11.28.2012

Differentiate in the Math Classroom & Have Students Think Deeply

Welcome Chicago! Here is the PowerPoint for this morning's session. Hope you find an idea that you can take back to your classroom and use with your students.

Exploring Subtraction of Fractions

With CCSS students will need to explore mathematical principles, look for patterns and routines, and demonstrate conceptual understandings. In a fifth grade classroom, our students were subtracting fractions and mixed numbers. I wanted our students to grapple with the process and not just be given the steps. Students were given the following task.


In groups, students were asked to look at the subtraction problems and identify rules and patterns that they noticed. Engagement and critical thinking were clearly evident during the small group discussions. The subtraction problems were purposefully arranged to build on each other. After verifying the rules and patterns, students completed the Try It Out! problems to demonstrate understanding. Then came the big challenge. How could our students then apply these learnings to the ultimate subtraction problem...a problem with uncommon denominators and renaming? Click on the image for your copy if you would like to try this with your students.

11.27.2012

Number Talks to Get Students Thinking Number Sense

I recently read Number Talks by Sherry Parrish. I thought I would give Number Talks a try to ramp up my fourth graders thinking with multiplication. Like many students, once they learn the algorithm, boom, it becomes a rote, automatic process. But my question is...do my students really understand the conceptual meaning of what it means to multiply and what the process really represents?

A Number Talk should take no more than 15 minutes. The ultimate goal is not the answer, it is the processes used. Yes, I said processes, multiple representations. Students are asked to solve the problem using mental math...no paper pencil. Put those pencils down and get those thinking caps on! Once students are able to determine the answer, they give a silent "thumbs up." It does not stop there. Students are encouraged to come up with other ways to solve the problem. When they determine another process, they put up another finger. Are you beginning to see how process is the focus. The silent "thumbs up" gives all students a fair chance to solve the problem while challenging those fast finishers to keep thinking.

The first problem we worked on was 25 x 7. I showed students the problem written horizontally. Remember no paper pencil is allowed. It was silent in the room, and then thumbs started to pop up. After a few minutes, everyone at least had their thumbs up. I asked students to share their answers. At this point, all answers are recorded and respected. Through discussion answers are confirmed, defended, or rejected. Students then went on to share the processes they used to solve the problem. One student explained that  20 x 7 = 140 and 5 x 7 = 35. Then the student went on to add 140 and 35 to get the answer of 175. Another process showed that 4 x 25 = 100. When doubled, it would be 200, but then 25 had to be subtracted because there were only 7 25s and not 8.

We then went on to 12 x 15 written horizontally. Now remember students are encouraged to think and solve using mental math. I will keep the examples short here. One student said he took (12 x 5) + (12 x 5) + (12 x 5) = 180. WOW! When I asked the other students why he did this, they chimed in, "Well, he broke down 15 into three 5s." Why 5s? "It is easier to multiply by. It is like a benchmark," they added. This was the first time my students engaged in a Number Talk. Conceptual understanding of number sense was definitely shown here. Give a Number Talk a try and see the different strategies students can use to a solve problem. Model and guide students to new ways of approaching problems to build their understanding of number sense and various processes. Manipulate and play with numbers to solidify understanding.

11.25.2012

Using a Word Bank to Foster Vocab Usage

The language of mathematics is important. With CCSS students are going to be expected to communicate precisely and accurately (Mathematical Practice 6: Attend to Precision). In addition, students are going to be expected to explore math concepts and use math vocabulary to explain  math processes (Mathematical Practice 3: Construct Viable Arguments and Critique the Reasoning of Others). Try adding a word bank to mathematical tasks to encourage the usage of specific math vocabulary. It is important that students have been explicitly taught the meanings and conceptual understandings behind the words before they are asked to use them. Repeated exposure and authentic usage can help math vocabulary to be meaningful, specific, and precise. See how the following activity was adapted using a word bank. Students are asked to use specific math vocabulary to defend their thinking. Click on the image to grab your copy.