These Are a Few of My Favorite Things: Common Core Math Resources

It’s a Friday evening and I have just drifted off into the loveliest dream.  I am the young and beautiful Julie Andrews falling for the dashing Christopher Plummer on the movie set of my favorite musical, “The Sound of Music”.  Things are progressing right on cue.  I have sung the opening theme song, met the Captain with his “ridiculous” whistle, set on the infamous pinecone, cut up the curtains to make playclothes, and then “Up in the nursery, an absurd little bird, is calling out to say “You’re” cuckoo, cuckoo….”

And we’re back!  I’m Renee’ Smith again and I have a blogpost due in three hours.  With the remnants of the dream still clinging to my consciousness, I decide to share “a few of my favorite things” for common core math.

Resources that I recommend for teacher training for common core:

Children’s Mathematics: Cognitively Guided Instruction – Carpenter, Fennema, Franke, Levi, and Empson

Extending Children’s Mathematics Fractions and Read more ›

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10 Things Jordyn’s Math Teacher Needs to Know About CCSS


Two months ago, Jordyn Marie was born.  Nothing can match the joy of having a child, unless it is the birth of a grandchild.  If you ask me, she is pretty darn perfect, and as a devoted Nee’Nee’ (my name for grandma) I would like to keep her that way.  I would like to make her life, most especially her school career, as smooth as possible.  Therefore, I have compiled a list for the future math teachers who will be tasked with ensuring Jordyn’s math understanding.   Here are the top 10 things that her teachers need to make sure they are doing by 2018:

1.  Problem Solving, Problem Solving, Problem Solving!!!-Children need to be daily problem solvers!  Their ability to do just that will be measured in our assessment system and is an essential life skill.  As a math consultant I believe nearly every math concept can be taught through problem solving with some “just-in-time” direct instruction.  Teachers need to be trained to facilitate learning through constructivist methods, schema based instruction (such as CGI), or inquiry based instruction (Dan Meyer model).   If Jordyn is to be prepared to live and work in the world beyond her formal education, she will need Read more ›

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M4: Midwest Mathematics Meeting of the Minds

I recently attended the M4 Conference in Kansas City, where math leaders from Kansas, Missouri, Nebraska, and Iowa met to discuss the Common Core Standards for Mathematics.  I was privileged to hear from Matt Larson the keynote speaker from Lincoln, Nebraska.  After humerously acknowledging that his state was one of the four who had, as of yet, not adopted the common core standards, Larson got right to work convincing us that the Common Core State Standards may be our last opportunity to get math education right!

Larson began his keynote address by looking back at the ten year cycle of math education beginning in the 1950’s.  He cited a 2011 article entitled, Slouching Toward a National Curriculum, when he said, that despite these previous reforms, instruction has remained largely the same.  Larson then posed the question, “Will the CCSS Matter Ten Years From Now?”.  He answered this question by first Read more ›

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I Couldn’t Have Said it Better

Are You Prepared for the Common Core Standards?  This is the question posed in the latest edition of Education Week Teacher.

I encourage you to read how five classroom teachers  from around the nation answered that question.  Their responses include information on the importance of the 8 Mathematical Practices; the importance of sequence, pace, and support resources; how critical teacher collaboration will be in the implementation of the standards; and how the standards encourage us to Read more ›

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Common Core Math Curriculum: How Do We Know It’s Aligned?


As more and more teachers become familiar with the common core math standards, the question that is beginning to crop up is,  “What curriculum (ie. textbook) is going to be aligned to the common core?”.  My standard response has been two-fold.  My inclination is that most companies will SAY they are aligned to the common core; after all, they cover most of the content somewhere in the book.  Of course my reaction to that is, “Buyer Beware”.   Like all good consumers, we will have to investigate the claims made by the textbook companies and make an informed decision.  We know that not only must the content match the grade levels to which it has been assigned  but we must also take into account the 8 Standards for Mathematical Practice and the College and Career Readiness Standards that play an equally important role in the effectiveness of the common core.  As districts look toward adoption of textbooks, or make a decision to write their own curriculum there will be certain criteria they need to follow to align to the common core.

The good news is we are not alone in this process.  Many groups have already begun to tackle this issue and have developed rubrics or checklists to make the search easier.  One such document, that contains a set of rubrics for elementary through high school curriculum is the Common Core State Standards Mathematics Curriculum Materials Analysis Project.  This work, supported by the Council of Chief State School Officers, the Brookhill Foundation, and Texas Instruments, will assist reviewers in using appropriate criteria for choosing mathematics curricula.

