Maths - trying the fishbowl technique

Hello friends,

I am currently working through the tips and tricks for learning your times tables with my students. This week we gave the 'Fish Bowl' a go (see this previous post) and it worked brilliantly :)
Your classroom culture MUST be established though as it is a 'risk-taking' exercise for the students to share their thinking and feel comfortable about being vulnerable with with this.

 We all used different materials at our table groups and also rotated around between activities so that the kiddies got to experience a variety of ways to model their  thinking.

Prior to this, we had looked at multiplying with 0,1, 2, 3, 5 and 10. Now we were moving to 4 and 6. These 2 numbers are special in that they have factors that we have already covered.

I asked the students if they could create a number story they could model, that showed this idea (factorisation). I didn't call it that - I wanted them to discover the concept for themselves. They were very inventive with the way that they used colour to demarcate for place value where needed (including for decimals). I found it very revealing and the kiddies all learnt heaps about misconceptions and factors. Here is the first video showing a common misconception. This students was modeling 6 x 23 or 6 groups of 23 with coloured sticks. He used colour to demarcate the ones and tens and the groups into their sets as well. He self corrected just after this video snippet when he realised that his total as explained did not match the workings in his book.

This video shows a students who had the correct understanding and could even interchange the factors. His story was 6 x 5 or 6 groups of 5. He demonstrates 2 x 3 x 5 and 3 x 2 x 5:

Finally this student used coloured jelly beans to demonstrate multiplying decimals. His equation is 6  x 8.4 or 6 groups of 8 wholes and 4 tenths. He also uses colour to demarcate wholes from tenths. Please note that this concept was devised originally by the first student with the misconception and adapted by this student after the first one shared.  

This little resource is great with helping to remember the times tables tricks for both teacher and student. You can print them into little foldable booklets for student mathsbooks or homework books too. They have been grouped into the sets that tables are usually learnt.

I quickly added these images from our maths books. We are just up to the 4 and 6 times:

Available internationally from:

Available in New Zealand from

 

How do you teach multiplication tables to your students?

Thank you for visiting. Come again soon.

Maths Knowledge #1 - What is it?

Hello friends,

Maths is one of those subjects you either loved or hated when you were in school. I'll bet that how you felt about it, strongly depended on the teacher you had and the lessons / resources that they provided, as well as their own attitude to the subject.

Having been the TIC (teacher in charge) of Maths at my school, I found it really deflating how many teachers held a negative outlook on this subject. Yet it encompasses daily skills necessary to function in our lives. Logic and reasoning applies universally to the choices we make...so lets make maths fun and REAL!.

One of the biggest gaps today is in the area of board games. The rich maths concepts that come out of them, not to mention the social aspect, communication skills, kin-aesthetic application, values examination, peer moderation and a competitive purpose to improve, to name a few of the benefits.

I see a lot of worksheet based maths lessons these days, and while there is definitely a place for this in your programme, it seems to have exploded since the accessibility of photocopiers and the continual growth of curricula that seems to cram more and more Learning Outcomes / Standards into a single year. No wonder the fun has been squeezed out - there is simply no time for it :(   . . . . . . . . or is there?

I am making it my aim to post a series of blogs about some ways to have fun while learning maths, but first, a little background about our maths curriculum for my international readers. I'm sure you'll see commonalities.

Over 10 years ago now, the NZ ministry rolled out the Numeracy Project in schools. This was a great way to up-skill teachers and get them all working from the same page, so to speak (because the programme came with its own set of teaching books (8) and many teachers would teach with these on their laps as a script, in the beginning).

Books 1-9 are viewable at NZ Maths.co.nz

One GOOD thing was it brought back emphasis on using concrete materials to model number concepts. YAY! Lucky kids. This meant that schools purchased math kits for all their teachers to use. Materials we didn't have before, like - counters, beans, film canisters, ice block sticks, array cards, fraction kits, 100 boards and large abacuses, etc. It was like Christmas.

The Numeracy Project focused of Number & Algebra at first. It divides up number into Knowledge and Strategy.

