##
* *Reflection: Developing a Conceptual Understanding
Powers of Ten: Review and Practice and Writing Clear Explanations - Section 4: Practice Work and Assignment

As thorough as I was in my teaching, almost all of my students could not explain what was done incorrectly, accurately. Even though my example was clear and well written with a good hook, students didn't bother with good openings.

See the Educreations clip explaining a few samples. I think this is the most difficult transitions about Common Core. It's going to take time!

*Samples of Work*

*Developing a Conceptual Understanding: Samples of Work*

# Powers of Ten: Review and Practice and Writing Clear Explanations

Lesson 12 of 19

## Objective: SWBAT write a clear explanation of the process of accurately finding powers of ten in a standard algorithm while demonstrating their knowledge of place value.

## Big Idea: Students will review powers of ten and learn to write clearly about the process after they identify the wrong answers from three given algorithms.

*45 minutes*

**Warming Up and Back in the Swing of Things:**

*It is the first day back from Winter Break...and we need to get back to thinking about powers of tens!*

To get my below grade level achieving students warmed up and reviewed, and to get the mindset focused for my other students, I assigned them this Khan Academy lesson. A few of my students tend to go back to repeated addition because their math facts are weak. This explanation is another way for them to see the importance of knowing those facts because he stresses that "it is easier to multiply." When they were done, I gathered them together and reviewed what was said using a small white board to be sure they understood the review lesson. Talking about Multiplying by 10 and what happens to the place value. This clip is just a little sample of reinforcing CCSS 4.NBT.A.1 (Recognizing that the next place value represents 10 times). I asked them if they thought they were ready to practice using larger values and learning about the powers of 10?

I wrote on the board: 10 x 10 = n. I asked them to tell me the answer. All shouted 100! I told them that I wanted them to think about how many times 10 was multiplied together. I asked them to think about how many times we multiply 10 to get 1000. I left them thinking about this as I moved on to the next portion of the lesson.

*expand content*

**Whole Group:** The goal of the prior section was a quick review to tap on prior knowledge of how to multiply by multiples of 10's when there are multi-digits to work with. They have mastered algorithms of 90 x 100. I wanted them to now explore the idea that 90 x100 is the same thing as 9 x 10 x10 x10.

I did a student constructed review on the white board so that students could take ownership for recalling prior knowledge and that all would be engaged. This engaged my above grade level achieving students because it created an atmosphere of support for struggling students. Those students benefit from a classmate model. We reviewed what we wrote and I guided them along to make sure everything was included. I liked how they included exponents in their example.

I asked students to write the notes from the board in their "Note" app on their iPad. *If you do not have this app or the luxury of iPads, they can take notes in their math journals. **This part of the lesson sets up the thinking for the next part when I teach students to write an accurate and clear explanation. *

As I got them ready to learn about powers of ten, we began connecting the discussion with the difference between multiples of ten and powers of ten. This Educreation Video is a sample of the instruction that went on just prior to my writing demonstration. I actually had planned to start them on homework after this section, but decided midstream that they really needed more instruction on the actual writing expectations. It was more important that I be precise about my writing expectations. I formulated a quick SB file to work from.

*expand content*

**Why Write About This ?** Writing about process and concepts in mathematics is a great way to solidify conceptual understanding and helps me develop understanding of what is going on in each child's mind about the problem. It is also a required skill for Common Core assessments and students need to be fluent in planning, writing and editing for non fiction pieces.

I told my students that I would be answering a new question in front of them and that I wanted them to only listen to my thinking and take notes about what they noticed I did to make my explanation clear. I told them that I wanted them to write JUST LIKE THIS! I constructed this think aloud and writing sample in front of them.* I find more successful results in writing when I tell them exactly what is expected from them for how to write and do a think aloud. They need strategies to make them feel confident in writing about mathematics and those strategies need to be modeled by the teacher each time there is an assignment to ensure success and growth both in language and in expressing mathematical concepts.*

I used the SB file and read the problem.

Write Like This about Powers of Tens

I began my instruction by telling my students...

Good writers of explanations use these strategies:

1. Read the problem and decide what the question is first.

2. Solve the problem first to check.

3. Make a plan.

4. Write from the plan.

5. Re-read the work aloud.

6. Edit for spelling, punctuation and grammar separately. Don't edit too many things at once.

7. Read again to be sure.

I told them they need to look for these things as I write in front of them:

1. Math words: Proper ones! ( We mentioned that some people use "ten to the power of" or "powers of" because they understand it.)

