Open Response Practice

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SWBAT explain their thinking and reasoning in writing about how to solve problems related to addition and subtraction of mixed numbers.

Big Idea

Writing about math provides students with an opportunity to communicate everything they know about solving problems.


5 minutes

Today, students will work on completing an open response question.  As a warm up for this lesson, students use the table of contents from the text book as a reminder of the many problem solving strategies we have practiced this year. 

Students discuss these strategies in a small group using the prompt:

• This problem solving  strategy is helpful because ________

• I use this problem solving strategy when __________

The strategies that we revisit through the year are:

• Look for a pattern.

• Draw a picture and write an equation.

• Break down multiple-step problems.

• Judge reasonableness of your answers.

• Missing information? Extra information?

• Is there a hidden question that needs to be solved first?

• Act it out with manipulatives.

Reviewing the strategies helps bring these to the front of their minds before the lesson begins. The objective isn't to make it "easier", it is to make sure students are applying mathematical reasoning by selecting and using appropriate strategies.


5 minutes

Before presenting the open response question to students, I bring their attention to the open response data wall hanging in the classroom to remind students of the collective class goal: Improving the average scores of our class on open response questions.  

Four tips for scoring a 4: 

1. Get the correct answer

2. Write about math the way you talk about math

3. Actually answer the question that was asked

4. Use the problem solving strategies you know

These focus questions are hanging in the classroom near the data wall.  They are posted in the kid friendly language that the students used when they generated these tips. 

Independent Practice

10 minutes

Today, students will be given time to collaborate with a peer as they answer the MCAS Open Response Question. Through the collaborative process, students are able to share with one another about their thinking as they approach a problem.  Students learn how their classmates approach a problem and can adopt these strategies on their own. 

For this lesson, I will choose the partnerships based on data collected student work on other open response questions.  I will place students who have a challenge with interpreting the question with a partner who can explain how they make the problem more accessible.

Before students get together, I set aside ten minutes of independent work time.  This way, when students meet in pairs, they can start by sharing their thinking.  This increases student ownership and accountability rather than having students work together from the start.

Guided Practice

25 minutes

Today, the guided practice is student centered.  They guide each other through the process of completing an open response.  

Before students begin working, I present them with a scenario in which I disagree with my partner about a possible solution.  I want to help the students understand that the focus of today isn't on getting the same answer, its about SHARING AND LISTENING to possible strategies.  If two partners have a difference of opinion, they should definitely have a mathematical argument.  In the end, if they can't come to an agreement, agree to disagree. 

I provide a few prompts for discussion to help keep conversations focused:

• What is this question asking us to find out?

• What problem solving strategy did you use to start solving this problem?  Why?

Aside from this facilitation, I remain in the background for the majority of the time.  I want students to work together on this problem without support from me.  


10 minutes

I project the sample student work that goes with this open response question on the board. Starting with the work scored 4, and then working down, we examine these as a group and discuss how and why the work earned the scores given.

Students take a minute to score themselves, based on what they have learned from the exemplars.