Dear Polly, 

I have been desperately trying to keep up with all the mathematical practices. With TCAP and progress monitoring all my students, I just don't know how to manage all the new learning and implement the knowledge into my classroom. I'm just exhausted! Help!

Sincerely, 

Exhausted

Dear Exhausted, 

Yes, it is that time of year! Stress levels are high as we are all in test mode, ready for spring, and looking forward to spring break. Hang in there - nice weather is just around the corner and the "spring in your step" will return after a restful break. As we have entered this busy period, I think this is a perfect time to marinate in the mathematical practices and reflect on the work your students are doing in the classroom. Take a deep breath, your students are on the right path to success!

Warmly, 

Dear Polly

Dear Polly Nomial:

I am frustrated that many of my students are not fluent with all of their facts. One colleague suggested giving students timed tests. Another suggested working on conceptual understandings. Is there one way that is correct and will help my students?

Signed:

A confused teacher

Dear Confused Teacher:

This is a topic in math that comes up in many conversations. Let me quote a famous author and researcher, John Van De Walle: "Timed tests cannot promote reasoned approaches to fact mastery" and will "reward few and punish many" that are not speedy writers. In his books, he suggests three steps to help get students to fact mastery:

1. Help children develop a strong understanding of relationships and of the operations. We do this in Stations and Number Talks!
2. Develop efficient strategies for fact retrieval through practice. We do this in Number Talks and EDM lessons! 
3. Provide drill in the use and selection of those strategies once they have been developed. Again, Number Talks and EDM!

Your colleague suggesting conceptual understanding first is correct. Students should not be drilling and practicing on skills or concepts they don't completely understand. During stations you need to provide opportunities for students to develop understanding, and during Number Talks and EDM lessons, they begin to practice more efficient strategies. While it might be an assessment for you to see what facts students know automatically, research is clear that timed tests do not promote fact fluency. If you would like more information and activities, check out Chapter 4 in the book Teaching Student-Centered Mathematics by John A. Van De Walle resource at your school.

Yours in counting, 

Polly

Dear Polly,

After reading last week’s letter, I feel a little overwhelmed in implementing all 8 mathematical practices. I see the value and I want to start right away, but where do I begin?  Is there one mathematical practice I should start with?  Can I implement them one at a time?  Please help!

Sincerely, Where to Begin

Dear Where to Begin,

Yes, you can absolutely begin by implementing the practices one by one and build on each other.  You can also be intentional about the practices that you choose to implement first.  The practices can be described as a doorway to the Common Core State Standards and no door can function without a frame.   The frame is the support system that holds the door in place.   The two mathematical practices that provide this support are the following: #1: Make sense of problems and persevere in solving them and #5: Use appropriate tools strategically (see picture).   

The threshold is another integral part of a door.  The function of threshold is to provide a transition between the inside and the outside or between rooms. Mathematical practice #6: Attend to precision, provides the threshold, allowing for students to use precise and effective communication that students are able to gain insights about how they think about mathematics.

Students who venture through this door are on a journey that promotes processes, proficiencies, and practices in the Common Cores mathematics classroom.  These three practices are pivotal, not only because they develop conceptual understanding to the content, but also because they play an integral role in the implementation of the other five practices.  These practices should permeate the mathematics classroom environment and become part of the daily fabric of both mathematics instruction and the students’ mathematics experience.   

As always, if you need help implementing these three practices, please do not hesitate to meet with your math coach.   

Respectively, 

Polly

Standards for MP

• Reason abstractly and quantitavely
• Construct viable arguments and critique the reasoning of others
• Model Mathematics
• Look for and make use of structure
• Look for and express regularity in repeated reasoning

Dear Polly,

I like the visual of the Mathematical Practices being the doorway to the Common Core State Standards. I feel like I want to focus on #1 Make sense of problems and persevere in solving them. I need more information about this mathematical practices and what it looks like in an elementary classroom!

Sincerely,

Persevere in Teaching

Dear Persevere in Teaching, 

We are creating problem-solvers so it does not matter what your objectives are or grade level, the eight mathematical practice standards are a guide to good math instruction. Mathematical Practice #1: Make sense of problems and persevere in solving them - is a great practice to start. It means that your students understand the problem, find a way to tackle it, and work until it is done. Basically, you will find practice standard #1 in every math problem, every day. The hardest part is pushing students to solve tough problems by applying what they already know and to monitor themselves when problem-solving. Mathematically proficient students start by explaining to themselves (or others) the meaning of a problem and plan a solution looking for entry points to the solution instead of just jumping into a solution attempt. They continually ask themselves, “Does this make sense?”