First of 8 levels - student profile sheet from NZ Maths

While different Strategies are the thinking processes one applies to solving problems, Knowledge is the content that is required to be instantly recalled and used when working with the different strategies.
Of course, as with any curricula, Numeracy is leveled and has 8 stages. Stages 1-3 cover the early basics and roughly equate to kiddies aged between 5-7yrs. These levels require students to spend a lot of time with manipulatives, exploring the concept of numbers. From around year 3 (age 7+), children are able to sustain focus on pair and groups games for more extended periods and group rotations are easier for teachers to manage.

Acquiring and practicing Knowledge expectations is an aspect that can be run through your independent work stations.

 

2 of my Year 4 boys from last year playing a game of Loopy to practice multiplication (Basic Facts Knowledge)

For younger students you might run it more structured for peer support, i.e. all kiddies working on the same activity for a week, then move on. For older students you can run it on individual goal based systems. This is how I have run it from year 4 up (age 8+) because it allows students to move at their own pace, be it slower or faster.

Finally, for today, each stage has several specific Knowledge learning outcomes that students need to acquire and demonstrate independently, most of the time. These fall into areas of Number Identification, Sequencing & Ordering numbers, Grouping & Place Value, Basic Facts and finally Fractions. I spent months and years sourcing games (both actual and virtual) to match each of these. In the end I wrote a set of games specifically for each stage and embedded it within a self-management and self-reflective programme for students.

I have used it for about 4 years now. Even when teaching in a digital classroom, I found that students loved the games centre, I suspect because of the human interaction aspect. While computer programmes are a great resource, the shine can wear off after a while and it can become just another worksheet type resource, whereas when you play games with fellow students, it will turn out differently every time :) I'll leave you with this video of a Bingo game in progress for practicing times tables.

Stage 4 and 5 are now available at my TPT store, my TNB store and at HML. 6-8 are in final proofing stages and on the way. Links are below.

Next time I will post about the ideas behind the resource so please link up or visit again soon :)

'Til next time

Super Speed Maths

Today I want to post about a cool way to practice Basic Facts in your classroom that doesn't involve paper and pen and encourages mental arithmetic. Chris Biffle from Whole Brain Teaching shared this resource a few years back and it just sat on my hard drive till this term. Such a shame, now that I see how much the kiddies are enjoying it.

This is my old copy. I believe it has been updated now to include Fractions too.

I have a few reluctant/slow writers that know their facts but just don't achieve on timed written quizzes, so I wanted to give something different a go.

We started with each student gluing the first level of facts and the matching answer sheet into their books (1 per page and side by side). There are multiple levels in the resource.

They work with a buddy. Person A gets 60 sec to read out and answer as many facts as they can. Person B monitors on the answer sheet. If a wrong answer is given, person B says "Beep! its x, go back 2 spaces". Person A then resumes 2 spaces before the incorrect answer.

Sorry if pics are a bit blurry. I cut them from the video.

When the timer buzzer rings, person A records a small 1 beside the last fact answered.

Person A now immediately gets a second go, with the aim of beating their first go. If they do so, the reward is to highlight off a row of facts at the top of the page. Tomorrow they start on the row directly below the highlighted one.

Repeat with person B.

I also gave out the STAR sheet that they record the  coordinate of the last answer given each day (the box where they write a small 2), to monitor their progress.

I have loaded up a short video (quicktime) of it in action today, on my classroom wiki page for this term. Feel free to visit and leave feedback here.

You can also watch a Chris Biffle webinar about it here here on You Tube but be warned, it is long (almost an hour). The resourse is available FREE* for download on their WBT website.

* resources are usually free with the pro visor that you share about WBT to your teaching community.

Times Tables

I make a big push to cement timetables in the year I teach (year 4) and we spend the whole of the second term on it, term 1 being about addition and subtraction basic facts. I made a Keynote for each set of tables to support the Visual learner and read them out as well. See more about times tables and resources I use, on the Maths Reflections page here...