# Category Archives: Hand-on activities

## Exploring fractions with “The doorbell rang” by Pat Hutchins

You may know the author Pat Hutchins and her books for young children, such as Rosie’s walk, Changes changes, Clocks and more Clocks, etc. I bought a few when my children Rosie and Tom were younger, and “The doorbell rang” was one of them. I had almost forgotten about them, until I recently heard Rosie, second grade, say:

“I recognize this book ! We read it in math today !”

So we read it again. The text is attractive as it includes predictable sentences that young children enjoys repeating out loud. And for older kids, the story opens the door to math. Ma made cookies for her two children, Sam and Victoria to share (equally). The doorbell rings, and two more children, Tom and Hannah come and share the cookies. As the doorbell keeps riging, more children come to share the cookies, until twelve children have to share the twelve cookies.

As I was reading the story, Rosie modeled it. She used flashcards to represent the cookies, similarly to what she has been doing with Time 4 Fractions.

1. At the beginning of the story, Sam and Victoria gets 6 cookies each. How many cookies has Ma baked?
2. Now that they have to share the 12 cookies among 6 children, how many cookies does each child get?

But a fun activity we added was to twist the story a little, and work not only with whole numbers, but also fraction. You may want to give it a try. I just let my child make sense of the problem, whether using paper to cut, or buttons to count, or the base Ten Blocks. Sometimes, she connects her model to symbols she has learned at school. But the goal is to let her make sense of the problem.

1. What if Tom does not want any cookie, i.e. three children share the twelve cookies, how many cookies does each child get ?

2. What if Peter does not want any cookie, i.e. five children share twelve cookies many cookies does each child get ?

3. What if Tom, Peter and Victoria do not want any cookie i.e. nine children share twelve cookies many cookies does each child get ?

9 children sharing 12 cookies: each child gets 1 whole cookie, and 1/3 of a cookie (or equivalents)

I always look for opportunities for my children to have fun exploring problems, and make sense of them.  “The doorbell rang” sure is a neat book to create such opportunities.

Give it a try ! I am here if you have any questions !

## Small, 2012 – Reaching out to all children

Here is another book I studied as a graduate student that I found interesting to share.

Small, M. (2012) Good Questions: Great Ways to Differentiate Mathematics Instruction, 2nd Ed., Teachers College Press, NY.

The author suggests 2 different types of math tasks to reach out children with different skills and needs. Makes sense in a classroom, of course, but it makes sense to me at home as I start seeing my son Tom, 4, willing to “do math” with his sister Rosie, 7 (see my previous post here on Doing Math outside, for instance).

Open questions:

The task is “framed in such a way that a variety of responses or approaches are possible” (Blanton, p6). Remember my post on Vygotsky  (here) ?  Well, the goal is to design the task “in the appropriate zone of proximal development for all students” (Blanton, p6), so that every student can be part of the discussion.

Here is an example of what we did recently:

“Go outside and take a picture of a pattern”.

Rosie came back with a pattern found on  a flower, while Tom came back with a  pattern he created with rocks and pine cones. Still, we were able to discuss patterns all together.

It is a set of tasks that children can choose from, that are close enough to be discussed at the same time.

For instance, this afternoon, I asked Tom and Rosie to create a story out of:

• Choice 1: 10 dinosaurs
• Choice 2: 3 cars

Again, even if Tom used a number smaller than Rosie to create his story, they still were able to share what they did with each other. Also, Rosie was able to create a math problem, while Tom invented “just” a story involving 3 cars.

Of course, with Tom and Rosie’s difference of age/skills/grade, I may not always be able to provide them with tasks they can explore together, but I really like the idea, and will come back to it regularly.

You may want to  check out the book, too ! It includes hundreds of Open Questions and Parallel Tasks organized by math concepts and grade levels.

## Making sense of subtracting in column

I thought I should complete my latest post,  making sense of adding in column (here), with a quick post on using Base Ten blocks to make sense of subtracting in column. My daughter is not there yet, but your child may be.