• Give students tough tasks and let them work through them.
• Allow wait time for yourself and your students. Work for progress and "aha" moments. 
• Have the students make a plan with you of how to solve problems that are challenging or have multiple steps. the math becomes about the process and not about the one right answer.
• Lead with questions, but don't pick up a pencil. Let students make headway in the task themselves.
• Allow productive struggle and don't rush in too soon to rescue, but ask questions to support them. 
• Highlight what the students are doing that is making sens of the problem and how they are persevering. 
• Have students reflect and share how they were performing this mathematical practice today.

Respectively,

Polly

Dear Polly:

It has been a lot of fun watching my students begin to use the Mathematical Practices Standards I have been encouraging in the classroom: #1 – Make sense of problems and persevere in solving them, #5 – Use appropriate tools strategically, and #6 – Attend to Precision. (See the ‘doorway’ illustration). I’m now ready to introduce them to Mathematical Practice #2 – Reason abstractly and quantitatively. Would you please help me understand this MP and give me some ideas of implementation in the classroom?

Signed: Fourth Grade Teacher

Dear Fourth Grade Teacher: 

Math Practice #2 has 2 parts: 1) Analyze abstractly – students should be able to break a problem apart and show it symbolically, with pictures, manipulatives, or in any other way than the standard algorithm, so they can go from numbers to words (contextualize) or from words to numbers (decontextualize), and 2) Quantitative reasoning – students can create clear symbolic representations with attention to units and other details with consideration of numbers and quantities. Many of the following suggestions for implementation you are probably already doing during different parts of the math block. Naming the Mathematical Practice ideas of #2 as students are solving problems will encourage them to think metacognitively about what they are doing to solve problems, especially when paired with perseverance. For example, when students are adding fractions with unlike denominators, they begin to reason about the meaning of adding fractions rather than just following a procedure. You can help them own this MP by having your students:

• Draw representation of a problem
• Build the parts of a problem with manipulatives
• Figure out on their own what to do with some data they have collected
• Answer questions you have posed to lead them to understanding a problem
• Build from concrete to pictorial to abstract

Naming MP #2 practices as you are roving among student groups during Stations and EDM lessons will help them own it. Other strategies for you to use include:

• Modeling using think-alouds
• Using guiding questions and then discuss reasonableness
• Emphasizing operational fluency and real-world problems

I appreciate hearing that you are making the Mathematical Practices an integral part of your math block!

Sincerely,

Polly

Dear Polly,

This doorway illustration of the Standards for Mathematical Practices has been so helpful. And now, finally, a Mathematical Practice my students are already doing! I see them using Mathematical Practice #3 – Construct viable arguments and critique the reasoning of others in our daily Number Talks. My question is, how do I provide my students with opportunities to do this throughout my math block?  I think there may be more I can do for my students in this area that will build on the Number Talk.   

Signed, 

Inspired Math Learner

Dear Inspired,

What a great connection you made to SMP #3 and Number Talks. And yes, we want our students to be involved with the SMPs in all parts of our Math Block, whether they are in kindergarten, twelfth grade, or any grade in between. The way it looks at your grade level may be different from another grade level. Basically, we need to provide opportunities for student discourse in all parts of our math block. Students may participate in ways ranging from a hand signal indicating agreement or disagreement to analyzing and discussing several responses to one problem. A helpful first step is to shift our teaching from…. mathematical authority coming from the teacher or textbook toward mathematical authority coming from student talk, interaction, reasoning. As we do with our Number Talks, we need to start with creating a safe environment.   

Have classroom norms to create a safe environment for discussion.

• Provide justification and explanations for ALL answers.
• Make sense of each other's solutions.
• Say when you don't understand or don't agree. 

What a great connection you made to SMP #3 and Number Talks. And yes, we want our students to be involved with the SMPs in all parts of our Math Block, whether they are in kindergarten, twelfth grade, or any grade in between. The way it looks at your grade level may be different from another grade level. Basically, we need to provide opportunities for student discourse in all parts of our math block. Students may participate in ways ranging from a hand signal indicating agreement or disagreement to analyzing and discussing several responses to one problem. A helpful first step is to shift our teaching from…. mathematical authority coming from the teacher or textbook toward mathematical authority coming from student talk, interaction, reasoning. As we do with our Number Talks, we need to start with creating a safe environment.   

