Tenzi Frenzy!

We are away for the summer at a cottage, with no internet or TV, which I usually love. We’ve already read lots of books, frolicked in the waves, swam to the Big Rock,  sailed to Seagull Island, canoed…dumped the canoe and had lots of good old fashioned fun; but my heart still felt the pitter-patter of excitement when I saw the clouds roll in, because that meant we could drive to the nearest town and spend the morning at Chapters!  

Don’t you love rainy days at Chapters? (Borders would probably be the US equivalent).The boys love playing with Thomas the train in the kids section, and looking at all the books, while I finally get a chance to peruse the latest best-sellers in person, instead of on Amazon! We go to the library every week, but it’s just not the same as a road trip to Chapters. And when we went yesterday, I felt like I hit the jackpot with my new find: TENZI!

Best. Game. Ever!!! Kevin and Steve (the game’s designers), made known by a little piece of paper in the game box with their story on it, may not have thought of the mathematical implications when they came up with the idea for the game, but kudos to them for unwittingly designing a brilliant game suitable for 3-103 year olds!!

Here is the general gist of the game, and I quote: “Everyone gets 10 dice. Then everyone rolls until someone gets all their dice on the same number.” Simple, right? Why am I so excited by this new find? Because of its GINORMOUS educational value! It’s like this game was conceived specifically with the pre-kindergarten to grade 2 curriculum in mind,  yet it’s intended for everyone!

Here’s why I love it:

Subitizing!

Subitizing is the ability to recognize number patterns without counting. Rory quickly grasped what the dot patterns stood for and although he still counted the dots on each new turn, the repetition of looking for the same dot pattern reinforces his learning. I am confident that after a few more rounds, he will quickly and easily know the dot patterns for 1-6 without counting.

Counting on!

If you have 3 of the same number and get one more, now you have 4. Rory was learning and Practicing math skills without even knowing it! He already has developed one to one correspondence and cardinality, but now we’re extending his knowledge. What is 3 and 3 more, or 4 more, or 5 more?! Because each turn is different, he is continually practicing different amounts of counting on.

Decomposition and recomposition of 10 (a very important bench-mark number)!

Because the goal of the game is to get 10 dice all on the same number, you are constantly looking for two numbers that make up 10: those you already have with the same number on them and those you have yet to roll. Rory quickly saw when he needed one more to make 10, and then we looked to see that he already had 9. Or he had 5 of the same number and needed 5 more. And that leads to….

Addition!

Decomposition of 10 is the building block to addition and although we didn’t concentrate on it today (it was our first time after all!), eventually we will use this game to practice our 10 facts. We can easily adapt it to practice our 5 facts first, just play with 5 dice each instead and yell, Fivzi!

Fun!

This game is fun for the whole family!  Oliver got in on the action too but only to yell “Tenzi! “ and steal our dice to make a tower, but I’m sure he’ll see the math value soon!! It was me that finally drew the game to a close after almost an hour; Rory could have kept playing forever!

So Kevin and Steve (fortuitous mathematical master-minds that you are!), thank you for a fun and easy game that everyone can play. It looks like you two have a whole new market to exploit and hopefully I’ve inspired some new fans here!

If you want to know more, check out their website at www.ilovetenzi.com. Thank heavens for rainy days!!

Have other great math games that aren’t actually meant to be math games?

Post them in the comments section below!

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Sorting and grouping

The thing with children is they change so quickly and if you blink, you feel like you missed the moment when a major milestone was achieved. For example, Rory used to say he wanted a hangaber for dinner. Alan and I thought it was adorable, and did nothing to encourage the proper pronunciation of the word! But then one day, we noticed he was asking for hamburgers instead of hangabers, and the moment was gone.

This week, I was playing with Oliver and noticed that he now knows some of his colours! This is a very recent development and one we’ve been anxiously waiting for. Rory knew all his colours by 2 years old, and Oliver is almost 3 and was showing no signs of progress; but then, just like that, he got them all right! This is so exciting for me as a mathematician because it now opens up so many more informal sorting activities!  

“As the children’s vocabularies increase, they will be able to label and describe how and why they are sorting and grouping things.” (Charlesworth, 2012)

Here is an example of Oliver engaged in naturalistic play. Notice how I commented any time he knowingly (although usually unknowingly!) put things into groups. Also notice he learned a new word (rectangle!) and now has additional sorting power for next time!

Because Oliver is now ready for more informal instruction on sorting, I started looking for articles about this important stage of development and was surprised when I couldn’t find many. I couldn’t even find agreement on what strand of math sorting falls into! In some books, classification was stuck under geometry, but the content was directed at a higher age level. For example classifying polygons versus nonpolygons; or triangles with the same area versus different areas.  Another resource I looked at, clumped sorting under data analysis because organizing data into groups is important for graphing. I myself, would have linked classification with logic and pre-algebra, because sorting involves reasoning and logical thought. It is also the precursor to addition (putting groups together) and subtraction (taking groups away).

