Other Archives - Shelley Gray

How the Friendly Number Mental Math Strategy Progresses: Elementary to Middle Years

Shelley Gray — Fri, 18 Apr 2025 14:57:55 +0000

As teachers, we know that strong mental math skills are foundational for developing number sense and math confidence. One strategy that can make a big difference for students is making a friendly number. This simple yet powerful strategy helps students approach calculations with flexibility by adjusting numbers to ones that are easier to work with. The best part is that this strategy can be used from very early years to middle years and beyond. In this post we will look at how this strategy might progress througout grade levels.

First things first, there is an important understanding that students must develop – when we add two (or more) parts, we can move objects from one part to the other without affecting the sum. In young students, this understanding is best developed with manipulatives that that they can physically touch and move around.

Now let’s take a look at this strategy in action, beginning in early elementary and progressing through to middle years math.

Using the Friendly Number Strategy With Ten Frames and Base Ten Blocks

When students are first introduced to this strategy, it’s best to use concrete manipulatives that they can physically move from one part to the other. Even though it may be easy for us to understand moving from one part to another, it can still be too abstract for kids. When we use manipulatives and students can move the actual pieces, it promotes a deeper understanding.

The ten frames below show 7+5. In the next picture, we move 3 from the 5 over to the 7 to make a friendly number – 10. Now we have 10+2.

We can also represent this pictorially on a part-part-whole model or a number line, or in an abstract form with digits and symbols.

We can also use base ten blocks to make this thinking visual. In the example below, we are using this same strategy to solve 14+38. We can physically take 2 ones from the 14 and give them to the 38. Now we have 12+40. Is this easier to compute mentally?

Friendly Number Strategy with Multi-Digit Addition

Let’s take a look at how this might look with a 3-digit plus 3-digit addition problem. Here we have 127+285. There are several different ways that we could approach this:

Take 3 from the 285 and give it to the 127 to make 130+282.
Take 5 from the 127 and give it to the 285 to make 122+290.
Take 15 from the 127 and give it to the 285 to make 112+300

and of course there are many more than this.

Which feels easiest to you? For me, the third option feels the best. Having conversations like this with your class about different ways to use the same strategy is a key to adding flexibility to your number sense routine. Notice that when we are working with numbers in this way, we have a real sense of the magnitude of the numbers – we are not simply working with single digits as we do when working with the traditional algorithm. This understanding is what will lead to stronger number sense.

Friendly Number Strategy with Fractions and Decimals

The part I love most about math strategies is that they are easily transferrable to other areas. This exact same understanding that first graders might use when adding 7+5, can be used by 7th graders when adding 3.2+4.95. How would you approach this problem? Personally, I would take eight tenths from the 4.95 and bring it over to the 3.2 to make a nice friendly number, 4. Then my expression becomes 4+4.15, which is simple to do mentally.

We can use the same approach with fractions with the same denominator.

Helping students make sense of numbers—rather than just memorize procedures—is one of the most meaningful parts of teaching math. Making a friendly number equips students with a flexible, intuitive approach that supports accuracy, efficiency, flexibility, and confidence. By introducing this strategy early and revisiting it in increasingly sophisticated ways across the grade levels, we give our students tools they can carry with them well beyond the classroom. Whether they’re adding within 20 or solving multi-digit equations, friendly numbers can be a familiar and empowering part of their mathematical thinking.

See a video about this strategy on Instagram HERE.

The post How the Friendly Number Mental Math Strategy Progresses: Elementary to Middle Years appeared first on Shelley Gray.

Free Halloween Number Talks to Build Number Sense This October

Shelley Gray — Mon, 26 Sep 2022 17:20:22 +0000

Regardless of whether or not you currently have a number talks routine in place in your classroom, your students are sure to love these free Halloween themed number talk activities. Number Talks are a fantastic way to help your students build number sense in an engaging way.

First of all, here are 5 great reasons to implement a number talk routine in your classroom as soon as possible:

Number talks teach students that math is flexible.
Students are introduced to new strategies and new ways of thinking.
Math confidence soars!
Conceptual understanding is built.
Number talks level the playing field between students. We are all equals!

Free Halloween Number Talks

If you are already using the full year Math Conversations number talk slides, you’ll recognize the familiar layout of these Halloween-themed slides. Students will be encouraged to think deeply about a variety of math concepts. They will share their thinking with the class, and reflect on other students’ thinking.

I’ve included ten different Halloween number talks in all. Choose the ones that best fit your goals for your students! Additionally, some come in differentiated versions so you can choose the version that best suits your classroom.