A third way to incorporate SMP#3 into our entire math block is to celebrate errors! Students should view errors as learning opportunities. Use errors as springboards for learning conversations as they arise and redirect to the correct reasoning and/or problem solving that leads to the correct answer.  Or, provide students with mathematical problems and solutions (some with correct solutions others with incorrect solutions). Let them analyze the problems and solutions. When you take the step of solving the problem out, you allow them to focus on the second part of the SMP (critique the reasoning of others). At other times, you can provide students with a sample argument and let them reason if it makes sense or not, ask clarifying questions, and suggest possible improvements to the argument

I know you will continue to find ways to incorporate opportunities for students to effectively discuss and critique reasoning in your math block!  It is a great next step to mathematical power!   

Signed, 

Polly Nomial

Dear Polly,

I am ready to support my students with the next Mathematical Practice. I am persevering and enjoying incorporating Mathematical Practices into my math block because I am seeing the benefits with my students as they improve and achieve. The doorway shows #4 Model with Mathematics is next. As TCAP approaches, I think about my mantra with my students about "showing your work with pictures, words, and numbers." Is that what Model with Mathematics is all about? 

Sincerely, 

Needs a Model

Dear Needs a Model,

You are on the right track with Mathematical Practice 4: Model with Mathematics. Mathematically proficient students in early grades experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect and explain the different representations. They should be able to use all of these representations as needed. By the time they are in 3rd grade and beyond, they continue to experiment with the things listed above. In addition they also evaluate their results in the context of the situation, reflect on whether the results make sense, and evaluate the models to determine which are most useful and efficient to solve problems. Students that can Model with Mathematics use math they know and understand to solve real-world problems. Make math relevant, meaningful, and real!

Keep Practicing and Keep Up the Good Work, 

Polly

Standards for MP

• Reason abstractly and quantitavely
• Construct viable arguments and critique the reasoning of others
• Model Mathematics
• Look for and make use of structure
• Look for and express regularity in repeated reasoning

Dear Polly, 

I am really excited by the depth of processing and reasoning that my students are exhibiting in my math block! Your last letter made it manageable for me to introduce Mathematical Practice (MP) #1  Make Sense of Problems and Persevere in Solving them. I am ready to introduce another. The doorway illustration makes me think MP#5 - Use appropriate tools strategically is my next step. Any advice? 

Signed,

Excited by my Students' Learning

Dear Excited by my Students' Learning,

I'm so happy for you and your students! Yes, MP#5 - Use Appropriate Tools Strategically is a great next step. Students need to know HOW and WHEN to use math tools. A first step may be to offer access to math tools in your classroom. Having tools available for student selection will free you to engage in student learning and not stuck searching for tools in cupboards and boxes. Avoid the temptation to tell students what tool to use. by asking students to choose which tools they wold use for certain types of problems, you are giving them the opportunity to show you they understand their math tools. In addition to offering a variety of tools, you can also ask students why they chose a certain tool to deepen their reasoning skills. Tools in math can e devices such as rulers, protractors, base ten blocks, colored cubes, etc. and as simple as paper and pencil or white boards and markers. 

An important step to keep in mind is asking about the reasonableness of solutions. If a student uses the wrong tool, or an efficient one, try asking about the reasonableness of their solution rather than simply directing them to use the correct tool. 

Signed, 

Polly Nomial

Standards for MP

• Reason abstractly and quantitavely
• Construct viable arguments and critique the reasoning of others
• Model Mathematics
• Look for and make use of structure
• Look for and express regularity in repeated reasoning

Dear Polly,

I have been implementing the Mathematical Practices into my teaching and expectations for learning this year. I have been working with my students on Math Practice #6 these past two weeks, which is all about students communicating precisely with each other. My students are doing well with explaining their thinking and reasoning during Number Talk and using their math vocabulary. I am proud of them, but I still have some students who will say, “I don’t get it” and will go no further. How do I help them become more proficient with their language and explanations.

