Throwback Thursday – “Summer Math” Suggestions to Boost Student Understanding

Over the summer, we thought it would be fun to run some of the most popular posts from the past. All of these options are still on offer. Let us know if you have used one of these or something else to counteract the typical “summer brain drain”.

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!


“Summer Math” Suggestions to Boost Student Understanding

Originally published 6/23/2016

School is out and summer is calling, but for many teachers and administrators, summer is a time to take stock and plan and budget for next year.

As a teacher, this is a glorious time of year, but also one of worry. I worry about my students.  I worry about those who needed extra support throughout the year understanding and retaining math concepts.  How will they fare next school year? Will they regress over the summer months if they don’t do any math work?

There are three categories of students who benefit most from summer math work:

  • Those who have struggled all year and maybe never quite achieved mastery on those critical grade level concepts,
  • those who easily forget concepts, and
  • those whose math confidence could use a boost.

With a Singapore Math program, there aren’t many ready-made options to pick up at the local bookstore.  Books that are available focus heavily on procedural understanding rather than underlying math concepts. So what’s a teacher to do?

Aside from recommending tutoring, I have found a couple of options that seem to meet my needs as a teacher and the needs of my students.

Workbook Work

Primary Mathematics Common Core Extra Prac 3

For those looking for a paper and pencil option, I recommend the Extra Practice books from Singapore Math’s Primary Mathematics series. Students should work at the grade level just completed (a rising 3rd-grade student should do summer work in the 2nd grade Extra Practice book).

The Extra Practice books offer parents and/or tutors “Friendly Notes” at the beginning of each unit that explain how to re-teach concepts in a way that is familiar to the student.  The notes are followed by practice pages that give parents sample problems appropriate for practicing the concepts and the student an option of working through problems independently.  Best of all, they include an answer key in the back so parents can check work and students can re-work problems, if necessary.

These books are written to cover a year’s worth of concepts; I am by no means suggesting that a child complete the entire book over the summer.  Teachers recommending this book will need to tailor the tasks to meet each student’s needs.  This can be as simple as highlighting the contents page to include units or pages that you would like the student to complete over the summer keeping those critical concepts in mind.

Another option for summer work can be found in online programs.  I have come across three online options for concept practice; Primary Math Digital, it’s twin Math Buddies and a program new to the US market, Matholia.

Online Options

Primary_Digital_Coming_Soon_Home_SchoolPrimary Math Digital (Free 15-day trial) and Math Buddies (Also a free trial) are backed by Singapore Math’s Primary Mathematics and Math in Focus series. Both offer students video tutorials that can be viewed by the student (and parent) an unlimited number of times.  These videos are scaffolded to follow the pictorial and abstract progression of learning.

Teachers can assign videos, practice and assessment tasks fMath Buddiesor students to complete over the summer at their own pace.  The practice pages can be a little challenging to navigate, but with some initial guidance, students should be able to complete the tasks independently.

Both programs require the school to purchase annual student and/or teacher accounts to gain access to the library of lessons. There are Homeschool accounts available. Expect a price tag of around $30 per student depending on the number of accounts purchased.

matholia logoAnother, more affordable option new to the US market is Matholia. Matholia was developed by two teachers from Singapore and has been used by teachers and students in Singapore as well as several other countries. This program also includes a library of video tutorials, practice and assessment tasks as well as fact fluency tasks and games.

The videos are easy to understand and are also strategically scaffolded for student understanding. The practice and assessment tasks are intuitive and easy for students to navigate. As with the other programs, teachers can assign tasks for students to complete over the summer.

Matholia also requires the school to purchase annual student accounts (teacher accounts are free) but is much more affordable at just $8 per student.

Don’t forget the concrete…

I can’t go without saying that any of these options will give students practice, but struggling students need more than just extra practice working through math problems.  They need more time in the concrete phase of learning using manipulatives; base-ten blocks, place value chips, model building with connecting cubes or paper strips, fraction strips or circles, etc.  So, please, consider not only sending these students home with books and login IDs but also with a bag of manipulatives for hands-on learning and practice.

Beach_of_Dreams_BeautifulNow…back to dreams of lazy mornings and time to relax and recharge.  Have a great summer and rest assured that your students will be prepared for the next grade with a little summer math work.

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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 – On the Topic of Math Sprints and Anxiety

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!


On the Topic of Math Sprints and Anxiety

Originally published 4/30/15

Reflecting on my time at the two national math educator’s meetings, one interesting dichotomy appeared over timed fact tests. On the one side was Jo Boaler stating that timed tests are the root of math anxiety. Pushback came from others, most notably Greg Tang and Scott Baldridge pointing out that kids are timed in real life. They are put under pressure in real life. Students should learn from these experiences, not freak out over them.

It’s a powerful discussion: How do we get kids from fluency (I can use strategies to solve 7 x 8) to automaticity (I just know 7 x 8)? Do we need to get them to automaticity? Do timed tests create math anxiety? Is there spelling test anxiety? Should the key anxiety word be “test”, not “math”?

This conversation appeared recently on twitter after someone posted the “How to Give a Math Sprint” pdf from this site:


Yep, I’d be worried if kids who couldn’t make connections were timed, too.

I’m a proponent of Math Sprints; thoughtfully structured timed tests designed to practice one skill. Sprints are not your typical timed test. Students compete against themselves to improve the number of problems completed in one minute. Then the sprints are thrown away, not recorded in a grade book. They are practice. Period. And just one way to practice math facts.

Do Sprints harm students or cause math anxiety?

