Ask the Experts: What’s the best way to organize my math manipulatives?

The answer to this question is complicated. So much of how to organize materials is dependent upon personal preference with procedures and arrangement within your classroom. One thing that I can say is true in all cases is that they DO NOT belong in the closet!

I highly recommend that you dedicate a shelf or area of your classroom to math materials. It’s equally important for students to choose the most appropriate tool, as it is for them to use them. Having materials out for students at all times will allow for that.

One of the joys of my job is that I get to visit schools and classrooms across the country. So, I will share with you some organizational tips that I have gathered from my journeys.

There are three schools of thought (no pun intended) when it comes to organizing manipulatives; individual kits, group kits or community tubs. You may find it helpful to use a combination of the three, depending on the item.

I’ll mention a couple of manipulatives specifically here.

Place Value Discs

Student Kits

Many teachers prefer to organize discs into student kits. The idea being that students will have easy access to the discs for lessons with minimal time getting discs out and cleaning them up.

This option works great if you have enough discs for each student to have 20 of each place value; 20 ones, 20 tens, 20 hundreds, etc. Students are expected to keep these baggies or boxes of discs in their desks.

Pros: Easy access

Cons: Relies on students to maintain the correct number of discs in their kits. (I was that teacher who couldn’t stand the fact that there was one ten disc on the floor at the end of the lesson that seemed to belong to no one!)

Group Kits

Like student kits, you’ll need 20 of each place value in each kit. With group kits, you don’t need as many total discs. The idea here is that students will use discs with a partner or in small groups. These kits can be stored in a community tub and pulled out for use during lessons.

Pros: Easy access

Cons: See above. (Which kit does this disc belong to?!?)

Community Tubs

In this case, discs are organized by place value into tubs. So, you would have a tub of ones, a tub of tens, and so on. In each tub, you can keep a set of small cups (Dixie cups work well) for students to take a scoop of the discs when needed. Clean up is a snap. Students simply dump the cups of discs back into the correct place value tub.

Pros: No more mystery missing discs! Very quick set up. (No more evenings spent counting out discs while watching TV.)

Cons: Requires a bit more practice with the procedure of gathering and returning discs to the correct tub.

Linking Cubes

Linking cubes are a multi-functional manipulative that each classroom should have. For a class of about 20 students, you’ll want to have at least 400 individual cubes. That’s enough for each student to have a set of 20 when needed for instruction. If you’re using them for modeling area or multiplication arrays, you might want double that amount.

Student Kits or Group Kits

You’ll want to put at least 20 in each kit.

Pros: Ease of access.

Cons: Whose cube is this?!?

Community Tubs

If you are keeping your cubes in tubs, for ease of passing out and cleaning up, organize them in rods of 10, preferably by color. That way you can quickly pass out 2 rods (or more) to each student or partner group.

Pros: Fewer materials in student desks. No more mystery cubes.

Cons: Need to establish procedures for keeping cubes in rods of ten. (Easy, peasy!)

 

Other manipulatives should be in tubs on a shelf in the classroom available to all students at all times!

If you have any organizational tips from your classroom that you’d like to share, please send us a comment.

 

 

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Events Recap – Jumpstart your Singapore Math® 2018

We were thrilled to welcome teachers, coaches, specialists and administrators from 18 states to our Jumpstart your Singapore Math® Instruction workshops this summer.

We are so very grateful that you took time from your summer to join us….And we are delighted that you found it valuable!

Scenes from Jumpstart 2018

What Attendees said about Jumpstart 2018

I have been in education for over a decade, and this has been one of the most engaging, practical, and meaningful Professional Development opportunities of my career. Thank you to these amazingly bright and helpful experts!

-Keith Grifffin, 1st and 2nd grade Math Specialist, City Academy School, St. Louis, MO

As an administrator, this training was invaluable to my understanding of the Singapore approach to teaching math!

-Melanie Stivers, 5-8 Principal, Springfield Christian School, Springfield, IL

This is the best training I’ve been to. Every minute was enjoyable and educational. I feel better going into the school year and am excited to teach the Singapore way. It was life changing and mind blowing!

-Jen Irish, 3rd Grade Teacher, Terra Academy, Vernal UT
There were so many things I was unsure how to teach in Singapore Math. Cassy and Beth explained the elements in layman’s terms so I could understand the material myself, then showed us, from a student’s perspective, how to solve the problems with a logical approach. The biggest difference between this training and others was, I didn’t feel like I had to be a Math expert to teach the curriculum.

