Being the "first" day of the "first" month of the new year, today is a good day to introduce your child to ordinal numbers such as "first", "second", and "third". What are the "second" and "third" months of the year? What position is your child's birthday month?
Ask your child to find her birthday on the calendar and tell you what day of the week it falls on this year. What about the birthdays of other family members?
Use a calculator to figure out how many months old your child will be on his birthday this year. Remind him there are 12 months in a year, so he has to add 12 for each year of his age.
Make pasta patterns. Get two or three different pasta shapes (e.g., elbow, bowtie, pinwheel). Start a pattern and ask your child to finish it (e.g., bowtie — elbow — bowtie — elbow — bowtie — ?). Challenge your child to come up with her own pattern .
Create two groups of objects, one with five items and the other with four items (use more items for older kids). Ask your child to look at both groups and tell you which one contains more and which has less? Then ask, "How many more?" and "How many less?"
You don't have to have snow to make a snowman! Cut out three different sized circles from white paper. Ask your child to glue them onto a sheet of dark paper, stacking them in order of biggest to smallest. Now give the snowman a face, hat, and scarf.
Ask your child how many ways he can make the number 7 (e.g. 5+2, 4+3, etc.). He can show you in a drawing, with groups of small objects such as coins, or by holding up fingers. There are lots of ways to make 7!
Celebrate the day by playing rock music and challenging your child to dance for one minute. She'll have fun and will also experience how long a minute is, a difficult concept for young kids.
Get nine pennies or other small objects. Ask your child to divide them up into three equal groups. How many are in each group?
See how far your child can count by 10's (or decades). Can she count to 50? 100? 200? More?
The number 11 is a palindrome, which means it is the same if you read it forward or backward. Ask your child if he can tell you some other numbers that are palindromes (e.g., 22, 33, 222, etc.).
Think of a number between 1 and 10 (20 for older kids) and challenge your child to guess your "secret" number by following clues such as "When you add 2 to my secret number you get 6," or "my secret number is bigger than 3 but smaller than 5."
Invite your child to think of a secret number between 1 and 10 for you to guess. Ask him questions such as, "Is your secret number larger than 5?", "Is it smaller than 8?", etc.
Think of a number, and then take your child on a safari around the house to find that number in as many places as possible (e.g., on clocks, phones, magazines, newspapers, etc.).
How many days are left in January? Give your child a calendar, and ask him to count the remaining days.
Ask your child to tell you what day of the week the 16th falls on next month. What about in July? In November?
Show your child that the number 17 is made up of one "10" and seven "ones", or 10 + 7 = 17. Use pennies to represent this concept. Separate 17 pennies into one pile of 10 pennies and another pile of 7 pennies. Do the same for the numbers 18 and 19.
Winnie the Pooh and his friends all live in the 100 Acre Wood. Explore the number 100 with your child. Ask her to count out 100 pennies, make a chain out of 100 paperclips, or string together 100 piece of elbow macaroni.
Fill a bowl with popped popcorn. Ask your child to grab a handful, and then guess how many piece she has in her hand. Now count them. Using what she knows about how many pieces she can hold in her hand, can she guess how many are in the whole bowl?
Use the classic "I Spy" game to help your child learn spatial relationships by giving clues about an object's location. Use position words such as above, under, on top of, next to, etc. For example: "I spy something purple under the table."
To pass the time at a restaurant, play a sorting game with the different colored packets of sweetener. Mix them up and ask your child to sort them by color. You can also create color patterns with them (e.g., yellow — pink — blue — yellow — pink — blue — yellow — pink — what comes next?)
How many different kinds of shapes can your child make out of drinking straws?
Draw an outline of your child's foot on a piece of paper. Cut it out. Place the foot cut-out end-to-end along the length of a piece of furniture. How many "feet" long is it? Do the same with a cut-out of your foot. Discuss why the measurements are different.
Measure your child's foot three ways (e.g., using paperclips, barrettes, and pennies), and compare the results. Using pennies, for example, line them up from the heel to the tip of the big toe. Count the pennies. Ask your child, "How many pennies long is your foot?"
Challenge your child to an opposites game. Take turns finding things that are small and big, tall and short, and narrow and wide. Start out by pointing to a short glass and saying, "Look, there is a short glass, can you find a tall glass?"
Here's an online game your child can play to explore geometry by showing how shapes tessellate, or repeat to cover an area without gaps or overlaps. A honeycomb, for example, is made by tessellating hexagons.
During bath time, use your finger to "draw" numbers on your child's soapy back. As you draw each number, challenge your child to guess what number you are drawing.
To celebrate Ernie's birthday, invite your child to play a game with Ernie!
Print out a picture, or cut one out of a magazine. Glue it onto a piece of heavy paper. Cut it into pieces to make a puzzle for your child to put together. Be sure to print out a second copy of the picture for your child to refer to as she puts the puzzle together.
Ask your child to count by 10's to 30, both forward and backward, and tell you how many tens there are in the number 30.
Count backward by ones from 20, and then count backward by fives. Challenge older kids to count backward from 100 by ones, fives, and tens. Add to the fun by asking your child to walk backward at the same time!