Structuring the Math Day

One of the questions I get most often is:

How do I use the materials with my Singapore Math curriculum and fit it all into an hour math block?

First off, kudos to your school for setting aside an hour math block for your youngest learners! Through math instruction, students will gain the skills and thought processes necessary to solve problems. Math needs to be given a priority in the schedule. Following is one of my favorite quotes from Dr. Yeap Ban Har, author, and contributor to several Singapore Math style curriculum.

“We are not teaching math. We are teaching thinking through the medium of math.”

What should I include in my lessons?
  • Ongoing cumulative review
  • Direct instruction
  • Guided practice
  • Independent practice
How much time should I spend on each component?

10 minutes – Ongoing Cumulative Review
20 minutes – Direct Instruction
30 minutes – Guided and Independent Practice

What does each component consist of?
Ongoing Cumulative Review (10 minutes)

According to Steven Leinwand, in his book Accessible Mathematics: 10 Instructional Shifts that Raise Student Achievement, in every classroom there should be signs of: 

A deliberate and carefully planned reliance on ongoing, cumulative review of key skills and concepts.

As you teach concepts, you will want to include them in your ongoing cumulative review. With such an emphasis on mental math strategies and the development of number sense, mental math should play a major role in your daily review.

Mental Math can be practiced through the use of:

Direct Instruction (20 minutes)

  • Teacher directed (follow the plan in the Teacher’s Guide)
  • Through student exploration (also known as, an Anchor Task)

Guided Practice (30 minutes combined with Independent Practice)

  • Textbook problems can be worked:
    • Whole group answering problems on individual whiteboards,
    • With partners working through problems together, or
    • Individually

Independent Practice (30 minutes combined with Guided Practice)

  • Workbook problems
    • As home enjoyment
    • As classwork
  • Fluency practice

Comment below with your questions or concerns about structuring your math day!

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Throwback Thursday – Direct from the classroom: Challenges & Successes with Singapore Math implementations

For our final post this summer, we thought it would be interesting to look at other challenges schools face in their adoptions. 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!


Direct from the classroom: Challenges & Successes with Singapore Math implementations

Originally published 12/1/2012

Some teacher challenges & successes with Singapore math one year or three months after adopting the program are below. Click to see larger images.

During follow-up in-services, I like to have teachers meet in grade level groups and spend time discussing the challenges and successes they have had thus far with their teaching of Singapore Math. Each grade level is then asked to list these challenges and successes on a poster and share with the group as a whole. This allows us time to compare and share lessons from the content fresh on their minds.

There is so much challenge the first year when implementing a new curriculum, it’s helpful to take a few moments to reflect on how many successes the teachers and students have had. These posters then guide subsequent teacher learning as we focus on the concepts that they are finding challenging.

 

 

 

 

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Throwback Thursday – Bar Model Solutions – by Students

Over the summer, we thought it would be fun to run some of the most popular posts from the past. It’s always interesting to see how students’ minds work. 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!


Bar Model Solutions – by Students!

Originally published 4/12/2016

After the post on Assessing Bar Model Solutions went up, Beth Curran sent a message: “We just did that problem!” She agreed to share some student work:


boys and girls 2

boys and girls 3

boys and girls 5

And when the students didn’t draw a model:

boys and girls 4

I see this as a comparison problem:

thinking blocks

5 units -> 125 students
1 unit -> 125 ÷ 5 = 25
7 units for boys -> 7 x 25 = 175 boys in all

(That’s the Thinking Blocks Model Drawing tool that allows you to insert your own word problems and solve – or you can use the pre-made questions!)

 

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Throwback Thursday – It can’t all be Singapore Math…

Over the summer, we thought it would be fun to run some of the most popular posts from the past. Here’s a look at some misconceptions around Singapore Math and Common Core Standards. 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!


It can’t all be Singapore Math…

Originally published 12/29/2014

This tweet posted by the National Council on Teacher Quality (@NCTQ) caught my eye:

NCTQ_Tweet

Now, I’ve heard decomposing called “branching” but can’t remember ever seeing this in a Singapore textbook. Where did this problem come from?

It’s nice that NCTQ recognizes Singapore’s Math as “tops in the world.” But it’s discouraging to see methods and terminology that are not a part of the Singapore curriculum attributed to it. Especially in the context of the nasty debate about CCSS. And especially since Singapore’s math curriculum–with its rigor, coherence, and focus–is often cited as a basis for more rigorous standards, including CCSS.

