I explain to students that they get to choose what they work on today and that their choices are to either practice some more with the cubes and two-digit addition with regrouping or, if they are successful with that, they can come to the carpet and I'll teach them a new, (I think fun) algorithm called equal and opposite change.
I remind students that learning is not a race, and that intelligent people know what they don't know and recognize that practice and productive struggle are integral parts of learning. Throughout the year I stop and share examples of times I have had to practice to master something. I also try to provide constant examples of how people make mistakes and learn and grow from them. I want students to know that it's one's persistence and intellectual curiosity that are the drivers of how successful they are in school.
I give students a little bit of think time and then have them choose their groups. On occasion I may override a student choice, but that's rare. Sometimes students don't yet understand their own thinking well enough to know what they don't know, but in my class of gifted students this is something that they can usually do.
There are two paths for independent work.
Extra Support and On Level:
Some students continue to work on using place value cubes (or other similar manipulatives - toy money works) to solve 2-digit addition problems. I let them know that my expectation is that they will be able to verbalize the steps using specific language as well as solve the equations.
Possible vocabulary terms to review: digit, place value, one's place, ten's place, hundred's place, trade, exchange, regroup, equal, equivalent, sum
I count out bags of 30 tens and 30 ones for each student prior to the lesson. Also, I give students the choice of working with a partner today. Partnerships should complete as much or more than individuals, not less. If working with a peer is too distracting, I state that fact and ask them to work by themselves. It is not intended as a punishment, but an acknowledgement that when working with a peer/friend it sometimes requires some extra self-monitoring to stay on task!
Students use the Take Time Tens Two Independent Practice to record their work.
On Level and Enrich:
I teach this group the equal and opposite change algorithm. I model it first with 2 digit addition and then have the students try a few. Then we move to 3 (or more) digit examples, as suits the need of the group.
I prompt students to think about something they learned today either about the math process (specific to the group they were in) or about their own thinking about math/this particular area of study. Time permitting, I randomly call on two students from each of the groups to share with the whole class.
I walk around the room and monitor students to insure that their conversations are on-topic and rigorous. For students who need extra support, either because they are still processing the math concept or because they are developing English vocabulary, I provide meaningful sentence stems and phrases to enhance the precision of mathematical and other language.
For on and above level students I provide supportive questions and, if needed, vocabulary to help them explain their extended thinking to others.
Student: “I learned that when I do equal and opposite change I do the same thing but opposite to the other side.”
Teacher: “What is it that you do to each number in the addition equation?”
Student: “If I add to one number, then I subtract from the other number… the same, the amount.”
Teacher: “So if you add an amount to one number in the addition equation, you subtract an equal amount from the other number in the equation.”
Teacher: “How do you decide upon the amount that you will subtract or add to the numbers in the equation?”
Student: “Well, I’m trying to get to an even one, you see…”
Student: “I mean, a ten, you know, that ends in zero.”
Teacher: “Why would you do that?”
Students: “So that one of the sides, the side of the equation, it can be either side, will be ending in zeros, like 90, or 900.”
and so on…