Daily Math Routines Archives - Shelley Gray

Five Engaging Classroom Routines to Energize Your Back-to-School Math Experience

Shelley Gray — Wed, 09 Aug 2023 00:27:05 +0000

As you gear up for the exciting back-to-school season, it’s the perfect time to plan the math routines that will keep your students interested and engaged in learning, as well as foster a predictable environment where students know what to do and when to do it. Let’s explore five different math routines – Number Talks, Mystery Numbers, Number of the Day, Dot Talks, and Math Games – that will provide opportunity for flexible, strategic thinking and can kickstart the new school year with a bang!

Math Routine #1: Number Talks: Fostering Mathematical Discourse and Flexible, Strategic Thinking

Number Talks are short, 5-15 minute whole-class discussions with the goal of building number sense. The focus of the discussion is on all the many ways to solve the problem, rather than on the answer itself. During a number talk, the teacher poses a problem and students share strategies, reflect on others’ strategies, and learn to see math in different ways. Number Talks are a fantastic way to promote mathematical discourse among students. These discussions encourage learners to articulate their thought processes and strategies for solving math problems. Students develop a deeper understanding of mathematical concepts through open-ended questions and peer interactions. Number Talks also help them realize there isn’t just one right way to solve a problem. This routine not only enhances students’ problem-solving skills but also builds their confidence in sharing ideas.

If you’re ready to implement this effective math routine, I’ve written a complete, comprehensive guide to beginning number talks in your classroom here.

Math Routine #2: Mystery Numbers

I hear from many teachers who use mystery number activities as their math routine at the beginning of math class or even when they enter the classroom in the morning. Mystery Numbers keep students challenged as they work through the clues, eliminating numbers as they go. Eventually, they are left with only one number remaining – the mystery number. One of the greatest advantages to using Mystery Numbers as a math routine in your classroom is that your students are building place value skills and math vocabulary without even realizing it.

If you’re interested in kicking off the school year with mystery number activities as your morning math routine, here’s a blog post where you can find more information.

Math Routine #3: Dot Talks

Let me ask you a question. How many do you see?

Now I want you to think about how you saw them. Chances are good that you didn’t count them one by one. Did you see 4 groups of 3? 2 groups of 6? Are there any other ways you can see them?

Introducing Dot Talks to your math class routine can be a game-changer when it comes to building a solid foundation in number sense. Subitizing, the ability to recognize the number of objects in a group without counting, is a crucial skill for early mathematical development. Dot Talks utilize visual representations of dots arranged in various patterns, challenging students to quickly perceive and identify the quantity without needing to count individually. By incorporating Dot Talks into your daily routine, particularly at the beginning of the year as you assess number sense, you’ll be providing students with an engaging opportunity to enhance their subitizing skills, fostering a deeper understanding of numbers and paving the way for more complex mathematical concepts.

Dot talks are also a fantastic precursor to number talks.

Interested in learning more about dot talks and subitizing for number sense? Here’s a blog post to help you get started.

Math Routine #4: Number of the Day

The Number of the Day routine allows students to explore a single number in-depth. Each day, a new number is chosen, and students engage in various activities related to that number. They might break it down into its parts (decompose), create equations that equal the number, explore its place value, and even represent it using different models. This routine helps students understand the versatility of numbers and appreciate the interconnectedness of math concepts.

Here are 10 ideas to include in your number of the day routine.

Math Routine #5: Math Games

I love math games for several reasons. First of all, they are an effective way to reinforce skills, particularly when it comes to fact fluency. Second, they can often be played with little to no prep and are a great way to break up a longer lesson. But the reason that I love math games the most is that they energize students and help them realize that math is fun! Although I love math games for the end of class, I also often like to begin a math class with a game. It gets students’ minds working right away, and puts them in a more energetic state before the lesson or independent work time begins.

If you’d like to start collecting a solid repertoire of math games to play with your Grades 2-7 students this year, here’s a weekly email series that you’ll love!

I hope these five math routines are useful to you! What are your favorite routines for math class? I’d love to hear in the comments below!

