Throwback Thursday – Anchor Tasks Demystified

Over the summer, we thought it would be fun to run some of the most popular posts from the past. It’s mid-July and teachers are already getting ready to go back to school. Here’s an article on planning for the concrete component of a lesson.


Anchor Tasks Demystified

Originally published 2/15/2016

With performance-based standards and 21st-century skill sets teachers are asked to teach mathematics with an emphasis on problems solving and inquiry learning, but how?  The answer is simple, with anchor tasks, of course, BUT HOW?

I have attended several seminars and sessions that have done a great job of explaining what an anchor task is and how using anchor tasks can transform my instruction while meeting the needs of all learners. Few, however, have explained how to implement them into my daily lessons.  I have been told anchor tasks are right there in the materials, but I have yet to come across a section labeled, “Anchor Task.”

In a recent seminar, hosted by Dr. Yeap Ban Har, I finally got the explanation I had been searching for… I had been looking in the wrong place!  Anchor tasks are not found in the Primary Mathematics Teacher’s Guides, but rather in the textbooks.

Dr. Yeap described the evolution of the term on his Facebook page:

Basically, an Anchor Task is the concrete component of any lesson!

How do I find an Anchor Task?

In Primary Mathematics 4A, Lesson 3.6c (Standards Edition) students will learn to interpret the fraction of a set as a whole number times a fraction.  The Teacher’s Guide leads teachers through an effective lesson where the teacher demonstrates how to find 1/3  of 24 using a couple of different methods.

TG - 4A - 3.6c_Page_1


I’ve included links to this same lesson in:


4A Standards TB p100To approach this lesson with more of an emphasis on inquiry learning, look to the textbook.

To create an anchor task, I took the example at the top of the page, find 1/4 of 20, and rewrote it as a word problem.  Students worked in partner groups to solve the following: There are 20 M&Ms in a bag. Three friends each eat  1/4 of the bag of M&Ms.  How many M&Ms did they eat altogether? Students were asked to find multiple ways of solving the problem and were given 20 chips to use if needed. Because our school has several Math Teachers that teach multiple grades, we devised a lesson planning document. (<-Click for a copy if you’d like to use it to plan your lessons)

Planning Sheet 4A - 3.6c Top

As students worked, I circulated around the room and quickly determined which students had mastered how to find  1/4 of 20, which students still needed support with this concept and which students were able to apply that concept to find  3/4 of 20.  Were they in the concrete, representational or abstract phase?

Planning Sheet 4A 3.6c MiddleAfter about five minutes, I gathered the students to share their methods of solving the problem.   This is where my direct instruction came in.  As students shared their strategies, I organized their independent learning into three methods.

I anticipated their strategies in my planning document and during my direct instruction I was sure to include any methods not discovered by my students on their own.

Planning Sheet 4A - 3.6c BottomStudents were then given the task of applying their newly discovered knowledge to solve the problems from the textbook, with my support, if needed.
The lesson ended with a journal prompt that was closely related to the concept learned.

A well-designed anchor task will engage students in the concrete and representational phases of learning a new concept.

Students will make connections with prior knowledge, reason and think logically to apply what they know to solve a problem with a partner or small group.  All students will be given time to work in the concrete phase to develop and hone their conceptual understanding.   As students are ready, they will naturally explore the representational or abstract phases of learning and discover strategies, or methods, for solving the given problem.  Sharing methods also allows students to communicate mathematically to explain and defend their thinking and consolidate their learning.

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Throwback Thursday – Personal Whiteboards

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


Personal Whiteboards

Originally published 3/25/2009

whitebds

In the post about Number Strings, I referred to a student’s “personal whiteboard”.  I use whiteboards throughout the day as a way of informally assessing students.

Instead of a store bought whiteboard, I prefer to provide students with a customized version.

  1. Start with a glossy page protector, a box of which can be purchased inexpensively on eBay or at Sam’s Club or Costco.
  2. Insert a brightly colored sheet of card stock. Cardstock makes the whiteboard a little sturdier and by using color on one side, I can instantly tell when the entire group of students is ready.
  3. Add appropriate pages. In the first grade, I might have a pre-made number bond page ready to go. When I’m teaching a lesson on adding or subtracting, I’ll insert a place value chart.

By keeping a classroom set of these on the shelf with the student textbooks, they would last an entire school year. Here are some printables to get you started:

You can find information on Alexandria Jones’ Pharaoh’s Treasure in the picture at Let’s Play Math.

These are also great for games and learning centers…

Sudoku, Kenken, Contig or

The Hex game:

white-board

Or any of the international logic games on the handouts page of this site.

