Saturday, August 11, 2012

Teaching Your Young Child Math

At 28 months old, Jett recognizes and can name numbers 0 to 100. (He says "ten-ten" for one hundred, for some reason.) He does count with me, but I have no idea if he has a concept of numbers yet. (Maybe he understands one, two and three? He seems to get those right...) He does know triangle, square, circle, rectangle and oval. At 34 months, he knows the concept of 0-10. He says "empty" to explain "zero." And he knows all his shapes, even complicated ones. I put both hands together and said, "a heart" and he tried to do it and said, "a polygon!" Late into his third year, Jett can also count by tens, identify patterns of 3 or less, sort and classify like items and add and subtract physical objects (not on paper, with symbols).

To begin, I'd read this article from RightStart Mathematics on Math and the Young Child. It's a 2-page overview on how to introduce math concepts early. You'll find a presentation called The Future of Primary Math that has no sound, but if you click through the slides, you'll get the idea of what they mean.

In addition to supplementation to improve Jett's cognition and memory, we do lots of educational activities. Here's a collection of blog posts (from blogs We Can Do All Things, Bill and Ria, Elaine Ng Friis, Hannah's Shenanigans, Special Connection Homeschool, Counting Coconuts, A Super Baby, The Pinay Homeschooler and more) as well as links to help you teach your child understand early math concepts such as:
  • Shape Recognition
  • Number recognition and formation
  • Counting, including skip counting and “counting on”
  • Pattern identification and creation
  • Sorting and classifying

Activities that Support Early Math Concepts


Toy Review Tuesday: Melissa & Doug Pattern Blocks & Boards
Shape Sorting Activities 
Tracing Shapes 
Voila Shapes & Shadows Wooden Recognition and Matching Game
Fun Activities using Pattern Blocks 
Elastic and Peg Board Shapes
Sensory Play with Ice Shapes
Educational Cubes: Shapes 
Magna Doodling Shapes
Light Table Play with Shapes 
Sensory Bag: Shapes
Lots of Circle Activities 
Oatmeal Banana Bars (Cooking with Shapes)
Numicon free printables including the numicon shapes.
Shapes with Popsicle Sticks


Toy Review Tuesday: Alphabet Beads
My First Sorting Bears Activities 
Toy Review: Super Sorting Pie by Learning Resources
Toy Review Tuesday: Birthday Cake (Melissa & Doug)
Number Recognition

Number Snowflakes
Toy Review Tuesday: Wooden Number Puzzle
Numbers and Shaving Cream & Scooping Numbers
Sew it: Sensory Numbers
A Tree Dice Game

Jett placing colored dominoes on chalk letters.

Understanding the Concept of Numbers 

Number Pom Pom Cards
Jumping Math
Homemade Number Matching Flashcards  
Ladybug Math
Homemade Flower Number Matching Cards
Fishing for Numbers
The Abacus
We started using one at 34 months old. It's a great way for kids to see and touch numbers to get a better understanding of number values. Jett loves the abacus!
The best type of abacus should have the first five beads colored differently from the next five. Like the Learning Resources 2-Color Desktop Abacus (LER4335). If you already have a Melissa & Doug abacus or one that needs 1/2 the beads painted, here are some nontoxic paint choices to fix the problem. 
Here is the overview on how to introduce the abacus.
You can get free sample lessons from RightStart Mathematics
Or you can purchase their entire program. Kay Ness, Jett's neurodevelopmentalist, highly recommends it.

To teach number concepts up to 100, play this simple game:
1) Say a number and slide the beads across to show it on the abacus.  
2) Say the same number and ask your child to slide the beads across. 
Then, if old enough, your child can say a number for you to show on the abacus. (Careful not to underestimate your child or bore them. In my first lesson, I was showing Jett how to move "1" bead across and I said it was his turn. So he used the palm of his hand and moved ALL of the beads in all the rows in a couple of swipes leaving 1 bead on each row. He pointed to each "1" that was left and quickly said: "One, one, one, one!" and was done with the lesson for the day.)

