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?

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?

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:

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?

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

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.

Shirley Davis shared her algebraic bar model solution:

How did you do?

**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.

*Originally published February 16, 2017*

For many, Spring brings with it those two dreaded words: **standardized** **tests**.

Whether your school is required to take PARCC, Smarter Balanced, state mandated standards-based tests or ERBs, you inevitably will want to make sure your students are prepared. Many teachers will plan to block out two to three weeks prior to the testing dates to review and teach content that may not have been covered, but is this interruption to instruction necessary?

It’s estimated that students and teachers lose an average of 24 hours of instructional time each year administering and taking standardized tests. This doesn’t include time taken out of the instructional day for test prep so that number may even be quite higher.

*Q: But, I need to review to make sure my students remember concepts taught at the beginning of the year.*

** ***A: Not if you have been teaching to mastery.*

Teaching math with a mastery-based program that is rich in problem-solving may all but eliminate the need for any test prep or review. If your students have a solid foundation in the basics and have practiced applying that knowledge to solving problems throughout the school year, then nothing a standardized test can throw at them should be unachievable. With a cohesive curriculum, where concepts build on each other, your students have essentially been revisiting concepts throughout the year. So, trust in what your students have learned and skip the review.

*Q: What about going over topics that I haven’t covered yet?*

*A: How much success have you had cramming for an exam?*

If material is thrown at students for the sake of a test a few things can happen.

- Students won’t retain information. If students have not been given enough time to progress through the concrete-representational-abstract phases of learning, they will likely not be able to recall concepts or apply those concepts to the unfamiliar situations they might encounter on the standardized test.

- Students will be stressed out. They will feel the pressure (that unfortunately, you are likely feeling as well) to get a good score on the test. Learning becomes just something to do for a test.

- You will get false positive results. Have you ever had the teacher in the next grade up comment that students couldn’t remember a concept that you know you taught? Or, better yet, had test scores reflect learning, but students couldn’t perform at the next grade level? That can be a result of concepts being taught too quickly.

So, rather than block out a few weeks to cram in topics that you haven’t covered, try integrating them into other areas of your day. Do some data analysis in morning meeting. Add some questions about telling time to your calendar activities. Play with measurement and geometry during recess (The weather is getting nice, right?).

If you follow the sequence in your well-thought-out curriculum and teach some of those missing concepts after testing, it’s ok. Your students will experience those concepts in an order that makes sense and will be able to make connections, apply their thinking and **master** those concepts. That mastery will stay with them into the next year and will be reflected on upcoming standardized tests.

After all, we don’t stop teaching after standardized tests. Well… that’s probably a topic for another post.

*photo courtesy of Alberto G.*

This problem was taken from Noetic Learning’s problem of the week and builds on the problem with the ropes from last month. Sign up to receive their weekly problems.

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

This problem was taken from Challenging Word Problems 2, a supplement to the Primary Mathematics series:

Dedicated reader, Shirley Davis submitted the following solution:

The problem reads, “There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”

Yes, this is that “new” math. This is the math that second graders will need to succeed as adults. Gone are the days when correctly completing 20 addition or subtraction problems is enough. Problem-solving and logical thinking is what employers are looking for. So, yes, this is a challenging problem, but not a problem we should be avoiding in our schools simply because the internet says it’s too hard.

I agree there is a flaw in this problem, but it’s not in the problem itself, it’s in the numbers that were chosen. Fortunately, the numbers are the least important part of solving a word problem. That stands worthy of repeating. **The numbers are the LEAST important part of solving a word problem.**

So, what is then? **Visualization and comprehension!**

Students need to visualize the problem and then represent it with models or pictures. This is why teaching bar modeling is so very important in the early grades.

Here’s a video that shows how easy it is to solve this problem if you focus on visualization first.

Any good teacher will follow up a lesson with practice, so here is your Word Problem Wednesday for February.

This problem was taken from Challenging Word Problems 2, a supplement to the Primary Mathematics series:

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

The previous problem came from *i-Excel Heuristic and Model Approach Primary 5* by Li Fanglan published by FAN-Math:

Dedicated readers submitted the following solutions, first an image from Shirley Davis:

And a video from Kristine Simonson, who has been using some of the problems with her fourth graders:

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!*

**Tulsa, OK | July 23 – 24, 2018:**

Register Now!

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

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

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