Counting and Catching with Captain Ball

Coaching a sport has forced me to learn a lot in one of my weaker areas. Our maths faculty is actually quite sporty, but I fit a more standard stereotype!

So learning to coach has been interesting. Just like all areas of my teaching, I like to make it all about games. I've learned to adapt a lot of games to the skills I need my kids to practise.

Recently I tried bringing one of my sports activities into my Numeracy Roll Call.

 The game is Captain ball and if you don't know it, it goes like this:

• Two or more teams line up. The first player from each team stands facing the rest of the line with a bit of a gap
• The leading player has a ball (or bean bag, or whatever you have that you can throw and catch)
• They throw to the first person in the line, who catches and throws it back then sits down
• The leading player throws to the next and so on until the last player in the line catches the ball
• The last player runs up to the leading position, the previous leader joins the line at the front and all players stand back up
• When all players have completed their time as the leader, the whole team sits down to show they are finished
• First team to finish wins

The Numeracy variation is pretty simple, you just call out numbers in a sequence as you catch. For example, counting by twos, fives or tens would be a good place to start.

Good for a learning activity with kids who are restless and need to move around. I think we all have plenty of those!

What other numeracy or mathematics skills could we adapt captain ball to?

"Make n" Grids - a numeracy game

Another numeracy game for my roll call group. Right now we are targeting the skill of knowing number combinations for numbers up to 20.

We played a game called "Make 10" from the NSW DET's "Developing Efficient Numeracy Strategies" (DENS) stage 2 booklet.

The grids for that game have numbers from 1-10, and you roll a 0-9 die. Players take turns to roll the die and colour in a square on the grid. Players use different coloured pens and the first to get 4-in-a-row wins. When they roll, rather than colouring the number they rolled, they colour the number needed to make ten from their number. For example, if you roll a 6, you colour in a 4, because 6 + 4 = 10.

These grids extend the game to make use of 8, 12, and 20-sided dice, and 10-sided dice with tens, hundreds, and thousands on their faces.

Make n grids.pdf

We played some of these variations today, and they went well. The students can play quite independently, and it's easy to vary the difficulty between different groups by which grid and die you give them.

Yes/No Game with Numbers

A simple premise, and very adaptable. Plus it gives us a nice opportunity to get up and get moving!

Here's how it goes:

• Label one area (e.g. one side of the classroom) with "Yes" and another area with "No"
• Give each student a number.
• Ask yes/no questions about the numbers.
• Students have to go to the correct area, holding their number where you can see it to check.

For example, today I played this with my Peer Numeracy roll call (which was extra good because it was a small group and the year 10 mentors helped check and helped the students who struggled). First I did numbers in the hundreds, then in the thousands.

Some questions:

• Are you even?
• Are you more than 50?
• Are you more than 400?
• Look at your tens digit. Is your tens digit more than 3?
• Look at your hundreds digit. Is your hundreds digit odd?
• Add up your digits. This is your digit sum. Is your digit sum even?

And so on. At the end of each set of questions, I got them to line up in ascending order and collected the numbers and gave out the new numbers.

I've also played as revision with year 7 classes, looking at number properties and special numbers, using questions like:

• Are you odd?
• Are you prime?
• Are you a multiple of 3?
• Is 4 a factor of you?
• Are you palindromic?
• Are you a square number?
• Are you a triangular number?
• Are you in the Fibonacci sequence?
• If you add 3 to yourself, are you a multiple of 5?

Some other ideas:

• Use decimal numbers and ask questions about the digits in certain places, to reinforce place value
• Use fractions and ask questions about the numerator and denominator (to reinforce those terms)
• Use algebraic terms and ask about "are you a like term to ...?" or "is .... a factor of you?"
• Give students shapes and ask questions about their properties

This also makes me think about getting students into groups for group work. Some ideas:

• Give students algebraic terms and get them to form groups in their like terms
• Give students numbers and get them to form groups of multiples
• Give students shapes and get them to find the same type of shape

Multiples Pig

When I was at high school, we played a lot of card games. A lot. All the time.