Using this method, your child will easily recognize 6, 7, and 8 beads without counting, just by visualizing. Also, let's say you choose 6 beads on one wire and 8 on the next one. You can show how the five and five on those two wires makes ten, and some are left over for early introduction to subtraction and addition. 
The M&D abacus that I painted with watercolors. I added painter's tape on the sides and wrote 10/ten, 20/twenty... in silver marker.
Learning how to count by tens and fives makes a lot of sense when you show your child on the abacus. The picture above shows how I modified Jett's abacus for teaching him to count by tens.

Number Puzzles 
The Learning Journey International has two and three-part puzzles called Match It! Puzzle Games Counting and Match It! Puzzle Games Numbers . They are large, self-correcting and Jett enjoys putting them together. You can control the level of difficulty by giving more or less choices for your child to choose from when solving the puzzles. I got the two-part puzzles when Jett was 30 months and the three-part puzzles when he was 32 months old, both from Ross for about $5. (I later used these puzzles to write the Japanese names and symbols for the corresponding numbers.)


Toy Review Tuesday: Beans, Beans, Beans
Early Learning Activities with "Teddy Bear Counters"
Loose Change
Counting Hearts 
Toy Review Tuesday: Felt Board Stories
Easy DIY Counting Cards
Counting using Bead Stairs
Counting Numbers 0 to 9 using Coins, Sticks and Beads
Counting 11 to 20 using beads
Counting by Tens with Legos
Counting to 100 with little cards
Counting Six Different Ways

Pattern Recognition

Paperclip Patterns and Numbers
Pattern Block Fun
Using 4-in-a-Row Counters
Stringing Beads
Patterns with Legos
Peg Board Patterns

Shape Puzzle Products

Learning and having fun with shapes can start with this durable Melissa & Doug Beginner Pattern Blocks set (left). It's sturdy and thick enough for little fingers to manipulate.

Jett doing the rabbit puzzle in the M & D Pattern Blocks and Boards.

The next step would be the Melissa & Doug Pattern Blocks and Boards (right). These puzzles are more complicated and have smaller, but still durable shapes. The wooden boards have pictures made from the shapes and your child places the matching shape piece on top to complete the colorful picture.

The Learning Journey Match It! Shape Shuffle has 88 shape pieces and 17 double-sided cards that teach shapes and patterns with progressing difficulty. Jett started this at 32 months old and likes it a lot. The first card has pictures of the shapes on it and the child simply puts the shape on top to match. The other cards have pictures made from the shapes (like the M & D one). Not good for children who still put things in their mouth since the shapes are smaller and made of cardboard. It would be better if these shapes were a bit sturdier because if your child sweeps his hand/arm across it, it does shift. But, if your child is pretty neat and careful, he won't get too frustrated. At 32 months, Jett was more successful with the M & D version even though he enjoyed this one as well. 

Activity Resources
The Down Syndrome Foundation of Orange County's (DSFOC) "The Learning Program" offers materials for free on their website. Registration required. They have an "Everyday Math" handout with plenty of activity ideas for prenumber concepts and early number concepts such as sorting, comparing objects and patterning. Early number concepts include rote counting, counting with meaning and number symbol (numeral) recognition. - from Bill and Ria's Blog.


Jett loves doing worksheets in his Crayola dry erase "folder." I enclose it so that he can write all over it and we can reuse the sheet as needed or give it away to others when we are done. If I forget, he follows me around insisting on doing his worksheets. Other moms call it "funsheets" but Jett thinks they are fun anyway.
Free kindergarten math worksheets from School Sparks.
Free Counting Pages  from Early Learning Activities.
Free P-K math worksheets from TouchMath.
Free Shapes Worksheets from Kids Learning Station.
Free Preschool Pattern Worksheets from Kids Learning Station.
Free Preschool Numbers Worksheets from Kids Learning Station.

At the Dollar Store and Big Lots, they have lots of worksheet workbooks to choose from. Here are some that are appropriate for early math skills:
Disney Shapes and Sizes (Dollar Store)
Teaching Tree Colors & Shapes Pre K/K (Dollar Store)
Little People PreSchool Vol.2 (Dollar Store)
Teaching Tree Counting Kindergarten (Dollar Store)
Sesame Street Let's Learn Beginning Math (Big Lots) $2  
Sesame Street Let's Get Ready for School (Big Lots) $2

Math Songs and Videos

You can check out/subscribe to my youtube channel "andiandi222" and see the over 700 short educational videos I've collected. There are a lot of videos that show shapes, songs, numbers and other math concepts as well as reading support.

