Grade Five: Exploring Place Value

“There are only three colors, ten digits, and seven notes, it’s what we do with them that’s important."

― Jim Rohn

Amazing that only 10 digits can make all numbers to "infinity and beyond."

First, post and review the standards.

• 5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
• 5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
• 5.NBT.A.3 Read, write, and compare decimals to thousandths.
• 5.NBT.A.4 Use place value understanding to round decimals to any place. 

Facilitate a review and conversation with students. It's difficult to begin a unit of study without a discussion that helps the educator understand students' knowledge, questions, and even misperceptions related to the topic. 

1. What do you know about place value?
2. How did place value come about?
3. Why is place value important?
4. Look at the models of Base 10 place value below, which do you feel is most accurate or useful and why?
5. If you were to make an ideal Base 10 place value model, what would you include and why?

4. What happens to the values of numbers as we move from left to right of the place value chart?  What does this model show us?

7. Watch these films and think about our past conversation, what would you change or add, and what questions do you have?

8. Let's work with familiar numbers, numbers that matter to us.  For each number we'll write standard, number name, expanded, and exponential form. We'll also write equations, expressions, and inequalities that show the value of these numbers. Finally, we'll make models of these numbers, models that show each number's value and the relationship between and within each number.

9. After this project, we'll solve problems that use our knowledge of place value as it relates to the standards. 

Common Core Resource

What's On Your Learning List?

I keep a learning list. A number of topics I want to learn about so when the time and mood matches, I learn.

The learning list comes from the places where I want to grow professionally and personally.

Currently, the list includes the following topics.

Collaboration
Getting to Yes
Getting Past No 

Educational Thought and Practice
Role Reversal 
Brain Rules

Math
Unpacking 5th grade standards and embedding learning experiences that lead deep thinking, understanding, model making, explanation, and debate.

Science
Similar to math, unpacking the standards and teaching each standard with hands-on exploration and investigation, STEAM Star connections, interdisciplinary STEAM reading and videos, writing, and presenting.

There's much to learn to teach and live well. As I state often, we're fortunate to live at a time where the learning we need and desire is close at hand.

Assessment and Completion Week Ahead

This week students will use four math periods to complete math assessments. We'll use the rest of the time to complete our ongoing ecosystem model and number quilt projects--projects that took much longer than I expected, but projects that I also deem worthwhile.

I'll focus on feedback, plans for upcoming weeks, and preparing for start-of-the-year family conferences.

I'll frame the assessments as a chance to "test yourself" and "show off what you know."  I'll also mention that teachers will use the test results to plan the program well so every student is getting the teaching and learning they need with respect to the long list of standards every child is supposed to master.

On these assessments students can use graph paper, scrap paper, and all the time they want.

I'll also observe how students tackle the tasks to gather more information about their individual learning needs and attributes.

Parents look forward to the data reports, and as educators, we profit from this information when it comes to planning student-centered learning experiences.  The key point, however, is that the learning program is not all assessment or two-dimension, paper/pencil tasks. The program for young children is best if it is differentiated, multi-modal, and focused on students' interests and needs as well as the learning standards.  Onward.

#mathchat5 Update

I started #mathchat5 by jumping in. Not unlike the farmers in the dust bowl, I didn't study the ecosystem of chats and chose a time that was filled with many, many other great chats. I also chose a very narrow audience (narrow for the Internet), fifth grade math teachers.

Since there wasn't much interest for that topic at that time, I'm going to stop the effort. If there are third-sixth grade math teachers out there that are interested in a weekly chat to review the standards, SMPs, and other topics related to fifth grade math, let me know, and perhaps we can start again with a better time.

In the meantime, #mathchat exists, and can offer us a great place to "talk and learn math." Thanks to those who jumped in with me and participated. As a lover of new ideas, I can't forget about the needed steps in the planning stage which includes surveying and studying the learning landscape, and collaborating to make the learning happen with strength.

A failed attempt at something new leads to new learning--another stair on the learning staircase.

Embed Enrichment into the Learning Program

In today's world of teaching and learning, enrichment is only a key stroke away.

There's no reason for an eager student not to have the challenge they yearn for or benefit from.

You may weave enrichment into your program in the following ways.

