The Math Year 2016 Starts

The math year began with a focus on STEAM and The Global Cardboard Challenge. The start also included a number of standardized tests and assessments. The STEAM activities, in part, foster teamwork, while the tests provide good data as to how to sensitively teach the curriculum standards, concepts, and skills.

Next week I'll combine the standards related to coordinate grids and place value with preparation for our upcoming nature field study. After that we'll explore place value more using facts and figures to prepare for our trip to the McAuliffe Science Center where we'll learn about space.

Following that work, students will focus in on numbers 0-10, math facts, number lines, addition, subtraction, multiplication, and order of operations. In the midst of this we'll study how to use Khan Academy effectively to learn, and continue efforts with Symphony Math and That Quiz.

1. Learning Math Begins with a Good Attitude

This With Math I Can website has many helpful links
for teaching and learning math. 

Today officially begins the math year. After spending the first few school days on team projects, today we'll begin our math focus.

Today's theme is that our attitudes affect math learning engagement and success.

We'll start with the the With Math I Can video listed on this page.

We'll then talk a bit about the video and a few organizational matters.

After that students will review the day's online learning menu and then follow the menu which includes completing an attitudinal/behavioral self assessment and math warm-up games.

Teamwork Matters: Making Math T-Shirts

Start the year by focusing on the fact that students learn better when they work together. Emphasize that your math class is a math team, and as a team the way you work together matters. 

Ask students if they belong to any teams. Then ask them to tell you what's important when it comes to successful teamwork. After that, you may want to show one of my all time favorite teamwork videos, and ask students to look for the attributes of successful teamwork as they watch the video:

After the film, acknowledge that like the Panyee soccer team, most teams have T-shirts. Say that the class will have some fun with numbers as they make paper T-shirts and a class bulletin board that celebrates your dynamic math team.

To make the T-shirts, do the following:

1. Set up a computer and printer in the classroom. Have students take a good picture of their face and print it. I use PhotoBooth for this. Students go to the picture stand, take their photo, and print it one after another.
2. Hand out the number activity guide which includes a T-shirt template.
3. Allow students to work with calculators to complete and check their work. 
4. As students work, observe their efforts and listen to their conversation. This observation will serve as a good initial assessment of student effort and need--an assessment that will inform future lessons.
5. Have students complete the task in pencil, check the work with a friend, and then check with you. Coach students with regard to correct completion of the work. When complete, have students write over the numbers and words with a fine line pen, write their number on their t-shirt and add the fact data to the front of the T-shirt or just below, tape their picture on top and hand it in for a class bulletin board that will display all the students pictures with a title such as "Teamwork Matters: Marvelous Mathematicians."
6. When students are done, they can work together on the enrichment activities included on the number activity guide. 

This project is a great start-of-year activity, one that provides assessment, fun with numbers, vocabulary/fact review, and an emphasis on teamwork. I recommend. 

Know Your Students: Assess Fact Skill and Knowledge

That Quiz is free and easy to use for simple student assessments and practice. 

While recent math research and writing points to a need to lessen our obsession with fact knowledge, an obsession that serves to make many students so nervous that they end up disliking math, it's still important to develop fact facility and fluidity. When students know their math facts well, they're more able to make connections, compute, and solve math problems.

How can math teachers do this in a sensitive and productive way.

First, it's important to assess students' fact knowledge. Who knows their facts and who still struggles with basic fact knowledge at fifth grade.

To assess this skill in an easy way that provides good data, I like to use That Quiz. That Quiz is a simple, free to use math practice and assessment site.

I simply put all students names into the program and create/assign assessments and practice sessions (outlined below). Generally I create a number of assessments that move from simple and easy to access to more complex and challenging. I have students start with the simpler assessments and move up as they can. Later I assess the assessment results by the number of problems completed, the time it took, and the complexity achieved. That gives me good data about who knows their facts with ease and who is still struggling.

After that I'll review fact results with individual students and parents, set goals with students, and work with the children to gain fact skill and depth of fact understanding through a varied array of investigations, practice, games, and projects as part of the fifth grade math program and during Response to Intervention and Math Tech times.