Pig was one I had forgotten about, until I was reintroduced to it by some students as Spoons. A good description of the game can be found here.

In Pig the aim is to get four of a kind. In Multiples Pig, the aim is to get 4 numbers that are all multiples of the same number (not including one, and I usually disallow twos as well).

All you need are some number cards. Here are some that go from 3 to 50 that work quite well:



My basic summary of the rules:

• Players sit in a circle
• Deal 4 cards to each player
• The rest of the deck is to the right of one player
• That player picks up from the deck then discards to their left
•  The next player picks up from those discards and discards to their left and so on. So each player picks up from their right, discards to their left.
• There are no 'turns', play continues as quickly as the players can play
• The first player to create a hand of 4 multiples puts their hand on their nose
• Anyone who notices this can also put their hand on their nose
• The last player to put their hand on their nose 'loses' (loses a life, gets a letter of the word pig, etc.)
• Shuffle, deal and play again!

The best part of pig is the subtle silent waiting for the last person to notice!

"I have...Who has?" for Simplifying Surds

My new addiction is "I have... Who has...?" cards. I'd seen the idea around a bit, also called "Follow me" or something like that, but never tried any.

Then I found a free example for telling the time from superteacherworksheets and used it with my year 10s.

The basic idea is that the cards make up a chain of matching items. They can be question-and-answer style or just different ways of representing the idea. The time cards have a clock face for "I have..." and a written time for "Who has...?"

We played just by calling out. So I took a card and read my "Who has...?" question. The students all look at their clock faces and whoever has that one answers "I have..." and follows by reading their question. When we got back to me, the game was done.

Of course, you have to have everyone paying attention! This was the hardest part for the class.

Other ways to play, I believe, include using it as a way to get everyone into a circle or a line in a random order, and you could also get the students just to put the cards into order as a kind of matching activity.

Today I tried my own little revision one with year 11 Mathematics. Yesterday we simplified surds, so today we checked our knowledge with these cards:

This was a bit of fun, quick revision and a good check of who still needed help with the work. Also they are very simple to make if you don't need images! So I plan to do lots of algebra ones.

I also suggested to my resident PDHPE teacher that it would be a hilarious game for revising knowledge of STDs. Not sure if he'll take me up on that one.

Numeracy Game: "50 and out"

My second numeracy game of the year for the Peer Numeracy roll call group was based on an idea I found on the internet when googling around. Naturally, I can't find it again. But it was called "50 and out" or something very similar.

Basically, everyone stands in a circle (I've found that a group of 5-10 is good) and they go around the circle saying the next number in the sequence. So for the basic game, they count up in fives. There is a target number, in this case 50. The person who says 50 has to sit down, then the others start back at 5 and you continue until only one person is standing.

There's no strategy to this game, but it leads neatly on to playing variations on "21". There, each person can choose whether to say 1, 2, or 3 numbers in the sequence to try not to get out.

For my numeracy roll call we are focusing on counting on and back by 10s, so we had variations like:

• Start at 10, go up by 10s, 100 is out
• Start at 200, go down by 10s, 100 is out
• Start at 37, go up by 10s, 157 is out
• Start at 182, go down by 10s, 62 is out

We've played for a week now and covered heaps of variations of counting by 10s off the decade, and they've also tried counting by 2s and by 5s.

With another Maths class, we used it more for times tables, up to the 12s. This was also a great opportunity to satisfy their desire to go outside on a nice day! We made two circles on the netball courts and they happily played for about half a lesson. They had a go at the variation with strategy, which I'll try with the roll call group tomorrow!

Numeracy Game for Counting by Tens and Ones

This is a simple group game for practising counting on and back by tens and ones. I used our recently-purchased pocket cubes to create dice for the game.

Players sit in a circle and takes turns to roll the dice and count as instructed. The worded die tells you whether to count on or back, and by ones or tens. The number die tells you how many numbers you need to count. Play starts at 100.

e.g.
Player 1 rolls "count on by tens" and "3", so they count "110, 120, 130".
Player 2 counts from 130. They roll "count back by ones" and "4", so they count "129, 128, 127, 126".

