This month’s Word Problem Wednesday problem comes from Math in Focus Grade 3.

**Farmer Fred makes 4 quarts of orange juice on Monday. He makes 2 quarts more orange juice on Tuesday than on Monday. He makes 2 more quarts on Wednesday than on Tuesday. He carries on making 2 more quarts of orange juice every day than the day before. In how many days will he make a total of 80 pints of orange juice?**

Submit your solutions by the end of the month!

Last month’s problem was from Primary Mathematics Challenging Word Problems 3:

How did you do?

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]]>Math Champions is happy to be returning to Palm Springs on November 2nd and 3rd to work with educators from Southern California. Cassy and Beth will be presenting three sessions this year, supporting the theme of Mathematical Journeys to Empower All Students.

Join us on Friday at 1:30 pm for **Ready, Set, Play!: Practicing Number Sense with Games**. Engage in tried-and-true math games that support the development of number sense and place value. Leave with ideas and materials to take right back and use immediately in your classrooms.

Continue your learning on Saturday at 8:30 am with **Navigating Word Problems with Models**. We’ll investigate methods of teaching and assessing tape diagrams for those persnickety word problems with hands-on materials. We’ll look at strategies to introduce model drawing to both beginning and struggling learners.

Come back again on Saturday at 10:30 am for **Using Mental Math Strategies to Deepen Number Sense**. Learn what we mean by mental math, explore strategies, and experience how to practice mental math in your classrooms. Having a deep sense of number will empower and build confidence in your learners.

Not registered? No problem! Registration is currently open.

Attend one of our sessions and identify yourself as a blog follower to receive a gift of thanks. We hope to see you there!

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]]>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.

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!)

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?!?)

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 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.

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

Pros: Ease of access.

Cons: Whose cube is this?!?

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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]]>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!

*-Keith Grifffin, 1 ^{st} and 2^{nd} 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*!*

*-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!*

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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]]>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…

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.

1^{st} – 2^{nd} 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.

3^{rd} 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.

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

Find Base Ten Blocks here and Place Value Discs here.

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

2^{nd} 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.

Cut them from paper found in the recycle bin.

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

2^{nd} 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.

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!

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

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

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.

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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]]>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.

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.

How did you do?

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]]>*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.

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 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.

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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