Productive Frustration: Implementing Math Learning Tasks

Winding down... While the school year is winding down students seem to be winding up!  With all that anxious energy floating around, we are tackling, wrestling, and basically pummeling Common Core math learning tasks.

Learning tasks are lessons that consist of word problems designed to make students dig deeper.  Tasks provide opportunities to play with numbers.   Students are encouraged to use words, pictures, and equations to explain their thinking.  Often, tasks do not ask for a simple put together or take away answer. Instead, they ask for a variety of solution paths, to compare or explain paths, or to make decisions about whether a given assumption/answer is correct.   

Here are some student examples. I have included a variety of skill levels. 

Lesson Format: 

• Set Up - Teacher explains the context of the problems and makes tools available. 
• Private Think Time - Students work independently to create possible solution paths.  Teacher monitors, using advancing, assessing, and guiding questions to correct misconceptions or draw attention to precision (errors).
• Small Group Discussion - Students work with partners to discuss differences and similarities between solution paths.    Teacher monitors.  
• Analyze and Share - Everyone engages in discuss that focuses on key mathematical ideas. Models /solutions are explained and critiqued.

Our classroom motto during a learning task is, "Try, try try! It's okay to make a mistake, because we have erasers!" So often, students hold back.  They don't want to make mistakes.  Students have come to expect answers to be given to them. That's just not happening in our class.  This is called productive frustration.  It's not easy, but it is so worth while to creatively work through tasks.  It builds stamina and deepens mathematical understanding. 

Where can fielded, high quality math tasks be found?
There are several places to find good solid tasks.   

• Illuminations - Lessons for learning is a great place to start. 
• Tennessee teachers have an abundance of tasks available through TNCore.org.
• K-5 Math Teaching Resources is another excellent site. You'll find tasks, lesson plans, literature connections and much more, all organized by grade level and standard.  There are printable journal tasks/word problems available for purchase. These are formatted to print on 30 per page labels. While a little pricy, they are convenient and good quality problems.   
• Envision math users will find that most quick checks located at the end of each lesson for K-5 can be tweaked to fit the format of a math task learning lesson.

Keep in mind when planning tasks that they should be open enough to allow for a variety of solution paths.  The goal is to create opportunities to play with numbers and use effective mathematical practices.  Remember it's all about productive frustration!

More student examples from varied skill levels:

Charlie Needs a Cloak: Math Bench Mark Review

Do you ever just have a moment when you think, "Hey, that's a GREAT idea!" It doesn't happen to often, but when it does you just gotta run with it.  

Second grade had been reading The Goat in the Rug by Charles Blood & Martin Link.  It was one of those weeks were everything needed to be completed at once.

Check List: 

• Prepare hallway for parent curriculum walk
• Wrap up literacy unit
• Review for math bench mark test
• Assess for standards based report cards

… You get the idea.   

I was settling in to create a review unit for our math bench mark test, when Tomie dePaola's Charlie Needs a Cloak came to mind.  It was a favorite read aloud from my  kindergarten teaching days.  A video version was on United Streaming, how convenient!  I quickly whipped out some labels and aligned our literacy theme with the math standards. Literally, I spent 45 minutes on planning and prepping.  My colleague proofed it and the students dove in! I was so proud of the stamina and tenacity they showed.  It never ceases to amaze me how students rise to the occasion when the expectations are high!

 Common Core Math Standards are listed for each sample. Here we go...

I Can Statements

2.MD.A.2  Measure the length of an object twice using length units of different lengths for the two measurements: describe how the two measurements relate to the size of the unit chosen.

2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g. by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

2.MD. 8  Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

2.MD.7  Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

This was a perfect opportunity to make anecdotal notes and engage in meaningful math dialog with students.  It rounded out the week nicely. 

Measuring Penny Update!

Measuring Penny is an amazing math picture book.  I wrote a lesson plan last summer and have been anxiously awaiting our second grade measuring unit to teach it.  Just imagine my frustration at having to wait so long.   Spring has arrived and the review is in…

After teaching this unit, I am happy to share that it is one of my favorites for the year.

Second Grade Common Core Measurement Standards focus on measuring, remeasuring, comparing, using different units, choosing appropriate tools, and problem solving.  With that said, I think this unit did a nice job moving through the skill set and tying everything together in the final project. 

As I approached this unit plan, I decided that a tool for reflection needed to be added.  I wanted this element to be something students could reference and share with their parents. Using three prong folders and loose leaf paper, students created measurement journals.  They recorded observations, created Thinking Maps, answered questions, etc. in these journals.

I found that as the unit was presented about 40% of my students did not have enough background knowledge in estimating and using non standard units. In response to this, I spent a bit more time on the initial dog biscuit activity then originally planned.  I displayed a very large dog bone and the small treat bone that students would be using for the actual measurements.  I used advancing and assessing questions to facilitate the manipulation of the idea that the size of measurement unit affects the number of the measurement and what a reasonable estimate would be?

