In the "Button Box" challenge, students have opportunities to employ all five process standards. They will:

• problem solve as they decide on a strategy for solving a problem where the answer is not immediately obvious.

• reason as they think about and justify their solution as the only possible correct answer.

• communicate about their thinking by discussing it with classmates, parents, and teachers, as well as by posting their written solution on the message board, and communicating via the message board with other students from around the world. Also, understanding the mathematical language in the problem is vital – half, twice, more, same as, even, etc.

• make connections between mathematics and real life experiences such as sorting buttons – and between mathematical concepts as they solve the challenge.

• use representations (drawings, charts, words, equations, manipulatives, etc.) to provide a record of their efforts to understand the mathematics of this challenge and make their understanding available to others.

About the mathematical content in these challenges:
The regular and harder challenges focus on the Number and Operations standard, and in order to solve it, students will need to use number sense as well as operational sense. For instance, upon reading that there are 26 total buttons, and 12 of them are small, the student must understand that to find the number of large button, the subtraction operation is called for.

The easier challenge and the extension activities focus on Classification. The ability to classify is the prerequisite to rational thought. Classification is the imposition of an organization on a set, to notice that some things are alike in some way and therefore, belong together. In other words, when we classify, we generalize attributes that are shared by all members of the set. This skill is a prerequisite for reasoning, for the organization, comparison, analyzing and judgment of data. Classification is really deductive reasoning, a big idea in algebra. In fact, classification is so important in children's mathematical development that it appears in three sections of the Pre-K: 2 Standards - under Reasoning, Statistics and Probability and Algebra and Patterns.

About the Challenge:
The regular challenge lends itself well to cooperative group work of 3 or 4 students each. Teachers could print out the clues on paper, cut them into strips, and put a set of clues into an envelope for each group to work with. The rules are that each group divides the clues as fairly as possible among themselves (some will get two and some will get three.) Once a student receives a clue, no one else in that group may touch or read that clue. In turn, each student reads one of his/her clues. After all the clues are read, any clue may be re read as many times as necessary, BUT ONLY BY THE PERSON WHO HAS THAT CLUE. (In this way, everyone is encouraged to work together to solve the challenge.) Because some clues are more important than others, and some clues must be solved before other clues can be used, lots of cooperation must be shown in order to arrive at the solution to the challenge. Teachers may wish to assign particular roles to the group, such as recorder, reporter, etc. However, it is very important that everyone in the group understands and agrees with the final answer before it is reported.

Note: With children unused to solving such problems, teachers may need to point out that each answer must be proven. There is no guessing allowed in such a challenge.

Younger children may need a copy of the Guess My Button Page or teacher may wish to make an overhead transparency as well. Beginning problem solvers may wish to use beans or other concrete objects of indicate when a button has been eliminated by a clue. When I play this type of "negative attribute" game ( using "not" clues) with my kindergarten classes, I often ask children which button they think it is, then ask them to give me a clue that would eliminate other buttons. I use their clue if possible, but in any case it involves them in thinking. When the children have played these kinds of games frequently, I let the children take over the game, making up "negative attribute" clues for their classmates. (One rule is that they have to whisper their secret button to me first so they don’t change their minds later!) Look in the extension activities for more games that can be played with this same button selection.

A Word From Aunty About Button Collections:
In this high tech world, it is surprising how much enjoyment children still get out of a simple button collection. My own grandchildren, ages 8 and 4, still spend hours sorting my collection into muffin tins. I love to look at the results of their sorting and see if I can figure out what they were thinking about as they sorted. I usually leave them alone to sort on their own but sometimes I ask them how they are sorting, and when I do, these are the kinds of things I hear:

• These are shiny and these are not

• These have no holes ( I was then able to teach them the word "shank")

• These have fabric on them

• These are my favorite colors

• These look like they are for queens – they look "spensive!"

• These look like men’s buttons

• These are made of metal

• These are really tiny and this is the tiniest on of all!

• These are not round

• We have 10 different shapes in here!

Just think of all the learning taking place in this simple activity – learning about using language to count, compare and order shape, size, texture, and material. This activity helps children learn to:

• observe and describe details using mathematical language

• become aware of the different attributes of similar items

• identify attributes that make it possible to sort and classify
  and communicate about what they see and think.

If your children or students do not have ready access to a good "old fashioned" button box, may I suggest you start one soon? Many craft stores have "starter" collections readily available.

Math/Literature Connection
There are many good math literature connection books on the subject of buttons. One of the best is Margarette Reids’ The Button Box by Dutton Publishers ( NY, NY, 1990). In this book a young boy sorts and classifies his grandma’s button collection. It’s a good introduction to a class sorting activity.

Another book Buttons, Buttons by Rozanne Williams is published by Creative Teaching Press, Inc. (1994) is clearly photographed.

Two classics remain Frog and Toad Are Friends by Arnold Lobel and Corduroy by Don Freeman. The "Guess My Button" can be changed to "Where’s Corduroy’s Button?"

Game #1
The secret button does not have 4 holes.
The secret button is not pink.
The secret button is not large.
The secret button is not heart shaped.
Which is Corduroy’s Button?

Game #2
The secret button is not on the top row.
The secret button is not large.
The secret button is not round.
Which is Corduroy’s Button?

Game #3
The secret button is in the corners.
The secret button does not have 2 holes.
Which is Corduroy’s Button?

Game #4
The secret button is not large nor is it heart shaped.
The secret button does not have 2 holes.
Which is Corduroy’s Button?

You and your students can make up many more games using this same collection or make collection cards of your own.

Button Patterns – Algebra, Geometry

Using Play dough or homemade dough, and buttons with designs, children can make linear, symmetrical or rotational symmetric designs using buttons.

A hole can be made using a soda straw. These designs can then be dried and painted. Then, a cord can be attached to make a pattern pendant.