The problem posted is based on the concept of “Number Bonds,” which calls for students to decompose numbers (this is the term used in Singapore and in all major Singapore Math® textbooks distributed in the U.S.). Below, I’ve posted some examples of how this concept is presented in Singapore Math® series available in both the U.S. and Singapore.

This matter points to my BIG concern: As publishers and others adapt Singapore’s Math for the American market, new approaches creep in. These often are not based on the curriculum that helped Singapore’s students go from mediocre to best in the world in a dozen years. I’ve written about this in my comparison of Singapore math textbook series available in the United States.

So my plea to NCTQ: please use examples from an actual Singapore mathematics text when citing the components that make it so successful. And feel free to ask if I can help you find those examples.

Number Bonds problems in Singapore Math® textbooks

Here are some materials covering Number Bonds and “decomposing” numbers from actual Singapore textbooks:

From My Pals are Here, the most-used materials in Singapore:

MPAH 3A Mental Addition

From the U.S. Edition of Primary Mathematics, available in North America since 2003:

PM US 3A Mental Addition

From the Common Core Edition of Primary Mathematics, released in the U.S. market in 2014:

PM CC 3A Mental Addition_0001

And finally, from Math in Focus:

MiF_3a_mental_math

 

UPDATE:

Ugh! One more similar tweet from NCTQ.

NCTQ_tweet_#2

 

 

 

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Throwback Thursday – Journaling in the Singapore Math Classroom

Over the summer, we thought it would be fun to run some of the most popular posts from the past. Journaling in math class has become quite popular. We’d love to hear your successes or challenges with math journals!


Journaling in the Singapore Math Classroom

Originally published 10/13/2016

Communicating mathematically is a critical skill and goal for all of our students to reach by the end of middle school. In fact, Common Core Standards for Mathematical Practices, MP3, states that students will, “Construct viable arguments and critique the reasoning of other.”

Singapore’s Ministry of Education would tell you that there’s nothing Singaporean about Singapore math.  When developing their highly successful math curriculum, they took theory and ideas from mathematicians and educational theorists around the world and put them into action.

What should a math journal look like?

I have attended many workshops and make-and-take sessions on planning and preparing for student math journals.  Many have focused on setting up the student journal with a contents page and tabs to divide the journal into “notes,” “vocabulary” and “practice problem” sections.  While this will create a journal that looks really nice, what I have found to be most effective (and one that I actually use in the classroom) is taking a simple composition or spiral bound notebook and beginning on the first page.  Students make their first journal entry of the school year on page one and continue with entries on subsequent pages. Less is more!

Here’s what a journal entry page might look like:

journal-photo

The journal entry number just grows as the year progresses.  We might come up with the title as a class, or students can create their own.  The problem in the problem box can be copied by students or printed out for students to paste in their journals.

What should students put into journals?

There are four basic types of journal entries; investigative, descriptive, evaluative and creative.

Investigative: Students explore a new concept, solve a problem and make connections to prior learning.

  • Example: Three friends share a sleeve of cookies.  Each sleeve holds 32 cookies.  If each friend eats ¼ of the sleeve, how many cookies do they eat altogether?

Descriptive: Students describe or explain a concept or mathematical vocabulary.

  • Example: Use pictures, numbers and/or words to explain a polygon.

Evaluative: Students argue for or against a strategy or solution to explain why they think an answer is right or wrong, explain their choice of strategies or justify the most efficient strategy.

  • Example: Which of the strategies discussed in class today would you use to solve 245 – 97?  Why?

Creative: Students write their own word problem or create their own number puzzle.

  • Example:  The answer is 465 lbs.  What’s the question?

Here’s a sample student  journal page (click on image to enlarge):

scan0018

When should I ask students to make journal entries?

Journaling can be a very effective tool to develop communication skills in your students.  Depending on the type of entry, you could incorporate journaling into many parts of your math day.  Open a class with an investigative entry to engage students.  Consolidate learning and reflect on thinking with a mid-lesson descriptive or evaluative entry.  Enrich students with a creative entry for early finishers of independent practice.

The benefit of journaling for the teacher is it provides a concrete formative assessment.  By evaluating student responses, you can determine their readiness to handle a new task and check for understanding of concepts.  Student journals also provide a great launching point for discussion at parent-teacher conferences.

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Check out a resource from a previous post: Singapore Math and Math Journal Writing

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