If you get to or below zero, restart at 100.

I have a roll call class called "Peer Numeracy", which involves a group of year 8 students who need help with numeracy working with year 10 students as mentors/leaders/tutors. We tried this game today in our first session for the year. They played in groups of 3 or 4 and the student leaders helped them mostly by remembering what number they were at, and providing guidance where it was needed to keep track of their counting.

Pocket Cube inserts for Counting On and Back Numeracy Game by

The inserts could be varied to increase or decrease the difficulty for students as they develop their skills. For example:

• starting at 1000 and including counting on or back by hundreds
• include counting by twos or fives
• use for higher-level kids studying decimals by counting on or back by ones, tenths and hundredths

Does anyone else use these pocket cubes? What have you done with them?

Day 10: Christmas Sudoku

Sudoku with Christmas symbols instead of numbers. Some kids ones here and here. Not a bad intro to sudoku for kids who aren't already familiar with it, but way too easy for those who are.

This one's a bit bigger and uses the words from "Merry Christmas and a Happy New Year" and "Seasons Greetings". Your handwriting sure deteriorates writing whole words. But it's very achievable for a learner too.

To teach kids the ideas of Sudoku, I also found this Christmas Sudoku to play online that takes you through filling in the gaps with increasing difficulty. It's a very short run through, but you could discuss it as a class as a starting point.

Day 8: Christmas Civiballs

What is it about me making a commitment to regular blog posting. It's an instant "get sick now" instruction to my body! I'm only feeling a little sick, but it's enough of an excuse (plus it's Sunday) to focus on another game today.

I got addicted to Civiballs a couple of years ago. The Christmas version is equally good. Again it's reasoning and logic, and also I think these strategies games require perseverence, which is a useful academic virtue. And it's super fun.

Enjoy!

Day 2: Christmas Tree Light Up

I love logic games. This one's a great one. Not maths as such I suppose but problem-solving and logic for sure. And a good one because kids can just play around and see what happens or try to strategise.

One way I judge the quality of a game is how much time I spend playing it. This rates pretty high.

Subtracting a Negative - The Third Umpire

My Lovely Year 7s are starting their topic on directed numbers/integers at the moment. Over the years we have had a lot of discussions about how to get them to really understand about adding a negative and especially subtracting a negative.

With some help from my lovely husband, it seems that sport or some kind of game is the way to go. He played a version of cricket where each batsman stays in for a fixed number of overs, but gets a negative score added if they get "out". I thought it was a great idea, and had lots of potential for negative numbers - what if the third umpire overturns an out?

Here's the game we played today:

Students came up in pairs, one pair at a time, to play. They had 30 seconds to throw a bean bag between them (from behind marked lines) as many times as they could.

Scoring:
1 point for each successful catch.
-1 points for each time the bean bag hit the ground but was picked up again in less than 2 seconds.
-5 points for each time the bean bag stays on the ground for 2 seconds or more.

Also I stopped them mid-game so we could discuss the scores on the board.

I considered the penalties for dropping as negative numbers, rather than subtractions, so that we could write our number statements that way. That also allowed us to subtract a negative score if a penalty was overturned.

For example:

A pair of students catch the bean bag 22 times, then drop it. I rule that it is on the ground for more than 2 seconds.

So I write 22 + (-5) =

Here we can talk about the use of brackets, how they may or may not appear and why we might use them. We can also talk about how we would say it. Do we say "22 plus minus 5" or "22 plus negative 5" or can we say "22 plus take-away 5"? Which ones make sense? Which is the most clear?

Now they know that the pair have lost points, because they did something wrong, so 22 + (-5) = 17.

But they did appeal that it was less than 2 seconds. We took a vote. My decision was overruled.

So I write 17 - (-5) =

I'm removing the negative score. They all know already that the result should be back at 22. So we can now discuss why that is.