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5 Great Reasons to Use Number Talks in Your Math Classroom

Shelley Gray — Thu, 11 Aug 2022 03:18:39 +0000

Number talks can be one of the most powerful additions to your math routine. Why? Because your students will explore math in a way that they may have never done before. During a number talk, students think about problems in flexible ways and then reflect on classmate’s strategies. The most exciting part for the teacher is often listening to all of the unique, creative problem-solving strategies that their students use.

If you’re not already familiar with how to do number talks, don’t be intimidated! It’s actually really simple to get started. Here’s a post where I guide you step-by-step through the process.

Here are 5 great reasons to begin using number talks in your classroom ASAP!

For the purposes of this article, when I say “number talks,” I not only refer to the traditional number talks where you present an expression and solve it, but also to other types of math talks like the ones you’ll find inside Math Conversations.

Number talks teach students that math is flexible.

Math often seems like a black or white, right or wrong subject. This is a common misconception by both adults and kids. But there is SO much more to math than correct answers, and when your students realize that it can be life-changing. The emphasis must be on the THINKING, not the ANSWER, and number talks are the perfect opportunity to reinforce this.

Consider the difference it could make when you ask your students to solve 15+25 in as many ways as possible, rather than to simply tell you the answer. Here are just a few of the ways your students might share after getting comfortable with number talks.

Students are introduced to new strategies…by each other!

As a teacher, you know how important it is to introduce students to new mental math strategies. But sometimes the most valuable strategies can come directly from your students! Kids often see things differently than we do, and it can be fascinating to listen to how they solve problems when they are given the chance to share. Too often classrooms don’t allow for this time – time for students to share their thinking and learn from each other rather than from the teacher or from a worksheet. Listening, sharing, and reflecting on classmate’s strategies is one of the most important aspects of a number talk.

Math confidence soars.

There are students who never speak up in math class because they have math anxiety or because they are scared of saying the wrong answer – I bet you can think of a few right now. The beauty of math talks is that the emphasis is taken off of this correct answer, and put onto the thinking. Some types of math talks literally have no right answer. When students realize this it can be empowering. They finally are comfortable to speak up because as long as they can justify their answer, it’s not possible to get it wrong!

Conceptual understanding is built.

We know how important conceptual understanding is, but it can be hard to set aside the time to build and reinforce it. The wonderful thing about number talks is that this is built right in. When you focus on the many ways that a problem can be solved, it forces students to think in strategic and flexible ways. This helps them build that conceptual understanding that will become the foundation for their number sense. When students truly UNDERSTAND math, rather than simply memorize it, it empowers them to be able to solve anything.

Number talks level the playing field.

In a number talk, all the students and teacher are equals. No one is “teaching” and no one is better than others. It is a time for sharing, for listening, and for reflecting. You might hear students saying things like, “Oh, I see how ______ is thinking! He added instead of subtracted! I like that strategy!” or “________’s strategy doesn’t make sense to me yet. Can you explain it again?” In a number talk, everyone learns – even the teacher. It can be empowering for students once they realize that number talk time is a safe place where answers are not judged as right or wrong, but respected and reflected on instead.

Ready to try number talks in your classroom?

Get 20 free slides here to get you started!

Yes, please!

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Three Types of Tasks You Should Add to Your Math Routine, Tomorrow!

Shelley Gray — Tue, 26 Apr 2022 20:57:22 +0000

Why should you shake up your routine in the Math Lab? In a word: equity.

It is more important than ever to provide engaging tasks for learners that they can actually learn from, that meet them where they are at, and that are rich in mathematical content. It’s been two years since the first COVID-related school closure, and this has me reflecting on what adjustments I’ve made to balance out the ongoing disruptions to learning and ensure that everyone coming to class, virtual or not, has the opportunity to think deeply about Mathematics.

Even under “normal” circumstances, it can be hard to curate the right tasks for your learners day after day. Let’s get to some supportive math routine ideas you can use in your classroom, tomorrow! Shall we?

Math Routine Task Type #1: Low Floor, High Ceiling

If you’re like me, you want to promote the idea that ALL learners’ thinking is valuable while at the same time ensuring your emergent mathematicians don’t feel lost, and that your proficient mathematicians feel challenged. Is it really possible to do that when everyone is working on the same problem?

Yes, if your task is “low floor, high ceiling.”

