Going Mental! Part 3
Post date: Mar 24, 2014 10:18:52 PM
In Going Mental! Part 2, I looked at oral counting, the counting stick and the sound of a number. In this post, I'm going to explore number line activities, the bead abacus and mini-white boards.
Number line activities
Number line activities can include a wide variety of activities and very important to help children develop their number sense. In Going Mental Part 2 , I recommended Maths out Loud, a video produced a number of years ago by the PDST, showing a cuiditheoir modelling oral and mental maths with a senior infants class. In the video clip (16:17-19:03) we see the children making a type of human number line using large laminated numeral/digit cards (1-10). Worth noting from the video is how the teacher asks the girl to explain why she thinks the children holding 5 and 4 should swap places, thereby asking her to explain her thinking and not just affirming straight away that she is correct. It is also interesting how the girl has to count from 1 to 6 to explain her thinking; thus reinforcing a point made in the previous post explaining how children can over-rely on counting from a familiar starting place i.e. 1.
A set of the large numeral/digit cards, as seen in the video clip, would be very worthwhile in the younger classes and would be well used. However, I'm not so sure if I'd recommend them in the older classes, as the scope and range of numbers would be much larger. Rather, Mini-whiteboards (explored more below) might be better; since they are less restricted can be used to represent any value that suits the topic.
"See it, Say it." When introducing an unfamiliar section of the number line to children, be it teen numbers, thousands or thousandths, the children should have the opportunity to see the numbers in sequence, and to become aware of their positioning in relation to each other. Then, through a process of saying out loud the numbers they see, they should begin commit those numbers to memory. Once comfortable with this, they can progress to the next stage: "Say it, See it to check". This is where they say out loud a number/numbers that are hidden, but then reveal what's hidden to check if they were correct. This use of blank/partial number lines promotes children’s ability to visualise numbers
A numeral flip (see opposite) can be useful for this if you have one, but if not, they are lots of alternatives available. Firstly, there are some great interactive number lines available on the net: This number line ITP, generates a customisable number line which can go anywhere from 0-500 and -50 to +50. This other number line, available both as an iPad and web app, allows you to count up 104 multiples of a chosen number. Both of these also allow you to use the number line to add on, count back and calculate difference. Also related (but not as customisable) is this great game called Estimate. You have to estimate to what number on the number line the arrow is pointing, based on its position in relation to the known numbers. There are lots of different levels, therefore it'd be useful in all primary classes. And if all else fails, you could write/draw up a targeted section of a number line on the IWB/board, add the numbers, with help from the class, and then hide them using a strategically placed shapes that could be re-positioned to reveal the hidden numbers.
As with many of the activities in Going Mental Part 2, the number lines can go up in intervals of ones, tens, hundreds, twos, fours, 25 etc., and can be used for fractions, (check out Fraction Monkeys or this ordering fractions activity) decimals, percentages, positive and negative numbers.
Another important point worth making, is that number lines should be used regularly as part of maths in all classes, not just in the junior classes. Current evidence suggests that, while teachers appreciate greatly the benefits of concrete manipulatives and exploration, we can often move children from this stage, straight to the abstract stage of just using numbers, symbols and digits. Rather, we should progress from Concrete to Pictorial (Representational) to Abstract (also know as CPA approach, based on research by Bruner and as found in Singapore Math). Number lines are an ideal strategy to use as part of this pictorial/representational stage and can be used very effectively in both the junior and senior classes, as can be seen in this fantastic InTouch article Keeping Numbers on Track . Personally, I use blank/open number lines all the time when teaching elapsed time and also for making change in money.
The counting stick (see Going Mental! Part 2) is in itself a concrete example of a blank/open number line. Also related are hundred squares, which are simply an adaptation of the traditional horizontal number line, and can be used in much the same way. For further ideas on both, check out Using number lines and hundred squares: A Maths to Share article from NCETM
Bead Abacus/Number Rack/Rekerek
Abacii come in many shapes and forms. Here, I am referring to the type of horizontal bead abacus, with ten beads on each row, not the vertical type that can be used for place value. The one in the picture is the type I have in my class, and is available from IKEA for the princely sum of €8. The most popular abacus in educational circles seems to be the Slavonic Abacus or Rekenrek, an abacus where each row of 10 beads is comprised of five beads of one colour and five beads of another, encouraging children to think about, and visualise, numbers in groups of tens and fives. This type of abacus also comes in various sizes eg the usual 10 rows (100 beads) and 1/2 rows (10/20 beads) suitable for younger classes. As with most educational supplies, the commercially available rekenreks can be quite expensive (approx. €50 for a similar size to the IKEA version above). However, you can access free virtual examples online (eg this slavonic abacus and this customisable rekenrek/number rack) and you can also make small versions for individual students.
In my own class, I find my IKEA abacus great for exploring number bonds of 100, decimals, percentages, making change of €1 etc. As well as for pre-planned oral and mental activities, I keep it handy at the top of the room, where I can quickly grab it, when needed to illustrate a concept or connection.
The Slavonic Abacus: More information, tips and a link to a virtual online abacus
Bead Frame Tens : an animation showing how the abacus can be used to show the 10s in hundreds
Using the Slavonic Abacus to Reinforce Five Grouping
Slavonic Abacus Recall the number of tens and hundreds in 100s and 1000s.
Dreambox teacher tools: Includes activities where children have to subitize the number on the mathrack (up to 10, 20 and 100)
Mini White Boards (MWBs)
By far the most used resource for math in my room are my mini-white boards (MWBs); I find them great for everything! The main way that I use them is for write-hide-show, where I get the class to answer questions on them quickly in pairs; and then a quick "aon, dó, trí, taispeán dom" later, and I can see straight away who is struggling and/or where they might have misconceptions. Their answers can be direct responses to my questions, or to questions from their textbook (usually displayed digitally in the IWB, so as to reduce distraction). We also use them to quickly "show our thinking" and explain how we came to a certain answer. I have found them to be invaluable; you can quickly assess understanding, immediately address any misconceptions, identify children who require more re-inforcement, re-teaching etc. They are great for stimulating mathematical discussions eg I asked the class to show me 40% as a fraction, some children wrote 40/100, others 4/10, others 2/5, then we discussed the validity of the answers, "same value, different appearance". Just earlier today, we were concluding a chapter on the circle; I called out various parts of the circle eg chord, radius, arc etc and they had to draw a quick diagram on the MWBs to show it.
Another way to use them in a class is for ordering:
Arrange the pairs with boards into bigger groups (eg I have 15 pairs usually, and I arrange them into 3 groups with 5 boards/pairs in each group)
Give each board in each group one of five letters (eg A, B, C, D, E) and give each pair a different instruction (A's write 8 thousandths as a decimal, B's write one quarter as a decimal etc).
Finally ask them to get out in a group and order themselves, smallest to largest or largest to smallest.
To be honest there's no limit to what you can do on MWBs; that's what's so great about them. And they don't have to be just on the maths table/trolley; I've used them for English, Irish, geography, you name it!
Keep an eye out for the final Going Mental post, where I'll look at some other useful mental maths activities and resources, as well as letting you know where you can purchase some of the resources mentioned in the series of posts