Fact Assessment Sets for Fifth Grade
50 addition facts
50 subtraction facts
50 addition/subtraction facts
50 multiplication facts
50 division facts
50 multiplication/division facts
100 multiplication/division/addition/subtraction facts
100 facts with simple variables
100 facts with more complex variables

Math Links and Tools

So many great math tools and links exist, so I'm starting a list here:

Number Models

Teaching and Learning: Numerical Expression

It's great to start the school year with a challenging, engaging math lesson. Children love to come to school at the start of the year and learn something new. This sets the stage for a vigorous, engaging year ahead.

Teaching numerical expression lends itself to engagement and provides students with a terrific skill to use as they learn, practice, and apply mathematical operations with numbers simple and complex.

Introduction: What Do These Expressions Equal?
Evaluate one or more of the expressions below in any order by hand or with a calculator. Giving students the chance to use a calculator takes away the pressure to remember facts and to calculate correctly. This frees up all students to reach for higher level learning in this lesson. 

8 + 6 X 5 - 1/2 + (8-3)

99 - 1 + 2 X 3

Let students play with it. Some will finish quickly, others will take a bit of time, and some may not know where to begin. Give the students about 10 minutes, then ask for children to come up to the board to explain their thinking about each expression.

Teach Order of Operations

Show Flocabulary's PEMDAS movie. While some mathematicians are not in favor of PEMDAS, I still think it's a good tool for early learning with regard to Order of Operations. As students work becomes more advanced, they quickly understand where PEMDAS doesn't exactly fit, hence I still believe it's a good starting point. 

Also introduce this graphic shared by a former student:

Study and Practice
Net talk with students about what they can do to remember, study, and apply the Order of Operations. List their ideas. Then let them work with classmates to do all or some of the following activities plus any good ideas they've come up with that you want to add to the list:

• Create a mnemonic, poem, picture, or mini poster that will help you remember the Order of Operations.
• Watch the PEMDAS rap over again, then make up one of your own.
• Make up your own expressions and evaluate them. Check with the teacher.
• Write 5 different expressions and 5 different equations that equal 50 (remember expressions do not have equal signs while equations do). Use at least two different operations in each expression. Make sure you use every operation at least once. Use parentheses, brackets, and/or braces in at least two expressions.
• Use exponents in at least two expressions. 

More Practice

Study the chart below. Then determine where you might add parentheses, brackets, and/or braces to simplify the challenging expression and puzzle below. Then solve the puzzle and expression.

ASSESS

After a day or two of practice and some Khan Academy review and study related to the topic too, it's a good time to assess students' skills. This is one assessment that provides the teacher with a good understanding of what students learned and still need to know.

Related Grade Five Standards

Teaching and Learning Divisibility Rules

Important Knowledge, Concept, and Skill: Factors, Multiples, and Divisibility Rules

Introduction: First Impressions
The introduction to a learning experience can last anywhere from 5-15 minutes. It's meant to wake students up to the topic, get them thinking, and make the lesson "sticky" or brain-friendly by connecting the concept to something they know, are interested in, and/or excited and even alarmed by.

"What does a first impression mean?' A first impression is what you notice first.

Students will likely list a number of descriptors of a first impression. Then say what can we know about a person from a first impression? And after that, can we know all about a person by a first impression, essentially, "can we judge a book by its cover?"

Then hold up the number above and ask, what's your first impression of this number--what do you notice? List all that students notice.

After that ask, "What can we know about a number just by looking at it?" And after that short discussion, can we know everything about a number by just looking at it?

Rationale:
After the introduction, share the rationale for the lesson. 

"Numbers are ingredients for mathematical thinking and process. The more you know and understand numbers, the better you'll be able to work with those numbers to describe situations, solve problems, and reason mathematically. Learning about the divisibility rules will help you to understand numbers better. What do you think the term "divisibility rules" means?" Take some ideas, then show the definition card.

One definition you may use is this one:

A Divisibility Rule is a way to figure out the factors of a whole number without performing division, usually by examining the digits.