In summary at the end of the games we talked about adding and subtracting positive numbers, and adding and subtracting negative numbers, since we had done a bit of all of these.

After we played that version a few times, we switched to a system where the scores started at -20. This allowed us to do the same types of calculations, but in the negative numbers and crossing zero. I have a number line across the front of my room which helps a lot in these situations.

Probability Games and Worksheets

My year 9s have been doing a topic on Probability. I like to start with some simple fun activities, including playing Deal or No Deal online. This group got so into it and wanted to play all the time, so I made a worksheet to justify us doing so!

My method of eliminating composite numbers first seems quite successful. Deal!

You can find my Deal or No Deal Worksheet at a lovely resource site called MathsLinks, in the Maths Faculty section. You have to login but you can do so through google or facebook or various other things as well as registering with the site individually. It is a valuable repository of resources and ideas provided by Maths teachers.

The other game I love is Higher or Lower at subtangent.com, so I made a worksheet for that to, which is also uploaded to MathsFaculty. The Higher or Lower Worksheet is simple theoretical probability.

With both of these, I like to run through the game a few times, discuss the theoretical probabilities on the board as we go, then follow up with the worksheet, and maybe a promise that if there's time the student who does the best work can be the next contestant.

(Oh and it was a good deal, I only had $2000 in my suitcase)

BINGO!

I love bingo. It seems to me that students do more drill questions playing bingo than they are willing to do in any other format, and don't care in the slightest that all they are doing is repetitive drill questions.

I know that as a classroom activity it is not exactly Quality Teaching, there is no deep conceptual understanding or exploration or critical thinking, but I like to think of it as a more engaging alternative to textbook work. I don't care for textbooks, especially in the junior years.

I used excel to randomly generate sheets, which means answers will sometimes be repeated. Usually I let them cross off multiples all at once, since I won't ask two questions with the same answer.

I generally write one question at a time and then every 10 or so go through the answers with the class so they can check if they missed any and to discuss method as we solve them. In some classes kids shout out a lot so this works well. With others I have found it works better to write up a few questions at a time then wander around helping people during the time everyone takes to find the answers. Obviously it depends how hard the questions are too.

All of my Bingo files are in this folder, and it contains the following items:

• Algebra Bingo (a, b and ab terms), and some questions.
• Algebra Bingo (with binomial answers in a, b, and constants), and some questions.
• Algebra Bingo Multiplication and Division (ab, ac, bc, and abc terms)
• Area Bingo (answers in centimetres squared) (Designed to work well as easy answers to square, rectangle, parallelogram, kite, rhombus, triangle questions), and some questions.
• Fractions Bingo (Good for simplifying, ok for multiplication and division too, or a mix, could also do "What fraction is x of y?" questions), and some questions.
• Indices Bingo (I used for the index laws for multiplication, division and power of a power), and some questions.
• Surds Bingo (Good for simplifying, adding and subtracting..?)
• Ratio Bingo (I used questions on simplifying ratios), and some questions.
• Also my colleagues and a class created a great powerpoint of student-written questions for area bingo as part of their year 7 area unit.

I've also used other versions where I've just given the students a range of values to choose from and had them draw their own grid. It's much easier as long as the values are simple (e.g. numbers from -10 to 10) and avoids repetitions. I've also given them a number plane to draw some points on and rolled two dice to randomly generate points.

Refraction

Refraction is an awesome game. Starts out as a fairly simple puzzle with simple fraction concepts but gets up to the concept of adding fractions by converting them to the same denominator, so it is pretty impressive! And loads of fun and addictive.

I've finished, but I still have a few coins and cards to win :)

Maths Taboo

I know someone else has done this, but I couldn't find it at the time I needed it, so I made my own. At first it was geared towards School Certificate content only, as revision for my lovely year 10s last year, then I added stage 5.2 and 5.3 content for further revision later.

If you haven't played Taboo, the idea is to give clues to get your team members to guess the top word, without using any of the words below (the 'taboo' words).