Math Programs

For a more multi-sensory approach to learning math using manipulatives, there are teaching resources like Numicon, which was developed in the UK and is available at downsed USA's online store. - from Bill and Ria's Blog. Here's Numicon's resources for children 3-5 years old.
Nathan Purdy's mom, Barbara, says that the Math-U-See program is the one curriculum she highly recommends for learning math. The man who developed it has a son with T21 so he understood the need for making the abstract concepts concrete. It isn't specifically for people with disabilities, but seems to work especially well for many of them. We also did Touch Math prior to Math-U-See and I found that to be very easy for Nathan to learn adding, subtracting and multiplying although it wasn't until the Math-U-See that he began to understand what he was actually doing, even though he was able to get the right answer with Touch Math. 

2+2 Free Math Software your child can work with when s/he is able to use the mouse. Counting, addition, subtraction, multiplication and division.


Teaching Math to People With Down Syndrome and Other Hands-On Learners: Basic Survival Skills (Topics in Down Syndrome) Book 1 by DeAnna Horstmeier has many activities for learning prenumber and early number concepts. 

Number Skills Development for Infants with Down Syndrome (0-5 Years) (Down Syndrome Issues & Information) (Pt. 1)

Fun Math For Young Learners 
This free e-book includes a brief discussion of the five main components of any basic math program including graphing. In addition, this e-book includes time-tested tips and strategies (plus 38 worksheets). 

One Two Buckle My Shoe: Math Activities For Young Children  by Sam Ed Brown You can get this for about a penny on Amazon.

Early Math Books for Children

These books are fun and educational all are Jett-tested and approved.

Is It Larger? Is It Smaller? by Tana Habon, a pictures-only book with photographs of objects of varying sizes.

BIG & Little : Board Book by Todd Parr has nice, bright pictures and big, simple text.

1, 2, Buckle My Shoe by Anna Grossnickle Hines is a nice first counting book only some pages have words.

Seven Hungry Babies by Candace Fleming is a fun math story. It has some big sized words, some small words with great, bright, expressive illustrations. Jett loves the "sound" words. (This is the first book that Jett started to read the words aloud.)

Five Little Chicks (Classic Board Books) by Nancy Tafuri Fun to read aloud with rhyme and repetition, sturdy board book, with nice, but detailed pictures and fairly big, bold words.

Five Little Pumpkins by Iris Van Renbach Big, bold words with rhyming. Pictures are a little too busy and detailed for young babies.

Click, Clack, 123 by Doreen Cronin and Betsy Lewin

Odds and evens : a numbers book by Heidi Goennel

Quack and Count by Keith Baker. This book is awesome for multi-age groups because although the text is simple there are two levels of math on each page. Simple duck counting as well as addition to arrive at the same number.

Just Enough Carrots (MathStart 1) by Stuart J. Murphy is a wonderful book about the concepts of less, more and the same amount.

Eggs and Legs: Counting by Twos by Michael Dahl

On the Launch Pad: A Counting Book About Rockets by Michael Dahl is fun to count down from 12-1.

1-2-3 Peas (Classic Board Books) by Keith Baker, with huge, colorful numbers and the corresponding amount of peas doing silly activities throughout the book. It covers the essential numbers between 1 and 100 and is helpful to introduce the idea of larger numbers.

Zero by Kathryn Otoshi learning about the shapes of numbers.

Mouse Count by Ellen Stoll Walsh, seems to be a counting book, it also serves as an early introduction to addition and subtraction.

Length by Henry Arthur Pluckrose, is from an excellent series called “Math Counts”

Inch by Inch by Leo Lionni, is a delightful Caldecott Honor Book that will appeal to all ages.

Ten Black Dots by Donald Crews This is a strangely written book and pictures are odd too. But, it has nice sized words and very simple, bright pictures. Jett enjoyed this one a lot, although we didn't. Good from the library!