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Throwback Thursday: Top 10 Tips for Using the Singapore Math® Curriculum

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


Top 10 Tips for Using the Singapore Math® Curriculum

Originally published 9/3/2014

I get LOTS of questions from teachers and administrators with questions about the Singapore Math® program. Recently, several fellow trainers have reached out to seek my advice (Wow!). One asked:

What would you are say the biggest 10 things to consider when using/implementing a Singapore Math curriculum?

Here’s my response. Did I miss anything?

Top 10 Tips for Using the Singapore Math® Curriculum

1. This isn’t the math most of us were raised on. It looks different and teachers cannot rely on their knowledge of themselves as elementary students. As such, the Teacher’s Guide is your math bible. You don’t have to read the lessons out loud as you teach, but you need to follow the sequence and pedagogy.

2. And that pedagogy includes Concrete, Pictorial, AND Abstract. Teachers are usually darned good at the abstract but above grade 2, not so hot with the concrete and pictorial. Yes, I know your students can solve the 3rd-grade word problems without the pictorial bar model, but if you don’t teach the bar model with content they know, you certainly can’t do it with content they don’t know.

3. Placement tests assess content knowledge. Keep in mind that a score below 80% on the Singaporemath.com Placement tests does not mean a student is not bright or capable – it does mean that they haven’t been taught the content yet. The Primary Mathematics materials are generally one year ahead of current U.S. materials and even bright students can’t just skip a year of content and expect to be successful.

4. When teaching Concretely, the SmartBoard is not enough. Students must actually use the manipulatives. Yes, they can work with partners, but students must use them, not just the teacher. Buy or make place value disks for whole numbers and decimals if you want your students to understand the content.

5. The equations are written horizontally to de-emphasize the process (that algorithm you’re so good at!) and focus on Number Sense. These mental math strategies are challenging for teachers as they were usually taught procedures only. Expect to practice the strategies yourself. Embrace the mental math!

6. Textbooks are not a curriculum. The teacher is the most important component of the curriculum. If you don’t understand the math in a lesson, how will the students? Read the Teacher’s Guide and prepare lessons. (See #1 – and below)

7. Get your own copy of the workbooks and work every problem as you expect the students to work them. It’s true that the Teacher’s Guides have the answers. You need the solutions to know if a student’s thought process is on target. In Singapore, 50% of elementary teachers have a 2-year degree – they aren’t math specialists either! The textbooks are designed to help teach teachers the math they need to know. (Same with any placement test you give: you work the problems first.)

8. Follow the maxim: Go slow to go fast. All teachers do not have to be on the exact same lesson at the exact same time. Sometimes you need to slow down and ensure that your students are understanding the content. In grades 2-4 it seems as though it takes f o r e v e r to get through the “A” books. Then applying the skills mastered in the “B” books is a breeze. (In Kindergarten and Grade 1, the “B” book will slow students down. In Grade 5, the books seem more evenly paced) Knowing what your students know and can do means you must be constantly informally assessing your students.

9. Rethink your Home Enjoyment. One big difference between the Singaporean and U.S. cultures is on the emphasis of mastering basic facts. Parents in Singapore believe it’s their job to do this. In the U.S.? Well, it’s the schools’ job. Just as we expect students to read very night to improve their reading fluency, so too should they practice math facts every night to improve fact fluency.

10. This isn’t your parents’ math either! (See #1) Many schools hold a Singapore Math night to introduce the new curriculum to the parents. Share with parents how the curriculum differs from what they’ve seen before, samples of the materials, some strategies, a couple of word problems and you’ll fend off weeks of questions and email.

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Throwback Thursday! Successful implementation: Buying books is just the first step

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


Successful implementation: Buying books is just the first step

Originally published 12/17/2010

Schools considering Singapore Math programs in their schools frequently ask me what the biggest challenges are when adopting the curriculum. Let me give you an example from a third-grade classroom I visited recently.

The math period started with a mad math minute type of activity of either addition or subtraction, depending on where the students were working.  For the lessons on multiplication and division by 8’s and 9’s, the teacher chose to list the tables from 8 x 2 through 9 x 9 on the whiteboard and have the students copy them down, like this:

Next, the teacher had the students make flash cards and quiz each other.  Finally, in a class of 27, they played around the world. The game where two students compete against each other to see who can get the answer to the problem on the flash card faster.

The lesson in the textbook does include some multiplication charts. The textbook was open on the teacher’s desk and she did refer to it at least once during the lesson:

Primary Mathematics 3A Textbook, U.S. Edition:

Notice how the textbook draws out a student’s prior knowledge to show the patterns behind the computation?

