Mental Math Strategies for Beginners
Mental math is a valuable skill that everyone should learn to perform calculations mentally, especially when paper and a calculator are not readily available. This article, Part 1, provides some introductory mental math strategies that parents can help their children learn at home.
Mental math should not be confused with the memorization of basic math facts, such as times tables. While memorizing these facts makes mental math easier, doing math mentally requires both memorized facts and the ability to manipulate numbers and operations to solve more complex problems.
The following mental math strategies are presented in a general order from the simplest to more advanced techniques that can challenge and strengthen mental math skills.
Strategies for Addition
Starting with addition problems is an excellent way to begin practicing mental math, even for young children aged 5, 6, and 7. The following strategies are suitable for beginners and can help build a foundation for mental math proficiency:
1. Adding One:
- Adding one means mentally hearing a number and then saying the number one higher or counting up by one.
- To introduce this concept, you can say a number out loud and have your child tell you the next higher number. Make it fun by taking turns.
- Start with low numbers and gradually increase the complexity as your child becomes more confident.
2. Adding Two:
- Adding two involves hearing a number and then saying the number that is two more.
- Children can either mentally add two or count by twos to arrive at the answer. For example, if they know the sequence 2, 4, 6, 8, 10, etc., they can add two mentally more easily.
- Encourage them to understand that adding two to any odd number will yield another odd number, and adding two to any even number will result in another even number.
3. Counting On:
- Counting on is a simple yet powerful mental math strategy. It involves mentally stating the larger number in an addition problem and then counting up the smaller number, one (or two) at a time.
- For example, when adding 5 + 3, start with the larger number (5) and count up: 6, 7, 8.
- Teach your children that with addition, the order of numbers does not affect the result (commutative property). So, they can start with the larger number and count up, which can be more efficient for mental calculations.
- Encourage your children to visualize and count in their heads, keeping both numbers in mind simultaneously.
These strategies provide a solid foundation for mental math development and are suitable for young learners. As they become proficient with these techniques, they can progress to more advanced mental math gymnastics.
Advanced Mental Math Strategies
In addition to the basic mental math strategies for beginners, there are several more advanced techniques that can help individuals perform complex calculations mentally. These strategies can be particularly beneficial for students who are looking to challenge themselves and enhance their mental math abilities further.
1. Making Tens:
- Understanding the combinations of numbers that add up to ten (e.g., 7 + 3, 8 + 2, 5 + 5) is crucial for mental math.
- Memorizing these combinations simplifies mental calculations.
- For example, knowing that 6 + 4 = 10 allows for easier mental manipulations in more complex problems, like 76 + 4, which can be simplified to 70 + 6 + 4 = 70 + 10 = 80.
2. Rearrange Numbers and Operations:
- Mental math allows individuals to rearrange numbers and operations for easier calculations.
- For instance, when calculating 6 – 3 + 2 + 4 + 8 mentally, rearranging it as (6 + 4) + (2 + 8) – 3 can make the process more manageable.
- However, this requires the ability to mentally remember and rearrange numbers effectively.
3. Visualizing a Mental Number Line:
- Encouraging students to visualize a mental number line can help them better understand number relationships.
- Physical number lines in classrooms can serve as references.
- Visualizing the number line can aid in more complex mental math problems by providing a logical arrangement of numbers.
4. Adding Ten:
- Adding ten is a simple and valuable mental math skill.
- When adding ten to any number, the ones digit remains the same, while the tens digit increases by one.
- For example, 5 + 10 = 15, 12 + 10 = 22, and 23 + 10 = 33.
5. Adding Nine:
- Adding nine involves adding ten first and then subtracting one.
- For example, 5 + 9 can be mentally calculated as 5 + 10 – 1 = 15 – 1.
- This strategy becomes almost as straightforward as adding ten once understood.
6. Using Doubles:
- Utilizing doubles (e.g., 5 + 5, 7 + 7) can be challenging but highly effective in mental math.
- Memorizing single-digit doubles helps students simplify calculations by combining known facts with other strategies.
- For example, in 76 + 6, students can think of it as 70 + 6 + 6, and if they know that 6 + 6 = 12, the problem becomes 70 + 12, which can be further simplified to 70 + 10 + 2 = 82.
7. Near-Doubles:
- After mastering doubles, near-doubles become accessible.
- For instance, in the expression 7 + 8, recognizing that 7 + 8 = 15, which is just one more than the double of 7 (14), simplifies mental calculations.
- Students do not need to memorize near-doubles separately if they know their doubles well.
8. Front-End Addition:
- Mental math often involves a different approach than written calculations.
- Front-end addition involves adding the tens and then the ones in a two-digit addition problem.
- For example, in 65 + 26, mentally adding 60 + 20 first (80) before adding the ones (5 + 6 = 11) results in 80 + 11 = 91.
9. “Friendly Numbers” Strategy:
- Certain pairs of numbers, known as friendly numbers, work well together in mental math.
- For instance, 75 + 25 equals 100, a commonly recognized relationship, making calculations more manageable.
- Combining friendly numbers with other mental math strategies can simplify complex problems.
10. Balancing Strategy:
– The balancing strategy involves redistributing numbers between two terms to make calculations easier.
– This approach entails “borrowing” from one number and “trading” to the other.
– For example, when adding 68 + 57, mentally borrowing 2 from 57 and adding it to 68 transforms the problem into 70 + 55, which is simpler to calculate mentally.
Remember that mental math should be an enjoyable and engaging activity. Some students may find these strategies fascinating and empowering, while others may prefer different areas of mathematics. The key is to go at your own pace and make mental math an enjoyable learning experience. A few minutes of mental math practice can be sufficient, so avoid making it tedious for your children. If mental math doesn’t appeal to them, consider exploring other mathematical concepts or activities that capture their interest.
