Teaching Column Addition and Column Subtraction

This is my lovely place value teaching tool. It was custom-made for me by my brother at Sen Clock and my dad. Prior to this I’d been using a paper sheet and laminated tokens, but I was fed up with them sticking together and getting lost. This magnetic version is much more practical.

I find this really useful because we if stick the tokens to the board, children have visual proof that once there are 9 tokens in a column there is no room for any more, so if they wanted to add another One in, it’s time to exchange 10 Ones, which won’t fit, for 1 Ten, which will. Physically clearing out the column, exchanging 10 One tokens for 1 Ten token really helps them to understand what happens when I want to add 1 to 109.

It’s great for subtraction too. When presented with – calculation lots of children will try to do 3-1. With this place value board, they can see that we only have one counter so we can’t take away 3. Then we can physically exchange 1 Ten for 10 Ones. I’ve made the column wide enough to accommodate them and the children can then see that they have enough in the column now to subtract 3, and that the tens column has one less token than it had before. I find this works really well side by side with a written column subtraction to iron out any misconceptions and to understand how the written method works.

35 activities for children in your own garden

I have noticed over the last few years, that fewer and fewer children know much about nature. In fact a few weeks ago I was surprised to discover than none of the children I was working with in school knew what a buttercup was.

I know it’s hard to find time in busy lives to get to the park or walk in the country, so here are a few suggestions of things that can be done without leaving your own garden.

 Important notes for the adults
This post contains lots of ideas to help your children connect with nature in your own garden. There are also ideas included for linking some of these activities to maths, English, science and art. Your child may need help or supervision carrying out these activities. These activities are suggestions only – it is your responsibility to ensure that it is safe to carry them out. Although I have used the websites and apps suggested, I have no control over their availability, content or any adverts that are placed on those sites and I cannot therefore accept responsibility for them.

Important notes for the children
There are some suggestions of things to eat in this list, but never eat anything you find in your garden without checking with an adult that it is safe to do so.
Make sure you ask an adult’s permission before doing any of these activities, and especially before visiting any of the websites or downloading any of the apps suggested here.
Always wash your hands after touching things found in your garden.

Thirty-five ideas of nature-related things to do in your home or garden.

