Introduction to Math Workshop

Tomorrow I'll introduce students to Math Workshop.

First, I'll restate why were learning what we're learning, and the many ways students can effectively support their own learning in school and outside of school.

Then I'll say that Math Workshop is a time for you to practice what we're learning in ways that help you learn best.

I'll ask students to practice the place value skills and knowledge we studied yesterday by completing the following tasks:

• Complete the worksheet
• Check in with a teacher anytime you have questions or upon completion
• If done, practice more using Khan Academy Place Value practice, and again when you have questions ask a teacher.

There's no simple way to learn tomorrow's focus skills and knowledge without simply practicing. Students can aid their practice by making the following steps:

• Work alone or with a friend
• Focus on the task
• Use a sharpened pencil or pen that you enjoy writing with
• Take your time and work with precision
• Work quietly so others can concentrate too

I'll set up shop at the big table so that I'm accessible and available to those that need me and for those when they complete the task. Also when students pass in their assignments I'll ask them to read a number of numbers to assess their ability to read numbers. 

The following day students will complete more practice items, then next week we'll focus on the "behavior" of the base ten place value system as we look closely at the ways number increase and decrease as you move up and down the place value system. 

Mathematical Reasoning: Number Sense

How many people live in Massachusetts?

We used five population statistics today as part of the place value unit students are studying.

Early in the day, I asked students how many students they thought were in the school. They made fairly good guesses that were close to our approximately 400 students.

Then I asked how many people live in the town where our school is located. Their guesses were about 100 or 200 more. Later when discussing this more they added rationale that increased the estimate with points such as the fact that there is more than one school, some students don't go to public schools, students have siblings who aren't in school, students have parents, and there are older citizens too. A few came close to 13,000 which is close to the exact number of people.

After that we estimated the amount of people that live in Boston. Students knew it was bigger than our town with more people and most made guesses that doubled, tripled, and quadrupled the town's population. Only a few used more reasoning and experience to compare Boston with cities they had visited or knew about thus guessing larger numbers. As for the United States and world population similarly only a few could come close to the actual number.

When watching the Presidential election debates, I was struck by the large amount of numbers thrown about--numbers that were difficult to imagine and compare when sharing with just language. I found myself wishing there were reliable infographics to help me understand the comparisons, proposals, and critique. I think the Presidential elections of the future will be blended presentations as the information is simply too sophisticated for words alone, thus the back and forth jabs.

Too often too many of us can't quickly make a numerical comparison or imagine a measurement or value. Yet, it's a very important critical thinking and decision making skill.

Working with numbers that relate to students' lives is a first step towards helping to build number sense, and then allowing students to estimate "how many" and explain their rationale for their estimations is a good way to share and develop mathematical reasoning and explanation.

Tomorrow we'll continue working with these numbers as students learn to write and think about numbers in many ways. Onward

Place Value: Population

Tomorrow students will consider the population of the small town where they learn, the state's capital city, the state, the country, and the world.

Using numbers that pique students' interest help them to learn
math with greater depth, interest, and skill. 

Town Population: 13,294 (2014)
Capital City (Boston): 667,137 (2015)
State: Massachusetts: 6,794,422 (v2015)
Country: USA: 324,718,574 (Census Clock)
World: 7,346,044,7784 (Census Clock)

First, I'll hang up the maps of the US, town, Boston, and State around our white board.  Next, I'll simply list the numbers on the board like this:

324,718,574       6,794,422         13,294      667,137   7,346,044,7784

Then I'll say what do you notice about these numbers?

I'll listen carefully to their responses as their observations will inform me about their number knowledge.

After that I'll ask students to order the numbers. I'll mention that mathematicians typically put numbers in order to help their analysis and number work.

I'll then tell them that these numbers represent the population, number of people, that live in the town, capital city, state, country, and world. I'll ask them to guess which number belongs to which location.

Once we have that information we'll focus on the population of Boston.

I'll suggest that we can write that number in many ways, and we'll practice writing the number in the many ways shown below. After that I'll say that it's difficult to remember that number and that's why people often use estimates instead. A ballpark number is easier to remember. We'll round the number to its nearest 100,000.

We'll then round the numbers of the other locations to the nearest highest value the number represents. Finally students will have a chance to write the other numbers in many ways to practice.

Why Math? Looking at Base Ten Place Value with a Systems Lens

We started today's lesson talking about the marriage between math and medicine. That was to provide some rationale for the importance of learning the early math skills we're focused on. Students understood the relationship and were interested in the related story.

Then we thought about the categories that belong to systems think including the parts, structure, function, purpose, and environmental affects.

We then used a systems' lens to begin to study the Base Ten Place Value System also referred to as the Base Ten Numeral System, Base Ten System, and Base Ten Number System.

We discussed the purpose with the question, Why would someone choose to spend their time inventing this system? Students had great ideas about this including communication, common understanding, making life better and easier, and more.

Then we looked at a model of its structure--on paper it looks a bit like a sports field. After that we started looking at the parts beginning with the decimal point which could be known as "The Separator" if it were a super hero since it separates whole numbers from parts or decimal numbers or fractions. We talked about the 10 digits that make up all the numbers in the Base-Ten System, numbers that go to infinity "large in value" and infinity "small in value." We'll watch the famous Eames Power of Ten video to make that more understandable tomorrow.

After that we began inserting powers numbers, words, exponents and expanded form to demonstrate the value of numbers from the ones place to 100,000's place. Tomorrow we'll complete the model by labeling up to the billion's place for the whole numbers and down to the thousandths place for decimal numbers.

Then we'll begin looking at the patterns that exist within the system. I'll have students work with each other to discuss what they notice and then we'll share.

It's a deep introduction to the the base ten system, one that will be followed by the study of how to write numbers in number name and expanded forms, rounding and its rules, and the "behavior" of the base ten system as we move up and down in value. We'll likely weave in the study of the metric system here too since it's directly related.

It's a lot of fun to reveal math concepts, knowledge, and skill with and for students--they're incredibly bright and curious especially when you match math with their lives, interests, and questions.

Teaching the Base Ten Place Value System

We'll complete and color code a place value chart like this. 

Students will begin the place value unit tomorrow. There are so many ways that we can teach this unit.

I'll begin with connecting this unit to the last unit, the coordinate system, with a focus on the word, system, which is the main concept of all fifth grade math.

I'll pass out a base ten model framework, and have students write the title, "Bast-Ten System." Then I'll ask remind students that "systems" is the main theme in fifth grade math and that we just studied the coordinate system.

I'll ask students to tell me what a system is? Then I'll ask, "What do you know about the base-ten system also known as the base-ten number system, base-ten numeral system, or base-ten place value system. We'll list what students say.

After that I'll focus on the following points:

• The base-ten system might be considered one of the world's greatest inventions. I'll ask students why that might be true.
• Only 10 digits can be combined to make numbers that go to infinity in with greater and greater values and to infinity with smaller and smaller numbers. That's amazing!
• Why is it called a "place value system?" This is true because the value of a number changes depending on its place.

Then we'll begin looking at the "parts" of this system by completing and color coding the chart. Once we complete creating the chart and looking at the "parts" of this system, we'll then look at the "behavior" of the system and how we use the system when using numbers to make sense of, order, organize, analyze, and make predictions about the world around us. 

We'll use the CCSS standards above to guide the first half or the unit.