Enriching Math Talent at Home

Marsha Landau, Ph. D.

Center for Talent Development

Saturday Enrichment Program

Parent Workshop

Saturday, November 3, 2012

Introduction

You are your child's most important teacher.

What are some ways in which you encourage mathematical thinking in your child?

Math is about Patterns and Relationships

For example, here's a number pattern I haven't had a chance to explore yet:

Understanding math involves translations within and among Modes of Representation:

In order to ENRICH at home, parents need to know what's happening in the schools:
Common Core State Standards
Common Core State Standards Initiative | Mathematics | Standards for Mathematical Practice
new directions for assessment, for example:
Grade K-2 performance task
Grade 3 performance task
Grade 4 Performance Task
Grade 5 performance task

Understanding Constructed Response Items

Math at Home:

Everyday life opportunities: measurement in cooking, arts and crafts, projects

Note about the afternoon session on Saturday: We talked about the fact that cutting an orange into eighths could lead to a discussion about non-Euclidean geometry. In the picture below, you can see how the "triangular" piece of the orange has three right angles:

Books
(for example, see: Math Books and Resources . Education | PBS Parents)

Almost any book will do if you are on the lookout for math connections.

Last week my granddaughter and I were reading There's a Zoo in Room 22 by Judy Sierra. (Preview here on Googlebooks.)

It is written in verse, so we discovered and labeled the rhyming PATTERNS.

This one is ABAB CDCD:

This one is AABBCC:

My granddaughter declared that "hexaflexagon is not a word."

Well!
I happen to HAVE hexaflexagons--in fact, all of the following:
trihexaflexagon
tetrahexaflexagon
pentahexaflexagon
hexahexaflexagon

So after finishing the book, we explored the flexagons.
For directions and patterns to make your own, go here.
And an exciting video here.

Planned learning situations: using manipulatives, games, software, internet

Big Ideas in Early Childhood:

numeration

seriation

classification

Early Childhood Math

counts and measures

meanings of operations: addition and subtraction
(in depth: Addition and Subtraction Problem Types )

Mathwire.com | Math Enrichment

Math and Literature

An excellent resource to use when creating a list of books to look for at the library is Math Patterns in Children's Literature.

Another is amazon.com's lists of books keyed to specific mathematics content. For example:

K-5 Math Teaching Resources - Counting

K-5 Math Teaching Resources - Place Value

FOR PARENTS:

Math And Literature, Grades K-1. Marilyn Burns, Stephanie Sheffield, Toby Gordon.

Math And Literature, Grades 2-3. Marilyn Burns, Stephanie Sheffield, Toby Gordon.

Math and Literature: K-3 Book 1 by Marilyn Burns

Math and Literature (K-3) Book 2 by Stephanie Sheffield

Math Through Children's Literature: Making the NCTM Standards Come Alive
by Kathryn L. Braddon, Nancy J. Hall and Dale Tylor. Math activities designed for 132 different children's titles. Designed for classroom use.

It's the Story that Counts: More Children's Books for Mathematical Learning, K-6. David J. Whitin, Sandra Wilde.

Project Resources

Example: Halloween (see page on this blog)

QUILTS

I was especially pleased to find a link to a free online quilt designer. Quilters made it easy for me to create my own patterns. Here's an example:

11/4/2012 Update on Quilters: Al Jarnow, the creator of Quilters, was kind enough to respond to my email about the application not working for me. Here's his reply (and both the link and the revised app worked fine today):

Here's a version that will work in a different way (I think). It might be too late for your demonstration, but for next time . . . .

https://dl.dropbox.com/u/72975954/QuiltRevision.zip

Click on the link to download a zipped app to your computer. It might unzip by itself. Otherwise find the downloaded zip in your downloads folder and click.

Further correspondence suggests that the first link above will work for PCs and the download from dropbox will work for Mac, but won't be available indefinitely.

TESSELLATIONS

To make your own tessellations, simple directions can be found here:

Making your own tessellations.

Cuisenaire Rods: Space, Color, and Mathematics introduces Cuisenaire rods and explains in detail how to get started with them. The rods are a very versatile manipulative, so worth the investment. They can be used to explore all the important whole number concepts and operations, but also factors and
multiples, fractions, area and perimeter, etc.

Speaking of manipulatives, here is a nice description (with pictures) of most of the useful math manipulatives you might consider purchasing for your home:
Math Manipulatives Page from USI STEM

Interactive Games and At Home Activities For Kids, LICM Kid’s Page is sponsored by the Long Island Children's Museum. There is another quilt designer here, and other interactive drawing games. The at-home activities include printable games for children 9-12.

The Math Kit "At Home with Math" at the TERC website has this description, from their introduction:

A word to parents This math kit contains activities and games to help you make math a natural part of your family’s everyday work and play. The kit contains two books, one for everyday math activities and one for math games.

Everyday math activities As parents, we use math all the time—as we shop, figure out how much time to allot for errands, and schedule time for cooking, eating, and cleaning. Often, our children are with us during these tasks. Perhaps they are even helping out. Why not involve them in the math?

The ten everyday math activities in this kit build math into the things most families already do—ordinary routines such as figuring out ways to save money, to share fairly, or to get somewhere on time. With these activities, children practice adding, subtracting, multiplying, dividing, and using other important math skills while doing tasks that are a regular part of life.

I particularly liked the activity using estimation and counting while putting away toys that are scattered about, and the one developing ideas of probability and statistics through collecting junk mail for a week.

Also try the activity Which holds the most?

This link, also at TERC, provides questions that can be the basis for a series of projects:

How many different ways are there?

Finding different ways to make fourths on a geoboard is one of my favorite activities when I work with gifted students.

Math manipulatives

for example:

tangrams

Explore geometry and measurement ideas using 7 easy pieces: similar triangles, equal areas, angle measures, etc. A wide variety of tasks are available to make this work well with students of all ages.

Wooden Geoboard 8 X 8 Single So much more than making a shape! Explore length, area, Pick's Formula, irrational numbers, composing and decomposing regions, congruence, and more.

Attribute blocks One of the central math tasks of early learners is classification. This manipulative allows the student to consider classifying pieces based on shape, color, size, and thickness.

pattern blocks

Note: The photo at the top of this blog shows a pattern block design tucked into a hinged mirror. I think it illustrates the beauty of the WOODEN blocks, which I much prefer to the only slightly less expensive plastic ones.

A better price is often available at EAI:

Pattern Blocks: Wood 1cm - Set of 250 | EAI Education

Pentominoes

All the shapes you can make in a plane when 5 congruent squares are connected along whole sides. The 12 pieces can be fitted together to make rectangles (6x10, 5x12, 4x15, 3x20) and many other shapes.

origami

Games

I do not recommend so-called games that are designed to make your child practice math facts--they are boring! The 24-game, featured below, gets the same job done many times over and is fun and exciting.

The other games are strategy games which promote logical reasoning and thinking ahead. The ones you can play with young students are Continuo, Gobblet, and Set, since they rely more on visual/spatial thinking than number knowledge.

Quarto Game