When you add, you combine two or more numbers. There are many strategies to add bigger numbers!
It is smart to estimate before adding. Then you will know “about how much” your sum should be.
Our estimate for the sum of 295 + 112 is 410.
We know our sum should have 3 digits and be close to 410.
One strategy to add is to simply count objects to find how many there are all together.
There are 407 blocks all together.
407 is very close to our estimate of 410.
Counting is simple and reliable, making it a great way to avoid mistakes. However, it can be slow, and by 3rd grade, it’s important to develop faster addition strategies. Let’s focus on methods that are both quick and accurate!
Strategy 1: Make 10 or 100
When you add, you can move parts of the addends back and forth across the plus sign without changing the sum. You are decomposing one addend and composing part of it with the other one.
For example, you can move 4 from 224 to 356 to make
360 + 220 = 580.
Let’s look at another example of make 10 or 100.
How can you manipulate the numbers to make a 10 or 100 that is easier to add?
185 + 325 = ?
You can move 15 from 325 to 185 to make 200 + 310 = 510.
But that is not the only way to make 10 or 100!
The sum is 510 no matter how you choose to reorganize the numbers!
Strategy 2: Front-End Addition
Front-end addition is separating addends into expanded form and adding each place separately, then adding again.
445 + 297 = ?
To use front-end addition, combine the value of the digits in each place.
Strategy 3: Partial Sums
Partial sums is really the same strategy as front-end addition. Solving with partial sums usually means the equation is set up vertically, with each place lined up.
You can add in any order, but you will be more accurate if your strategy is consistent.
How can you use front-end addition or partial sums to solve the problem?
408 + 218 = ?
There are 2 ways to solve it!
Solve using front-end horizontally:
Solve using partial sums vertically:
The sums are the same!
Strategy 4: Counting on
Counting on or counting up is fun and good for mental computation. It can be done on a number line, number chart, or in your head.
Choose a place to start. You can count by ones first or hundreds first. You will be more accurate if your strategy is consistent.
Here is counting on a table or chart, starting with the hundreds again.
We counted up 2 hundreds, 8 tens, and 5 ones, or 285. This is the same strategy you can use mentally.
Practice Problems
Find the sum.
237 + 125 =
Find the sum.
354 + 265 =
Find the sum.
Choose the correct statement that describes the regrouping in the following problem.
