Not-your-usual-shape Lesson!

Not a box!

One of my favourite books is “Not a box” by Antoinette Portis. I love it because it reminds me of my own children who refuse to let us throw out boxes. They have all these great ideas of what the boxes can be turned into and although the mess drives me nuts, I’m always inspired by their creativity!

As a math teacher, I also love the book because it is a great spring-board for conversations about shapes as well as real-world applications. Here are some math talking points you could use to talk about the book:

  • Where is the box now in the drawing? (Can they still see a box shape when it is incorporated into a drawing?)
  • What would you have made out of the box? (Can they think of real-world applications?)
  • What shapes do you see in the box? (Do they connect it to squares and rectangles?)
  • What things could you NOT make with a box? (Understanding non-examples helps solidify the concept.)
  • What makes the box different from a rectangle or a square? [Is it fat (3D) or is it flat (2D)?]

My goal with these questions is to have students recognize some attributes that are unique to certain shapes as well as to have them make connections between shapes and the real-world. These can then lead to lines of inquiry such as: why are most buildings box-shaped? Why don’t tissues come in triangular boxes?! Or why are most drink containers ‘circle-shaped’ instead of box-shaped?

Not a shape!

After reading the book, I have the students pick a shape (always think differentiation!) and create a picture of their “Not a shape” idea! For kindergarten I started with the box (a 3D shape), but then we did examples with 2D shapes (because that is what they are learning). Here are some drawings my son came up with:

My favourite is the happy face…it is a self-portrait!

Not a Triangle!

Math4Love has many great activities and lots of them for free. I like their “not a triangle” game, although I adapted the rules a little for kindergarten. The goal of the game is to NOT make a triangle. Each player takes a turn to draw a straight line between two of the points. In my version, they have to work together to create a shape, but it can’t be a triangle. Here is a video of Rory and I playing the game.

I love this game because students see that shapes can be irregular (all sides aren’t equal) which is sometimes overlooked especially in the early years. Teachers often concentrate on shape recognition of regular shapes, but it is important for students to learn that polygons don’t always look ‘nice’.  The other great thing about this game is the opportunity for extensions. Can the kids name the shapes they created? What shapes can you NOT make with the 6 dots? What if the dots were in different places? How many different shapes can you make? What if we played a game with more dots or less dots? Would it be easier or harder? What about playing, ‘Don’t make a rectangle’? Is it easier or harder?

I can’t find their original post of the game, so here is the copy I downloaded (click here), but all credit goes to Math4Love! When I did this lesson with a full class of  kindergarten students, the conversations were rich and rewarding. They talked about regular and irregular shapes, names of shapes, what constitutes a polygon, how many lines can meet at a corner, straight lines versus curvy lines; all important learnings about shapes while trying not to make a triangle!

The sign of a good mathematician is one that can reason with you about WHY something is the way it is. They haven’t just memorized a rule and are regurgitating it, they have made deep connections with the concepts and can justify their thinking. So if my students can explain why something is NOT a certain shape, then they have a true understanding of what attributes DO make that shape.

Have other unique ideas for shape lessons? Leave them in the comment section below!

Ordinal numbers are anything but ordinary!

The other day, a Grade One teacher asked me to do a demonstration lesson on ordinal numbers. She wanted to see how I would approach it. I had to think for a moment because I have never explicitly taught ordinal numbers. Usually, by the time students get to me, they’ve already learned them. I just assumed it was something children picked up naturally; the evidence being my children who have fought many times, with lots of tears, over being first or second!

I became curious and wanted to know whether children’s understanding of ordinal numbers developed in the same way cardinal numbers did (to find out more about the development of cardinal numbers, read my earlier post here), so I did a bit of action research with my boys! See the video below.

As you can see, Oliver ( 3 and a half years old) knows the words for the ordinal numbers, but just like his development of cardinal numbers (see Learning to count…baby steps.), he has no understanding of what first or third actually means. Rory on the other hand (kindergarten) has a rational understanding and could count up to 18th before he found saying ‘th’ too hard (when is that front tooth going to grow in?!). I am pretty sure he hasn’t been taught ordinal counting in school and I know I haven’t taught it to him, so this result supports my initial hypothesis that children pick up ordinal numbers naturally!

So what could I add to a Grade one class then? Three things:

First (ha!): I can teach for understanding. Neither Rory nor Oliver could articulate what the difference was between cardinal or ordinal numbers. It is important to explain that cardinal numbers are for counting. Ordinal numbers are to describe positions. I emphasise this with the alliteration Counting-Cardinal….Ordering-Ordinal. Always embed this learning with real-life scenarios.

Second: Relate the ordinal words and symbols to patterns. Is there a rule we could use to know the ending of each ordinal number? The Grade Ones were great at seeing that every number ending in one, is first; two is second, three is third and all the rest end with a ‘th’ ending. We also discovered why the teen numbers don’t follow this rule. How silly would it be to say the twelvesecond position!

Third: Connect to cardinal numbers. Notice the similarities and differences in counting with both sets of numbers. In our video, we counted the people on the train, but then we described their order. Have a conversation with your child about when we would want to know the count and when we would want to know the position. A great example to use for this discussion is waiting in line for tickets to an event with a finite number of seats.

Techniques for teaching? Bring in the 100 chart, read step-by-step books and refer to the steps using ordinal numbers, role-play! What a fun lesson to act out: have a race, build a train, stand in line. Happy ordering!