The picture above presents a concrete illustration of 43 – 15. It is quite helpful for kids to visualize that, when subtracting 15 to 43, they trade a Ten from the Ten column into Ones. Then, they can subtract 5 Ones to 13 Ones, 1 Ten to 3 Tens, and end up with 2 Tens and 8 Ones i.e. 28.

I just spent the morning in my son’s classroom. He is 4 and attends a Montessori school. Their approach to teaching math is amazing. Indeed, using concrete objects, little 4-5 years old kiddos solve 4-digits addition without even thinking about it.  I should write a special post on the Montessori approach to Math. Quite inspiring, indeed.

## Making sense of adding in column

Adding in column 23 + 14 ?  3 +4 = 7, 2 + 1 = 3… so the answer is 37. Adding 37 + 44 ?  7 +4 = 11, 3 + 4 = 7… so the answer is 711. Wait, Mom. It does not make sense, doesn’t it?

Nope, Rosie, 711 doesn’t seem to make sense. So let’s step back an inch, with the Base Ten Blocks (click here if you want to read more about these blocks).

Here is an example of 32 +23, and the connection between the blocks, and the addition in column. While adding in column, you add the Ones, then the Tens, then the Hundreds, and so on, and the blocks provide a neat concrete representation of such process. Indeed, it shows why you have to “align” digits (because if you don’t, you end up adding Ones to Tens !).

But what I like the most with these blocks is how they  help children  make sense of carrying an over to the next column. Here is an example with 37 +44.

From the 11 Ones you get from the right column (i.e. the Ones column 7+4), you trade 10 Ones from 1 Ten that you carry over to the left column (i.e. the Tens column).

Here you go, Rosie, 711 does not make sense, but 8 Tens 1 Ones aka 81 does.

## Crochet and hyperbolic geometry

A dear friend of mine made me discovered an amazing project this morning: the Crochet Reef Project.

The fact that a mathematician could have thought about using the art of crochet to model a form of geometry is so inspiring to me. It just makes me feel like helping my children develop their creativity in math even more :-)

“The Crochet Reef Project was inspired by the technique of hyperbolic crochet originally developed by Dr Daina Taimina, a mathematician at Cornell. In 1997 Dr Taimina discovered how to make models of the geometry known as “hyperbolic space” using the art of crochet. Until that time many mathematicians believed it was impossible to construct physical models of hyperbolic forms; yet nature had been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry in their anatomies – among them kelps, corals, sponges, sea slugs and nudibranchs. Thus the Crochet Reef not only looks like a coral reef, it draws on the same underlying geometry endemic in the oceanic realm.” – From http://crochetcoralreef.org/about/hyperbolic_space.php

I had on my list to teach my child how to knit over Summer, but I may start with crochet !

Fascinating !

French and US version of the game “Mille Bornes”

A fun game to practice addition up to 1000 is the French card game “Mille Bornes” (same name for the US version, available online).

Not sure if you are familiar to this game or not but basically, each player pretends to be on a road race, and the first one to complete 1000 kilometers (or 1000 bornes) wins the race. Players do so by displaying borne cards (25, 50, 100 and 200 kilometers), stopping others with a red light,  a speed limit, a flat tire, etc. Quite fun. I loved it as a kid. And my 7 year old child seems to enjoy it a lot to.

But I am sharing it here because it is an easy way to practice … math: adding 25s, 50s, 75s, 100s and 200s to reach 1000, here we go.

Quick tip if you play with a child not quite yet familiar with a 4 digit number, try to use a base Ten blocks. It is quite helpful, indeed, and so instructive in discovering such a BIG number. We use a Thousand block as a reference. As my child displays borne cards, she sees, thanks to the Thousand block, how far she has left to race, adding Hundreds, Tens and Ones blocks until she can trade them for the Thousand block. And win !

50 kilometers left on the left ! 900 kilometers left on the right !

## Fancy dice ! Music dice !

By now, if you have been following our journey, you must have noticed that I like… dice, and so do my children. You can find fancy dice in toy stores or online (e.g. eNasco). But I thought I should share a new online ressource I just found : The practice Shoppe (http://www.thepracticeshoppe.com). They offer dice related to music ! I will order a few and let you know ! Indeed, music is just another beautiful example showing that math is indeed all around !