How do the units change?

What happens when the unit of measurement gets larger? smaller?  Why?

What happens to the number when the unit changes?  

Explain to a shoulder partner your opinion about, why the numbers change? Do you agree with your partner?
What should a reasonable estimate look like? How do you know this?

The goal here was to illicit viable arguments and critique the reasoning of others (MP4).  Once we activated that prior knowledge and put a little experience under our belts, we were ready for the fun to start!  Students had a blast. With materials in hand, students explored measurement with purposeful movement and productive math talk.

Final Performance Task

The unit closed with a final Performance Based Task.  Students brought stuffed animals from home, chose tools, measured, compared, and took ownership of the standards.

I Can Statements

Class Display

Individual Examples

Common Core Mathematics Standards

2.MD.A.1  Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.A.2  Measure the length of an object twice using length units of different lengths for the two measurements: describe how the two measurements relate to the size of the unit chosen.

2.MD.A.4  Measure to determine how much longer one object is than another, express the length difference in terms of a standard length unit.

2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g. by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

This lesson plan is available for free download at my Tennessee Trending Teacher Wiki Space.  Please look on my Second Grade Common Core Lesson page.

Now & Ben: A Common Core, STEM Lesson

While perusing through Even More Picture Perfect Science Lessons by Morgan & Ansberry, I was excited to find a STEM lesson for Now & Ben by Gene Barretta. Now & Ben just happens to be the final reading story for the second grade Journeys series.  I was inspired to create a second grade lesson plan that incorporates several Common Core ELA standards and TN science standards. 

The lesson is available for download in both Smart Notebook and powerpoint formats on my Tennessee Trending Teacher Wikispace.  The Smart Notebook version has several interactive pieces that are not included in the powerpoint. These include quizzes, drag and drop Thinking Maps, and a hyperlinked content slide. 

Now & Ben: Common Core STEM Lesson

The lesson begins by brainstorming circle maps and a read aloud.  Students are encouraged to activate prior knowledge and read closely for new information.  

The next step is to take a closer look at the differences between discoveries and inventions.  What were Ben Franklin's discoveries and inventions? What impact on history did Ben's accomplishments have?  Why would someone from long ago still be important today?

Students are then asked to contemplate problems.  With small groups, they discuss, design and even create inventions (solutions) for their problems.  Students critique their inventions and present their findings to the class.   

ELA is further incorporated by the introduction of cinquain poetry.  This simple 5 line form of poetry is tweaked to incorporate a review of nouns, verbs, & adjectives.  Students create their poems independently with teacher support & scaffolding as needed. Finally, poetry readings are digitally recorded for students to review and share with their families. 

This lesson is going to be a wonderful way to wrap up our school year. Those last two weeks of school can often drag on. I'm looking forward to engaging my students to really stretch their thinking and make connections between scientific ideas, history, and modern life.   

  

Journeys Common Core Resources

Implementation of a new series is a wonderful excuse to freshen up our out look on curriculum presentation. This year brought in the adopted of Houghton Mifflin Harcout's, Journeys Common Core series. While the website offers a plethora of online resources, there is plenty to expand on.

With some help from my second grade colleagues, I am almost through building a second grade  Journeys resources wiki page.  At this moment you'll find weekly, lesson plans, Tic Tac Toe homework assignments, and Magic Vocabulary. This is a work in progress, so you'll notice that the collection is growing.

Weekly lesson plans arrange Journeys curriculum  into a TEAM friendly format.  Microsoft word format allows for easy editing, so you can add or subtract throughout the documents.

Lesson Plan Images

Tic Tac Toe homework assignments include vocabulary/spelling,  comprehension, and grammar/language skills. The assignments compliment the various tasks we are completing in class.  They increase with rigor as the year progresses.  Tic Tac Toes are designed to engage parents and keep them informed about what we are learning at school.  A brief list of "I can" statements are included in the document.  

Directions for Magic Vocabulary can be found in an early blog post.   

Non Fiction: Biographies

Second grade has been busy, busy!

After reading My Name is Gabriela, by Monica Parra Brown, we jumped into the genre of biographies.  This was an amazing opportunity for students to practice close reading with complex texts.

The process began by reading several different biographies. Students collaboratively decided what a good biographer would include in an article.  Once important elements were identify, they were used to create a basic format.

Students chose a person to research and identified texts.  Pupils used Thinking Maps to record important information.  Peer discussions about their notes lead students to determine whether or not additional information was needed.  Internet resources were utilized to fill in missing elements and locate appropriate illustrations for final projects.

Thinking Maps

Final Projects

Differentiation

Differential supports were used to scaffold this lesson. Both of these examples utilized dictation. The example on the left illustrates dictation followed up by the student tracing and reading aloud text. Here the student needed physical support to get the information on the paper. The second example is from an emergent reader. This student had adequate verbalize skills, but lacked the repretoire of written language and reading skills needed.  Both students participated in the writing process and followed the basic format for research and reporting.