When children are learning basic math facts it is important for them to make sense of number combinations. Concepts that may seem like common sense to an adult often need to be explicitly taught to a child, with clear examples demonstrated so they know exactly what strategies to use to complete the problem.
Multi-modal teaching, which is an evidence-based practice in which the child is taught concepts through a variety of modes (e.g. hearing, seeing, touching), is discussed in this article as well. The ultimate goal of this lesson is that the child will be able to figure out similar problems in their mind without having the numbers/items in front of them. However, every child is different and some children may always need to see the problem to solve it.
Below are some common strategies to help kids start to understand basic addition. Remember to give the child opportunities to explain these concepts back to you to the best of his/her ability and recreate examples on his/her own. Many kids learn best when they have the chance to recreate what they learned.
3 Mental Math Strategies
1 – Adding ‘Zero: Teach the child that when you add zero to a number you will be adding nothing, so the answer will always be the larger number. (e.g., 5 + 0 = 5, 0 + 9 = 9, 3 + 0 = 3, 0 + 6 = 6, etc.). Let them know that the rule is the same no matter what number they add zero to. Visually show the child on paper or a board so they hear and see the rule. Then let them practice making some of their own equations. They can draw the equations or use real objects. Here is an example:
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As one reader pointed out, adding zero to an integer such as -2 will give you an answer of -2 which is technically smaller than zero, however, the methods in this article are for children first learning basic addition concepts and apply to all positive numbers (above zero). You could also say “whenever you add a number to zero, the answer is always the other number.”
2 – Adding One: Teach the child that when a problem asks you to add one, the answer will always be one number higher than the larger number. For example if the problem is 6 + 1 = ?, and the child knows that adding one means to go one higher than six, they will be able to figure out the answer is 7. If the child cannot automatically think what number is one higher, have them count to figure it out (1, 2, 3, 4, 5, 6, 7). Have them work the problem out on a piece of paper or board, so they can visually understand the concept.
3 – Adding Two – Count Up Two: Teach the child that when a problem asks you to add two, the answer will always be two numbers higher than the larger number. If the problem is 6 + 2 = ?, have the child start with the number six and count up two. If he struggles to count up two in his mind, have him use his fingers or use objects to represent the problem as shown in the examples above. Let’s say you use Cheerios; have the child put six Cheerios on one side and two on the other. Once he/she has identified that one side has six, have him/her touch the other two Cheerios one at a time and say “seven”, “eight.” If this is still too difficult, have the child count all six Cheerios on one side of the line, and then move over to the other side to say “seven”, “eight.” Practice this example with all different problems that require adding two (e.g., 1 + 2, 2 + 2, 3 + 2, 2 +4, 2 + 6, etc.)
Make sure to teach the child that the rules are the same whether the larger number comes first or the smaller number comes first (e.g., 1 + 0, is the same as 0 + 1, 6 + 2 is the same as 2 + 6, etc. This concept is called the commutative property.
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MathLink Cubes are a great example of math manipulatives that can be used to visually represent math problems. Since there are 100 cubes, students can practice with higher numbers as their skills improve. However, you can use any item for manipulatives (e.g., toys you already have, food, rocks, etc.)
Using a number line is also an excellent way to help a child learn the concepts taught above. Have the child put his finger on the number on the line and then count up however many numbers he is supposed to add. So if the problem is 6 +2, have the child put his finger on the 6 and then count up two numbers to 8, moving his finger as he goes. Carson Dellosa Student Number Lines Desk Tape (shown below) is a number line that you can easily tape to a desk or table for the student to refer to as needed.
It is also important to note that digital learning has become a common method used in the classroom because it allows the students to see pictures accompanied with verbal math problems or explanations and interact in a fun/game-like way. Many teachers use the IPAD and free IPAD math apps to allow students to play math games in which graphics are part of the learning experience. You can also find several free math apps for your android smartphone or tablet. Allow your child to play digital math games at home for a fun, visual, and interactive experience.
Keep in Mind:
Every child is different. Some respond to several strategies, others respond to a few, while others may not respond to any strategies you try. If your child is significantly struggling with math or acquiring other academic skills, despite consistent practice and guidance, talk to your child’s school and/or doctor. They should be able to refer you to the appropriate professionals to determine what might be interfering with your child’s progress and what additional strategies might help.
Remember to always stay calm when working with a child or student, even if you think they should be getting something that they are not getting. If you get frustrated with them, they may start to feel anxious, angry, inferior, stupid, etc. which will lead to a less productive learning session. Keep sessions short (5 to 10 minutes for younger children or children who get easily frustrated and 10 to 15 minutes for older children or children who can work for longer periods without frustration), unless the child is eager to keep going. I also recommend reading 3 Ways to Use Timers to Encourage Homework and Chore Completion and How to Use Schedules to Improve Children’s Behavior for suggestions on how to encourage homework completion, especially when homework is taking a long time and the child is giving up, frustrated, rushing through the work, distracted, or refusing to complete the work.
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Rachel Wise is a certified school psychologist and licensed behavior specialist with a Master’s Degree in Education. She is also the head author and CEO at educationandbehavior.com, a site for parents, educators, and counselors to find effective, research-based strategies that work for children. Rachel has been working with individuals with academic and behavioral needs for over 20 years and has a passion for making a positive difference in the lives of children and the adults who support them.