As teachers, we know that strong mental math skills are foundational for developing number sense and math confidence. One strategy that can make a big difference for students is making a friendly number. This simple yet powerful strategy helps students approach calculations with flexibility by adjusting numbers to ones that are easier to work with. The best part is that this strategy can be used from very early years to middle years and beyond. In this post we will look at how this strategy might progress througout grade levels.
First things first, there is an important understanding that students must develop – when we add two (or more) parts, we can move objects from one part to the other without affecting the sum. In young students, this understanding is best developed with manipulatives that that they can physically touch and move around.
Now let’s take a look at this strategy in action, beginning in early elementary and progressing through to middle years math.
Using the Friendly Number Strategy With Ten Frames and Base Ten Blocks
When students are first introduced to this strategy, it’s best to use concrete manipulatives that they can physically move from one part to the other. Even though it may be easy for us to understand moving from one part to another, it can still be too abstract for kids. When we use manipulatives and students can move the actual pieces, it promotes a deeper understanding.
The ten frames below show 7+5. In the next picture, we move 3 from the 5 over to the 7 to make a friendly number – 10. Now we have 10+2.
We can also represent this pictorially on a part-part-whole model or a number line, or in an abstract form with digits and symbols.
We can also use base ten blocks to make this thinking visual. In the example below, we are using this same strategy to solve 14+38. We can physically take 2 ones from the 14 and give them to the 38. Now we have 12+40. Is this easier to compute mentally?
Friendly Number Strategy with Multi-Digit Addition
Let’s take a look at how this might look with a 3-digit plus 3-digit addition problem. Here we have 127+285. There are several different ways that we could approach this:
- Take 3 from the 285 and give it to the 127 to make 130+282.
- Take 5 from the 127 and give it to the 285 to make 122+290.
- Take 15 from the 127 and give it to the 285 to make 112+300
and of course there are many more than this.
Which feels easiest to you? For me, the third option feels the best. Having conversations like this with your class about different ways to use the same strategy is a key to adding flexibility to your number sense routine. Notice that when we are working with numbers in this way, we have a real sense of the magnitude of the numbers – we are not simply working with single digits as we do when working with the traditional algorithm. This understanding is what will lead to stronger number sense.
Friendly Number Strategy with Fractions and Decimals
The part I love most about math strategies is that they are easily transferrable to other areas. This exact same understanding that first graders might use when adding 7+5, can be used by 7th graders when adding 3.2+4.95. How would you approach this problem? Personally, I would take eight tenths from the 4.95 and bring it over to the 3.2 to make a nice friendly number, 4. Then my expression becomes 4+4.15, which is simple to do mentally.
We can use the same approach with fractions with the same denominator.
