##
* *Reflection: Rigor
Problem Solving Division Day 2 - Section 3: Concept Development

As you can see in my reflection video, this lesson went well, although not all students got as much done as I had wanted. I had a few groups only get about halfway through the problem page and about half of the class complete through number 9. Knowing this helps me adjust my instruction for tomorrows lesson. Since most students did not complete the last two problems, those two problems will be the focus of tomorrows lesson when students complete a gallery walk activity.

I think most students are doing a great job at thinking about what the question is asking. Thinking about remainders and making sense of a division situation provided productive struggle for most of my students. A few students wanted to just "do" the division and write that quotient as their answer. As I circulated around the room and saw this happening occasionally, I was able to have great conversations with those groups and be able to guide their thinking about situations. One student did get upset when I pointed out that he had not answered the questions. He had done all the division for each problem, but reported his quotient with remainders as his answer to the problem. When I began questioning him about if his answers made sense, he knew they didn't. He was frustrated that he had to go back and "think" about what the problem was really asking. This student is really great with procedures and skills, but has trouble applying those skills. This is such valuable information for me and in my feedback to him and his parents.

*How did we get such different answers?*

*Rigor: How did we get such different answers?*

# Problem Solving Division Day 2

Lesson 14 of 16

## Objective: SWBAT solve word problems while practicing division skills.

## Big Idea: Students solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

*52 minutes*

#### Warm Up

*7 min*

Students will start today's lesson with a fluency assessment. This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results. It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions. (It also happens to be the quietest time in my math classroom all week!!)

This is what my classroom looks like as students work on this assessment.

This is sample of a student's graph. You can also click here to hear my thoughts about this graph below.

Click hereto see an example of a typical fourth grade fluency decrease since students are completing the fourth grade fluency set that incorporates division, multiplication, addition, subtraction, and adding and subtracting fractions with like denominators. (At this point, students have not had many fraction lessons, thus very very students are able to complete the fraction problems)

*I do not start my students with the fourth grade skills, but at this point in the year, all students are using the fourth grade set.. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards. By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics. I want to make clear that this assessment ONLY measures basic math computation. It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year. Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.*

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#### Concept Development

*45 min*

Students continue solving problems today just as in yesterdays lesson using the 3 ÷ 1 worksheet. This is day 2 of a three day problem solving activity. Students continue using the Think Aloud Partner Problem Solving approach and talk through problems with their partner in order to solve all the problems on the page.

A major focus of the Standards for Mathematical Practice is on using problem solving to reinforce important concepts and skills to demonstrate mathematical understanding. In *Improving Mathematical Problem Solving in Grades 4 Through 8*, published in May 2012 under the aegis of the What Works Clearinghouse (NCEE 2012-4055, U.S. Department of Education, available online from the Institute of Education Sciences) reported and made some recommendations about problem solving in mathematics. This report provides educators with specific recommendations that address improving mathematical problem solving. The first recommendation was to *Prepare problems and use them in whole-class instruction.*

Students utilize Math Practice Standard 1 and 3 in this lesson along with content standard 4.NBT.6. CCSS MP1 states mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. **Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different ****approaches.**

One of the strengths in this lesson is directly related to the above bold text. The *think aloud partner problem solving (TAPPS) *instructional strategy allows and encourages students to share their thinking with peers and allows peers to help or guide checking work and reasonableness of answers. Student partners can continually check each other's work and ask each other if their answer makes sense. Often times, one student's strategy or method differs from their partners which creates an opportunity to see and hear other approaches and build students' abilities to think flexibly.

The goal for today's lesson is for partners to work on the problems presented on the problem set worksheet. I know that students will not finish this worksheet in the time allotted, but I encourage them to work wisely and efficiently so they are able to finish in tomorrow's lesson. As students work, I am constantly moving around the classroom to observe students thinking. As much as I can, I resist the urge to re-direct students thinking until I am certain they have talked with their learning partner about the problem. By doing this, students partners often help correct misunderstandings and errors.

In this video you can hear two students talking and thinking through a problem utilizing the TAPPS strategy.

This pair of students are thinking about a problem and trying to figure out what they will do with a remainder. They have some incorrect calculations happening. Listen and watch my questioning process as I help guide their thinking.

This is a sample student work paper for a partnership that finished all problems. Many students are very close to finishing.

You can see that this student had quite a few comments and a few questions. This student also listed all of the problem answers on the left hand side of the comments.

Students worked right up to the end of the class period. I collected their work and problem so they may finish tomorrow.

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- UNIT 1: Getting to Know You- First Days of School
- UNIT 2: Multiplication with Whole Numbers
- UNIT 3: Place Value
- UNIT 4: Understanding Division and Remainders
- UNIT 5: Operations with Fractions
- UNIT 6: Fraction Equivalents and Ordering Fractions
- UNIT 7: Division with Whole Numbers
- UNIT 8: Place value
- UNIT 9: Geometry
- UNIT 10: Measurment
- UNIT 11: Fractions and Decimals

- LESSON 1: Place Value Chart and Division
- LESSON 2: Dividing with Place Value Chart - Decomposing Tens
- LESSON 3: Place Value Chart to Divide Hundreds and Thousands
- LESSON 4: Using an Area Model to Divide Tens and Hundreds
- LESSON 5: Using Area Model to Divide Thousands
- LESSON 6: Division Quiz and Snowflake Symmetry
- LESSON 7: Expanded Notation for Dividing Hundreds
- LESSON 8: Divide thousands using Expanded Notation and Pizza
- LESSON 9: Picasso Pizza Day 2
- LESSON 10: Holiday Stroll with Multiplication and Division
- LESSON 11: 12 Days of Christmas
- LESSON 12: Reviewing Division with Jeopardy
- LESSON 13: Problem Solving Division Day 1
- LESSON 14: Problem Solving Division Day 2
- LESSON 15: Gallery Walk Division
- LESSON 16: Division Unit Assessment