Sunday, July 29, 2012

3.OA.4

Pin It 3.OA.4 Determine the unknown whole number in a multiplication or division quotation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

Unpacking this standard, I found the following I CAN statements.

  • I can write a FACT FAMILY using multiplication and division.
  • I can label the positions in a FACT FAMILY.
  • I can identify the PARTS and WHOLE of an equation.
  • I can use an array to show related facts.
  • I can identify symbols used for missing numbers.
  • I can find the missing number in an equation using the FACT FAMILY.
  • I can write an equation (number sentence) to match a word problem.
  • I can write a story problem to match a fact family.

The familiar FACT FAMILIES are the backbone of this standard. However, some 3rd grade students will need support to understand the vocabulary of the standard. Jenn at Finally in First offers an engaging activity with pictures of family members labeled with sticky note numbers to help students develop the meanings of "relate" to "relative" to "relation."


Using this as a jumping off point, I made a graphic to illustrate the connection between operations and size of units.



This
flash resource from Teacher Network (requires log-in with FREE registration) is part of a downloadable lesson packet that can be used with a projection device to practice creating multiplication and division equations with a set of numbers. Simply insert the three numbers and drag the circles to the proper position within the equation blanks.



Update: 8.4.2012

I found a set of
multiplication strategy posters at the math learning center.

Thursday, July 19, 2012

I Can Statements

Pin It
The Common Core Standards format very easily into I CAN statements for students. Many of these simply restate the standards in easy to understand language. However, when unpacking . . . the skills or tasks can be analyzed further.

For instance, when working with 3.OA.2, multiplication arrays tasks require students to understand horizontal and vertical lines on a grid. They need to connect the vocabulary of rows (horizontal) and columns (vertical) with the process of following with the finger along to count. This is one of my favorite skills to assess because it is foundational for so many visual problems ---graphing, coordinates, area, multiplication, fractions. You get the concept.

If a child can't follow rows and columns visually, the deficiency will cross over domains. I believe that's the center of the Core. As a teacher, I must uncover the misconceptions or gaps that keep my students from performing with the new expectations.

During this time spent on my creative journey with my Student Interactive Notebook on 3.0A, I'm also exploring interesting and efficient mediums to include that will help students understand concepts. The I CAN STATEMENTS will be a foundational tool in lesson planning. I can make a taxonomy of layers that will highlight a student's level.

Kids love working in levels. All the current "hot" games use levels. And, I can teach the children how to draw icons for problem solving and skills to infuse their writing.

Here's an example of my process today. I made my first digital doodle. First, I created the pen drawing. Then, I scanned it as a jpeg (in color mode). As soon as it appeared on the desktop, I opened it in my photo editor. Using layers, I put the can inside the border. I colored it and erased some of the dust.

Instead of writing "I CAN", we can draw an EYE CAN!



Wednesday, July 18, 2012

A Calendar of Problems for Homework

Pin It

Sometimes, simple things just make me smile. I found the Carroll County web site when searching for problem solving strategies. While there, I stumbled upon their digital warehouse of resources for K-5.



Inside the elementary math curriculum pages, they have review calendars for each grade level for the summer months and benchmark dates throughout the year. As soon as the printed page was in my hands, I imagined using these calendars for homework in conjunction with a math journal. I also thought "SUBSTITUTE FOLDER." And, they would make great center rotational activities.



Common Core Standards call for RIGOR and DEPTH building layers of understanding. I could easily assess where my students become deficient by giving them the review calendars in order from K to 5, stapled together.



Here's the site. Click on over there and look at the calendars.

And from the great state of North Carolina, NCDPI still has the Math Stars program online available for download. These pdfs have many open-ended problems useful for homework or centers. All the problems need is a Common Core Standard attached. Find your grade level and browse this resource.

You can also find Problem Solving Decks at Math Learn NC.



Tuesday, July 17, 2012

How to teach students to EXPLAIN in math!

Pin It
  • I'm working on the 3.OA standards. And I found a blog in Bright Hub that explained how to teach subtraction with the strategy of breaking-it-down in context, focusing on how teachers should be relevance to math problems.
    Isn't that the rigor of common core standards in math?

