Wednesday, May 19, 2010

Differentiation in First Grade Math

Sometimes it is hard for teachers to know exactly how to differentiate in a classroom. This post explains what a series of differentiated lessons in math looked like in a first grade classroom.

I have been working with a group of gifted first graders for a few months now. From some early assessments, their teacher and I knew that they were working at a higher level than their classmates. We decided to put seven students in my group. The teacher took the rest of the students. The teacher’s group has been walking through the textbook. In this particular unit on addition, they are solving problems with regrouping such as 14 + 7= __________.

My group of students needed more challenge but I didn’t want them to stray too far from what the topic their classmates were studying so we started by solving regrouping problems with larger numbers such as 48+37= __________. We used place value mats and base ten blocks to model each problem. We have been doing lots of trading this year (trading pennies for dimes, dimes for dollars, etc.) so once I reminded them that they would need to trade, it was easy for them to solve these problems which all involved trading units for longs (ones for tens).

The next day the teacher’s group practiced different strategies for solving their two digit plus single digit problems (counting on and building with blocks).

My group was already proficient at counting on and building the easier problems with blocks. The next challenge for them was to solve problems that involved two trades – units for longs and longs for flats. These would be problems such as 129 + 83= ______________.

Before we started, however, I wanted to check that the students knew how to build the larger numbers. The students were confident using the base ten blocks to build numbers up to 100. With larger numbers, their understanding was not as solid. We practiced building and writing numbers such as 110. Many students built it correctly but then wrote it as 10010. Once they saw that their model only used three columns, they realized that the numbers they wrote down needed to correlate to their place value mat. They had one flat in the hundreds column, one long in the tens column and zero units in the ones column. They could then record this as 110. Next they were challenged to build 203. Some built 230 and some built 203. We continued to practice until they could build numbers up to 999 with accuracy. They were then able to solve the more complex addition problems confidently.

Throughout this process, one student correctly built and recorded each number without fail. I made a note of this student’s solid understanding of place value. This would help me plan next steps for him in math.

The next day the teacher’s group continued to need more practice with regrouping. It was clear, however, that my group did not need this practice. What they did need was to solidify their understanding of the place value of larger numbers that they had been building over the past few days.

I decided to have them work on counting strips. If it had been the beginning of first grade, I would have had them start their counting strips at number 1. Since we had been working on numbers over 100, I had them start with 100. They placed one flat on their place value mats. Then they added a unit and recorded 101. They then added another unit and recorded 102, etc. Soon the students were able to work abstractly and did not need the blocks to represent every number but used them at tricky times such as going from 149 to 150.

For the past few days, the class had been benefitting from the two math groups. At this point, it became clear that we needed to split yet a little bit more to meet everyone’s needs. The one child who had a solid understanding of place value from the start did not need to do a counting strip in base ten. I did, however, want to keep him on the same topic so I started him on a counting strip in base five. This would test his understanding of place value and strengthen it. He was thrilled to be working on something at his level and actually went home and asked him mom if he could do counting strips in bases two and three as well!

The day we started working on counting strips, the students in my group were beaming. They were so happy to be working on work that was just at the right level for them. They asked me why the one child was working in base five and the others were working in base ten. I told them that everyone’s brain was getting what it needed. They accepted this idea and continued to work quietly and happily for the rest of the period.

While this level of differentiation was achieved by having two teachers in the classroom, it could have easily been done by one teacher. One group could have worked with the teacher while the other group did some independent work (Marcy Cook math tiles, playing math games, reading, etc.). The teacher could then switch groups.

The biggest hurdle to differentiation is realizing that different students have different needs. Once a teacher acknowledges this, meeting those needs does not mean creating twenty different lessons. It does mean having two or three different levels of a topic available to meet the range of needs in the class.

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