Signed, 

Proud and Pushing

Dear Proud and Pushing,

As you know, Math Practice #6 “Attending to precision” means students try to communicate precisely to others. They learn to use clear definitions in discussions and in their own reasoning. Students should communicate, whether speaking or writing, precisely, using clear definitions and math vocabulary along with explaining the meaning of symbols, and calculating accurately and efficiently. Students must label accurately when measuring and graphing and provide carefully formulated explanations. Just as we teach our students to ask questions of one another in a Number Talk, we need to teach and encourage our students to state what it is they need help with when solving problems or when they are in a discussion with other students. One tool that may help you and your students is the Math Clarifying Bookmark, which I have attached to this email. Rather than saying “I don’t get it,” students learn to use the sentence frames on this Bookmark to explain exactly what they do or do not understand and where their understanding falls apart. This helps the student clarify their own thinking and begin to become “precise” in their thinking, calculations, and the language they speak when explaining their thoughts to others. You are well on your way with your expectations for precision in Number Talks. Continue those expectations in your math lessons and Stations. When we give students ideas for what to say and how to say it, such as using this Bookmark, they will become more precise in math.

Sincerely, 

Polly

Dear Polly, 

You have explained in depth all the mathematical practices except #7 and #8. As the spring in my step has returned, I am ready to tackle these last two and to be honest, they seem to be the more confusing practices. So, please help me to understand the purpose of #7 "structure in math" and what a student would have to do in order to be proficient.

Sincerely, 

Spring in my Step

Dear Spring in my Step, 

Looking at the title of the mathematical practice #7, Look for and make use of structure, does not on the surface provide a deep understanding of this standard. However, this standard focuses on understanding the structure of mathematics. When people see structure in math, they understand the predictability and find that math makes sense. 

In every day situations we use structure, patterns and properties, to understand our daily tasks. As we add our monthly bills, we don't worry about the order in which we add them because we understand the way math works (math properties). We know that the order in which the numbers are added will never change the total. We also look for patterns to understand rising prices or stock market changes. We break apart numbers as needed to perform tasks (e.g. when we can't find the 3/4 measuring cup). We apply what we know about the structure of math - its patterns and properties - as we use math each day. 

If our students understand the structure of mathematics, they will find that math makes sense. Our students need to be proficient in the following ways:

• See the flexibility of numbers: numbers can be composed and decomposed
• Understand properties: commutative, associative, distributive, and identity
• Recognize patterns and functions: identifying patterns in our number system from the hundreds charts to decimals and fractions; using function tables to recognize patterns. 

I have also attached a document breaking these elements down explaining simple ways that you, as the teacher, can focus on developing this standards. As always, please contact your math coach for additional ideas or suggestions. 

Sincerely, 

Polly

Dear Polly,

I have been working with my students and their use of all the Mathematical Practices #1-7. I am ready to start focusing on the final Standard of Mathematical Practice #8, Look for and express regularity in repeated reasoning. Can you explain it in more detail?

Sincerely, Eager for #8

Dear Eager,

As I learn more about the Standards for Mathematical Practice, I am starting to see how some of them can be grouped together.  If I consider the Mathematical Practice from last week, Look for and make use of structure, and this week’s MP, Look for and express regularity in repeated reasoning, both are focused on having students seeing structure and generalizing that structure.  More specifically, in Mathematical Practice # 8, students can express this by seeing patterns that exist and make generalizations based on those patterns. Some examples of patterns students might see are:

• When playing “Snap‐it” to find combinations of a given number, they always get “turn around facts” – when working with 6 cubes, they see 2 and know 4 is hiding or see 4 and know 2 is hiding.  
• After practicing adding ten to number, followed by adding 9 to the same number, students start to notice a pattern to the sum.   
• Students might notice a pattern in the change to the product when a factor is increased by 1:  I know 5 x 7 = 35 and 5 x 8 = 40.  I notice the product changes by 5.  I know 9 x 4 = 36 and 10 x 4 = 40.  I notice the product changes by 4.  I can generalize that when I change one factor by 1, the product increases by the other factor. 

What can you do as a teacher to help students start to notice these patterns and make generalizations?   

• What can you do as a teacher to help students start to notice these patterns and make generalizations?   
• Allow students to practice using “If/Then” reasoning strategies for obvious patterns.  
• Provide rich and varied tasks that allow students to generalize relationships and methods, and build or prior mathematical knowledge.
• Provide time for exploration, dialogue, and reflection.
• Ask deliberate questions that enable students to reflect on their own thinking.

What are examples of questions you could be asking or encouraging students to be asking each other?

• What pattern did you notice?  How did this help you?   
• What pattern did you notice?  How did this help you?   
• What pattern did you notice?  How did this help you?   

When you begin looking for patterns in mathematics, you will find they are everywhere! Students that are numerically powerful make use of this structure and make generalizations all of the time!