  1. Race two raindrops down the window pane. Describe the path they take – straight or curvy, fast or slow?
  2. Count ladybirds in the garden. How many did you find? Make a tally chart of how many have two spots, four spots, etc. What was the highest number of spots? Which amount of spots was most common?
  3. Close your eyes outside for two minutes. What sounds can you hear?
  4. We talk about the seven colours of a rainbow but they don’t really have 7 colours. Look at a rainbow. What colours can you actually see?
  5. Choose two pretty stones from the garden. What is the same about them? What is different about them? Look at the patterns. Draw one of the stones.
  6. How many different coloured butterflies can you see? Have a look at a butterfly identification chart- can you identify any of them?
  7. Place a blade of grass between your fingers and blow. What sound does it make? What happens if you use a thicker or thinner piece of grass?
  8. Look at the flowers in the garden. Either find one for each colour of the rainbow, or find 3 the same colour and order them from lightest to darkest.
  9. Make a daisy chain.
  10. Touch the soil on a dry day. What does it feel like? Touch it again after it has rained. Describe the difference in texture (how it feels).
  11. Watch the bees. Which sort of flowers do they like best?
  12. Count how many different sorts of birds visit your garden. How many can you name? If you don’t know what sort they are, have a look at the RSPB site to try to identify them.
  13. Open the windows early one morning and listen to the bird song.
  14. Plant some meadow flower seeds to attract the wildlife to your garden. Don’t forget to water them on the days it doesn’t rain.
  15. Make your own rain gauge and measure the rainfall. If you measure it over a few days, you could draw a graph of your results.
  16. Eat your lunch outside.
  17. Look for spiders webs. How many different sorts of spiders did you spot?
  18. Lots of people don’t like wasps. Find out about wasps and write down one reason why we should be grateful to them.
  19. Tie a ribbon to a stick. Which way is the wind blowing? Watch it for a few days. Does it always blow in the same direction?
  20. Plant some runner bean seeds and wait for them to grow – don’t forget to water them if it doesn’t rain. When the beans develop, you can pick and eat them!
  21. Ask five different people what their favourite flower is and why. Write down their replies.
  22. Make a bark rubbing.
  23. Lift up a stone or log. How many different insects do you see? Note which insects like which habitats. UK Safari is a useful site  to help you identify what you have found.
  24. Count the number of petals on different flowers. How many arrangements can you find? How many had 3 petals? How many had four? How many had 5? How many had more than 5? Draw a bar chart to show your results.
  25. Lie on your tummy and look at the grass. Have a look at the tiny insects you can see. Can you see any more if your use a magnifying glass?
  26. Smell the flowers. Which one do you like best?
  27. Make a collection of leaves. Pay attention to the size, colour and shape. Are they smooth, prickly or furry? Are the veins (the lines running through the leaves) hard or easy to see? If they are leaves from trees, see if you can identify them from the Woodland Trust website or download the free woodland trust app.
  28. Watch a sunrise or a sunset to find out which direction is east/west. Remember the sun rises in the east and sets in the west. Paint / draw what you can see, or write a description/poem about it.
  29. Plant some nasturtiums. They are climbing plants, so they look really pretty growing up walls and fences and you can eat the flowers and leaves on bread and butter!
  30. Look at the clouds. How many different types can you see? Have a look at the Royal Meteorological Society website to help you identify them. What colours can you see? How quickly are they moving? Can you see any pictures in the clouds?
  31. Grow your own potatoes.  Grow your own potatoes has some instructions for how to plant them and some instructions for how to look after them.
  32. Make a sundial. You can also do this with a stick in the ground instead of using a board and a nail, and by placing a stone where the shadow falls each hour, instead of marking the board with a pencil. Don’t forget to paint the numbers 1-12 on the stones!
  33. Enjoy a thunderstorm. Work out how far away the storm is. Is there sheet or fork lightning or both? Learn how to spell the word lightning (tip – there’s no ‘e’ in it)!
  34. Look at the sky at night and try to pick out some constellations. SkEye is a useful app for knowing what you are looking for, or you could try the Astronomy Now website.
  35. Feed the birds. Use proper birdseed – bread is really not good for them. Make sure that if you decide to put out peanuts, they only go in a proper peanut feeder – otherwise very small birds can choke on them.

And above all – have fun!

 

Subtraction by Adding On

This is also sometimes called “subtraction using a blank numberline” and I’ve even heard it called “that nonsensical modern method”. This latter is a real misnomer since it is neither nonsensical nor modern. In fact it’s a method that dates back to before I was born, in days before we had calculators and electronic tills. It’s also a really useful method involving counting forwards, which is always easier than counting backwards – even for maths geniuses!

Let’s return to those old-fashioned little shops. I buy some sweets for 24p and hand over a £5. To work out my change, the shopkeeper needs to calculate £5 – 24p. Now she could count £4.99, £4.98, £4.97 until she had subtracted 24p, but what you actually would have heard is this:

24 and 6 makes 30, and 20 makes 50 and another 50 makes £1. 2, 3, 4, £5. And while doing this they counted the change (£4.76) into your hand.

This is the method that schools have returned to. To begin with, Children use a “blank numberline” – that is, a line that they can write the numbers on themselves. They then write the lower number at one end, and see what they need to add to make the higher number. Here’s an example:

96-38

numberline

The children first of all use their knowledge of number bonds to add to the next 10 (38 + 2 = 40).
They then use their ability to add multiples of 10. In the example above the child has done 40+10 = 50 and then 50 + 40 = 90. They may have been able to see straight away 40 + 50 = 90 and done this as one step, or they may have needed to do 40 + 10 = 50, 50 + 10 = 60, 60 + 10 = 70 and so on up to 90. The method isn’t about having to complete it in a certain number of steps, it’s about each child breaking it down into the smallest number of steps that they can manage.
When they reach the multiple of 10 before the higher number, they add on whatever units are needed to make the higher number, in this case it was +6 to make 96.
Finally, they add up all the numbers they added on to find the answer: 2+10+40+6 = 58 so 96 – 38 = 58.

When they are confident with this, they move on to jotting down only the numbers they are adding on, and they keep the tally in their head, until eventually they develop their working memory enough to hold all of the numbers in their head and write down just the answer.

Related posts: Teaching the Times Tables, Teaching Sequencing and Column Addition