In a previous article on the power of mathematical discourse, I wrote about these types of tasks as a way to level the mathematical playing field. Math education guru Jo Boaler describes them as having a low access point that everyone can creatively approach and discuss deeply, with a high ceiling that provides opportunities to enrich and challenge learners at higher and higher levels of understanding.

One of my favorite tasks from Boaler’s site (though it was adapted from an original task by Mark Driscoll) is called Paper Folding. It took me more than a year to find a solution to the fifth step! Ian Byrd writes that this is a telltale sign you’ve found a low floor, high ceiling task: there are solutions for learners to uncover that you’ve never even thought of!

Math Routine Task Type #2: Open Tasks

An open task is exactly how it sounds: the answer is not limited to one thing.

Open tasks allow for divergent thinking, instead of expecting all learners to arrive at the same answer. I first learned about this type of task from Marian Small who has an entire book series dedicated to them! She says that open tasks:

Demand thinking (not regurgitation)
Focus on big ideas in Math
Allows all learners to participate
Get learners talking about mathematical ideas

Open tasks can be as simple as giving students an answer and asking them to write the question.

Another way to open up a textbook or worksheet task that you already have would be to let the learners pick their own values. Small (2016) says, when you incorporate open tasks, “One question can meet the needs of many learners because the question is not overly tight and so benefits a broader range of students.”

Math Routine Task Type #3: Parallel Tasks

Last but not least, another great way to differentiate and reach more learners in your group is to use parallel tasks.

Here you need at least two variations of your task, both connected to the same big mathematical idea. This is important because if your tasks do not align with the same expectation or standard, then your learners can’t discuss their work with each other or make connections during a group discussion.

Present all variations to the learners, and let them choose which one to work on. In the same way that low floor, high ceiling and open tasks invite everyone to think and do math, giving learners parallel choices helps them more readily approach Math and again, see themselves as valuable contributors to their math community. Here we are back at one: equity.

Try One, Try Them All

In the wake of COVID-19 it seems inevitable that as educators we will see the most varied classrooms of our careers in the years to come. Of course, learners, parents, educators and administration have been doing their best to pivot from in-person to remote and back again but, the fact remains that recent learning has been inconsistent. Regardless of your classroom context, there is a lot of content out there so I have generated a short list below under Resources that should help you get started without having a lot of extra planning on your plate. All are designed to meet your learners where they are, whether they are struggling with the basics or reaching ahead for more.

Give one or all of these task types a try and let us know how it improves the quality of learning in your classroom!

Resources

For the readers:

Creating Low Threshold High Ceiling Classroom article – https://nrich.maths.org/7701
Aim for High Ceilings and Low Floors article – https://www.byrdseed.com/to-differentiate-lower-floors-and-raise-ceilings/
Numberless Word Problems – https://bstockus.wordpress.com/numberless-word-problems/

For the grab and goers:

Low Floor, High Ceiling Tasks:

Open and Parallel Tasks:

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Wondering How You Can Integrate Literacy and Math? Here are SIX Easy Ways!

Shelley Gray — Wed, 02 Feb 2022 15:16:29 +0000

As teachers, the amount of content we need to teach in a year can be overwhelming. But integrating subject areas is one way to work smart in the classroom. Literacy and math may not seem easy to integrate, but there are some simple ways that you can encourage reading and writing in your math class!

Reading In Math Class

One way to incorporate literacy with math is to do a math-based read-aloud with your students. While reading, stop to ask questions and discuss the book. This can spark problem-solving conversations among students. They will have so much fun with math-related conversations!

Some great math read alouds for your students:

Equal Shmequal by Virginia Kroll
Elevator Magic by Stuart Murphy
Inch by Inch by Leo Leonni

Math-Themed Reader’s Theaters

My students love reader’s theater plays. They have the chance to act out different roles and pretend to be another person. Reader’s theaters are a great way to introduce and practice math academic vocabulary. They can also be good review for comprehension and fluency.

Exit Tickets

Another great way to incorporate literacy and mathematics is to use exit tickets. Exit tickets work well at the end of math units or lessons and can be used as informal assessments to drive future instruction.