Sincerely, 

Polly Nomial

Dear Polly, 

I am so impressed by my students' ability to discuss and understand mathematical concepts due to their increased opportunities with the Standards for Mathematical Practice. But I'm a bit confused between the Mathematical Practices and the Standards. Can you clarify for me?

Signed, 

Stumped by Terms

Dear Stumped by Terms:

I am glad your students are seeing success in their experiences with the Mathematical Practices! Briefly, the differences between the two terms are as follows: The 8 Standards for Mathematical Practice are about student behaviors when they are engaged in mathematics – they solve problems with precision, stick with it (perseverance), use what they know to solve problems, and so on. Grade level Content Standards, such as in math and literacy, are about the level of performance and what it looks like by grade level for students. We often speak of it and use the Content Standards as a basis for whether or not a student is performing at their grade level expectation. To learn more about the Standards for your grade level, consider taking the ‘Deep Dive into the Standards’ class offered this summer through District 6. And although all Math Professional Development classes will include some elements of the Mathematical Practices, for a more focused learning experience with them, consider taking the ‘Mathematical Practices K-12’ blended learning class. Keep calm and Teach On! The end of the school year is approaching and we want to keep our students engaged and getting the most out of their learning every day. You can do it!

Signed,

Polly

Dear Polly, 

At times, I feel like my math block is disjointed. Sometimes I don't know how to make the Number Talk, the EDM lesson and the Stations work together. It seems like I am teaching three different things during the 90 minutes. 

Signed, 

Seriously Disjointed

Dear Disjointed, 

The State Standards are what the students are to learn and know and the Mathematical Practices are the student's behavior when performing the Standards. No matter what grade level you teach or what Standards you are teaching, you are trying to create a mathematically proficient student. My best advice for you is to let the 8 Standards for Mathematical Practices be a driving force when planning what students should know and be able to do. Whether you are doing a Number Talk, interacting with your students during Stations or facilitating an EDM lesson, give your students opportunities to:

• Make sense of problems you present to them, and giving them time to persevere in solving them. 
• Reason abstractly by asking them questions that help them see relationships, and quantitatively so they can attend to the meaning of the quantities whether they be whole or rational numbers. 
• Construct viable arguments by requiring your students to engage in mathematical discourse and critique the reasoning of others because you expect your students to explain their reasoning and use previous learning to explore plausible alternative strategies. 
• Model their understandings with mathematics giving you insight into their thinking so you know where to go next with your instruction. 
• Use appropriate tools strategically and allowing students to make errors along the way so they can learn from their mistakes. You are giving them tools to choose for so they can figure out which ones are best for the situation or problem. 
• Attend to precision as they communicate precisely to others using math vocabulary you are teaching. You have high expectations for calculating accurately and efficiently. 
• Look closely for patterns and make use of structure by asking them what they notice and what they already know to help them analyze and solve a new and different problem. 
• Look for patterns and generalities in the math they see and express regularity in repeated reasoning giving them the ability to explain why short cuts work. 

Even though you may be teaching geometry in your EDM lesson, working on computational fluency in your Number Talks and have students working on several different concepts during your Station time, you are helping them become mathematically proficient by keeping a focus on the Mathematical Practices stated above. This is how the 3 components of the math block can work together to give your students the opportunity to learn and become successful in mathematics. 

Sincerely, 

Polly

Dear Polly Nomial:

Why do we have to chart our number talks on chart paper? It's a waste of paper when I have such great technology with my Promethean Board, and it takes me extra time! Plus, I can use the models on ActiveInspire. I just don't see the point. 

Sincerely, 

Second Grade Teacher

Dear Second Grade Teacher:

The purpose for charting our number talks on paper is so that students can easily look back at another child’s strategy that was used in a previous day and attempt to use it to solve a similar problem the next day. Sharing strategies between students is part of the purpose of scripting, or charting, student answers and strategies to problems. If a student only hears it the day before, it may not be enough to help the child attempt to use a similar strategy to solve today’s problem. But if they see it the next day, they have a better chance of remembering the strategy and a better chance of being able to "copy" or use it themselves when presented with a similar problem. What if you displayed your number talk on the Promethean Board then had a chart stand beside the board to scribe student thinking on chart paper? This could then easily be displayed beside or underneath the Promethean Board. Similarly, if you chart the thinking on the Promethean Board, you can print it out and hang it beneath the PB. Another way is to do all Number Talks on chart paper and post them for a week at a time so students can see the thinking behind solving a problem.

