## Ask the Experts: What manipulatives do you suggest for my grade level?

Singapore Mathematics instruction – or, really, just good math instruction – will have students working through three phases of learning, referred to as the Concrete-Pictorial-Abstract approach. In order to teach following this approach, you need to start at the concrete level. Jean Piaget, a Swiss psychologist, believed that in order for students to be able to visualize and abstract mathematics they first must manipulate materials. He called this the concrete operational phase of learning.

So, what do you need to teach concretely? A complete list of recommended materials by grade level can be found here.

Really, though, with a few basic items you can get started…

Kindergarten – used for counting with one-to-one correspondence, measuring with non-standard units, and for modeling basic addition and subtraction situations.

1st – 2nd grade – used for place value understanding, to model story problems and mental math strategies, for measurement with non-standard units, building array models for multiplication, and for beginning bar modeling.

3rd grade – used to model part-whole and comparison word problems involving addition, subtraction, multiplication, and division, for building array models for multiplication and division, and for modeling area.

4th grade and up – used to model word problems for multiplication, division, and ratio, and to model area and volume.

### Base-Ten Blocks and Place Value Discs

Find Base Ten Blocks here and Place Value Discs here.

1st grade – Base-Ten Blocks are used to model place value for numbers to 100

2nd grade and up – Place Value Discs are used as a more abstract (and manageable) model for place value understanding for numbers from thousandths to millions, and for modeling and developing a conceptual understanding of the four standard algorithms. Base-Ten blocks can continue to be used for those students needing a one-to-one representation.

### Paper Strips and Squares of Equal Size

Cut them from paper found in the recycle bin.

1st and 2nd grade – used to model fractions of a whole.

2nd grade and up – used to model the four operations of fractions with the same size whole and for modeling part-whole and comparison word problems.

### Number Cards (Playing Cards) and Dice

Find number cards on our resources page or pick up some playing cards at your local dollar store. Dice can be found here.

All grades – for playing games and making math fun!

Get creative and have fun building your inventory of math manipulatives!

Share:

## Announcing: Jumpstart Your Singapore Math® Instruction Workshops for 2018!

Back by popular demand!

We are pleased to announce the return of Jumpstart, an intensive, two-day workshop for current and potential users of Primary Math and Math in Focus, as well as any teacher interested in incorporating these techniques into their own classroom, regardless of current curriculum. If you are:

• new to the Singapore approach to math instruction…
• needing a refresher to boost your math teaching skills…
• wanting to incorporate the best practices from Singapore into your current curriculum…or
• curious about the reasons for Singapore’s remarkable success…

…then this workshop is for you!

Click here to get all of the details on this exciting program!

#### Location and dates currently available:

Tulsa, OK | July 23 – 24, 2018:

Fort Collins, CO | July 26 – 27, 2018:

Minneapolis-St. Paul, MN | July 30-31, 2018

Do you want to be notified when a Jumpstart Your Singapore Math Instruction is scheduled near you? Fill out the form below:

Share:

## 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

Share:

## 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.

Share:

## Event Recap: Jumpstart Your Singapore Math Instruction

[Several teachers from Minnehaha Academy in Minneapolis attended Jumpstart. We are stunned and saddened by the news of the explosion at Minnehaha’s Upper School and our thoughts are with the Minnehaha community and families of the victims.]

Beth Curran and I had wonderful time hosting Jumpstart Your Singapore Math Instruction, our recent two-day workshop (and first self-produced event) in Saint Paul, Minnesota.

Our goal: to offer an intensive learning opportunity covering all the essential elements of Singapore’s highly-acclaimed math program, including strategies, number sense, model drawing, and curriculum.

We were thrilled to be surrounded by such an enthusiastic group of co-learners, including teachers from many of the region’s finest schools and some from as far away as California.

What did teachers say about their experience?

I couldn’t imagine teaching this year without this class. It was amazing!

-Joanne Pilon, 6-8 Math, Holy Family Academy

Wonderful experience! Amazing! Thank You!!!

-Sarah Gerlach, 2nd Grade Teacher, St. Raphael Catholic School

OUTSTANDING!! After all of our training, it’s all making sense now. I LOVE IT!!

-Kim Schafer, 4th Grade, Breck School

Amazing and informative CEU that I can apply instantly to my teaching practices.

-Sharleen Blanco, Kindergarten Teacher, Excell Academy

Very informative, fun, and safe space to learn about and practice Singapore Math. Thank you!