How to Introduce Exit Tickets in the Classroom

It will take time for your students to understand your expectations for their exit tickets. Demonstrate how to respond to questions thoughtfully. Model what a good answer looks like as compared to a great answer. Have your students practice this! Over time, use exit tickets as a way to grow your students’ writing skills and conceptual knowledge about math strategies. After using the tickets for a few lessons, challenge your students to write longer paragraphs.

Sequence of Events Writing

Incorporate writing and mathematics together by having your students write the sequence of steps to solve a math problem. For example, you might have your students write down the steps to solve a multiplication/division problem or the area of an irregular shape. (Use transition words like first, next, then, and last.) After completing this as a whole group, have your students try it independently.

Math Journals

Math journals are fantastic for getting your students to write at the beginning or end of your math period. Allow your students to let their creativity shine through with their writing style.

Some possible journal topics include:

What is the difference between multiplication and division?
Tell me everything you know about fractions.
Write a multiple choice question about area. Include one correct answer and three other options that students could easily mistake for the right answer. Why could they easily be mistaken for the correct answer?

Tip: Designate a time where students can share their journal passage. I love having my students share some of their journal entries at the end of our math block.

Creating Word Problems

One of my favorite lessons to teach is writing word problems. Start this lesson by looking at some sample word problems. What is the problem telling you? What is it asking you to do?

After analyzing several word problems, have students practice writing their own. I like to emphasize that they can tell a story with their word problems. Students can also be creative when writing by using their names, names of friends and family members, favorite athletes, etc. Encourage students to be imaginative and incorporate their hobbies, favorite foods, passions, or pets into their word problems.

To foster teamwork and collaboration, students can even work with partners to create and discuss their word problems. When everyone finishes, students can share their word problems.

What are your favorite ways to integrate literacy and math? Share in the comments below!

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Making My Own Three-Act Task: What I Learned and Why You Should Try It

Shelley Gray — Thu, 27 Jan 2022 19:13:05 +0000

A three-act task is a whole group problem-solving activity, presented in three “acts” to engage and immerse students in authentic and meaningful math learning. Three-act tasks encourage curiosity, perseverance, and growth mindset (“We can do hard things!”). And even better – they are fun!

The Hero’s Journey

My Hero’s Journey Begins

As it turns out, and as the literary lovers out there probably know, the Hero’s Journey is a mono-myth template developed by Joseph Campbell (Matthew Winkler on TEDEd summarizes it well here). What I need you to know is: it will also save your math lessons.

This past September I started a new gig that changed my life. I had been a full-time educator for seven years prior and, especially with the past couple of COVID years, “teaching” for me had started to become synonymous with “draining.” I kid you not I was digging deep and doing the work to make a career swap… and then I found my current school. Though I’m not technically a teacher anymore, I am still very much an educator. It’s just that now the learners call me a Guide.

So what exactly does a Guide do that is different from a teacher?

You may have heard of these expressions before, the “sage on the stage” or “meddler in the middle” – well, I am the “guide on the side.” Each refers back to various learning theories and tries to define the educator’s role in the classroom. The semantics might not seem like much, but for me, moving through the roles of traditional teacher to even a reformed meddler does not nearly compare to the dynamic power shift that occurs quite dramatically as a Guide. And if I’m being perfectly honest, I’m failing at this all the time because it requires that I step back from the learners and let them truly lead. And when things don’t work for the learners, I am supposed to step back some more. Failure is the goal because it will be their greatest teacher (not me). They are on a journey together as a community, and as a Guide, so am I.

The Call To Adventure!

In between considering leaving teaching and still teaching, I had been wanting to expand my approach to math education in particular. When I came across the practice of Three Act Math Tasks I was instantly intrigued. They are typically multimedia-driven, with a real-life hook, they capture EVERY learner’s attention and they make math accessible to all learners where they are using the power of intuition. And, cue serendipity, they often follow the Hero’s Journey as a template. When I found out that my new school uses this as the arc for every school year, every sessional quest, right down to the weekly and daily narratives too, I couldn’t help but feel that little spark from the universe that I was on the right path.

Assistance

Dan Meyer (one wise mentor I discovered on my journey) explains how this refreshing approach helps rectify many “symptoms” you’ve likely encountered at some point in teaching mathematics. Though he is coming from a secondary perspective, I find the same applies for primary/junior-aged learners:

They often hesitate to try something new or perceived as hard and,
give up easily, and/or,
don’t seem to truly make meaning of the math, and,
have easily caught on to the notion that “word problems” are the ones we boycott.