Not when administered correctly. I work with a school for students with ADHD and learning disabilities. Initially, teachers there said things like, “I can’t time my kids, they are slow processors”. It turns out that students at this school LOVE sprints. They can always improve by at least one problem on the second sprint. With all the content flying at them, practicing facts is one thing they can do and feel successful with.

Allison Coates runs the non-profit Math Walk Institute that works with schools and students to build a bridge to Algebra.

In every school we’ve ever worked, nearly all students enjoy sprints. They don’t see them as tests if the teacher doesn’t present them as tests. They see them as another fun game they can play against themselves (or against the teacher). Practice makes permanent their knowledge, and students love knowing they have knowledge. Knowledge is power.

Are Sprints from Singapore?

Nope. Sprints were created by Dr. Yoram Sagher as a fluency program to work with any curriculum. I’ve considered them a way to compensate for differences between Singapore and the U.S. In Singapore, parents drill fact fluency while schools teach the conceptual understanding. It’s not unusual for a first grader in Singapore to know all their math facts. It’s the school’s job to then get the understanding of multiplication into such a student. Contrast that with the U.S., where it is less likely that parents practice math facts at home with their child. Few American programs include a fluency component, often farming it out to the web or an iPad app.

Scott Baldridge has a great blog post on sprints: Fluency without Equivocation. I suggest you read it now.

My favorite Sprint books are Differentiated Math Sprints as they offer two difficulty levels with the same answers.

Eureka Math Sprints are aligned to Eureka Math (referenced in Scott Baldridge’s post above).

Wondering about the emphasis on math facts? Read: Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores

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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: If I had a million dollars, ok $1000…

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!

I updated the cost of the materials to current 2017 prices (in bold) for the US Edition of Primary Mathematics, which are higher but include shipping on orders over $50. That puts us over the original $1000 threshold, but not bad…

For students that struggle, I would now recommend a recently published series: Visible Thinking in Mathematics with A & B titles at most grade levels that run from $12.80 to $14 each.


If I had a million dollars, ok $1000…

Originally published 6/20/2013

Recently, I received a question from an excited teacher who had just received a grant to spend on her classroom: “If you had a $1000 dollar grant and taught second grade, what would be the most important pieces of Singapore Math you’d buy?”

If I had a million dollars, ok $1000… here are two scenarios.

#1 Using the curriculum in 2nd grade as your main curriculum

  1. A classroom set of the 1B & 2A textbooks @ $9.00 each, so if you had 24 students + 1 for teacher: 25 x $18 = $450     ($735)
  2. Possibly a set of the 2B textbooks: 25 x $9 = $225     ($367.50)
  3. A Teacher Manual for 1B, 2A & 2B: 3 x $21 = $63     ($88.50)
  4. A workbook for reference and problem ideas for 1B, 2A & 2B = 3 x $9 = $27     ($44.10)
  5. Challenging Word problems level 1 & 2: 2 x $8.50 = $17.00     ($29.40)
  6. Intensive Practice: 1B, 2A & 2B: 3 x $8.80 = $26.40     ($38.40)
  7. Process Skills in Problem Solving L2: $10.70     ($12.80) 
  8. Math Sprints Masters, Levels 1 & 2: 2 x $31 =$62     ($68)
  9. Elementary Mathematics for Teachers by Parker & Baldridge: $29     ($33)
  10. Place Value Strips: $12.50     ( $13.95)

That’s $625.80 (Currently: $1430.65 including shipping)

I’d spend the rest on linking cubes, base-10 blocks, place value disks or other manipulatives and containers to keep them organized.

Keep in mind that for Number Disks/Place Value Disks you’ll need about 20 each of ones, tens and hundreds disks per student or pair of students sharing. Many companies sell these:

Place Value Disks, 100 Ones DisksPlace Value Disks, 100 Ones Disks

Place Value Disks - 100 Tens DisksPlace Value Disks – 100 Tens Disks

Place Value Disks (1-3): HundredsPlace Value Disks – 100 Hundreds Disks

#2 Using Singapore Math to Supplement another core curriculum:

  1. Start a library at your school with one set of the textbooks and workbooks for every grade level at the school as reference (4 per grade level)  x $9.00 each book – k-6 would be $36 x 7, k-5 would be $36 x 6    ($14.70 x 4 per grade level for grades 1 – 4  and $15 x 4 for grades 5 and 6)
  2. A Teacher Manual for each level:  $21 each book, 2 books per grade level = $42 per grade level     ($24.50 – $31.50 each)
  3. Challenging Word problems are $11 each and there are 6 levels (1-6)    ($14.80 and $15.20)
  4. Process Skills in Problem Solving vary in cost from $10.20 to $12.80 – levels 1-6   ($12.80 – $14.80)
  5. SpeedMaths Level 1 – 4: $8.20 each (no higher than level 4!) ($12.80)
  6. Math Sprints Masters, Levels 1 -5: 5 x $31    ($34)
  7. Elementary Mathematics for Teachers by Parker & Baldridge: $29 several copies for staff ($33)
  8. The Singapore Model Method for Learning Mathematics: $29 for grades 5 & up ($32)
  9. Teaching of Whole Numbers by Dr Yeap Ban Har, Singapore’s renowned math educator, $30.50     ($32)
  10. Bar Modeling A Problem-solving Tool also by by Dr Yeap Ban Har, for lower elementary. $30.50     ($32)
  11. Place Value Disks: get plenty of ones, tens and hundreds. $15.95 per 100 disks     ($7.95 per 100 disks)
  12. Place Value Strips: $12.50 and other manipulatives (if you don’t already have them on campus).    ($13.95)

What did I miss? Are there any books or tools that you consider “must-haves” in your Singapore Math classroom?

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