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My recommendation for kindergarten math

The goal of kindergarten mathematics is to prepare children for first grade math. Please see below a list of objectives and goals for kindergarten math:

• To count by rote at least to 20, but preferably a little beyond.
• The concepts of equality, more, and less
• To count backwards from 10 to 0.
• To recognize numbers
• To be able to write numbers
• To recognize basic shapes
• to understand up, down, under, near, on the side, etc. (basic directions)
• To have a very basic idea of addition and subtraction
• It also helps to expose the student to two-digit numbers.

Children may also get started with money, time, and measuring, though it is not absolutely necessary to master any of that. The teacher should keep it playful, supply measuring cups, scales, clocks, and coins to have around, and answer questions.

During 1st grade, children will then learn addition and subtraction facts, two-digit numbers, some adding and subtracting with two-digit numbers, and some basics of measuring, time and money.

Counting

Mathematics starts with COUNTING. Let children count all kinds of things they see or use. Use simple counting games, such as:

• Have a deck of regular playing cards minus the picture cards. Each person draws a card. The one with a higher number wins all the cards played in that round. This can teach both number recognition and counting, because the child can count those little pictures (hearts, spades, clubs, or diamonds) on the card.
• A variation of the one above: deal two cards to each person. The person with a higher TOTAL wins all the cards played in that round. Children will learn basic addition!
• Use any board game. Have the markers advance as many steps as a die or dice show. The child will need to count the dots on the die or dice, and then count steps to move his marker.
• Lay a bunch of dominoes face down on the table. A child picks one, you pick one. The person with a higher "dot-count" gets both dominoes.
• Lay a bunch of dominoes face UP on the table. A child picks one and places it on the table to start the "train". The next person picks one so that its end matches one end of a domino already laid.
• Play with marbles or blocks or similar objects. You take some objects, and ask the child to take for himself as many as you have AND ONE more. Then it's the child's turn to take some, and you need to take the same amount plus one more. Reverse the game later to do ONE LESS.

A 100-bead abacus

One extremely helpful manipulative to buy is a basic 100-bead abacus (10 racks, 10 beads in each).

This is the prime "toy" to teach numbers beyond ten. With such an abacus children will naturally learn their "tens and ones". I've written about the usage of abacus for learning place value here.

The best kind of abacus has each five beads in alternating colors. Some are pricier than others, but all have the same basic idea. Nasco sells an abacus with each 5 beads in alternating color. The AL Abacus from RightStart is also very good. Melissa & Doub wooden abacus is sturdy. You can browse Amazon's abacus selection here.

Number recognition

It is helpful to have concrete numbers (plastic or foam) that the children can touch. Other than that, games are again an excellent way to reinforce learning.

• Here's a simple game: Have a bunch of foam numbers and/or plastic magnetic numbers, and make a heap of them between you and the child. You pick one, hold it up high and call out loud its name, such as "Number five!" and put it to you personal pile.

  The child will then find the same number (make sure there are at least two of each number) and does the same, calling its name out loud and gathering the number to himself.

  Then you reverse it so that it is first the child's turn to pick any number from the pile, call out its name, and put it to his pile, and you have to find the same number. After all the numbers in the middle pile were gone, the task is to arrange the numbers you have in order.

• Play all kids' favorite card game: UNO. That'll motivate children to learn to recognize numbers quickly.
   
• DotMath for kids practices number recognition based on the dot patterns on a die. Several pages of the book are available online (as images).
   
• Check my list of online addition and subtraction games.

Worksheets for shapes, matching, equivalence, more, and less

To recognize shapes and practice matching, you can either use ready-made worksheets or workbooks, or make some of your own.

If you make your own, you can just draw three circles on a page and then 2-5 triangles on a page, and ask the child to match each circle with a triangle by drawing a line from shape to shape. Vary the shapes and the amounts. Sometimes the amounts should be equal, sometimes not.

Another variation is to ask the child to draw. First make some sticks, circles, squares, or other shapes on a page, and encircle them. Make for the child a big "bubble" to draw in, and ask the child to draw either the same amount, one more, or one less.

Also have your child practice writing numbers on paper.

You can find lots of different kinds of basic kindergarten workbooks at LearningThings.com. You don't really need anything too fancy to practice these concepts, so workbooks from many different publishers can work equally well. Singapore Math's EarlyBird Kindergarten math is praised a lot. Dorling Kindersley's kindergarten math workbook is of good quality as well.

There are also several fine websites that have free worksheets for kindergarten math, such as:

• Kidzone.ws kindergarten math worksheets
• Maths is fun kindergarten worksheets
• Kindergarten math worksheets from About.com
• ...or search Google for kindergarten math worksheets.

Math Mammoth 1st grade

A child is ready for Math Mammoth complete first grade curriculum (Light Blue series) once he/she:

* can write numbers
* can count well at least to 10 and back, but preferably a little more.
* has some idea about basic addition.

If you do not want to get a complete curriculum, but shorter worktexts or workbooks, then the Addition 1 book is the first and easiest one in math Mammoth Blue Series. It best suits 1st grade.

Both the Light Blue first grade and the Addition 1 book start out dealing with addition within the range 0-10, but they also include missing addend problems such as 3 + __ = 7 and word problems. Kindergartners or younger children MAY get confused with the missing addend concept. If that happens, don't worry - just wait and let the child's brain mature. A lot of the lessons are accessible for kindergartners as well.