Educators have a variety of techniques and resources available to teach the properties of addition to first graders of all ability levels.

A child's knowledge of mathematics expands rapidly during first grade. After establishing a foundation for numeracy in preschool and kindergarten with activities like naming numbers and counting to 100, children are ready to start learning the principles of addition.

Understanding addition is essential to success in all future math activities, from subtraction to multiplication (or repeated addition) and beyond. In fact, by the end of first grade, most core competency standards require that students demonstrate a mastery of addition and subtraction with numbers up to 20, working with equations to come up with correct answers.

This is where learning the properties of addition come in. Learning the properties of addition enables a child to master the core concepts that can be applied to add any numbers whether they are big numbers, small numbers, two numbers, or even three or more numbers.

Children up until this stage often learn by rote and to ensure that they are able to shift to a more understanding-based functioning of addition in daily life, teaching them the core properties of addition is key.

The Three Properties of Addition

There are three properties of addition that kids at this stage are mentally well equipped to understand and apply: The additive identity, commutative and associative properties. Let's first understand what these properties are and then move on to how we may best go about teaching them.

The Additive Identity Property

This property simply means that if you add zero to any number or any number to zero the sum remains the original number. Even though it might seem trite to us adults, learning this property is essential as it will enable the child to work with the column method of addition for bigger numbers later. Also, it teaches the value of 0.

This one is pretty easy to teach and kids generally love it. It's a good idea to start with it before moving on to the slightly tougher ones to build the child's confidence and ease with equations. Sometimes an equation itself can look intimidating. After all, there are 2 numbers and 2 signs (+ and =), and one big blank spot waiting to be filled.

The Commutative and Associative Properties

The commutative property means that even if you change the order of two numbers that are being added the sum remains the same. Therefore, 2+3 is the same as 3+2. While the associative property tells us that when adding 3 sets of numbers the order is irrelevant. Meaning when adding 2,3 and 4 it does not matter if we do (2+3) + 4 or (3+4) + 2 or even (4+2) + 3, the sum will remain the same.

This property of changing the order of the numbers being added, or the addends, can also be referred to as 'turn around facts' and is the core of the commutative and associative properties. But before we go about teaching them it's important to understand the relevance of the turnaround facts in mathematics.

Turn Around Facts

The idea behind teaching the properties and turn around facts is to make numbers flexible values in the child's mind that can be manipulated for convenience and speed rather than fixed symbols on the page. The end goal after all is that the child is able to add in the head and use addition in day-to-day matters confidently without relying on digital assistance, most of the time.

To achieve this, it's important to teach that it's possible to change the order of addends. Once a child can do this, they will naturally use whatever order feels most workable for them. Most children find it easy to add to tens (10, 20, 30...) and factors of five (5,10, 15...). Further, adding smaller numbers to a larger number is generally found easier as well. This is because children can use 'counting on' and 'fast fingers' methods quite confidently by this stage.

Teaching Turn Around Facts

Since recognizing these turn-around facts doesn't always come naturally, fun math worksheets such as those available through the internet for free are especially helpful in providing practice.

These visuals help students see that reverse-order questions actually represent the same values. Realizing that 6+2 gives the same answer as 2+6 helps kids discover that they know the answers to twice as many math problems. This can be a great confidence booster.

Since concepts are integrated with practice over time. These worksheets are designed by experts to subtly introduce the turnaround facts to a child first visually and then bring in the equations.

For example, in the 'Boomerang Addition' practice sheet, notice how the boomerang is flipped to reveal the correct answer in each column. Children and even educators often don't notice this subtlety however, this can be a powerful memory aid once it sticks.

Similarly, in the 'Turn Around Dominos' sheet, finding the correct number of dots to find the answer can draw upon the already mastered concept of 'using manipulatives' where the child learns addition through counting physical objects and then adding more.

Once the child has grasped the basic concept and has been familiarised with the topic you may introduce worksheets with equations. Although these are designed to capture a child's interest and keep things visually stimulating, if you find the child nervous, just ask 'what's 100 + 0?' and watch them beam!

These types of digital resources are especially popular with first graders, who see math games and interactive electronic worksheets as a fun break or even reward when used during class time.

It helps to have auto-scored worksheets and games with immediate feedback as the child can correct any misunderstandings before deeper learning occurs. It also helps teachers offer different activities to students of different ability levels and interests.

Also, when kids have fun learning math, they often want to continue the activity at home. Thus, educational websites and apps give kids opportunities to continue reinforcing math skills outside the classroom, helping them gain a solid understanding of course material.

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