Keep on Counting, 

Polly Nomial

Dear Polly Nomial:

I thought as long as we give our students choices during Nermacy time that they could choose between EDM games and Math Perspectives activities. One of my team members thought we couldn't do EDM games at that time. Another team member thought we could do the games as long as we added manipulatives. Another team member said we couldn't do any writing during that time. Please help me understand Numeracy time expectations.

Signed:

A Numerical Teacher

Dear Numerical Teacher:

Our math block consists of 30 minutes for numeracy time. It is not a review time, number talk time, finishing the EDM lesson or games time. For our students to have number sense, we need to provide them time to gain a deeper understanding of mathematical concepts by working at their edge of understanding at their current critical learning phase. At numeracy time, we meet their individual needs by interacting with them while they are at work:

• Asking questions
• Providing support
• Posing challenges when appropriate

Since EDM games are practice activities, students are figuring out what strategy will work for that particular game. The strategy may or may not work for other problems. For example, "Name that Number" might be great for fact fluency, but do they understand number relationships? If we use "Top It", we would need to add counters so students can see which number is bigger. 

As far as writing goes, it needs to be purposeful writing. If a child is spending most of the time writing, it is taking away time from his concept building. But, if the writing is part of the station, it helps the child keep track of the work or discover patterns. For example, we don't need to have the child write all the combinations of numbers when "Building a Floor", but we do need to see what umber was rolled at the "Roll and Multiply" station or "Roll to 100 or 1,000" station. Numeracy is all about being purposeful.

Conceptually Yours, 

Polly

Dear Polly,

I am hearing and reading a lot about scaffolding in math in our district.   Do you think that means to differentiate?  In order for all my students to be successful when I am teaching a concept, I differentiate my lessons, choosing harder problems for some and less difficult problems, or even less of them, for others.    Why do I need to scaffold too?

Sincerely

Breaking it up is hard to do!

Dear Breaking,

Good question as we often feel like there is more to do without taking anything off our plates as teachers.    With that in mind, we need to figure out how to support all our students in the learning environment of today.  With our Common Core Standards it is essential that we increase accessibility and amplify our instruction, and not simplify or make the task easier when planning our lessons.    To scaffold lessons means to support learning as students become more secure in their understanding.     There are several ways to accomplish this process.  You are already doing one of them when you choose models or examples as supports suited to individual students when developing a concept.  Another way to support learning is to explain and review with students after an assignment.  An effective way to get students involved is to include partnering or grouping students to discuss problems when reviewing either homework, tests, or journals, rather than as a whole group.  This promotes mathematical thinking and discourse among the students, part of Mathematical Practices.  And as you are developing conceptual understandings in Stations, another effective process is to include Sentence Frames to promote math talk and language among students.    As students are working together, you can circulate and listen for misunderstandings and/or misconceptions that you can address in their small groups. In addition to using Sentence Frames, other ideas to increase accessibility to math content for students include:  Think‐Pair‐Share,  Quick Write, Four Corners, Collaborative Posters,  and doing a Gallery Walk.  All of these structures can be better explained by your Math Coach and the Coach will help you with implementation.  These classroom strategies support integrating scaffolding content for students into your lessons to help them become successful in math.

Happy Scaffolding!

Polly

Dear Polly,

As spring break approaches, I want my students to take a break but I also want them to practice their math skills to reinforce their learning. So, what activities can students do to have fun with math during break?

Sincerely,

Fun With Math

Dear Fun with Math,

You are right! We want students to take a break and enjoy their time off, but we also would love for them to spend time practicing those math skills. Below you will find different activities that you could send home for families to use to practice those math skills but also have fun:

• Egg Hunt - Fill plastic eggs with math problems and spread them throughout the house or the yard. Your child can hunt for the eggs and must solve the problem inside each egg in order to keep them!
• Jelly Bean Graphing - Jellybeans are a popular spring break treat. Have your child sort and graph the different colors in a bag of jellybeans. Then, ask your child questions about his/her completed graph. Also, how about an estimation? Estimate how many of each color and count them before graphing!
• Coloring Eggs - While your family is coloring eggs, work to color only a fraction of each egg a chosen color. Example: Can you make 1/3 of the egg blue? Can you color 1/2 of this egg red? After you are done coloring, write math problems to represent the eggs you have dyed. Example: 4 blue eggs + 8 red eggs = 12 eggs; 3 colored eggs + 5 plain eggs = 8 eggs
• Park Visit - While playing at the park, look for shapes or patterns. Measure the playground equipment. Estimate first! Then see how many times you can go down the slide in one minute. Figure out what fraction of the swings are empty. math is everywhere!
• Board/Card Games - Games are a great way to reinforce math skills. Take some time out to play Chutes and Ladders, Monopoly, Yahtzee, or other board games that our family enjoys!
• Spring Treats - Have your child read a recipe and help them measure out the ingredients. Have a picnic and enjoy your creation outside!

