Y.5 Add ones to two-digit numbers using place value – without regrouping

Place value tells us what each digit in a number is worth. The place a digit holds decides its value. In a two-digit number, the digit on the left is in the tens place. The digit on the right is in the ones place.

Adding ones to two-digit numbers means we start with a number that has tens and ones. Then we add a small number that is 9 or less. We add only to the ones place. The tens place stays the same. This is called adding without regrouping because we do not make a new ten.

Place value helps us add because we can break the two-digit number into tens and ones. Then we add the ones together. Finally, we put the tens and the new ones back together. The tens stay the same. The ones become a new number.

When the ones add up to less than ten, we write the sum in the ones place. The tens place stays exactly the same. This is the easiest kind of addition because nothing carries over. The answer is just the same tens digit with a bigger ones digit.

We can add ones to two-digit numbers up to 120. That means we might start with a number like 115. 115 has 11 tens and 5 ones. When we add ones to 115, we add to the 5 ones. The 11 tens stay the same. The answer will be between 116 and 124, depending on how many we add.

Regrouping is when we have ten or more ones and we trade them for one ten. In this lesson, we do not regroup. That means the ones add up to 9 or less. The tens place never gets an extra ten. The number of tens stays the same from start to finish.

Checking your answer is an important math habit. You can check by looking at the tens place. Did it change? It should not change. You can also check by counting up from the two-digit number. If you start at 34 and add 5, you should say 35, 36, 37, 38, 39. Your answer should be 39.

When a two-digit number ends in 9, we can still add ones without regrouping if we add 0. If we add 1 or more, we will get 10 or more in the ones place. That is regrouping. So in this lesson, when we add to a number ending in 9, we can only add 0. That might seem small, but it is important to know!

Adding zero to any number does not change the number. Zero means nothing. When we add zero ones, the number stays exactly the same. This is called the identity property of addition. It works for any number, big or small.

Adding one to a two-digit number is like counting up to the next number. If the number does not end in 9, the tens digit stays the same and the ones digit goes up by one. If the number ends in 9, we regroup. So in this lesson, we practice adding one to numbers that do not end in 9.

We can add any number from 0 to 9 to a two-digit number, as long as the ones do not add up to 10 or more. That means if the ones digit is 5, we can add up to 4. If the ones digit is 7, we can add up to 2. If the ones digit is 0, we can add up to 9. We must look at the ones digit first.

We can add ones to numbers up to 120. That means we might add to 100, 101, 102, and so on. These numbers have a hundreds place, a tens place, and a ones place. When we add ones, we only change the ones place. The tens and hundreds stay the same if we do not regroup.

Adding without regrouping is the first step in understanding addition. It is simple and builds confidence. It helps you see that the tens place is strong and does not change when you add small numbers. Later, when you learn regrouping, you will see that sometimes the tens place does change. But for now, we practice keeping the tens the same.

Even careful students make mistakes. Here are some common errors when adding ones to two-digit numbers, and how to fix them.

Mental math means solving problems in your head without writing them down. You can add ones to two-digit numbers in your head by saying the bigger number and counting up. This is fast and useful in everyday life.

Word problems tell a story with numbers. You have to find the math in the story. When you see words like "add," "more," "plus," "in all," or "total," you are probably adding. Look for the two-digit number and the small number being added.

You can practice adding ones anywhere. Look at numbers around you. A house number, a page in a book, a score in a game. Add a small number to it. This makes math part of your world.

Here are the most important things to remember about adding ones to two-digit numbers without regrouping.

Ready for a challenge? Try these problems. They follow the same rule: add ones to the two-digit number. No regrouping allowed! The answers are at the end.