• Start lessons with big ideas through short videos, quotes, problems, or conflicts: That approach sets the stage for the learning experience. This alone is enriching because at its simplest level, this kind of introduction "wakes up the mind for learning," but at the enrichment level these are the kinds of introductions that one can revisit to analyze with greater and greater depth and thought. For example, I often start the Place Value unit with Eames' "Power of Ten" video. 
• Scaffold the lesson: Always think 1-2-3 when you're planning the learning experience. 1: review, 2: grade-level content, and 3: the enrichment level. I like to have all levels there for the taking for all students, but typically I expect students to complete level 2 and reach for level 3 if desired. 
• Embed learn-at-your-own-rate programs and games into your curriculum: Today the Internet offers multiple learn-at-your-own-rate sites that students can access.  Two of my favorites include Khan Academy and SCRATCH. Students also profit from Minecraft and Sumdog, but those are not allowed at our school. I plan to identify more of these programs this year, and if you have favorites, please share. These programs allow students to level up as they are ready.  A bright young student could begin learning high school math in fourth grade on sites like Khan Academy and make sophisticated learning models using SCRATCH, Khan coding, and Minecraft. Sumdog offers playful review in a way that students K-8 can play against each other and students from all over the world. Multiplayer platforms are engaging, motivating, and help students to solidify skills they've learned.
• Let students teach: Advanced students can typically solve a problem or complete a task, but are challenged by application and explanation. It is always enriching to offer students the opportunity to create a presentation on a topic, and then to teach the topic to younger students using that presentation. Teaching to younger students prompts one to think deeply about the content and present it in the simplest terms using multi-modal methods. For example, students could create a short blended lesson that teaches third graders the vocabulary and meaning of multiplication. Willingham's book, Why Don't Students Like School, points out the richness and strength of revisiting concepts repeatedly, and each time gaining new insights and information from the analysis and study. 
• Spread the learning: Similar to letting students teach, also prompt students to spread the learning by making videos and posters to share with classmates, the school, and possibly others. Integrating your learning in a way that helps others is a very challenging and worthwhile learning task. Last year my students worked with high school buddies to create math films--it was deep work related to math vocabulary, work that served both high school students and fourth graders well on many levels.
• Challenge the teacher: Give students the opportunity to use the current concept focus to write a problem that will challenge the teacher. Make sure that the student writes the problem neatly, solves the problem herself, and then reviews the teacher's work. Students' first instinct is to write a really challenging problem, one that they can't solve so it's important that students' solve the problem before offering the challenge as this is where the best learning happens. In some cases the student may need to help the teacher if the teacher needs more learning. Young students LOVE to challenge and teach the teacher.
• Online home study list: Using a Google doc or other venue to host home assignments and enrichment helps students and families at all levels. Students can quickly use links, read the assignments, and know how to get help via other documents and sites or emailing the teacher. The enrichment list can include videos that deepen students' understanding of content. For example, our class is about to start the place value unit, and watching one of the History of Math videos on the Internet serves to enrich and deepen this unit. 
• Email the teacher: If you're a student who is not challenged today, you can email the teacher asking for greater challenge. I have a student who does that, and the more he emails, the more I know how to challenge him well. Again, I typically give him a task that will support the whole class's learning, and he eagerly problem solves and completes the task. The challenge for me is finding good time to review his work after completion, and I'm working on that challenge. 
• Class contests using brackets: Last year we played Illuminations' Factor Captor game online with a class tournament. Like a wrestling match, we used brackets so students more capable with the concept kept leveling up and playing other strong students, while more challenged students played students at their levels. This is a good process as when you get the chance to play with someone stronger than you at first, you witness and learn new strategies, but as the tournament continues you are playing with students that are at your level which fosters greater thinking, a good pace of playing, and well-matched challenges. 
• Debate: Creating multi-level debate teams and making the strongest student the captain is another way to enrich students. The captain has to demonstrate leadership as she and her teammates gather information, prepare for the debate, and work to prove their point. This is an excellent enrichment opportunity. 

Enrichment routines and efforts can be embedded into the typical program in the ways above. If you have other ideas, please share as the teaching program is stronger when every child is working at a just-right level of struggle, challenge, and learning.