I have also attached a 20 Questions activity to send home with the older students. These are great math questions to get students thinking about math but also to force them to problem solve and make sense of the problems. Try them - they are not as easy as they may seem!

Sincerely, 

Polly

Dear Confused Teacher: (Follow-up to letter, 10-30-13)

When writing to you last week, I neglected to tell you that the Chapter 4 recommendations can be found in the K-3 edition of "Teaching Student-Centered Mathematics" by John Van de Walle as I know you and/or your schools also have the 3-5 edition. In the 3-5 edition in Chapter 4, you will also find information about fact fluency and some activities for students, which you probably have already found!

Polly Nomial

Dear Polly Nomial: 

One of my team members thought we couldn't do EDM games during Stations. Another thought we could do the games as long as we added manipulatives. Another team member said students shouldn't do any writing during Stations. I thought we could just give them choices. Please help me understand the purpose of Station activities. 

Signed:

A Numerical Teacher

Dear Numerical Teacher:

In order for our students to meet Standards, our math block includes 30 minutes dedicated to developing number sense. For our students to have number sense, we need to provide them time to gain a deeper understanding of math concepts by working at their edge of understanding while moving them through the Critical Learning Phases and beyond. As teachers, besides providing the appropriate activities based on our student data, we meet their needs by interacting with them while they are at work - asking questions, providing support, posing challenges when appropriate. When choosing activities, we need to be certain that we are developing a concept, not simply providing practice activities. Before moving in EDM games, all AMC grade level goals must be met. Many EDM activities are practice activities, but not appropriate for developing understanding of number relationships. If we choose to use EDM activities, we need to add manipulatives to support understanding of a concept, not just writing numbers by rote, or practicing a game. We also need to be careful about requiring too much writing of numbers. If a child is spending most of the time writing, it is taking time away from concept building and sharing thinking. In some stations, writing is a component to help them keep track of their work or to discover patterns. Providing the stations activities as they were intended from the DNC books will help us make those decisions. Our 30 minutes of Stations every day is a time we can help our students achieve grade level expectations and beyond by providing opportunities to gain number sense, which is the basis of all mathematics. 

Conceptually yours, 

Polly

Dear Polly Nomial,

I am noticing a trend in my classroom during Stations time. My students work hard and they want me to test them. Unfortunately, when I interview them, they are not "ready to apply" at their concept. I see them counting on their fingers, taking a lot of time to try to figure, and using inefficient strategies. I don't understand. They are doing lots of writing and recording of their equations and are very excited by all their work. What can I do to provide them with supportive questioning and instruction so their learning transfers over to the interviews?

Signed:

Fed Up with Finger Counting

Dear Fed Up with Finger Counting:

Students who spend more time writing equations than processing their learning may not be learning at all - but giving us that "illusion of learning." To support students to see relationships and patterns, we can ask them questions that guide them to see relationships and patterns within a concept. We should also do brief instructional groups using teacher directed activities in Developing Number Concepts Books 1, 2, 3. Another structure to implement is to take away the writing piece of a station for a period of time and give them sentence templates to support partners talking together about their math. Partners can work on the same problem and either share materials and work together, or work on the same problem with their own materials. The important part is that they are sharing their thinking and learning with each other. Ask your students if they know what it is they are practicing and learning. Finally, making learning objectives clear to students during Stations time will also make this time more conducive to learning and not just a time for "doing” but really encourage students to know what they are responsible for learning and how that makes them better at doing math.

Conceptually yours,

Polly

Dear Polly,

My kids sometimes have a hard time paying attention to their work in stations. I feel like I need to change their stations a lot to keep them interested and engaged and I just don't have the time to do it! How can I manage my stations so that my students are more engaged?

