Since this post is part of a series, it may be helpful to read over and Beginning a Lesson Using Guided Discovery to put it in context. You may also want to look over the podcast posted earlier on the Partner or Folding Pages to see a model of the content of this post.

Earlier this month, we posted an outline approach to integrating assessment into a math lesson. Teacher and student ongoing assessment run throughout that initial step. Equally important, doing something about what is observed, with every student, is also integrated into that step.

This post takes up the second step in the guided approach – working with a folding or partner page of problems. This engages students in quickly reconstructing and re-experiencing the work they did on the graphic manipulative. Both the graphic and partner pages are deceptively simple looking, while being highly flexible and engaging tools for building understanding and fluency together – in a way that can be directly observed.

On the left is an image of a negative number partner page with the problems at one end and the answer key facing the opposite direction at the other end. (Our March 2 post has an image of a Soccer Teams partner page.) The same teaching approach laid out in the post on Guided Discovery should be used here – 1. use short phrases, 2. begin with an action verb, 3. model your directions as needed, and 4. look around to make sure everyone is on track. There is no point in having students construct and build visual memories of a wrong procedure or amount!

These steps for delivering a lesson with the partner pages follow on the approach with the graphic pages. While not prescriptive, they do help keep students actively engaged in the work.

Start by saying:
1a. “Fold the partner page in half and set it down on top of the graphic page.” The partner page takes the place of the blank paper described in the earlier post.

1b. “Read the first problem on the partner page and move it to show that many…” teams, weeks, squares or roots, dollar bills, tickets, shirts, gallons, fractions of a cake, cheese slices, negative temperatures, “quadratic hearts”, or whatever graphic starts the lesson.

Then
2. Ask “How many players (teams, fractions, weeks…) do you see?”

3. Respond to correct answers with a simple “good” or “correct.” Respond to every correct as well as incorrect answer. By doing this, there is no question as to whether the answer is correct or not. For an incorrect action or response, never give the answer. Instead, guide students to correct themselves with: “Try again” or  “Show me on the chart how you got that answer.” As they reconstruct and rethink their solution, many will see for themselves what they did wrong and how to do it right. A few may require further guiding questions.

Do the next problem or two as a class as needed. Then ask the class to work the rest of the problems like that individually. Ask them to read the problem; move their paper; and say the answer in a quiet voice. So that students won’t copy each other, have some work the problems going across the page; some going down (from top to bottom); and so on. Circulate around the room checking on their work responding to correct and incorrect answers.

4. Ask for a volunteer to do the first row of problems for the class. Remind them that it is not cheating to use the graphic page. Ask for others to do the next rows. Have the rest of the class follow along with the answer key to make sure these students are answering each problem correctly.

5. Ask for two volunteers to model working in partners, one doing the problems, the other checking the accuracy with the answer key. The partner checking the answers follows the model in step #3, never giving answers and saying “good” for every correct answer. And the partner simply says “try again” if the answer is incorrect. They have the graphic page to refresh their understanding of the procedure and the basic facts. The rest of the class follows to make sure these two are doing it correctly.

6. Now have everyone work in partners following the model in step #5.

Summary: The partner pages build understanding and fluency together – in a way that can be directly observed. They involve cooperative learning with individual accountability, students receive immediate and ongoing feedback (but no answers), so they engage teacher, peer, and student in student self-correction. Going in different directions on the partner pages enables non-rote repetition. Like music students, math students benefit from going over a familiar exercise more than once. Getting better at what they are starting to get good at builds confidence along with competence.

At this point, students have achieved the first two levels of success: 1. they understand what they are doing, and can accurately solve problems slowly, with the aid of the graphic page; 2. using a partner page, they connect manipulation with computation and gradually wean themselves from the graphic page, accurately solving problems with greater fluency. The next level, developing independent speed, accuracy, and understanding, using the progress chart, will be addressed in an upcoming post.