As a prerequisite to the 10 more 10 less skill, your students should be very comfortable building two-digit numbers. Your students should also have a solid understanding of addition and subtraction. 

Making the leap of finding 10 more or 10 less mentally is just a matter of allowing your students to put together the information they already know! 

Start by asking your students to build a number with base ten blocks. Experiment with the blocks. What happens when we add a ten stick?

Record the starting number and the resulting sum when ten is added. 

Repeat this activity many, many times and ask your students what they notice is happening to the numbers. 

An easy way to prompt your students to make a rule about the patterns they are seeing is to ask them to predict the outcome after they add a ten and then to simply ask them why they made that prediction! 

Record your students’ rules about what happens when you add a ten to a number and test their rules out to see if they hold up! 

Using the same method, ask your students to build a two digit number and to take away a ten. What is the result? 

Ask your students to, again, generate a rule for subtracting 10. Test a number of examples to see if their rules continue to work.

In order to be sure your students are understanding the skill rather than learning a procedure for finding “10 more and 10 less with base ten blocks” introduce a new hands-on material! 

Linking cubes, $10 bills, place value disks or bundles of straws are all perfectly acceptable models. Your students are manipulting tens only so using a pre-grouped model is perfectly supportive. 

At this point it would be very easy for your students to think that adding and subtracting means simply changing the tens place- we don’t want our students to make this overgeneralization! 

Mixing in examples where your students are adding or subtracting a ten OR a one will help your students to attend to place value as they practice this skill. 

Consider introducing yet another hands-on material as well. When you use a variety of materials you are encouraging your students to make connections between materials used previously and their new manipulative. Their understanding will become more solid as they make these connections. 

Ultimately, you want your students to have the ability to find 10 more or 10 less mentally which means that hands-on supports need to be stripped away. 

One step away from math manipulatives is to move towards a representative model such as a place value drawing or place value chart. 

Allow your students to use their representative model directly alongside the hands-on tools they are comfortable using until they are successful using these representative models alone. 

As your students are working with representative models begin to ask for predictions before they draw or chart to model their thinking. They can then confirm their thinking using these representative models. Asking for predictions will help your students to take another step in the direction of mental math. 

If the ultimate goal is for your students to solve 10 more 10 less problems mentally you need to build in time for your students to practice this skill using mental math. 

That doesn’t mean any and all supports need to be taken away! 

Provide your students with an example either in the form of an equation or a story problem. First, ask your students to solve the problem mentally (here’s your practice!). Next, ask your students to use a representative model to confirm or change their thinking. Lastly, you can even ask your students to use a math manipulative to further confirm their thinking. 

As you see your students “predicting” the correct result consistently, you will know that they have mastered this skill at the abstract (mental) level.