Estimating Addition and Subtraction of Mixed Numbers

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SWBAT estimate the sums and differences of fractions and mixed numbers using numbers sense and benchmark fractions.

Big Idea

Students become "test makers" today as they write multiple choice questions and possible choices for finding the BEST estimate.


5 minutes

To warm up student's thinking for this lesson, I spend time discussing the homework assignment due today.  This assignment, from the text book, provides students with a mixed review of skills and concepts.  This review worksheet includes multiple choice and short answer questions.  I spend time reviewing multiple choice questions to help students get into the frame of mind of a "test maker".  

As we review the assignment, I focus on the content, ask students to share strategies for approaching various problems, and ask questions to help students consider the reasons behind the choices that are given.

Guided Practice

15 minutes

I present students with a question, "Which of these is the BEST estimate".

We just talked about the fact that no answer is the right answer when it comes to estimation, how can there be a best estimation? 

It should be that the best estimation is reasonable and it is the best fit for you.  A Multiple Choice question don't always consider what is the best choice for you, neither do your partners when you are working in groups and explaining your thinking.  

Next, I ask students to consider:  If estimates do not have to be the same for every person, then why do some test questions ask, "What is the best estimate?" and allow you to choose A, B, C or D.? If there are many ways to find a reasonable estimate, how can we all be expected to make the same choice?

This question is used to set the purpose of the lesson.  I don't hear answers from students at this point, instead, I ask if anyone has ever encountered one of these questions.  Then ask if they have ever wondered the same thing.  

Today, we will work on uncovering the thoughts of test makers when they write questions like that. Then, next time any of us encounter one of these challenges, we will attack it with confidence, rather than confusion.

When faced with questions like this, I know you can attack them with confidence, because you can consider each of the choices provided and consider what the "test maker" was thinking about when he put each of those choices there.  

For these purposes, it is important to think about the various methods that are used for estimating addition and subtraction of mixed numbers.

Use probing questions and interactive modeling to generate a list of estimation strategies:

1. Round to the nearest whole

2. Round to a benchmark fraction (one number of both)

3. Think of compatible numbers

(Provide an example of a problem for students to refer to when they are listing these strategies).  I used 1 and 3/7 + 1 and 2/6.

Independent Practice

20 minutes

Students are provided with an open ended task:

What is the best estimate?

1. Write a problem (that involves adding and subtracting mixed numbers).

2. Use the estimation strategies that we have discussed and your expert knowledge of multiple choice questions :) to create the 4 possible choices of a multiple choice question.

3. Circle the best answer.

4. Write about why this is the best answer.  Use appropriate persuasion strategies to justify for reasoning.

I leave the content instructions open ended intentionally because I want to see what the students generate with these parameters. 

While students are working in pairs, I move from group to group and stop to ask questions about their approach.  I am not asking questions to check for understanding as much as I am to understand their thinking.  

Group Share

5 minutes

Students are prompted to  share something about their question that makes it challenging. The strategies they use to reason through their problems offer insight into the powerful thinking and reasoning of the students. 

We made our question challenging because:

• We only showed the estimation answers as part of the choices.  Even though when we were making the choices, we used different estimation equations.  But, we only wrote down the choices because that it was it is like when we have to take a test.

• We used larger numbers as our whole numbers to make to more challenging for students.

• We made sure that the fractions in our problem had different denominators

• We made we tricky choices that were really similar, and then we added one that could be ruled out, because that is usually the case on a multiple choice test.

• We included the answer that someone would get if they estimated using the wrong operation my mistake.

• We put down the actual answer as one of the choices, because someone might not read the question carefully and they might not estimate.