## Friday, May 17, 2013

### Combinations of 100 and the Common Core

We have been hard at work in second grade this year on combinations of numbers that make 100.  Having students who understand how to combine numbers to reach 100 expands their repertoire of strategies for solving addition and subtraction problems.  It makes them much more fluid in their reasoning around operations and place value.  Having this concepts supports a huge chunk of the common core standards for grade 2.  Here are the main standards this supports

## Use place value understanding and properties of operations to add and subtract.

• CCSS.Math.Content.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• CCSS.Math.Content.2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
• CCSS.Math.Content.2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
• CCSS.Math.Content.2.NBT.B.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
• CCSS.Math.Content.2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.1

Here is a peek at some of the activities, routines and manipulatives we use to support this important idea.

#### Base 10 Pieces

We use our base 10 pieces and a deck of cards from 1-100 to make a simple practice game for students who are learning about combinations of 100.

Kids flip over a card and find what goes with that number to make 100.  Once they place the number of pieces they flipped over the 100 mat, what is left is what they need to get to 100.  Kids start noticing patterns right away and some move quickly away from needing to use the manipulative while others spend a lot of time at the concrete stage with the manipulatives.

I will sometimes do this as a warm-up, a math center or even as a whole class activity.  Sometimes we use record sheets and other times we just share our answers orally.

Another manipulative to work on combinations of 100 that we use often is our 100 bead strings.  We purchased some plastic lanyard material and beads from the craft store and made a set of bead strings.  We alternated colors every 10 beads so that the groups of 10 would be highly visible.   We use some of the same routines/games with the 100 bead string that we do with the base 10 pieces

 This student has pushed 41 beads to the left and uses the beads on the right to figure out what goes with 41 to make 100

Sometimes we use record sheets.  My students like to make their own on an individual white board.

 A simple game where students flip a card and find out using the bead string or base 10 pieces or mental math what goes with that number to make 100.
And we extend it to subtracting from 100
 Almost the same game as above but instead of thinking about the missing addend, the students are thinking of subtraction.

Are your students fluent with combinations of 100?  What experiences do you provide for kids to practice this important skill?

Check out this lesson on how my students apply this skill to three digit subtraction.
Here is a fun, free app to work on combinations of 100!
Need a computer activity to work on combinations of 100?  My students love this one!