The file is here, it requires editing to make sure the tables aren't split across pages and so forth. And I recommend adding more, as I plan to in future.

AngleJack and other games with a Deck of Angles

Ok so bear with me here, I might rant. I got a bit excited about this one.

I found a piece of paper on which I had scribbled the idea of a game of making shapes out of angle cards, to practise angle sums of triangle and quadrilaterals (there is a post still to come about another game on this topic I made earlier). I made a test deck and started to play with the idea.

Basically the deck is angles in increments of 10 up to 170 degrees. There are more of the ones from 10 to 90 to provide more balance in the games. My first version of the deck only had the numbers, except for right angles which had a diagram only, but I'll add diagrams to them all (Firstlyl to remind them that they are combining angles, not just numbers, and secondly in the hope of subconsciously familiarising them with size of angles to help them visualise and estimate in future). The games focus on combining angles into right angles, straight lines, revolutions, complementary and supplementary pairs, triangles, and quadrilaterals.

Here are some ideas:

• Go fish with complementary or supplementary pairs. Seemed quite successful in the playtest with year 10 at the end of term. The kids these days seem to really like go fish. Low on strategy, but easy to explain and get going.
• Snap with complements and supplements. Never as good because a difference in skill swings the game a lot but always popular with some groups.
• AngleJack (or Revolution). I was inspired to create Blackjack-style games by this one for negative numbers and also the fact that some students seem to know this game idea quite well. Instead of 21, the aim is to get as close to a revolution as possible (optional - without going over). Can be adapted to getting as close to a straight line as possible but you need to be allowed to go over (or remove the cards above 90), otherwise you can go bust as soon as you start. This was our favourite at home (I have the best, most tolerant boyfriend!)
• Texas Hold 'em Angles - still some fine details to work out, including rankings and the tricky "betting" thing. But basically two cards in hand, five face up, from which the players have to make the best "hand" they can by combing the cards. So far the ranking of combinations is quadrilateral, triangle, revolution, straight line, supplementary, complementary. (Even though a supplementary pair should be less common than a straight line made of any number of angles, there is more thinking involved in the latter, so I ranked it higher). I think to split within the levels, the largest unique angle wins. I did contemplate introducing suits or colours of some kind but I think it's unneccessary. Not sure what the suits would have been but I do like the idea of someone anouncing "quadrilateral of abacuses" or something.
• My original one was a Numero-ish game where each player has a hand of 5 and the table has 5 cards face up. On your turn, you combine cards from your hand with one from the table to make a triangle or quadrilateral to put into your pile. Replenish hand and table. Most cards in pile at the end wins (therefore quadrilaterals are worth more, which is fair, they require more thought). Could also be allowed to make supplementary and complementary pairs to keep the game going.
• At a lower level, the cards could also be all spread out and players take turns to make and take a quadrilateral or triangle (or whatever else mentioned above).
• We also pondered the idea of a Scrabble-like board where you play your triangle or quadrilateral onto one already on the board, using one of their angles. This will take some more thinking about! (And probably the kids would think we had gone insane)

Heaps of thanks to Michael and Bennie for developing these ideas with me.

Some thoughts about games

Further to my previous post about up-skilling my students, I'm dwelling on one of my favourite things - games.

I love maths games and I try to use them in class, but I do find they meet with mixed success, and it often isn't the maths that is the problem. I began by thinking "Kids these days don't know how to play games" and feeling sad about that. But sometimes I go to a friends place for dinner or a party and a board game comes out, and sometimes there is an adult who doesn't seem to really "get" how to play the game. So I suppose it isn't generational, it's just that not everyone plays games and I don't normally associate with that sort of person.

I think I should persist though, because using maths in a game seems like another level to me. Once the student has a good grasp of the concept, playing a game about it can work on using the knowledge/skill strategically, reasoning about the knowledge, and gaining more fluency at applying the skill. Which potentially also provides differentiation, (although I might be reaching here) as one student makes the most obvious move while another considers multiple options and chooses the best one for the situation.

