Applets for Intermediate Level Fractions November 15, 2007

Hey there…
I wanted to pass along 2 new applets (ok, new to me) for modelling fractions – both on a number line and using an array model.

The first is a game, in which you have to select a fraction that is equal to or less than the fraction you’re given, with a goal of moving all your sliders over to the far side of the screen – in as few moves as possible. My best score was 12 moves… Try out out by clicking here… Here’s a game board:

The second applet asks you to create fractions equivalent to a given fraction on a number line. You have to slice a box into sections and then shade the correct number of sections in order to get the point to align on the number line. I like this one because there are lots of ways to do it… Check it out by clicking the link here!

A screen shot of the game…

By the way… I’m thinking that the rectangular array model is a far more powerful and visually meaninngful model than the “pie” model for representing fractions. Those pieces are so hard to slice, to draw and to compare that they seem more trouble than they’re worth. I get the whole pizza reference and all, but right now I am leaning towards square pizzas for the sake of conceptual understanding.

Carole

Actual Size – A book about measurement, visualizing and asking questions November 13, 2007

Hello there!

A while back I was introduced to the book Actual Size by Steve Jenkins. The illustrations in the book are – you guessed it – the actual size of the creature being described. That makes it a wonderfully engaging and interesting book for children of all ages – and for anyone just learning English, the images are captivating enough to convey plenty of meaning.

I was asked to do a lesson in a grade 2 classroom in Richmond. The school was working on strategies for non-fiction reading, and I was to focus on the strategies of visualizing and asking questions. We read the book together, talking about the images the children made (the pictures in my head) and the questions we had (what I wonder about). After reading and exclaiming :O at the illustrations for a while, I gave each child a card with a picture of one of the creatures and small bit of text on it. I asked them to look at their card, to read the text and then to do 2 things: to draw the picture they had in their head and to write one question they had about the image. Not surprisingly, every single question the kids had about the creatures was mathematical in nature, and their questions inspired many many math lessons after that day… I’ve used the book in intermediate classrooms as well, where the notions of proportional reasoning and scale come in nicely!

I’ve been asked to include the Actual Size fact cards in this post so that others can try this task. I’ve summarized, in kid-friendly language, one fact about the animal on each the card and included (in METRIC) some information about the creature’s length, weight or height. Feel free to download them, understanding that they are drawn from Steve Jenkins’ work and should be credited to him. The file is very very big…!

Let me know how it goes in using these cards and this wonderful book!
Carole

Integers, anyone? On-line experiences of negative numbers November 6, 2007

Hello to the folks in the grade Math Makes Sense group! It was great to see you all yesterday. For those of you who weren’t able to attend, we talked a bit about the notion of integers and students’ experiences with modelling them on number lines. I described this particular applet to you, but thought it best if I sent it out for real…

Try the JUMPING NUMBER LINE. It asks students to arrive at a target number by “jumping” a certain distance in either a positive or negative direction… In this example I am aiming for the number 4. I have to use all four of the arrows. I must start at zero. Fortunately, I can reverse the direction of the bounce my clicking the direction button in the middle of the page…

This next applet uses green and blue bars to represent positive and negative integers. You create 2 bars of any length, then indicate by dragging dowon on a pull-down menu the operation that is happening between them. They are placed on a number line and you can choose to show the total or figure it out yourself. I liked this one… It’s simply called NUMBER LINE and require Flash Player to run… I had more success using Firefox with this one.

Here’s a screen shot of the game. I created 2 bars – one was -10, the other was +10. I chose the operation of subtraction, and asked that the answer be displayed…

Carole