In her blog post,Teacher Checklist:  How to Choose the Right Textbook, Jennifer Chintala shares a checklist she found online which could be used by districts to evaluate curriculum for the common core.

Al Cuoco recommends choosing curriculum attuned to the 8 Standards for Mathematical Practices and his comments can be found in this two page essay.

Each of these resources will be posted to the resources tab on this site and as we find more that might be helpful to schools who are in the process of textbook adoption we will continue to add them,  so check back often.

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When the Stars Align

Yesterday, it was as though the stars aligned and things I have been working on for over twenty years converged and crystallized in my mind.

Years ago when my children were young, I was the public speaking leader for their 4-H club. I taught 4-Hers how to write and deliver interesting and engaging speeches. They learned how to hook the audience by peaking their curiosity, deliver the bulk of the message in the body of the speech, and end in a clever way, usually leaving the audience wanting more.

When I returned to the classroom, I knew the essential elements of a speech also applied to a math lesson. I had to find ways to intrigue my students, engage them in the lesson, and then sum things up at the end. However, I don’t believe I have ever seen this done in a more deliberate and creative way than I did while listening to Dan Meyer present on real-world problem solving yesterday.

During our time together, Meyer led us through his version of the “Three Acts” of a math class. He equated these acts to the scenes of a movie. In “Act One” Meyer uses a visual, either picture or video, to peak the students’ curiosity. He relates a short story to draw his audience in and with as few words as possible he sets the hook. He lures the students into wanting to know something mathematical.

According to Meyer there are several important aspects of this opening act. The first thing is allowing students to pose all sorts of questions based upon the visual presented. As all the questions are posted, the teacher should ask for a show of hands about other people who had the same question. This is one of the methods Meyer believes helps reluctant students buy-in to the process. After all questions have been posed, each question is addressed by the teacher and then eliminated until one remains. This is the problem that the class will solve.

Another important feature of “Act One”, is having students estimate what they think the answer might be. Meyer also requires students to write down a guess they know is too low to be the correct answer and one that is too high to be the correct answer, thereby establishing a range within which a reasonable answer would be found. According to Meyer, “Everyone can hazard a guess, and it only costs you about 7 seconds of class time. This is one way to engage some of your more reluctant math students.”

In “Act Two”, the teacher asks students to help solve the problem but does not initially supply all the needed information. The participants determine what information they might need in the form of a list and then the teacher addresses each item on the list and supplies only enough information, in a visual format, so the problem can be attacked. The teacher then acts as a facilitator, or guide on the side, as students do the bulk of the work on solving the problem. At no time during “Act Two”, does the teacher dictate a strategy that students must use to find their solution. The teacher merely circulates, asks questions about the work, redirects students as necessary, and takes notes on different strategies.

During “Act Three”, Meyer believes teachers should ask students to check the reasonableness of their answer; does it fit within the range of numbers that were chosen in act one? The remainder of this act involves leading a summary discussion of the different strategies that were used by various groups of students. The teacher can also use this time to formalize the mathematics. Meyer noted another way to engage students during the summary discussion is to assign them a task at the beginning of the discussion. He asks students to think about which group was the “laziest” and used the most efficient method to solve the problem. At the end of the act, Meyer again returns to a visual method to show the correct answer. He also suggests acknowledging the student with the closest original guess, thereby letting the class know that estimating at the beginning of the lesson was not busy work.

I look at this “Three Act” script as a perfect opportunity for math teachers of all age groups to address most or all of the common core practice standards. It might also lead to students who are more engaged in math and see its usefulness.

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Sense Making


One of the reasons I am so passionate about basic math understanding is a beautiful 24 year old girl named Cameron.  She was a wonderful student, but in her final years of high school she struggled with math.  In a very matter of fact tone, this daughter of mine will tell you she hates math.  Now, I don’t think math needs to be “one of her favorite things” (Sound of Music reference in honor of our favorite musical of all times), but I do think it would benefit her life to at least understand and feel confident that she can do math.

Last year, while Cameron was home from Chicago for the Christmas holidays, I happened to be working on a blog post about the division of fractions. (The reason this is still timely a year later is because of  the two national presentations I have done recently on the subject and my work with the common core.)  I decided to pose the problem in the post to her and her initial reaction was negative.  Being a mom, and a teacher, I wouldn’t let it go.  Being a good daughter she decided to humor me and play along.