Over the years I have played a lot of games in class, that I have discovered or invented (mostly invented). I spent a lot of my early part-time years throwing myself into making cards for cool games I came up with and then they didn't work that well or I got bored of them. The legacy I will leave behind me in the teaching world is a large pile of neglected hand-made games. But I will be sharing my more successful creations here in the hope someone else might enjoy them. Stay tuned!

What kind of students do I want to pass on?

I've been thinking a lot about what it is I am actually trying to achieve as a maths teacher. With good students it's easy to not question the standard form of maths education, but with middle and lower-achieving classes I question the relevance of a lot of content.

I've been slowly reading through some of the blogs I found in my first over-excited blog weekend, and after reading all of exzuberant and infinigons, I've thought a lot about quality teaching, assessment, problem-solving skills and engaging, relevant learning activities. Reading this post today made me think about what the key, transferable, whole-of-life skills are that I should be trying to impart. If I taught at the kind of school where many kids went to university I might not care as much about this, but probably 50% of our students won't do maths in year 11 and 12, and only a handful will be studying any mathematics after school. So what the hell are we doing? And why?

This is a big problem and I have a short attention span but I kind of continued the thought on a slight tangent.

Today I was also making up a new maths game (as you do), and I though about how most of my students aren't great at playing games that require much strategy. And in fact a lot of the "cool", engaging activities we want to do, anything that requires independent thought, critical thinking, deep understanding, dealing with open-ended problems, etc. etc. seems to stump our kids.

So I thought, that's something to start thinking about. This type of thinking, dealing with these types of problems and activities, these are all just skills too. They need to practise them. We need to be persistent, and we need to maybe scaffold learning how to learn that way?

I have the top year 7 class. They are pretty good at maths so far (most of them) and from here I have to try to turn them into hard-working, keen, interested, engaged, skilled maths learners. And maybe that means I need them to be:

• used to learning games, playing games, strategising and coming up with variations to games
• used to solving problems
• used to working on projects
• used to working in groups
• used to reasoning about and communicating concepts
• used to tackling open-ended problems

as much as, or even instead of:

• doing lots of drill questions from textbooks or worksheets 

Which means I need to make sure I'm doing these things. I've made a start on games and have some group projects about communicating concepts planned, but need lots more problem-solving especially.

Week 2 Challenge Review, and end of the stupid challenge idea

The Counting On activity went well, and we used blu-tac to create the giant graph on the wall. We did run out of room for the prime numbers column and had to overlap.

Edit: Here is a picture of the graph. In future I would consider using a large floor space instead of the wall, so that we could fit all the prime numbers in properly! And discuss what would happen to the graph if we did more numbers. And if I put it on the wall again I would include labelled axes.

They loved the active "yes or no" categorising game. Each student had a number, and two ends of the room had "Yes" and "No" up on the wall. I called out questions like "Are you a prime number?", "Are you an even number?", "Are you divisible by 3?", "If you add 5 to yourself, do you have 4 as a factor?" and so on. It provided a good opportunity when someone was unsure to ask the whole class relevant questions like "How can you tell if a number is divisible by 3". And they loved it.

I'm already over the challenge thing

 Not surprising, but with contributions from a personal situation, I lost a lot of motivation. Plus two of my classes annoy me. But Year 7 continue to be lovely, so I will keep doing my best for them at least.

Year 7: We're going to be looking at prime and composite numbers and factors. The main activity I want to use for primes and composites is one from the Counting On numeracy framework. Students draw rectangles to find the factors of numbers (a different number on each sheet) then lay them on the floor (or stick to the wall) to create a bar graph of how many factors they have. Then you can instantly see prime numbers, and how one is not a prime, but has a special column all to itself. It also separates square numbers from other composites. After they've got the general idea I want to try an idea from Brent Vasicek at Scholastic for an in-class assessment of their understanding. I think I will give each child a number and then get them to sort themselves according to different criteria, e.g. primes over here, composites over there, sit down if you have 4 as a factor etc.