What is a Three-Act Task?

So, what exactly is a Three-Act Task and how does it work? Simply put, this is a whole group problem-solving activity, presented to learners in three “acts” to engage and immerse them in authentic and meaningful math learning. Let’s dig in!

A Tasty Task

Full disclosure: when I was younger I used to eat A LOT of Starburst candies and my friends and I used to fold up and keep the wrappers. I kept them all these moons and finally found a use for them (no, I never did quite make them into origami or a purse).

ACT I – Present a teaser, a short clip, something recognizable from daily life but curious! Everyone can participate because we are bringing thinking down to shared experience and intuition.

What do you notice and wonder about my candy wrapper collection?

Side note: I just learned about the real power of the word wonder from queen Brené’s new book where she says that, “wonder fuels our passion for exploration and learning, for curiosity and adventure” (Brown, p. 59, 2021). If the learners have nothing to wonder about, what do we expect them to learn? Furthermore, we might know what we hope they’ll ask about, but putting the power in their hands here is key. Whatever the learners decide they want to understand about your prompt is where we’ll head in Act II – so make sure the context is math rich! Inevitably, the learners ask me: how much candy did you eat, Ms. Mel!?

ACT II – Continue by asking what information is missing? This gets some problem-solving going; what information matters and does not matter, what do we keep and what do we toss? The learners, again, drive the sub-steps and are not given them (or even “taught” them) in advance! What mathematical processes would help us determine how many there are? What information is missing or hidden? As they ask questions, provide more information.

ACT III – Similar to the consolidation part in a three-part lesson, bring everyone together to discuss strategies and solutions. Bonus points if you have monitored learner thinking and selected or sequenced the sharing to portray a coherent storyline (another blog post on the The 5 Practices soon to come!). Even if you just invite a show and tell style discussion, as Meyer says, “The math serves the conversation, the conversation doesn’t serve the math.” If no one gets to the goal (there are 792 wrappers by the way), the discussions about why not are just as powerful in terms of turning students’ mathematical reasoning on and grounding it in something interesting to them.

My Three-Act Task: What I Learned

What Failed: I have used this in a traditional Grade 6 Math classroom and in an alternative multi-age studio, and both times the learners never quite got to the strategies I was hoping they would. I anticipated they would use measurement concepts like area and volume to make precise estimates based on Metric measurements of the container and/or an individual wrapper. While there were accurate estimates and some smaller case arguments, the advanced spatial reasoning wasn’t captured and shared as I had hoped.

What Worked: Everyone participated. Everyone shared an idea. Everyone was excited. Some of us made connections between area and perimeter. Some of us built smaller models. We practiced other important rituals like “say more about that” and asking questions of our peers. Learners had fun in the Math Lab.

A Challenge to You!

So, next time you’re planning a mathematics activity, I challenge you to try to:

Incorporate real-life multimedia into your problem-solving
Extend the invitation to all learners with a sense of wonder and the three-act template
Let the learners drive the questions
Let them struggle (it is a Hero’s Journey after all!)

If you try it out, let us know how it goes in the comment section below!

Resources

For the readers:

From Teaching Children Mathematics Volume 24 Number 2 (2017) check out the article “Trying Three-Act Tasks with Primary Students”

For the grab and goers:

Explore these banks of free tasks for primary/junior learners:

Graham Fletcher

Dane Ehlert

References

Brown, B. (2021). Atlas of the heart. New York.

Meyer, D. (n.d.). Math class needs a makeover. TED. Retrieved January 23, 2022, from https://www.ted.com/talks/dan_meyer_math_class_needs_a_makeover?language=en#t-122859

TEDEducation. (2012, December 4). What makes a hero? – Matthew Winkler. YouTube. Retrieved January 23, 2022, from https://www.youtube.com/watch?v=Hhk4N9A0oCA

FREE MULTIPLICATION ACTIVITIES

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Ten Important Things to Include in Your Number of the Day Routine

Shelley Gray — Mon, 22 Nov 2021 18:19:31 +0000

There’s no doubt that students thrive on routine. Using a Number of the Day routine starts your math class off with a predictable activity that gives students a chance to make connections, problem-solve and apply what they already know to what they’re learning. It also gives students the chance to continue working with important number concepts even after you’ve moved on to other concepts in your lessons. Number of the Day gives kids opportunities to work with numbers in many different ways. Here are ten concepts to include in your routine to build strong number sense skills and boost your students’ confidence in math.