Teaching and review of multiples and factors is an engaging and valuable focus of the fifth grade math curriculum. Though this focus is more closely matched to fourth grade standards, it's integral to fifth grade standards related to numbers and operations, fractions, measurement, and more.

Teaching/Learning

Day One
Once you've introduced the learning experience and main definition, it's time to explore. A good way to explore is to teach and play Factor Captor online or off. Encourage students to think about their "first impressions" of numbers as they play. Start by playing a simple version of the game with the whole class, then give students time to play at the level they desire with friends.

At the end of the time available gather students, and ask what "first impressions" of numbers they had as they played. Also ask them to share any strategies, patterns, or other observations they made as they played the game.

Days Two and Three (an more possibly)
Review the definition of a divisibility rule, then review the rules below. 

image reference

Watch the video below and singing the song. After that students can practice using this divisibility rules exercise and chart above with classmates.

Once that's complete, students will be ready to play the Factor Game game again. You may even want to encourage students to play the game at home with friends and family members to practice more. At the end of the lesson, add to the chart students made yesterday about game the strategies, patterns, and number observations they made during the game. Ask students if they used the divisibility rules while they played and if those rules helped them to play better.

At this point, you may want to sponsor a Factor Captor Tournament to give students plenty of practice. This tournament provides students with the opportunity to teach one another, practice, and deepen their knowledge and skill. The tournament also provides the teacher with lots of time to coach students with this knowledge, concept, and skill as well as others.

Day Five: Learning-to-Learn Mindset, Behavior, and Science Connection
Before students assess their skills, engage in a conversation about how students can move this knowledge from "short term memory" to "long term memory." This is a good opportunity to teach students about the limited space and accessibility our short term memory has while our long term memory ensures, for the most part, that facts, figures, and concepts are well rooted and easily accessed. You may ask students to think of information they never forget and facts/figures that are easily forgettable, and after that, the students and you can list ways that help us to learn information well--ways to embed that information into our long term memory. Your list will likely include learning tasks such as writing notes, making flash cards, testing one another, making an mini poster or infographic, turning the concept into an image, singing a song, creating a rhyme or poem, acting it out, and teaching the concept to others. Give students time to choose a strategy, work with friends, and learn/study divisibility rules.

Assessment
Following that, it's time for a quick online or offline assessment like this example. I suggest using Google forms now that they have the new quiz feature embedded right on the forms. That's a quick way to create an assessment to see who knows their divisibility rules and who still needs to study. Allow students to take the assessments as many times as needed until they grasp the learning. Provide extra support where and when necessary.

Blended Learning Resources

Related Videos:
These were a couple of great videos that added to the teaching.

Use Amazing Numbers in Math Class

Math class becomes a lot more interesting when you use amazing numbers.

You may easily teach math concept, knowledge, and skill by analyzing the math in current events articles and situations. Today's amazing space article is an article that will be understood much more with mathematical reasoning.

Below I'm going to collect a number of articles that provide a good stage for mathwork--articles that will lead students to use math well to understand the world around them.

Space Articles
New Planet with Three Suns

Early School Year Focus on Landmark Numbers

Last year I began the math year with a focus on landmark numbers. The introduction proved to be helpful with regard to creating a community of math learners who had common language, patterns, tools, resources, and routines.

I will weave the landmark number lessons into the early year math curriculum again this year. In the days ahead I'll revisit this unit to revise, add, and enrich. In the meantime if you have ideas for change and enrichment, let me know.

Math Direction: Ten Questions Lead the Way

Ten questions will lead the 2016-2017 fifth grade math teaching/learning program.

1. Who are we? What do we know and what do we want to know?
As we discuss who we are as a learning team of students, teachers, and family members, we'll think about the ways that we can collect and analyze data to create an infographic and other models of who our learning team is. Then we'll draw from that data all year.

• Line Plot Lesson
• Assessments: Behaviors/Mindset, 5th Grade CCSS Standards, Facts
• Coordinate Grids - Where we live and learn?

2. How does our community behave?
We'll engage in a number of teaching/learning experiences that focus on apt discipline and behavior for optimal math study, practice, and share.