-Penny Hagerman, Interventionist, 3-5, Vanguard Classical School West, Aurora, CO

Truly appreciated the lesson planning information. The teacher’s guide does not have enough information to assist teachers with teaching strategies. I feel I can teach better and help my students better understand and build on the concepts. Awesome Class!

-Cheryl Kenney, 1st Grade Teacher, Augustine Christian, Tulsa, OK

Thanks to Jumpstart 2018 Hosts

Clayborne Education – Charlottesville, VA
Augustine Christian Academy – Tulsa, OK
Liberty Common School – Fort Collins, CO
Mounds Park Academy – Saint Paul, MN

We will announce details regarding 2019 Workshops soon. If you would like to receive notice of upcoming workshops and are not already on our email list, please complete our Training Needs Survey or give us a call.

 

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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…

Linking Cubes

Find linking cubes here.

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!

What questions do you have?

Next: Ideas for organizing manipulatives.
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Word Problem Wednesday – Jason and Louis

This month’s Word Problem Wednesday problem comes from Primary Mathematics Challenging Word Problems 3.

Jason and Louis picked up a total of 30 cans. For every 2 cans that Jason picked up, Louis picked up 3 cans. How many cans did each boy pick up?

Submit your solutions by the end of the month!


Last month’s problem was from Dimensions Math 6A:

 

Here’s a solution from Reader Shirley Davis:

How did you do?

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Word Problem Wednesday – Laiza’s Dress

This month’s problem comes from Dimensions Math 6A and highlights the unitary method of solving problems:

Laiza spent 38% of her money on a dress and the rest on a purse. If she spent $114 on the dress, how much did she spend on the purse?

Submit your solutions by the end of the month!

 


Last month’s problem was from the website TestPapersFree.com, which provides past copies of continual and semestral assessments from Singapore Primary Schools. This is a great resource if you’re looking to see questions directly from Singapore classrooms. The problem is from Raffles Girls School,  Grade 4, and is a Semester 2 assessment, which is the final term of the year.

Pei Ling had 3 times as many cards Zandy. Sulaiman had half the number of cards Zandy had. There were a total of 1278 cards.
How many more cards did Pei Ling have than Zandy?

Here’s a solution from Reader Shirley Davis:

 

 

 

 

 

 

 

How did you do?

 

 

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Word Problem Wednesday – Pei Ling, Zandy, and Sulaiman

This month’s problem comes from the website TestPapersFree.com, which provides past copies of continual and semestral assessments from Singapore Primary Schools. This is a great resource if you’re looking to see questions directly from Singapore classrooms. This problem is from Raffles Girls School,  Grade 4, and is a Semester 2 assessment, which is the final term of the year.

Pei Ling had 3 times as many cards Zandy.
Sulaiman had half the number of cards Zandy had.
There were a total of 1278 cards.
How many more cards did Pei Ling have than Zandy?

Submit your solutions by the end of the month!


The prior problem was from the Grade 6 STAAR 2013-2017 Released Test questions from lead4ward aligned to the Texas Essential Knowledge and Skills or TEKS.

There are 176 slices of bread in 8 loaves. If there are the same number of slices in each loaf, how many slices of bread are there in 5 loaves?

 

How did you do?

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Word Problem Wednesday – Rulers and Bread

Word Problem Wednesday was such a hit, we’re going to continue throughout the year with one problem a month.

This problem popped up in my Medium feed last month:

Algebraic expressions — the return! Guess the Misconception author Craig Barton noted that on a quiz website for test prep in the UK,  only 1 in 3 students could answer this problem correctly. At the time, I was also analyzing the value of model drawing by reviewing released problems from the 6th-grade STAAR tests, so my first thought was, hmm, how would this work as a bar model?

Pretty well, actually. If I know that:

I can find:

The AQA is an independent education charity that offers GCSE testing in the UK. DiagnosticQuestions.com provides multiple choice questions so you can build your own assessment, or use one of their collections.

Check out a bar model solution:

 

Finally, this month’s problem comes from the Grade 6 STAAR 2013-2017 Released Test questions from lead4ward aligned to the Texas Essential Knowledge and Skills or TEKS. It aligns to the standard:

6.4(B) (New) Proportional Reasoning: Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates.

There are 176 slices of bread in 8 loaves. If there are the same number of slices in each loaf, how many slices of bread are there in 5 loaves?

Submit your solutions by the end of the month!


The prior problem was from the Teacher’s Guide for Primary Mathematics US Edition 5A.

We had a couple of submissions.

Here’s Shirley Davis’ model and algebra combo:

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Word Problem Wednesday – Alice, Betty, & Cassie

Word Problem Wednesday was such a hit, we’re going to continue throughout the year with one problem a month.

