MATHS HIDDEN TRAP: THE DANGER OF IGNORING HALVING ODD NUMBERS

“What is half of 5?” Many kids in grade 5 would answer “There’s no such thing as half of five!” This is based on their misconception that only even numbers can be divided evenly by 2. And unfortunately they are not taught that half is two parts the same, and all numbers can be divided into two parts the same. In fact, if you divide a number into half, and half it again and again, there’s no ending to that.

At Mathnasium, we build children’s concrete understanding of division by teaching them half of odd numbers from 1 to 25 as soon as they are skilled in halving even numbers from 0 to 24, and we teach them starting as early as grade-1. Introducing basic fractions early gives a strong foundation for later mathematical concepts and number sense.

Mastering the art of halving odd numbers. With the Mathnasium magic behind her, this kindergartener has already mastered the skill of halving odd numbers - which puts her on the right track to zoom ahead and skyrocket her grades next year and beyond! Her parents can kick back & relax knowing that she is all set for an epic school year. 

Why students need to learn to halve odd numbers?

1. Strengthening Number Sense: enabling students to manipulate numbers and understand the relationship between numbers.
2. Building Arithmetic Skills: enabling them to do division and introducing them to the concept of fractions, which are the fundamental arithmetic operations. This would make them comfortable working with fractions and decimals.
3. Sharpening Problem-Solving Abilities: mastering this skill would make them easier to solve various context in real-life situations – such as dividing resources and sharing quantities. If one big loaf of bread requires 5 cups of flour, how many cups you need to make a loaf of bread half the size?
4. Higher Math Concepts Preparedness: when they know half of 7, then solving half of bigger odd numbers like half of 47, 97, 127 or 707 would be easy. Knowing halving odd numbers also serves as a stepping stone to understand concepts like ratios, proportions and algebraic expressions.
5. Logical Reasoning: the thinking process to determine the most efficient way to divide a number evenly will strengthen their logical thinking and fosters a mindset of approaching problems strategically. If a kilogram of meat costs $25 how much is a quarter kilo? Since a quarter is half of a half, a quarter is half of half of 25, that means it’s half of 12 ½, so the answer is 6 ¼ or $6.25. Quick & painless, while their classmates have no clue how to solve that without a calculator or paper & pen. Using Calculators – Yes or No?

How to teach them halving odd numbers?

“OK, I get it. Halving odd numbers is an important concept. But how to teach it to my kids?” you might wonder. The prerequisite skills before learning this concept are doubling and halving even numbers. Then explain that 7 is just one more than 6. Half of 6 is 3, half of 1 is ½. Please use ½ instead of 0.5 as decimal knowledge will come later, and 1 out of 2 as expressed in ½ would make more sense for beginners.

For young learners, using manipulatives is really helpful because they can touch the objects and the calculation becomes less abstract. As shown in the picture, we used dog biscuits - with the dog's approval 😊 -  to explain concretely why half of 1 is ½ or half of 5 is 2 ½ . 

After they master halving odd numbers from 1 to 25, we can go to the next level (as long as they're ready) and explain halving bigger odd numbers, by breaking them down into smaller components. What is half of 47? 47 is 40 + 7. Half of 40 is 20, and half of 7 is 3 ½ ; combined altogether you'll get 23 ½. Don't forget that the key to math success is practice and practice - using the right way of course. 

Let's prepare your child's math success!

Your child might be one of those students who can easily solve doubling but lack of awareness of the equally important concept of halving, especially when it comes to odd numbers. Failing to master this fundamental concept could impact their future math success. This summer, let’s ignite our children’s young minds by exploring the concept of halves across all types of numbers. As a start, we have provided you with practical guidance that you can apply when teaching your kids. You’d be surprised to see that it could unleash their math potential!