Sincerely, 

Struggling to Keep Up

Dear Struggling to Keep Up:

Have you tried offering your students choice in stations? Teachers are finding that student engagement increases and students are receiving a more well-rounded station experience when they have the opportunity to choose to work with a concept in multiple ways. A question you may have is how do teachers manage choice? One way is to provide multiple stations within each concept. Students can either choose to stay at the same station during the entire numeracy time or they could have the choice to move to another station. Something important to note is that students need time at a station. Sometimes teachers feel the need to change the stations too quickly and that doesn't give students the chance to really dig into the mathematical thinking. Remember that students start by learning the procedure of how to do that station first, then they start to develop the mathematical thinking required in the station after the process is practiced and learned. 

Consider how you will organize this time with choice. Will you dismiss students to go to the stations and once a station is "full" students can choose from other open stations? Will you have station tubs with multiple station choices in the tub? Will you set a timer for 10-15 minutes and then ask students to make a different choice if they want to do so? 

Another way to increase student engagement is in the questions that you ask while roving and collecting data. Asking good questions that dig into the concept within the station will take a station to a new level for students as they think about what they are doing through a new lens. 

Happy Choosing, 

Polly

Dear Polly:

I keep hearing about clipboard checks, and I want to begin to use them during Numeracy/Station time to help me with formative assessment and next step instruction, but I don't know where to get them or how to use them effectively. Any help would be greatly appreciated!

Thank you, 

Clipboard Check Novice

Dear Clipboard Check Novice, 

I am excited that you want to learn about clipboard checks.  They are a great way to assess students as they work and provide a record of growth.  There are many ways that teachers use clipboard checks in math.  During Stations, teachers use clipboard checks based on the Critical Learning Phases and AMC assessments, whereas, clipboard checks in EDM are focused on the Standards. For Numeracy/Stations time, you can find a document called “AMC at a Glance” on blackboard (in the numeracy section, which is in the support documents folder.)  This document can be used for informing instruction during Numeracy.  Many teachers use this document in different ways, but the document provides a way to record student assessment data from the share drive, which provides a snapshot of where students fall.

Once students are recorded on to the document, you can begin to “assess at work.”  As you walk around the room during Stations, you can ask questions based on the data you recorded.  The document provides the test questions at the top for each AMC test section and indicators for instruction, practice, and application.  This will help you know what type of questions to ask and know exactly where each student needs to be working.  By asking the students as they work, you will begin to see what skills they are mastering, connections they are beginning to apply, or where their misconceptions may be leading them astray.  This provides you information that can guide your instruction for mini‐lessons, small group learning, or changing students’ stations in the moment.

As always, your math coaches can help you implement the clipboard checks in your math block.  Just ask and they will be more than willing to model the use or show you different ways to use clipboard checks.

Happy Checking! 

Polly

Dear Polly:

My students often struggle to recall basic facts. I see students using their fingers and I hear them counting on. I have them using fact triangles but I don’t notice much improvement. How can I help my students? Sincerely, Flustered with Fact Fluency

Dear Flustered:

We need to consider several things before we begin to work with students to become more fluent in their facts and the first is to be certain they understand the concept, whether it be addition, subtraction, multiplication, or division. Common Core State Standards says: “Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected.” Additionally, the Standards state: “Wherever the word fluently appears in a content standard, the word means quickly and accurately…a key aspect of fluency in this sense is that it is not something that happens all at once in a single grade but requires attention to student understanding along the way.” For support, I have attached to this email the Common Core Standards for each grade level that include fact fluency. I also recommend that you have a conversation with your school’s Math Coach. They have many ideas of ways to support your students with fluency. Using fact triangles is one way, but you can expand on that idea to make sure you are individualizing the practice for each student. A couple of other tips: introduce small sets of related facts; correct errors immediately; to make practice efficient, increase or decrease the difficulty depending on a student’s proficiency; use small sets of facts until they are mastered; and never use timed tests, which have been proven to be ineffective and cause many students anxiety and frustration. The research is clear that timed tests do not support fluency. Most importantly, students should have conceptual understanding before starting to work toward developing fluency. Again, your Math Coach can support you and your students!

Sincerely, Polly

Here are the Common Core Standards for each grade level that include fact fluency:

• Kindergarten
  • K.OA.5 Fluently add and subtract within 5
• 1st Grade
  • 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
• 2nd Grade
  • 2.OA.2 Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.
  • 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 
• 3rd Grade
  • 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
• 4th Grade
  • 4.NBT.5 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
• 5th Grade
  • 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
• 6th Grade
  • 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
  • 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.