Our problem this month comes courtesy of a 5th grade teacher who was excited that for the first time, her students understood and easily modeled this problem from the Teacher’s Guide for Primary Mathematics US Edition 5A.

Alice, Betty, and Cassie have $70 altogether. The ratio of Alice’s money to Betty’s money is 1 : 3. Cassie has $10 more than Alice. What is the ratio of Alice’s money to Betty’s money to Cassie’s money?

Submit your solutions by the end of the month!


The last problem was taken from the Dimensions Math 3A Textbook. (Click to learn more about this recently released curriculum):

Shirley Davis shared her algebraic bar model solution:

 

How did you do?

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Word Problem Wednesday – Pinecones

Word Problem Wednesday was such a hit, we’re going to continue throughout the year with one problem a month.

Singapore Math, Inc. will be releasing a new series April 25 at the National Council of Teachers of Mathematics Annual Conference. This problem comes from a chapter on two-step word problems from 3A

Mei and Dion together made 11 turtles. Mei made 3 more turtles than Dion.
How many turtles did Mei make?

Submit your solutions and we’ll post all interesting solutions.


The last problem was taken from Noetic Learning’s problem of the week Sign up to receive their weekly problems.

Robin’s age is 3 times Marcia’s age. Anna is twice as old as Marcia. The sum of their ages is 30. How old is Marcia?

Shirley Davis shared her algebraic bar model solution:

 

How did you do?

 

 

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Come see us at NCEA and NCTM

Spring educators’ conference season is upon us and we are thrilled by several opportunities to speak at upcoming events.  The descriptions below are from conference programs.

NCEA 2018 Convention & Expo (April 3 – 5 at the Duke Energy Convention Center in Cincinnati, OH) is the largest private-education association gathering in the nation!

Strip Models, Tape Diagrams, Bar Models, Oh My!
Presenters: Cassy Turner and Beth Curran
Date: Tuesday, April 3, 2018
Time: 1:30 PM – 2:45 PM
Room: 251

Improving students’ problem-solving abilities is a major focus of mathematics education. Model drawing is a powerful tool that students can use to attack complex problems. In this hands-on, minds ­on session, presenters will investigate methods of teaching and assessing tape diagrams for those persnickety word problems, and explore interactive model drawing technology. Walk away with strategies for guiding student learning that you can use tomorrow!

Using Mental Math Strategies to Deepen Number Sense
Presenters: Beth Curran and Cassy Turner
Date: Thursday, April 5, 2018
Time: 11:15 AM – 12:30 PM
Room: 251

Number sense = mental math. Participants will actively explore mental math strategies used throughout the elementary grades. Engaging in mental math activities allows students to develop a relational understanding of numbers and their magnitude. Students begin to see numbers as being made up of parts and develop an understanding of how numbers can be composed and decomposed for mental calculations. Discourse around mental math allows students to expand their toolbox of strategies for solving problems and to evaluate strategies and answers for efficiency and reasonableness.

NCTM Annual Meeting and Exposition 2018 (April 25 – 28 at the Walter E. Washington Convention Center in Washington, D.C.) is the premier math education event of the year!

Do Not Invert and Multiply! Building the Bridge to Algebra Through Fractions Tasks
Date:  Friday, April 27, 2018
Time:  1:30 PM – 2:30 PM
Room:  159 AB

Join Cassy Turner, Beth Curran, and Allison Coates as they work through hands-on tasks for fractions. We’ll investigate how the progression of fractions problems helps students build mastery of algebraic concepts such as naming unknown quantities, writing expressions, and laying the foundation for solving for x.

Using Anchor Tasks to Engage Learners: Deepening Understanding through Exploration and Discourse
Date:  Saturday, April 28, 2018
Time:  8:00 AM – 9:00 AM
Room:  146 B

Participants will engage in active math lessons and learn how to use learning objectives to create anchor tasks that spark student interest and allow students of all levels to build on prior knowledge, explore concepts with concrete materials and engage in productive discourse to deepen conceptual understanding with a focus on problem-solving. Cassy Turner and Beth Curran will lead this interactive workshop

Beginning Bar Model Boot Camp: Getting Started with Model Drawing
Date:  Saturday, April 28, 2018
Time:  9:45 AM – 11:00 AM
Room: 144 ABC

Improving students’ problem-solving abilities is a major objective of Common Core and state standards, and model drawing is a powerful tool that students can use to attack complex problems. Join Cassy Turner and Beth Curran to investigate methods of teaching and assessing tape diagrams for those persnickety word problems, and explore interactive model drawing technology.

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