    But then, students need to explain and/or justify their solutions.

    I found there are two levels that students need to organize for writing in math. First, they need to have a structured problem solving process. You've probably seen a 4-step problem solving process before that labeled the steps with Understand, Make a Plan, Try it Out, and Look Back. Or, it might say Explore, Plan, Solve, Examine. However, I found an alternative 4-step process that looks less wordy (complicated) and most Common Core of all that I previewed. I call it the SUPER SLOOTH process because it includes the same language used in reading comprehension skills (who, what, how). You can read more about this problem-solving process here.
    Here's a school resource that has links for problem solving with graphic icons, templates, a problem-solving song and testing samples. It doesn't follow the SUPER SLOOTH process, but it's all good stuff.

    The second level includes helping students write an explanation for their work. They need a list of strategy tools. How many strategies are there? Common Core standards strive for rigor and depth. Student writing is evidence of strategy ownership. My previous question should be revised. How many strategies does Johnny have in his toolbox?

    I'm working on a list of statements for students to use to explain math problem solving work.

    I put the problem in my own words.

    I decided to ______________.

    I drew a picture.
    I checked to make sure it was right by _____________.
    I noticed a pattern.
    I added.
    I subtracted.
    I multiplied.
    I divided.
    I made a list.
    I made a table.
    I made a graph.
    I wrote a number sentence.
    I wrote an equation.
    I used the fact family.
    I used the inverse operation.
    I worked backwards.
    This pdf list sample responses.

    Do you need problem solving graphic icons to use in your class? Click here to visit FCPS and download.

    Here's a template I made (with some 3.OA specific icons) to show student work and help with written explanations. (There's a color jpeg and a BW!)









Situations that require writing explanations: EXEMPLARS

I appreciate the tasks included in these samples on a WIKI . . . even thought the old typed copy is difficult to read in places.

Here are some EXEMPLARS and rubrics for grade levels.

Here are some NYC EXEMPLARS (listed by grade level).

Ontario EXEMPLARS and rubrics (3rd grade)

IOWA EXEMPLARS

NYSED Peformance Indicators and samples of student work





Sunday, July 8, 2012

3.OA Notebook

Pin It

I enjoyed the Kindergarten Kindergarten Blog by Kathryn. She presents engaging activities with math journals and Reading Workshop. But, I was most interested in her great pictures and details about her students work with measurement and their notebooks. I thought the examples might inspire even upper elementary students to show work in a journal.

Why was I so interested in these Kindergarten journals? This summer I am working a sample for a Student Interactive Notebook to document performance tasks. I'm starting with 3rd grade, Multiplication Strand. (Each strand will have a separate notebook.) My choice for the notebook itself is a 120 page composition book. I think the smaller format will be easier to store. Also, the students will not be so tempted to tear out pages. And, best of all . . . my handouts can be printed two to a page!

The main schema for problems solving shown in the notebook will be structured following Singapore Math model drawing. It will also include a strong vocabulary and process guides. But, the part that will require the most research is finding relevant performance products.







This is a sample of a foldable in the 3.OA. Student Interactive Notebook. On the outside of the bottom petal (the one folded on the front), write the essential question (How do I know when to Multiply? Click here to print or download.






Here's a sample performance prompt included in the notebook.

Click here to print or download.

Another question,

How do I help student EXPLAIN problem solving processes in content writing?

Here's a great resource that gives details about strategies and background for writing in math class! MCREL.org. Look for more about this on my blog entry (to be posted soon).

Reference sites for lessons:
These are the places I stopped while researching activities for 3.OA!