• Lessons from Learning Mindset and Behavior website. 
• Building Team
• Global Cardbard Challenge
• Khan Academy Introduction, Study

3. What are the digits? What are numbers? What do we know about the landmark numbers 1-12, 25, 50, 75, 100, 200, 500, 1,000?
As we review operations, math facts, math vocabulary, and order of operations, we'll explore the world of the number 0-12. This study provides a good review and lays a valuable foundation for year's math study. This focus also provides a terrific way to introduce multiple math tools including rulers, calculators, tech tools, and coordinate grids.

• Landmark Number Lessons
• Divisibility Rules
• Numerical Expression

4. In what ways can we analyze, discuss, and measure?
Students will create and study two-dimensional and three-dimensional figures as they learn about geometry, area, perimeter, and volume.

5. How does the base ten system behave?
We'll explore the "behavior" of the base ten system in multiple ways, and hopefully work to make models and code animations that demonstrate this behavior.

6. How do we "operate" on numbers?
Students will study, review, and apply number operations as they create and solve real-world multi-step math problems.

7. When and how do we measure length, capacity, and mass? What is proportional reasoning?
Practicing measurement with problems related to matter.

8. What's the difference between whole numbers and fraction/decimal parts?
We'll look at the relationships between and amongst whole numbers, fractions, and decimals. We'll explore where and why we use the various numbers and how we manipulate these numbers using many models, operations, and algorithms?

9. How does math help us to solve real world problems successfully?

10. What place does math hold when it comes to STEAM projects, exploration, and study?

I am just starting to explore the use of big questions to lead each math unit. I am not yet satisfied with these questions, but will continue to brainstorm more about this as I consider the strength and areas for growth with regard to this year's teaching and learning in math.

I welcome your wisdom in this regard. 

Twelve: Goal Setting and the Language of Learning

Note that much of this language came from John Hattie's book, Visible Learning for Teachers, Maximizing Impact on Learning 

Today students took a math assessment. The assessment will provide a baseline for an individualized math fact program.

Prior to the assessment we discussed learning.  I told the students that true learning causes change--a change in action, attitude, ideas, and/or knowledge.

Then I told them that there is a success process when it comes to learning.  I showed them the diagram above and we reviewed each step with the story of how I learned to teach my son to ride a bike, and how they'll use this process to meet their fact fluency goal:

Step One: A desire or need to learn.
My son was seven, and he couldn't ride a bike.  The children in the neighborhood were riding bikes, and we were going on bike rides as a family.  The fact that he couldn't ride a bike meant he was left out of friend and family activities.  He desired to ride a bike, and we knew that this was a need.

Similarly, students need to become facile at math facts in order to learn math at a higher level with ease and success.  This isn't true in all cases, but it is true in most cases, hence this is a fourth grade goal. 

Step Two: Determine Success Criteria
In this case, it's easy, the success criteria is riding a bike.

For facts, our goal is 50 facts of each operation in three minutes or less with three or fewer errors. 

Step Three: Assess
What did my son know at the start of this learning journey?  He could ride a bike with training wheels.

What do students know as they start their math fact learning journey.  Students took a series of That Quiz tests to find out.

Step Four: Plan and Strategize
I planned to hold on, push forward, and run close to my son to help him learn.  

Students will make a plan to reach their fact goal. Students will choose from a number of strategies.

Step Five: Act, Adapt, and Assess.
At first I tried to teach my son to ride his bike on a bumpy, hilly tar road.  That didn't work.  Then I brought him to a flat, part pavement-part grass school playground.  I also added a $ bribe to encourage him to try.  That worked.

Students will try out their plan.  We'll assess regularly and adapt the plan as needed so that they reach their goals.  There will be in-school parts of the plan and at-home parts.

Step Six: Final Assessment/Next Steps
My son's final assessment was done by observation.  I observed that he had learned to ride and was ready to ride wherever he wanted to.  The next step was to take him on some bike hikes and teach him about safe bike riding.

In class, students will choose when they are ready to take the test for each operation.

Step Seven: A New Goal!

We'll revisit this learning process regularly this year as children begin to understand that they're in the driver's seat of their education--they are the most important people when it comes to setting and meeting worthwhile learning goals.