Mental Computation During LOCK DOWN
As teachers spending all of our day on our computers due to us being in strict stage 4 lock downs in metropolitan Melbourne we are all probably going a little “MENTAL.”
It’s been 7 weeks since the Primary Maths Specialist Team presented our Mental Computational professional learning in the gym ensuring we were all socially distanced.
During the many days planning, what I hoped would be engaging maths activities for the Year 5 students while they were learning from home I was wondering how I could incorporate a mental computation sessions for my students.
Unlike our first phase of lock down way back in Term 2 as a school it was decided that we would connect with the students via a virtual classroom on WebEx. Immediately I saw this as an opportunity to work with smaller groups and trial a new strategy to engage the students in some fun approaches to incorporating Mental Computation during a maths lesson.
As a school we have been fortunate to have the opportunity to participate in some inspiring Professional Learning online facilitated by Rob Vingahoets and Michael Minas Using
Using Games to Develop Fluency and Ramp Up Engagement (F-2)
Using Games to Develop Fluency and Ramp-Up Engagement (3-6)
After attending both of these wonderful PL sessions I decided to try and adapt some of the games that they presented to us.
The games that I trailed were:
- How’d you Solve It?
- Five Moves to 100
- Greedy Pig
The students in my grade loved the games and I felt that it was a really fun and engaging way to incorporate a little Mental Computation to my weekly WebEx maths sessions.
Feel free to give them a go with your classes and if you would like copies of any of the power points please just email me.
How’d you Solve It…..
Students were given 2 minute to solve these problems in the head. They couldn’t use pen or paper or a calculator.
As the students were sharing their strategy I was able to ask questions like: Did anyone else solve it this way? Did anyone else have a different strategy? Could you re-explain how x solved that problem?
I used the annotate function in WebEx to represent student thinking on a number line for the addition problem and I was able to demonstrate student thinking using an area model for the multiplication problem.
Five Moves to One Hundred
This game is a game of skill and chance and requires students to draw on their Place value knowledge and mental computational skills with regard to addition.
Set up and share a split screen so that students can see the game board and the dice. Students make a copy of the game board on a piece of paper.
Roll the dice. Players choose whether the number rolled goes in the tens or ones place value column. For example if teacher rolled a 3 it could be 3 or 30.
The aim of the game is to get as close to 100 as possible. If you go over 100 you do not bust as the aim of the game is to get as close to 100 as possible.
After the five rounds the student or teacher who is the closest to 100 is the winner.
Often I would stop and get the students to share their score verbally or through the chat function on WebEx. I also asked before the last round what numbers students wanted to roll next and why.
When I first started playing with the members of my class I played and annotated the scoreboard by inserting my scores.
After the first game I stopped doing this and kept my own score on a piece of paper. The students loved this game and ask to play it again and again.
Another classroom favourite that I adapted to play with my students during a WebEx session is the game Greedy Pig.
Within the virtual WebEx classroom it is difficult to know if the student is standing up to indicate that they would like to keep their score and not risk losing it due to rolling a 1. This was modified so that if a student decided not to “risk” it they would switch their camera off.
Students being able to see my game board and the virtual dice added to the student’s engagement.
As the rolls of the dice progressed the tension grew and the numbers that they would soon need to add grew as well.
This was a fun way to talk to the students about probability and build in a sneaky element of Mental Computation without them even knowing.
The Rob V and Michael M professional learning referred to an article written by James Russo “Five principles of educationally rich mathematical games.” I believe that Greedy Pig covers each of these thus making it a rich and educationally valuable maths game to play with students.
James Russo’s “Five principles of Educationally Rich Mathematics Games”
Watch the video .https://screenrec.com/share/X4cE3RYerv
These are the multiplication facts to 10. There is 100 facts. It is expected that students in Year 4 know all these facts by the end of the year. That means if we say 9 x 7 you would reply 63. In the past students were expected to memorise all these facts. As it is difficult to learn and remember all these, we teach multiplication strategies to help you.
These are the multiplication strategies. Doubling x2 and multiplying by 10 are the most important. Once you know those you can work out the remainder of the facts very easily.
This is a multiplication grid. It has all the multiplication facts listed in a different way. Here is 6 x 8 = 48 and here is 4 x 3 = 12. It shows the fact family. Here is 5 x 7 = 35 and here is 7 x 5 = 35.
You can see the x2 is just double the number, then double again to find the 4 facts. 3x is double the number then add another. 5s are half the 10s. 9s are x10 then take one away.
So we can see that we know the 1s, 2s, 3s, 4s, 5s, 9s and 10s, so if we highlight them and their turn arounds, most of the facts are already learnt.
There are these 9 facts left to learn. 6 x 6, 7 x 7, 8 x 8 are what we call square numbers because they make a square.
7 x6, 7 x8 and 6 x 8 are the only multiplication facts you need to memorise.
These strategies also help us to solve problems with larger numbers in our head. We sometimes can’t use a written method to work out an answer so the strategies help to solve the problem mentally.