Samples of Performance Tasks:

Monday, July 2, 2012

Classroom Tools

Pin It
Teaching is a job always just short of perfection! There's a perpetual door to the room labeled "Improvement- Under Construction." However, our profession builds hope at the end of each year. Fall is the new spring. Everything is reborn fresh.
"Next year, I'm really going to be organized!" or "Next year, I'll get a handle on behavior!" are the rally cries of continued enthusiasm.
Here are some resources for my current ROOM FOR IMPROVEMENT folder:
  • Foldables - I'm going to get back into these this year. They use less copies because students use regular notebook paper or copy paper for most of them. The Center for Math and Science WIKI gave me tons of great templates and ideas for foldables and graphic organizers by categories.
  • Behavior Management: Class DOJO is a behavior management system. Very easy to use. Colorful and interesting for students. APP available to update from your phone. Avatars can be customized with your own photos. You can mark attendance (great for the morning entrance SmartBoard activity) and award points.

Also, check out all the math games and interactives at Fuel the Brain including hundreds board activities, money, base-ten blocks, customizable number line, and a global weather center!
These links will be added to Edujourney's teacher page!

Sunday, July 1, 2012

Vocabulary Context is BIG!

Pin It

Have you ever picked up a book and opened it up to the last few pages to begin reading? I have developed a bad habit of skipping to the end. Probably because I'm limited on time. I want to see if the writing is any good before I spend my valuable, precious, quiet moments reading all the words.
And so it goes with research texts. I usually scroll down to the summary first as soon as the PDF loads. Along the scrolling way, I find headings, charts or visuals that might grab my attention. Today, I'm searching for help with vocabulary instruction. I did uncover some interesting information to keep in mind while I'm planning deep vocabulary tools for my classroom.
The challenge is: VOCABULARY COMPREHENSION ASSOCIATIONS
There is a triangle of learning including Vocabulary, Decoding, and Comprehension.
I feel secure in giving my students strengths with decoding. Much like math sequences, the parts of words can be categorized and compared. However, vocabulary acquisition is a reflection of unequal opportunity. It is the bridge crossing the great cavern of comprehension. Some students come with rickety, wooden slat swinging bridges and towering fear at every step. Others enter the classroom complete with steel beams and wide-eyed views.
Understanding of the vocabulary context of use, idioms and collocation will be one of the focus changes for new Common Core language arts rigor. I was unclear about the difference between idioms and collocation (which is a new word for me!). Found this explanation by an anonymous responder on Blurt It.
A collocation is the way words combine in a language to produce natural speech and writing. For example when you say "pay attention", it could be "give attention, or put attention" but it is not, it is pay attention because it is the natural way in which native speakers express that.
An idiom is a sequence of words which has different meaning as a group from the meaning they would have if you understood them separately. For example, when you say "it's raining cats and dogs" you do not really mean that cats and dogs are falling down from the sky but that there is a heavy rain.
I found a few relevant research pieces to add to my understanding of language acquisition. For instance, according to a Cambridge study, Teaching Vocabulary -Lessons from the Corpus Lessons for the Classroom by Jeanne McCarten,
"Since there are so many things to learn about each piece of vocabulary
  • The meaning(s) of the word
  • Its spoken and written forms
  • What "word parts" it has (e.g., any prefix, suffix, and "root" form)
  • Its grammatical behavior (e.g., its word class, typical grammatical patterns it occurs in)
  • Its collocations
  • Its register
  • What associations it has (e.g., words that are similar or opposite in meaning)
  • What connotations it has
  • Its frequency
  • . . . it is important that we as teachers only introduce a little at a time, starting with the most frequent, useful, and learnable vocabulary, and returning later to more difficult vocabulary and less frequent uses of previously learned items. We need to repeat vocabulary often, because students must work with a word or phrase many times before acquisition takes place, and we must offer variety to keep the exercises fresh and to cater to different learning styles. Finally, we need to help students understand that learning is a gradual process that takes place in small, manageable increments over time, and to encourage them to seek additional information on their own, personalizing the learning experience and tailoring it to their own specific needs."

    Thus, the DEPTH of understanding demanded by Common Core!

    Whew! Just to be clear, I did go back and read the whole article . . . and will re-read it again.

    Here's a fun book with activities and games to explore vocabulary. There are several chapters available for FREE download. WordPlay Cafe

    Quote

    "Those that are burdened to believe in the impossible need to get out of the way of those that are breathing reality into exceptions!"---V. S. Bell

    Visitor Stats