Here are some notes and worksheets to help children work through some of the potentially difficult areas of mathematics…lots more resources will be added soon…
Learning addition and subtraction
The best way for children to grasp the concepts of addition and subtraction is with the use of a set of identical objects that can be counted. (I usually use the smooth glass stones that are used to fill vases.) The items to be counted must be identical and boring so that they do not become a distraction from the activity of counting.
To show 2 + 3, just make a group of 2 stones and a group of 3 stones and push the groups together and ask the child to count how many. When counting, always move the stone you are counting to the side so that you can tell which stones have been counted.
Same process with subtraction: Using the idea of candies usually catches their attention: “You have 5 candies and eat 2. How many to you have left?” If you take two away from the group of 5, the answer will be easy to see. After the concept is understood, the stones can be used as a counting aid. Here are a few worksheets for practicing these concepts:
Once addition and subtraction are well-understood, and the addition facts are able to be recalled quickly, the child is ready to work on addition and subtraction with numbers of 2 or more digits. Here are a few worksheets for practice with addition and subtraction with larger numbers. Borrowing and carrying are introduced part-way through these worksheets.
Learning multiplication and division:
The skip counting worksheet is the best way to learn multiplication tables. Ideally, this work should start in grades 1 and 2 so that kids have learned many of the easier multiplication facts by grade 3 and then they can learn the harder ones by grade 4. Skip counting worksheets should be done often! Division should only be worked on once multiplication is understood.
If you want to work with your children, dice are fun. Use two dice and have your child multiply the two numbers together. To make it more challenging after a while, cover up the 1 and 2 and 3 on one die with 7 and 8 and 9. Nines are fun to learn.
Flash cards work well also – but only if the child is given a bit of time to get the answers. You can have a white board handy or some paper. These flash cards should be printed on card stock (heavy paper) so they hold up well. Cut them out so that each question is on one card. Start with just the 2 and 3 times tables, then add more. Once they have been introduced to times tables up to 9 x 9, I like to teach children that 2 times 2 is the same as two squared – it makes a square of 2 x 2 and I show that with grid paper. If you want to emphasize the squaring, there is an extra page of flash cards that you can include. The nine times tables are fun – see the Nines Trick worksheet below.
Once children have done several of the skip counting worksheets, and some flash cards, it is good to practice their multiplication skills using worksheets, online quizzes or math drills out loud. Once accuracy is established, work on speed.
I recommend this online math quiz for all types of math practice (you can set difficulty, number of questions, which areas to work on, etc.):
Once children have become more accurate with multiplication, it is time to work on the harder questions and develop speed. Completing Multiplication Review 2 several times a week will build speed and confidence. Accuracy is always more important than speed.
Grades 3 and up: new areas covered
Starting in grades 3 and 4, children will start to use the addition and multiplication skills to solve problems – usually area and perimeter. In grades 5 and 6, the questions include area of triangles and parallelograms. Other extensions of the multiplication and division work include fractions and percentages, which are usually covered in grades 5-7.