The 3A Teacher’s Guide includes a more comprehensive lesson based on a deeper understanding of the number 8 and it’s multiples. I couldn’t find the Teacher’s Guide in the room.

(Click to enlarge)

Can you see the difference in the depth of a student’s understanding after the Primary Mathematics lesson?

Note that the subsequent three lessons are:

  • Multiplying a 2 or 3 digit number by 8.
  • Dividing a 2 or 3 digit number by 8.
  • Word problems that require multiplying and dividing by 8.

The sequence of lessons follows the same pattern for the number 9.

When I asked the teacher about the lesson, she essentially said, “Well, I didn’t think to look at the teacher’s guide. I’ve always taught this way.” She’s new to the school and only had about 2 hours of training.

Back to the original question. One of the biggest challenges for schools adopting the Singapore Math curriculum is the need for adequate training. If teachers don’t understand what makes Singapore different or if they lack content knowledge,  they’ll continue to teach the way they always have. Effective training will give teachers an understanding of Singapore Math’s philosophy and approach and leave them with confidence in their ability to teach it.

Buying the curriculum is the first step. Successful schools invest in content-based training.

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How can I fit it all in?

In 2015, Beth wrote about the Primary Mathematics adoption process at St. Anne’s-Belfield School. Here’s an update on the school’s progress.


stab_logoAs the year winds down and I look back at all that my students have learned this past year, I still feel panicked at what’s left to be covered.  This is the end of a 3-year adoption cycle of Primary Mathematics and while I’ve been able to cover more curriculum than in the previous 2 years, I am still left wondering, “How can I fit it all in?”

In the fall of 2013, we adopted the Primary Mathematics curriculum in Kindergarten through sixth grades.  We knew this would come with its challenges but felt strongly that if we were going to offer our students the “world’s best mathematics curriculum,” then we needed to offer it to all, not just those who made the K, 1, 2 cut.

With this plan, we knew there would be time spent filling in holes in our first year, teaching skills and concepts that the students were missing, and building a solid foundation in number sense and place value.  We accepted the fact that we would not cover all of the curriculum that first year, and worked with Cassy Turner to develop a sequence for each grade level that included teaching critical lessons from prior grade levels.

Year 2Beth with grade 4 student

In the second year, teachers were feeling a sense of relief.  We’d made it through that challenging first year.  We experienced the curriculum from start to finish, well – at least our version of it, and we felt confident.  We weren’t faced with the need to back-teach (as much). Our students entered the year having learned and retained a deeper understanding of those critical math concepts.

With Cassy’s advice, we created a new plan for our second year.  We knew the lessons that had been skipped the previous year and teachers worked together to map out a Kindergarten through sixth-grade sequence that allowed us to get further through the content, and more importantly, accounted for previously omitted lessons.  If we didn’t teach a lesson on geometry to our third graders our first year, we made sure those students would get those lessons in fourth grade our second year.

The year ended, and our standardized test scores showed slight increases in problem solving and algebra readiness, both areas of statistical concern with our previous curriculum.

Year 3

Entering year three, we felt confident in our abilities to deliver lessons.  Along with our students, our staff had developed a deeper, conceptual understanding of math.  We were able to effortlessly explain new concepts, differentiate on the fly, and anticipate misconceptions.  We incorporated anchor tasks, journaling and finally had a grasp on how to effectively use all of the materials.

We entered the year with the goal of teaching the entire curriculum.  Halfway through the year we were teaching material nearly a month ahead of our previous two years and felt really good about it.  Then came…

  • rehearsals for performances
  • grandparents’ day presentations
  • spring field trips…
  • field day…
  • and all sorts of other school commitments.

By April, we had just about lost the scheduling lead that we had enjoyed in December.

So, here I find myself once again faced with the task of choosing one lesson over another and prioritizing the importance of skills and concepts that I may or may not have the time to teach.  Fortunately, the list to choose from is smaller than in the years before. I’ve been able to cover almost all of the material, nearly reaching the goal.

I consider myself lucky to have been in a situation of specializing in math in the lower grades over the past 3 years.  I have been able to experience the strengths of the sequence, which in my mind, is one of the pillars of success of a Singapore Math curriculum.  Going forward, I know it will be easier to thoughtfully prioritize content to eliminate the risk of creating gaps or holes in student learning that could potentially weaken their foundation.

As I leave the school, I look forward to bringing this wealth of knowledge that I gained over the past 3 years to Math Champions and look forward to assisting other schools that are facing the question of, “How can I fit it all in?”

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