Mary Ellen Kanthack BROOKWOOD MIDDLE, GENOA CITY, WI
4th Grade Math : Unit #13 - Multiplication Unit : Lesson #12

Powers of Ten: Review and Practice and Writing Clear Explanations

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.
Standards: 4.NBT.A.1 W.4.1b W.4.2 L.4.1f L.4.2 L.4.2a
Subject(s): Math
60 minutes
1 Getting Back in the Thinking Groove! - 10 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.

 

 

 

 

 

 

 

 

2 A quick reviewof powers of 10 in multi-digit algorithms - 10 minutes

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.

 

Appreciation of Math Skills
Coherence

The Educreations Video shows some interesting discussion and clearly demonstrates student's level of understanding. I thought the discussion about 5 x 10 and 10 x10x10x10x10 was invaluable. Their faces were intense and showed their thought process as we discussed a lot. I talked about everyday use of powers of 10, figuring out wrong answers, and explanations because I want them to appreciate learning how this skill sharpens their number sense.  Common Core emphasizes this in its design. Their questions and their realization in that short clip was so exciting.

3 I want you to write an explanation about powers of ten, like this! - 10 minutes

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. Explain 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.)

 

 

 

 

Writing is Coming Along!
Writing Across the Disciplines

I noticed that my more advanced writing students were really engaged and not as anxious about writing about math this time. I think what happened was that in this process, true understanding for the more skilled writers clicked in gear. They have mastered the other work in writing in math easily.  I think now they understand what I am talking about when I am referring to the power of ten and it happened through showing them how to write about it. These students are usually caught up in "let's just get the answers done!" because process comes so easily for them.

The value of writing in mathematics is clear: it really advances student thinking. Common Core is very clear in the writing standards that students need to write across the curriculum. They seemed to enjoy it and I think it helped that I was so precise about what I wanted them to write. It was spoon-feeding them a little bit, but I expect to see lesser things on their assignment. They simply aren't used to it. Maybe I will be surprised. As I have seen in the past, the effort to be so thorough in conceptual work pays off.

 

 

4 Practice Work and Assignment - 15 minutes

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.

Samples of Work
Developing a Conceptual Understanding

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!