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* *Reflection: Student Self-Assessment
Division: Quiz 1: Assessing division of 2,3, &4 digit by one digit divisors - Section 2: The Quiz

I passed back ungraded quizzes because I wanted them to see their own progress and evaluate themselves. They used checking pens and graded their own papers as I solved each problem on the board. The discussion was lengthy and questions were rich. We discussed reasonableness of answers and checking using the inverse.

As quizzes were graded, I noted that a handful of my students had various issues going on. One student is not thinking through what it means to subtract. She is trying to subtract larger numbers from smaller ones and therefore missing the whole concept that division is repeated subtraction.

Other students were forgetting to regroup. Subtraction appears to still be very weak with my lower students. Knowing that, I need to spiral around and work on subtraction with them again using IXL.com or other apps on their iPads.

I was impressed with some of the conceptual writing, however. It was pleasing to see that some students wrote in depth about understanding how division and multiplication are related. They used words from the word bank correctly.

Prior to CCSS, I would not have bothered to assess their written responses. I would not have demanded an explanation of concepts. I used to teach them only "how" to solve. It's rigorous to have to write in depth about mathematical understanding.

This Educreations video shows some work of students who need help and intervention, and some whose writing is coming along nicely as well as their conceptual understanding.

*Goal Setting*

*Student Self-Assessment: Goal Setting*

# Division: Quiz 1: Assessing division of 2,3, &4 digit by one digit divisors

Lesson 12 of 21

## Objective: SWBAT show they can divide up to 4 digits by one digit and explain the relationship between division and multiplication.

## Big Idea: Students write solutions to 2, 3, & 4 digit by one digit equations using rectangular sections (box) method. They show and explain the relationship between division and multiplication.

*40 minutes*

Using a recipe is a great real world application to review multiplicative comparisons and help students see that 1/4 of something is the same thing as dividing by 4. I decided to warm up on this because this light and fun activity would relax them. I chose a recipe from The Math Chef by Joan D'Amico and Karen Drummond to get my kids thinking about heart healthy recipes as we celebrate Heart Health Month.

*We talked about how many students had eaten cooked carrots or baked apples before. Most had never had baked apples. I explained how you can easily bake a whole apple and what a delicious treat it is! One student asked me to share a written recipe; he wanted to try it out. We talked about the nutrients in carrots and apples and how they help our bodies grow and keep our teeth and organs healthy. A little chat like this sets the tone for being interested in the real world situation that would help master the standard regarding multiplicative comparisons.*

I wrote down the recipe on the SB. I had photographed it on my iPad and showed it up on the SB so that students could easily see the original recipe.

Their task was to figure out what 1/4 of this recipe would call for.

4 medium apples

12 carrots

4 TBS of firmly packed brown sugar

1/2 tsp nutmeg

8 TBS butter ( the recipe calls for margerine) crossed it off and wrote butter.

I quickly asked about what 1/4 OF something meant. I have posted their vocabulary around the room to remind them of which vocabulary meant **to divide **and which meant to multiply. *I wondered if they would be able to figure out 1/4 of 1/2. They hadn't been exposed to that concept yet, but I like to challenge their thinking with everything. Mastery of this wasn't important, just the immersion in critical thinking and problem solving. It was a risk...and I encourage risks!*

**Someone said " Multiplying by 1/4....of means multiply. That's the same as dividing something into 4 pieces."**

Their completed work was their ticket to getting their quiz. When they were done they had to show me their work. Some of my students drew out the 1/4 of 1/2 and I was thrilled to see the thinking. 1/4 of 1/2 Others could just explain that they multiplied the fractions because of the word "of".Apple Carrot Recipe

Students who could not draw or figure out what 1/4 of 1/2 was used the manipulatives on the board as I helped them achieve the concept. I leave these magnetic fractions up all year. They get used a lot! Magnetic Fractions.

*expand content*

#### The Quiz

*30 min*

I wrote this quiz to measure how well students can divide using the box method. It is a straightforward quiz for the first 4. Then, I thought it was important to measure what we had learned through the lessons "The Sieve of Eratosthenes" and "The Bubble Wrap" lesson.

Preparing them for Smarter Balance Test or PARC tests requires that they write, write, write! Every chance I get, students need to write and explain their thinking. The last problem makes them show equations and explain their understanding of the inverse.

I encourage and write in directions that I expect complete sentences. As teachers of mathematics, I believe that they need to be able to write clearly and exceptionally about math. That means that language skills need to be at their best. I included a word bank to help the light bulb go on in their heads to use math vocabulary in their explanation. On the test, I will expect that they remember the words without a word bank and just a prompt to be sure to use appropriate math terms.

#### Resources

*expand content*

##### Similar Lessons

Environment: Suburban

###### Shopping Comparison Problems

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*Resources(44)*

Environment: Urban

Environment: Urban

- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Divison Pretest
- LESSON 2: Ants, Ants, Ants! Using discovery to understand the meaning of division.
- LESSON 3: An Intro to the Box Method: A Conceptual Approach to 2 digit by 1 digit division
- LESSON 4: A Remainder of One: Practicing Box Method
- LESSON 5: Multiply or Divide? Exploring Word Problems that Compare.
- LESSON 6: Developing Our Division Skills
- LESSON 7: Two Games for Practicing Fluency & Dividing 3 -4 Digit Dividends Against 1 Digit Divisors
- LESSON 8: Oranges,Social Studies, Sister Anne and Studying the Whole: An integrated lesson
- LESSON 9: Talk the Talk of Division: Recognizing "Division" Words in One Step Word Problems
- LESSON 10: The Sieve of Eratosthenes: Prime Numbers, Multiples & Inverse
- LESSON 11: Understanding Division Through Bubble Wrap
- LESSON 12: Division: Quiz 1: Assessing division of 2,3, &4 digit by one digit divisors
- LESSON 13: Supporting Their Writing in Math: Class Collaboration and the Google Doc
- LESSON 14: In a Heartbeat! Connecting Informational Text to Multistep Word Problems
- LESSON 15: Assessing Understanding of Division Word Problems
- LESSON 16: Game Day! Review Day!
- LESSON 17: Bowling for fluency: A game for number sense, fluency and equation development.
- LESSON 18: Writing: Showing our Understanding of Entry Points & Place Value in Dividing
- LESSON 19: Division: Getting Ready to Test
- LESSON 20: Dear Mrs. Kanthack: A letter from students about mastering Division Standards
- LESSON 21: Assessing Division