Dump out a pile of base ten blocks onto your table. Write the number 234 on a teacher white board. Give each student their own white board with the number 234 at the top. Ask students to build this number from the base ten blocks.

Repeat the entire activity adding 100 to the start number rather than ten. What do your students notice? Can they generate a rule about adding 100 to a number? 

After each student has built this number, ask students “What would I need to do to my blocks if I wanted to add ten more?” As you ask this question, note “+10” after the 234 on your white board. Students might ask you to add ten ones but if they do, ask immediately if there is a more efficient way to add 10. After you have all arrived at the conclusion that students should add a ten stick to show ten more, have each student do just that; add 1 ten stick to their blocks and then note 234 + 10 = 244 on their whiteboard.

ASking your students to pair their place value models with an equation right from the start of your study of this concept will help your students move toward abstract thinking more quickly! 

Ask students to look at their white board and circle the number that shows how your blocks started and then what the blocks looked like after ten was added. Discuss if there is a rule or pattern they think might apply when they add ten to other numbers. Allow your students to test a variety of examples to see if their rule holds true! 

Repeat the same activity you completed with base ten blocks but this time in the context of subtraction! In this lesson you will take 10 away and form a rule and then take 100 away and form a rule. Again, your students will have the opportunity to test their rule through multiple examples. 

In your exploration of subtraction, consider moving to a new tool! Play money ($1, $10 and $100 bills) is a non-proportional model. Unlike base ten blocks where the 1s, 10s and 100s are each a different size, play money is all the same size regardless of what it is worth. Moving towards non-proportional models is a helpful step in moving from hands-on to abstract because it strips away a piece of the scaffolding that is in place. 

Your students have taken in a lot of information in the past two lessons creating and testing rules for adding and subtracting 10 and 100.

Next,  you will want to support your students in gaining flexibility in moving between these four scenarios by thinking about place value. Allow your students to use a new hands-on math tool to help ensure that they are able to generalize what they know to a new tool. 

Your new tool can be any place value tool! This might mean moving towards place value disks or a teacher created material! 

In the example below you can see teacher created spider cards that are engaging and allow students to generalize their place value understanding to a new tool. 

A strong concept development in math moves students from a concrete experience to a representative model through to abstract thinking. So far, your students have experienced a number of concrete models and have linked these models to the equation which is more abstract. The next goal is to transition students away from the need for concrete models in order to solve these problems.

In the first phase, you will link a student’s concrete understanding to a drawing representation. Ask students to build the number 231 using base ten blocks. After they have built the number, ask them to draw a picture of their base ten blocks on their white board to match the number they have drawn.

Next, ask students what they would need to do to the blocks to add one hundred more. Once they add a hundred flat, ask them to show one hundred more in their drawing the same way. Ask students to count their blocks and drawings to confirm that they got the same result. Ask students to write a number sentence that matches the action that just took place- 321 + 100 = 421.

You can repeat this exact activity with subtraction having the student cross off the hundred that is being taken away.

As students begin to demonstrate proficiency, flip the expectation for their base ten blocks. Give each student an equation and ask them to solve it first using a picture and then using blocks only to check their work. 

Begin by telling your students that there were 125 cars in the grocery store parking lot this weekend. Ask students “If I was going to build 125 cards using blocks, how many hundreds, tens and ones would I need?” Students should respond using place value language by saying 1 hundred, 2 tens and 5 ones. If students do not have this rote understanding at this point, go back and have them spend more days building numbers with blocks or drawing place value drawings.

Next, tell your students that 10 more cars entered the parking lot. I model the thinking aloud for my students “If I had 1 hundred, 2 tens and 5 ones add another hundred…. Now I have two hundreds, 2 tens and 5 ones.” You can even go as far as to mime as if you are looking at a pile of 1 hundred, 2 tens and 5 ones and adding another hundred.

Ask your students to use blocks or a place value drawing to check your work and tell you the total number of cars in the parking lot.

Repeat examples in this manner where your students are first working mentally to visualize and calculate but are then checking their work using a visual model or concrete manipulative.