In addition to the controversy over what strand this falls into; sorting and classification only really appears in the pre-k to k curriculum, and as a result it is minimized in the teaching resources or believed to develop naturally. This surprised me because classification is such an important skill not only at school, but also in our daily life. This skill, although it may appear basic, is the basis for further logic and reasoning. It provides an introduction to graphic organizers such as Venn diagrams and to me, it is a life-skill that may even precede executive functioning ability! (New research project?!) Think of the importance of learning how to sort and classify in this day and age, with all the information we have access to.

Now that I have convinced you of the importance of this seemingly natural ability, I want to share with you how to nourish this skill in your child. In the early years, classification activities fall into three categories:

Stage: Your responsibility:       Example:
Naturalistic: Provide free time, material and space
  • Blocks, cars, farm animals, nature things
Informal instruction Provide comments or tasks that identify or encourage sorting
  • Your picture has lots of red.
  • Can you separate the forks from the knives?
  • Could you put your cars in the car bin and your balls in the ball bin?
  • I see you’ve arranged your dolls from smallest to largest.
Guided instruction Give specific objects and guide classification strategies
  • Find some things that are___.
  • Tell me why these belong together.
  • Sort these into groups, how did you decide?
  • Is there another way to sort these?

 Rory has a larger vocabulary than Oliver and a larger understanding of the universe. For his sorting activity, I used guided instruction. You’ll notice he came up with interesting ways to sort things: by function (button, sticker), by colour (red, blue, yellow, green) and by category (animal, vehicle, shape).  I guided him by encouraging him to think of different ways to sort his materials; however, it was ultimately his decision.

Next time, I might choose different objects that force him to make different decisions. For example, choosing all cars but different sizes, or choosing all art mediums (canvas, paper, felt etc.) and let him sort by texture, or all natural objects and have him sort by common features. I would also provide objects that relate to different content areas. For example, objects that float or sink (science), pictures of workers and different materials (social studies), or sorting plants into edible and non-edible. The possibilities are endless! The only thing to keep in mind is that classification activities should follow the same progression as manipulatives (see my post on this here), so start with 3-D objects and then move to cut-outs and then to pictures.

Although I couldn’t find much on how to teach classification, I found bucket-loads of activities that involve sorting.

Click here  and sort through these for starters!

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Making Math Meaningful with Manipulatives!

If you’re not a teacher, you may not be familiar with the term manipulatives, but you can probably infer what they are. Manipulatives are models that help children think and reflect on new ideas in math. They include resources that allow children to explore, question, guess and check, but more importantly, to play with the problem. Counters, toys, linking cubes, abacuses are just a few examples.

Why use manipulatives?

We all know the old adage: we learn better by doing and math is no different! Manipulatives give students, of all ages, opportunities to have a hands-on approach and develop deeper understanding of concepts. Research has shown benefits to using manipulatives all through life! That means, don’t be in a rush to move your child into more abstract ways of solving problems. There is a natural progression to manipulatives and you need to assess your child’s readiness before pushing them to a more abstract level. When choosing materials, they should be sequenced from concrete to abstract and from 3-D to 2-D. See the chart below for more information.

Transitioning from concrete to abstract manipulatives (Charlesworth, 2000)

1) Start with real objects. Sensorimotor stage.
2) Move to real objects supplemented by pictures. Pre-operational stage
3) Once the first two are mastered, you can use cutouts of real objects. This is the transition from 3-D to 2-D, but the objects can still be manipulated. Pre-operational stage.
4) Now move to pictures. Transitional stage
5) Finally (and much later!) use paper and pencil. Concrete operations stage

So where do virtual manipulatives fit on this spectrum? Good question! I’m not sure! My guess is that they act like real objects because you can move them, but because they are 2-D, they might be more on par with the cut-outs level, in terms of concreteness (see step 3 above). Let’s see what Rory thinks. I’m going to get Rory to do a task with real objects and then do the same task with on-line manipulatives. Then we’ll see what he has to say! This task is an introduction to addition but it would also be great to use for lessons on one:one correspondence, decomposing numbers, counting on and  cardinality.

Well it looks like Rory prefers virtual manipulatives. It may have been the novelty of it or the fact that the computer images acted more life-like than the real objects! He claims that the boat was more real compared to my egg carton version and he liked that the bears kept looking at him (in case you couldn’t tell)! The important thing is that children are given the freedom to choose their own manipulative so that they aren’t restricted to one method. That way, they can discover their own way to reach a solution that makes sense for them. If he likes the on-line tool, on-line tool it is! But I’ll make sure he has the real objects on stand-by in case he’d like to use them as well.

Looking for manipulatives? Look no farther!

Click here for a list of manipulatives that teachers often use with this age group!

Are you a parent? The great thing is that anything can be a manipulative! You don’t need to run to a teacher supply store in order to help your child.

Click here for a list of great things to use at home!

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