For example, 37 x 4 would use the double, double strategy. Double 37 is 74, then double again would equal 148.
Hope this helps you to understand why we teach multiplication strategies and makes it easier to learn the multiplication facts.
Today I played what appears to be a simple card game in Foundation. It goes like this-
In pairs the children are given the cards 1-5 (we’re working with numbers to 5 in this year level)
Place the 5 cards face down. Taking it in turns, flip one card over and place it where you think it would go in the counting sequence of 1,2,3,4,5. Now its the other partners turn. They flip a card and place it where they think it goes. This continues with students taking turns until all 5 cards are in order.
The cards are not always flipped over in sequential order. This is where the difficulty lies. Although children can often count up to large numbers when they enter Foundation, that doesn’t always go with understanding what it is they’re counting, what makes 3, what number comes before, what numbers comes after etc.
What skills, understandings and strategies do you think children can develop from playing this game?
This would be a fantastic game to apply the 5 Practices Model to.
This game is a wonderful opportunity for children to engage in the Mathematics Proficiencies of
- Problem Solving
The maths discussions that took place helped students who found the task challenging to develop their understandings as well as those who were very proficient the chance to think deeply about their understandings and justify, explain and elaborate their choices.
To further challenge the children, cards 1-10 were given and they were off and running placing them in order from smallest to largest. Many children went to resources around the room including the number line and hundreds chart. It was great to see them utilising the resources at their fingertips so confidently.
A big thanks goes to Doug Clarke who shared this game with us at the February PMSS conference. Not only was it fun but a great task/game for assessing student understanding.
Welcome back everyone! I can’t believe it’s week 3 already.
At one of our PMSS conferences last year, the name Jo Boaler was mentioned as someone doing great work on Growth Mindset in mathematics. Her Ted Talk is amazing. Growth Mindset is not always something we tend to think about when it comes to mathematics. She discusses some of the newest neurological findings that directly link Growth Mindset and mathematics achievement and that our brains ‘see’ fingers when we calculate. ‘Finger perception’ is directly linked to students ability to calculate with more accuracy than standarised testing. Now consider this statement
‘When we stop children from using their fingers to count, its akin to halting their numerical development.’
So take 12 minutes out of your busy day- you can just listen to it and pretend its a podcast if that’s more your scene. It will get you thinking- guaranteed!
For many years we’ve used the Maths Online Interview to assess students. Each time I complete the interview Im reminded of how rich the interview is not just in terms of ‘right’ or ‘wrong’ answers but in the way in which the interview reveals so much more about what the child is thinking, doing and not doing. We’ve been working hard this year to use this information more effectively in our classrooms and across cohorts of students. We’ve introduced an ‘hour of counting’ lesson each week and seen our counting results in MOI grow dramatically. The hour of counting incorporates a range of learning activities and we try and integrate it with our Curiosity Unit or other aspects of mathematics where it fits. Sometimes we just count! We’ve loved a game called ‘Chicken Scramble’ from Scaffolding Numeracy in the Middle Years. These resources called SINE from Catholic Education Office and resources from Kathy Palmer have all been instrumental in helping us to really target the point of need for students within the Growth Points of MOI.
Scaffolding Numeracy in the Middle Years (SNMY) is a program we run here also which has been fantastic for helping those students still struggling with early numeracy concepts, when they themselves are no longer in the early years of schooling. Chicken Scramble comes from there. Although it is from SNMY the concepts behind the game are just as pertinent and important for our younger students. This game probably has lots of names but regardless of its name the children LOVE it!
So who are we these PMSS people?
There are three of us! Brett McGinniskin, Robyn White and myself (Elicia Briggs) are the Primary Maths and Science Specialist (PMSS) team at Greenvale Primary School. Although the title includes Science we are focusing on the mathematics side of the program.
What is this PMSS business?
Greenvale Primary School was a successful applicant for funding of the PMSS initiative. The Primary Mathematics and Science Specialists (PMSS) initiative is a successful Victorian Department of Education and Training (DET) program that upskills primary teachers in government schools to become mathematics or science education specialists. The Victorian Government has provided $27m to train 200 specialists over four years (2016-19). The initiative aims to: • increase student engagement and achievement in mathematics and science, • increase teacher confidence and capability in teaching mathematics and science, • increase understanding of Science, Technology, Engineering and Mathematics (STEM), • have a sustainable impact in schools beyond the life of the initiative’s funding. This website was created to document our journey as we strive to teach mathematics with the best, research informed models of teaching available.
We are not ‘the experts’, instead we are three fortunate teachers who have the opportunity to work with amazing teams of people including our own staff, professionals from the field of mathematics and a host of other real experts! In the coming weeks and months, you can expect to see the professional learning delivered to staff, student work and articles by the experts who are guiding our journey. We hope to inspire, excite and motivate you.
Elicia Briggs on behalf of the PMSS team
Elicia, Brett and Robyn.