NUMBER OF THE DAY ROUTINES

Routine #1: Word Form

We assume that as students learn to count, recognize, and quantify numbers, they also learn to read and spell number words. This is often not the case! In order to be able to write numbers in word form, children need exposure and practice. Including word form in your daily number routine also gives opportunities to connect the words with the numerals they represent.

Routine #2: Place Value

Many mathematical concepts build on place value. Truly understanding place value provides students with a solid base for many future concepts including regrouping, multi-digit multiplication, decimals, and percentages. Place value practice gives students the opportunity to truly understand what the digits in each number mean.

Routine #3: Representing Numbers

A number is not just the numeral we print on a page. A number can be represented in so many different ways! Exposing students to multiple representations allows them to make connections and “see” how numbers can have the same value but be represented differently. Some of the representations that can be used in your Number of the Day practice include ten frames, number lines, base ten blocks, equations, arrays, dots, tally marks, pictures, words, money, fingers, dice, rekenreks and hundred charts. We can connect these representations to real, concrete materials as well as abstract representations (CRA Model) to help students build their understanding even more.

Routine #4: Skip Counting

Skip counting is a fundamental skill used in many other math practices. We use skip counting in real life to solve problems where multiplication and division are needed, count money, tell time, and keep score in a basketball or football game. Skip counting also makes counting larger quantities quicker and more efficient. It’s also important to remember that we don’t have to start at zero when skip counting. For example, we can practice counting by 10’s starting at 13, or practice counting by $0.25 starting at $1.50.

Routine #5: Odd and Even

The concept of odd and even goes hand-in-hand with skip counting. Identifying odd and even numbers help children make sense of the number system and identify mathematical patterns. Once students learn that some numbers can be divided into two equal groups (even) and some cannot (odd), they can extend their understanding to multiplication, division, prime numbers, factors, and multiples.

Routine #6: Expanded Form

Writing numbers in expanded form is an important way to reinforce place value. By breaking a number apart, or decomposing it, students can see the value of the number they’re working with. As numbers get larger, they become more abstract. Expanded form makes large or more complicated numbers easier to work with.

Routine #7: Money

Recognizing, counting, and calculating values with coins and bills is not just an important math skill, but a life skill. With daily practice, children become more fluent and confident when dealing with money. Adding money to your daily routine prepares children for financial literacy throughout life.

Routine #8: Greater Than/Less Than/Equal To

When comparing two numbers, your students may be able to draw the correct symbol, but do they really know what it means? “Alligator mouth” is a common trick used to remember which symbol to use, but we want to encourage real understanding rather than tricks. With regular practice, students learn that the relationships between numbers are more than just a symbol between them. Comparing numbers builds skills that we use in the real world.

Routine #9: Number Lines

A number line presents numbers in relation to each other and provides a visual representation that students can see. It is a versatile tool that can represent all types of numbers – positive and negative whole numbers, proper, improper and mixed fractions, decimals, and percentages. A number line encourages children to see the relationship between numbers and, as a result, develop a deeper understanding of number.

Routine #10: Equations

Incorporating equations into your Number of the Day routine can help students see patterns and connections. This practice also allows them to continuously reinforce addition/subtraction/multiplication/division skills. Equations can give you a chance to differentiate your instruction as well. For example, one student might incorporate fractions into her equations, while another focuses on whole numbers only.

Number routines build foundational skills by giving students the practice they need to build their mathematical thinking. Number of the Day is a simple but effective activity that you can do without any pre-made materials. Just write the activities on the board in the morning, and have students complete them in a notebook! However, if you are looking to simplify your prep, here are some ready-made packages that might come in handy for you. {Find links below.}

Number of the Day activities for numbers 1-50 (50 activities)

Number of the Day activities for numbers 51-100 (50 activities)

Number of the Day activities for numbers between 10 and 1,000 (75 activities)

Fraction and Decimal of the Day

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