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Adding with 3 numbers up to 20

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Adding with 3 Numbers up to 20

This lesson teaches students how to add three numbers with a sum up to 20. It covers the associative property (adding in any order), the make-a-ten strategy for grouping addends efficiently, and step-by-step worked examples to build fluency and confidence with multi-addend addition problems.

What Does Adding Three Numbers Mean?

When you add three numbers, you are combining three separate amounts into one total, or sum. For example, \( 7 + 3 + 5 \) means you start with 7, then add 3 more, then add 5 more. In this lesson, every sum stays at or below 20, so it builds directly on skills from adding with digits up to 20 and from knowing your addition facts up to 20.

The key idea with three addends is that you do not have to add them in the order they are written. You can pick whichever two numbers are easiest to combine first, then add the third number to that result.

Strategy 1: Add in Any Order

Because addition is associative, you get the same answer no matter which two addends you add first. This means:

\( (7+3)+5 = 7+(3+5) \)

Both sides equal 15. This flexibility is powerful: instead of always adding left to right, look for two numbers that are simple to combine, such as two numbers that make a double or a ten.

7 3 + 10 5 + = 15
Grouping 7 and 3 first to make 10, then adding 5, gives a sum of 15.

Strategy 2: Make a Ten First

Ten is an easy number to add to, so a useful trick is to scan the three addends for two that combine to make exactly 10. Then add the third number to that 10.

Example: \( 8 + 6 + 2 \)

Notice that \( 8 + 2 = 10 \). So the problem becomes \( 10 + 6 = 16 \). This is much quicker than adding \( 8 + 6 \) first, which does not make a friendly number.

Ten frame for 8 + 2: + 6 = 16
Eight blue dots plus two orange dots fill the ten frame, and adding the leftover 6 makes 16.

Worked Examples

Example 1: \( 4 + 9 + 6 \)

Look for a friendly pair first. \( 4 + 6 = 10 \), so \( 10 + 9 = 19 \). The total is 19.

Example 2: \( 5 + 5 + 8 \)

Here \( 5 + 5 = 10 \) is a double, so \( 10 + 8 = 18 \). The total is 18.

Example 3: \( 2 + 7 + 3 \)

Grouping \( 7 + 3 = 10 \) first gives \( 10 + 2 = 12 \). The total is 12.

If grouping into a ten is not obvious, you can also add the numbers in the order given, using strategies like counting on or a number line, which are covered in more detail in using a number line to add up to 20.

Practice Problem

Try this one before checking the answer: \( 9 + 6 + 1 \)

Solution: \( 9 + 1 = 10 \), so \( 10 + 6 = 16 \). The sum is 16.

Quick Tips

  • Scan all three numbers before adding anything, looking for a pair that makes 10 or a matching double.
  • Adding three numbers in a different order never changes the total, so choose the easiest path.
  • Every sum in this topic stays at or below 20, so if your total is larger, check your addition again.

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