’ know. Work on the pile you don’t know, gradually getting that pile less.
✦Continue reading large numbers up to millions. Use the odometer of the car and read these numbers. What is one more? One less? Ten more? Twenty more? A hundred less? A hundred more?
✦Reading phone numbers as a number rather than as digits e.g. 3126533 – three million, one hundred and twenty-six thousand, five hundred and thirty-three.
✦Gather some decimal numbers from magazines, newspapers, advertising flyers etc. Place these in order. Be careful to use more than just prices. Do the same with fractional numbers.
✦Use the car sales pages or house sale pages in a Saturday paper and get the children to say and then order some large numbers. Which is the most expensive car? The cheapest?
✦Use contexts to solve multiplication problems eg. cans of soft drink – 6 packs of 4 cans – how many altogether? What is the total volume? Or if a packet of 10 cakes is $2.50 – how much would each cake cost? Or 8 pies shared among 3 people – how much would each person get?
Advanced Multiplicative (AM) - Stage 7
Advanced Multiplicative thinkers can choose from a range of strategies to solve problems in the best way including problems with fractions. They can work with decimal numbers to three decimal places. They are able to make use of more complicated strategies where one or more of the numbers may need to be broken up, manipulated then recombined. Children working at this stage need continued reinforcement of their basic facts both in addition & subtraction and multiplication & division.
✦Encourage children to use more than one strategy to solve a maths problem and check their answer. ✦Use flash cards of the basic facts to get the children to state what the basic family of facts are. eg.
8 x 4 =, ? 4 x 8 =, ? 32 ÷ 4 = ? 32 ÷ 8 = ?
? x 4 =32 ? x 8 = 32 ? ÷ 4 = 8 ? ÷ 8 = 4
4 x ? = 32 8 x ? = 32 32 ÷? = 4 32 ÷? = 8
Use addition and subtraction facts as well. eg.
3+ 6= ? 6+ 3= ? 9–6= ? 9–3= ?
? + 6 = 9 ? + 3 = 9 ? – 6 = 3 ? – 3 =6
? x 4 =32 ? x 8 = 32 ? ÷ 4 = 8 ? ÷ 8 = 4
4 x ? = 32 8 x ? = 32 32 ÷? = 4 32 ÷? = 8
Use addition and subtraction facts as well. eg.
3+ 6= ? 6+ 3= ? 9–6= ? 9–3= ?
? + 6 = 9 ? + 3 = 9 ? – 6 = 3 ? – 3 =6
3 + ? = 9 6+ ? = 9 9- ? = 3 9- ? = 6
✦Gather some decimal numbers from magazines, newspapers, advertising flyers etc. Place these in order. Be careful to use more than just prices. Do the same with fractional numbers.
✦Use the car sales pages or house sale pages in a Saturday paper and get the children to say and then order some large numbers. Which is the most expensive car? The cheapest? What is the difference between the two?
Advanced Proportional (AP) - Stage 8
Advanced Proportional thinkers find solutions using common factors, the multiplication of decimals and the calculation of percentages. These thinkers can find the relationship between two different measures. The children at this stage can make use of a variety of complex strategies to solve problems involving fractions, proportions and ratios.
✦Children should be encouraged to say decimal word sequences counting forwards and backwards by the thousandths, hundredths, tenths, ones, tens etc, starting at any decimal number.
✦Children need to practice saying the number one-thousandth, one-hundredth, one-tenth, one, ten, etc before and after any decimal number.
✦Gather some decimal numbers from magazines, newspapers, advertising flyers etc. Place these in order. Be careful to use more than just prices. Do the same with fractional numbers. ✦Use the car sales pages or house sale pages in a Saturday paper and get the children to say and then order some large numbers. Which is the most expensive car? The cheapest? What is the difference between the two?
✦Make use of percentages. eg. 20% discount, how much will we save? What will the final price be?
✦Continue to encourage children to use more than one strategy to solve a maths problem and check their answer.
What about basic facts?
Children should be able to make sense of addition and multiplication before they try to memorise their tables. When they do understand it, it is important that they learn these basic facts until they can recall them instantly. Each of the basic facts families are linked to the stages mentioned previously. Ask your child’s teacher when or how they feel it is appropriate for you to support your child in learning these basic facts.
What about bookwork?
Most children will have untidy sections in their maths books especially where they have been thinking through problems. They should also have tidy sections where they will have written out important ideas or their answer. Children are often involved in classroom discussions and hands-on activities. Therefore there may be less formal written work in their books than you may be expecting from years gone by. Your child should be able to talk about their learning though, so ask them about their work and ideas.
What about calculators?
Children are encouraged to work towards doing most calculations in their heads. They should only use pencil and paper or a calculator when the numbers are too hard. There is a place for children to explore numbers and number patterns using a calculator.
Websites
Here is a list of some websites that could be useful to assist your child with their basic facts homelearning:
From the home page, click on ‘Interactive Activities’, then ‘Maths Zone’. Other places on this site could be worth a visit for activities in other curriculum areas
Place cursor on ‘Key Stage 2’ at the top of the home page. Click on Numeracy on the drop down window to access the maths games
Click on ‘1/2/3’ on the home page for Numeracy games. Games are then listed down the right hand side of the page
From the home page, click on ‘The Playground’ for sample activities
This is a game based on the TV show ‘Who wants to be a millionaire?’. Children are asked numeracy questions and have to answer them correctly to move on to the next level where they can bank, or risk it all! There is also ask a friend etc.
A lot of links to a variety of websites - I have not tried them all!
A variety of entertaining educational games, choose maths games on the menu and there are plenty for your child to work on.
A great basic facts challenge where children compete with others around the world in a basic facts race to the finish.
Another maths based site with a collection of maths games for your child to choose from.
Another site with a collection of maths games for your child to choose from.
Cool Math Games
IPod Touch Apps
Here are a selection of apps available to help your child with their maths learning. Many of these are free and most that are paid apps cost between $1 - $3, with a few exceptions.
•Basic maths
A free app that helps with practice of basic facts in addition, subtraction, multiplication and division. Suitable for all levels.
•Rocket math
A free or paid app which not only helps with practice of basic facts but also can be used to help with the practice of different strands such as geometry, time and numbers. A huge child favourite! Suitable for all levels
•Dino Math
A free or paid app, great for the lower stages of numeracy, models counting in sets and using materials with low numbers. Excellent for the younger children.
•Frac Factory
A free app which helps with learning of fractions and decimals. Great for the year 7 and 8 students. •Sudoku A free app, suitable for most ages, a great way for children to learn numbers and ordering while really using their brain to think about the puzzles!
•T.A. Math
Free app. An entertaining basic facts game where you compete against the mouse trap to get the cheese. Good for middle to senior learners.
•Number crunch
A free or paid app. Great for basic facts across all areas. Most suitable for ages 8 and up.
There are many more apps out there which are great for your childʼs learning. We encourage you to check them out and see which suit your child best.
The majority of the iPod apps are also available on iPad. There are a few apps which are only available on iPads.
•Math board
A free or paid app. A bit more expensive than most but an excellent app for all stages. Good for teaching those in the higher stages how to use algorithms (stacking).
•Sequence Pro (Free app.)
This is an excellent game which will teach children about sorting and sequencing numbers.
No comments:
Post a Comment