One More Bunny Board Book : Adding from one to ten by Rick Walton Illustrated by Page Miglio Great book. Eleven big words per page. Nice big words, separated from picture. Fun to read, exclamation points, rhyming words, about activities that toddlers can relate to. Great introduction to addition.

Help Me Learn Addition by Jean Marzollo, is an adorable book using photographs of figurines and rhyming narrative to introduce basic addition equations in a way that appeals to young readers. 

Math Appeal: Mind-Stretching Math Riddles by Greg Tang and Harry Briggs. At 3 1/2 years old, Jett loved all of their books with short, fun math poems. Including Math Potatoes, Math for all Seasons, Math Fables and The Grapes Of Math.

How Do Octopi Eat Pizza Pie? Pizza Math (I Love Math) is part of the I Love Math Series... At 3.5 and 4 years old, Jett loves these books!

Math TV Shows

Team Umizoomi is on Nick, Jr. and is the first preschool show that focuses on early math skills. It's a half an hour long and features counting, pattern recognition, shape recognition, search and seek, puzzles and sorting and classifying--all in a fun way. At 37 months, Jett loves the show and excitedly participates to answer their questions. He even eagerly wears his "TV glasses" (therapeutic glasses) in order to be allowed to watch it--even putting the glasses on himself! 

Some reviews:
Commonsensemedia 4 stars Parents give an average of 4.8 stars

There's even a Team Umizoomi math kit. Here's a review of it at You can purchase it at ToysRus for about $20. Looks very interesting!

Math Apps

These are the ones that I like because they are free, easy for a new iPad user to navigate, getting the answer right is not a huge deal, so they encourage the child to try and Jett likes them because they make learning math fun: 
Injini There's a great free version, but the full is $25. (Maybe even worth it!) It has find it, puzzles, matching, a simon-says-type game, a fun writing game and more. It is very good.  
Eurotalk Math age 3-5 Love this app! (I think it's $5?) It shows how to do each lesson very simply, both visually and verbally. It slowly expands on each concept (except patterns, I think it goes a little too fast. And the writing is hard too. I'd do the Injini first before getting to the writing part). It's only positive, no "wrong," just try again, and doesn't go overboard with "WOW! YOU DID IT!" kind of response for each little thing. It's very low key. It covers a lot, including number recognition, patterns, shapes, sorting and writing in a friendly, colorful, fun but not crazy way. It's also not loud or flashy.
Patterns by EdNinja has cute pictures and lively music to teach patterns.  
Monster Math uses monsters and animals in simple equations. 
i learn with Boing has cute games to learn counting. 
Math in Action helps with sorting. 
Little Writer by Alligator Apps helps the child learn to write numbers. 
Trash Stash with Peep and the Big, Big World is a simple sorting app.

Math Apps List and Reviews for Pre Schoolers

Kindergarten Level

According to, this is a list of objectives and goals kids should be able to do by the end of kindergarten:
  • Count by rote at least to 20, but preferably a little beyond.
  • Know the concepts of equality, more, and less
  • Count backwards from 10 to 0.
  • Recognize numbers
  • Be able to write numbers
  • Recognize basic shapes
  • Understand up, down, under, near, on the side, etc. (basic directions)
  • Have a very basic idea of addition and subtraction
  • The should also be exposed to two-digit numbers.
At almost 37 months old (just turned 3), Jett's only missing these kindergarten skills: 
  • Know the concepts of equality, more, and less (he uses the words: empty, full, half and a lot appropriately so we are getting close)
  • Be able to write numbers (we are working on this--his fine motor skills are improving!) and
  • Have a basic idea of addition and subtraction 
Next Level Math Activities
Large Numbers

Large Numbers and Bead Activities


Addition with Beads and Bears
Chicks Addition Game
Addition Boxes

Advanced Shapes
3D Shapes


Clock Faces and Time
Learning how to tell time


Dinosaur Egg Graphing 


Learning how to Measure with Fruit

Related Posts


We Can Do All Things said...

Andi, this is a great list, thanks for adding us as a link, I am going to add this post to our collaborative Ds math board on pinterest. Are you on pinterest I would love to add you to the board so that you could also add more of your reading, math and homeschool stuff

Anonymous said...

Andi, you're great! ;) thanks