First you need to know that Cameron was driving us down the interstate at the time, so there was no opportunity for paper and pencil calculations or the use of manipulatives.  The whole “math lesson” occurred through mathematical discourse and sense making.  My first question to her followed the tack of my blog post, “Banished From the Math Classroom, Don’t Ask Why….”.  At first, Cameron insisted she couldn’t think of a reason to divide 3 1/2 by 3/8 but before long we arrived at 3 1/2  pizzas and 3/8 of the pizza being a serving.  (For those of you who know me, I apologize.   I never let my students use pizza as the example but I was working with a reluctant learner who is a self avowed math hater.  I wanted her to continue and I was trying to build self confidence.)  With some step-by-step logical thinking Cameron arrived at 9 servings with one piece left over.  With only a little coaching on my part, she also identified the leftover piece as 1/3 of a serving.

Now, I am not deluded enough to think I converted my daughter that day, but she did say no one had ever helped her understand division of fractions in that manner before.  I am sure there were a lot of other concepts that she never had a chance to “make sense of” and that has led to her “attitude” about the subject.  I will continue to work on her over time but I hope that we can eradicate this “hatred” of math from our classrooms by spending more time in activities that lead to dialogue and sense making.

“Sum”thing to work on!

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Deep Not Wide

For years, teachers have bemoaned the fact that they were forced to teach a mile wide and an inch deep.  The new Common Core State Standards for Mathematics are designed to reduce the number of concepts that will be taught at each grade level, thereby allowing teachers to devote more time and depth of instruction to each standard.

The concepts placed at each grade level were determined based on prerequisite topics that were to have been taught in a previous grade, international comparisons and the professional judgment of educators, researchers, and mathematicians.

These standards do not dictate a predetermined order of instruction or a particular curriculum.   As it says in the Common Core document, “These Standards are not intended to be new names for old ways of doing business.  They are a call to take the next step.  It is time for states to work together to build on lessons learned from two decades of standards based reforms.  It is time to recognize that standards are not just promises to our children, but promises we intend to keep.”

Just “sum” thing to think about!

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New…and Improved? Assessments

When it comes to discussions of the common core, the conversation quickly turns to the question uppermost in teachers’ minds,  “What will the new state assessment look like?”   The truth of the matter is, we aren’t sure yet.

Initially, the word was that the new math assessment would be groundbreaking.  It is supposed to include selected response, multiple mark, constructed response, computer simulation,  and open-ended questions as well as performance based tasks.  Both of the assessment consortiums, as outlined by Deb Haneke, in Assessments and Common Core Standards, are charged with helping ensure students who graduate from high school are college and career ready.  Their plans for the new assessments are similar but not identical.   The Smarter Balance Assessment Consortium, of which Kansas is a governing state, is planning an adaptive assessment; one in which the computer aligns the difficulty of the questions to the student’s performance level.

At this point, there seems to be some backpedaling when it comes to the news about the new assessments.  According to an article in Education Week, Experts See Hurdles Ahead for Common Core Tests, there are several factors that may impede the creation of a truly innovative assessment.  As in most areas of education today, the lack of money rears its ugly head.  Although both consortiums received Race to the Top Assessment grant funds, this does not include long-term funding for test administration or revision.  With this in mind, there is pressure to get the test right the first time.  The timeline for development is also a factor that may impede the amount of innovation that we see in the final product.

So my advice to teachers at this stage of the game is to focus on the standards themselves and leave the test, for now, to the test makers.

Just “sum”thing to think about.

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A Whole New Look

or teachers who are proficient at navigating their current state standards, the Common Core Standards may have a completely different look.  In the area of mathematics, the content of the document is divided into domains, clusters, and standards. Domains are the overarching term and refer to a large group of related standards.  Clusters are groups of related standards.  Because mathematics is a connected subject, standards from different domains and clusters may be closely related.  Finally, the standards define what students should understand and be able to do.  An example from fourth grade would be:  Domain – Operations and Algebraic Thinking; Clusters – Use the four operations with whole numbers to solve problems (three separate standards), Gain familiarity with factors and multiples (one standard), and Generate and analyze patterns (one standard).

Within the document, each grade level does not necessarily have the same domains or number of domains as the preceding grade.  However, the standards are aligned vertically from one grade to the next.  Unlike some current state standards, the Common Core State Standards do not spell out every step in the instructional process and some do not have example problems.  Therefore, educators are going to have to investigate the new standards thoroughly and translate them into new instructional practices.

“Sum” thing new to think about!

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