Adding and Subtracting Within 100: math lesson, Grade 1 – download the PDF

Every number up to 100 is built from tens and ones. In this chapter you will use that idea to add and subtract in smart, speedy ways. You will use drawings, number lines, and your own words to show how you think.

1. Tens and Ones

A two-digit number is made of tens and ones. The first digit tells how many tens. The second digit tells how many ones.

Look at the picture. Each long rod is one ten. Each dot is one one. You can see 3 rods and 6 dots, so the number is 36.

Moving 10 more or 10 less is easy. The tens digit changes by one, and the ones digit stays the same. For example, 10 more than 36 is 46, and 10 less than 36 is 26.

2. Adding a Two-Digit Number and a One-Digit Number

When you add a few ones to a number, you only need to add to the ones. The tens wait quietly.

3. Regrouping Ones into a Ten

Sometimes the ones add up to 10 or more. Then you can trade 10 ones for 1 new ten. We call this regrouping.

There is another way to regroup. You can make a ten first. To add 27 and 5, notice that 27 needs 3 more to reach 30. Split the 5 into 3 and 2. Add 3 to reach 30, then add the last 2.

4. Adding a Multiple of Ten

A multiple of ten is a number such as 10, 20, 30, up to 90. It has tens but no extra ones. When you add one, only the tens change.

5. Subtracting Multiples of Ten

Subtracting tens works just like adding tens, but you take tens away. Think about 80 as 8 tens. If you take away 3 tens, you have 5 tens left.

The crossed-out rods are the 3 tens we take away. Five rods are left, so \(80 - 30 = 50\). You can also check with an addition: \(50 + 30 = 80\).

6. Using a Number Line

A number line shows numbers in order. To add, hop forward to the right. To subtract, hop back to the left. Hops of ten are fast, so use them for multiples of ten.

Here we start at 80 and hop back three times by 10. We land on 50, so \(80 - 30 = 50\).

7. Explaining Your Strategy

Good mathematicians do more than find an answer. They tell how they found it. Use words such as tens, ones, regroup, hop, and make a ten.

Here is a sentence you can copy and change: “I added the ones first. \(8 + 5 = 13\), so I made a new ten. Then I had 4 tens and 3 ones, which is 43.”

You can also draw a quick picture with sticks for tens and dots for ones. A drawing is a clear way to show your thinking, and there is often more than one good strategy for the same problem.

Key takeaways

• A two-digit number is made of tens and ones: \(47 = 40 + 7\).
• To add ones, add the ones and keep the tens: \(52 + 4 = 56\).
• When ones make 10 or more, regroup 10 ones into 1 ten: \(38 + 5 = 43\).
• To add or subtract a multiple of ten, only the tens digit changes: \(34 + 20 = 54\) and \(80 - 30 = 50\).
• On a number line, hop forward to add and hop back to subtract.
• Explain your strategy with words, drawings, or hops.

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