Hands down, this is one of my absolute favorite math skills to teach. You take something that seems like such an abstract mix between place value and operations and without fail teach 6 and 7 year old how to be successful in manipulating these numbers.

It's almost like magic.

As with most (all?) other math strategies, I find a CRA approach is the most effective way to support students towards proficiency.

Yes, ultimately this will be a mental math skill... but that doesn't mean that's where we need to start!

Concrete
I prefer to begin teaching this skill with a focus on adding ten with base ten blocks or linking cubes and then move to subtracting ten using money. I'm not as fussy about groupable models vs. pre-grouped models when teaching this skill because we aren't asking our students to compose or decompose a ten.

If your students struggle to subtract using money, you can always use base ten blocks or linking cubes for that skill as well, but be aware! You are looking to get all of the way to the abstract/mental math stage on this skill in first grade so using a non-proportional manipulative such as \$1 and \$10 bills.

The Ten Dollar Store
A really fun activity I like to do with my students is called the "Ten Dollar Store". I put out a number of items and everything in the store costs \$10. Students then get a "wallet" and have to represent that amount of money using \$10 and \$1 bills. They choose one of the items from the store and model what it looks like to subtract \$10 and then write a related equation. The students get very into it and have a lot of fun but they also practice building 2-digit numbers and subtracting ten over and over. It's a win-win!

Representational
Moving away from hands-on materials, using a place value drawing to show how to add or take away a ten is a step in the direction of less scaffolding to perform this skill. When you first introduce the place value drawing, do so directly alongside a tool like linking cubes or base ten blocks that visually looks a lot like a place value drawing.

At this point (if not sooner!) I also like to be sure to mix in adding and subtracting 1. It may seem like a skill that your students have already mastered but mixing in addition, subtraction, tens and ones will ensure that your students are attending to place value when they are this skill rather than just "changing the tens place".

Abstract
Alongside each of the concrete and representational activities above, asking your students to talk about what they are doing with place value language and asking your students to write related equations will ensure that they are ahead of the game when it comes to being ready to demonstrate this skill at the abstract level. With no hands-on math tools of drawings at all!

In fact, you can even take it a step further! When your student shows you their "wallet" with \$57 and tells you they are going to buy a microphone for \$10 ask them "How much money do you think you will have left if you take \$10 away?" Asking your students to make these predictions and then carry-out their work to confirm their thinking will allow them to get a head start on being able to demonstrate this skill at the abstract level!

The Guessing Game
Another fun game you can play to reinforce this skill is the guessing game. One partner is the "picker" and chooses a starting number, whether they want to add or subtract, and whether they are going to change by a 1 or a ten. Both players record the "picker's" choices on their recording form. Next, with a divider between the students, the picker builds the scenario using a math manipulative while the guessed writes a related equation and solves mentally. When both partners are ready, the divider is lifted and both players check their work. Students trade who is the "picker" and the "guesser" and play continues!

So, as with any other math skill:

• Think C-R-A. Know your end goal of abstract thinking but start in the concrete to build a strong foundation.
• Link Along the Way. When you are using hands-on materials, ask for related equations and predictions to activate abstract thinking! When you are drawing place value drawings, link back to the hands-on materials your students have already had success with!
Comment below if you use any or all of these strategies! If you are looking for a more comprehensive unit, the unit linked below is ideal for small group math and walks through a 5-lesson progression that will bring your students from concrete to abstract!

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