2. Place value language.

3. Order

4. Any other thing they notice that made this written answer clear and well written.

This SB file is what I used to lead the writing. I did a think aloud and used the white board for my plan. I reinforced in my think aloud that good writers always plan what they are going to say when writing an explanation in order not to leave anything out.

So I listed my plan as follows:

**My Plan:**

1: **Good hook!** ( I talked about how important it is, especially in an explanation that I get the reader's attention by using a good opening sentence. I write two or three and go back and choose. Sometimes I write the hook last...it just depends if I can think of a good one right away or not.) My hooks: I could tell right away that this problem is answered completely wrong! Or I could say: There is an obvious mistake in the product of this algorithm! The solution shows that the person didn't understand some important place value concepts!

2.** Explain** **how I pull apart the tens **from the factors and multiply using Associative Property and basic facts.

3. E**xplain how many times I multiplied by powers of ten and why I need to do that,** which shows that each place value increases each time we multiply, giving us one more zero each time in our product.

4.** Explain how the person must have left off a group of tens** in their multiplication process, or they just neglected to count the zeros correctly.

5.** Good closing: I talk aloud about how a good closing ties up the paragraph and makes the reader know that I am done explaining. Example of a closing for this topic: **It is important to consider place value and that the zeros match the amount of times ten was multiplied.

**Read Out Loud: **I then went back and re- read aloud my paragraph and told students that I read aloud any time I have finished writing. This lets me hear my own voice which is helpful in finding mistakes in grammar or in wording. I ask aloud "I wonder if I can improve a sentence or two. Is it clear enough?

**Edit Out Loud:** I told my students that when we are being asked to write "on the spot" we still edit our work and look for errors. I started with spelling. I looked for key "common mistake words" (in this case their really wasn't any, but we reviewed what we sometimes misspell.) I then checked for any math words for spelling. I then checked for any other words by starting from the last word and checking each one just to be sure. Any I was unsure of, I circled to look up, because this time, it is not a test and I have time to edit my spelling. I told them that there is no excuse for not striving for perfection! ( I think it is extremely important to establish accuracy in mathematics both in language, explanation and in process.)

#### Resources

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#### Practice Work and Assignment

*15 min*

I passed out their Multiples of Ten and Explanation assignment as soon as I was sure they were ready to work on it. I gave them about ten minutes and checked for understanding by walking around. I wanted them to feel confident about writing their answer.

I noticed there were several that were not making plans as I had asked. I let them be. I want to see how they write without one and will correct it if need be tomorrow. I think that part of mastering standards in writing is letting kids figure out their planning niche. I can insist on a plan, but unless I can somehow get right in their heads, I cannot prove that the plan is not mentally organized. So, I wait for the finished product and adjust my teaching referring back to my lesson if need be.

#### Resources

*expand content*

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- 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: Pretesting The Multiplication Unit
- LESSON 2: Introduction to Area Models
- LESSON 3: Area Models: Extension of Understanding
- LESSON 4: Area Models: 4 Digit by 1 Digit Multiplication
- LESSON 5: Getting Ready to Quiz: The Greatest Product Game
- LESSON 6: Quiz 1 in Multiplication: Area Model fluency 1x2,1x3 & 1x4 digits
- LESSON 7: Estimation of Products Using 1 Digit up to 4 Digit Equations.
- LESSON 8: Multistep Word Problems, Algebraic Concepts & Equations: Strategy Toward Mastery!
- LESSON 9: Quiz 2 : Multiplication Word Multi-Step Problems: 1x2,1x3,1x4 digit and estimation
- LESSON 10: An 1870's Classrom Meets Common Core: Drilling Math Facts & a Game of What's Wrong with This Answer?
- LESSON 11: Double Digit Multiplication and the Area Model
- LESSON 12: Powers of Ten: Review and Practice and Writing Clear Explanations
- LESSON 13: Multi-step word problems: Review and Support to Mastery
- LESSON 14: Quiz 3: Double Digit Multiplication, Estimation and Solving Word Problems
- LESSON 15: Estimating Double Digit by Double Digit Multiplication
- LESSON 16: Reviewing for Multiplication Assessment: A student jigsaw presentation.
- LESSON 17: RTI: Making Solving One Step Word Problems a Piece of Cake!
- LESSON 18: Estimation Scenarios: Writing Estimation story problems.
- LESSON 19: Assessing Multiplication