Get your set of free Halloween Number Talks here.

The post Free Halloween Number Talks to Build Number Sense This October appeared first on Shelley Gray.

Here’s an Easy Way to Incorporate Subitizing into Your Math Routine

Shelley Gray — Wed, 24 Aug 2022 00:51:11 +0000

Subitizing – if you teach elementary math you’ve probably heard this word, but may be unsure of what it actually means or how it can be used effectively in the classroom. Before I get into the definition of subitizing and tips for using it to help your students build number sense, let’s try a couple of fun activities.

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?

Let’s try another one.

How did you see them this time? Do you see 4 diagonal groups of 3? Do you see 3 horizontal rows of 4? Maybe you saw 2 groups of 6. Are there any other ways you can see them?

What you just did is called subitizing. You recognized a quantity of objects without counting them one by one.

When you practice subitizing, you become a flexible thinker, realizing that there are many different ways to make a number. You also build a strong foundation for number sense as you visualize numbers in different ways.

Subitizing is common in kindergarten and grade 1, but did you know it can be just as beneficial to students in older grades? Imagine the conversations you might have with a class of grade 3 or 4 students using subitizing images like this:

Or what about the conversations you might have with a grade 5 or 6 class using a visual like this?

Research supports the relationship between subitizing and strong number sense. But it can be a difficult routine to implement if you don’t have the proper visuals available to you.

Dot Talks are here to support you as you implement this routine in your classroom and work to close the number sense gaps that your students may be struggling with.

Dot Talks are intended as a whole-class, low-floor high-ceiling activity that will get even your most reluctant students involved. There is no wrong answer, as long as you can justify it!

Simple Tips for Getting Started Subitizing with Dot Talks

Begin with visuals that seem “too easy.”

Even though you might think the visuals look too easy, it can be fascinating to hear how different students see the dots. This is also an opportunity to begin with something that seems “low-risk” to students who don’t generally participate in classroom discussions. As students get better at subitizing, use slides with more dots or more complex patterns.

Consider leaving images on the screen before getting into Quick Looks

Often, subitizing activities are done as quick looks. This means that the teacher flashes the image for the students, giving them enough time to see it, but not enough time to count the dots one by one.

But when you first introduce subitizing to your class, you may want to simply leave the dot image on the screen and have a discussion about different ways to see the dots. Then move to quick looks once students are comfortable.

Use Dot Talks as a way to ease into number talks.

If you plan to implement number talks this year for the first time, it can be intimidating to get started. Dot talks are a great way to ease into the number talk routine. It only takes 5 minutes, and your students will beg to do more! When you are ready to get into more complex math talks, your students will be used to the routine and more willing to participate.

About the Dot Talks Subitizing Routine

Using Dot Talks for your subitizing routine will help your students:

build number sense
visualize numbers and strategies
become strategic and flexible thinkers
boost math confidence

Dot Talks are available in three different grade level packages and can be found here (be sure to download the free previews using the links below for an in depth look at what’s included):

Or grab them as part of a Number Talk Bundle along with Math Conversations to have your entire year of Math Talks planned out (no prep required)!

Three Fun Math Games Your Students Will Love

Games are a great way to incorporate learning into the classroom. It’s easier to learn when you’re having fun! Here are three low-prep, fun math

Do You Need Help With Number Talks? Here’s The Quick Start Guide.

Number Talks have gained in popularity over the last several years – and for good reason! They are a powerful and collaborative way for students

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

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

The post Here’s an Easy Way to Incorporate Subitizing into Your Math Routine appeared first on Shelley Gray.

5 Fun Ways to Use a Multiplication Chart

Shelley Gray — Sun, 07 Aug 2022 15:41:29 +0000

Multiplication charts are a staple in many Grades 3-6 classrooms. But how can you use this important tool in a fun way to reinforce multiplication facts? Multiplication charts are more than just a reference tool to find answers to problems – they can support students in a fun way as they learn and practice the times tables!

Here are five fun ways to use a multiplication chart in your elementary classroom. (And be sure to download your free multiplication chart printables down below!)

Cut it up to create a puzzle.

Cut the chart into about ten different pieces and have students put it back together at a math center. To do this, students will need to find products and understand how it works.

Find patterns.

Multiplication charts include lots of different patterns. In the different rows and columns we see skip-counting patterns that we can use when we solve multiplication problems. Have students notice the patterns and make connections to the multiplication facts. For example, in the 5’s row we skip-count by 5’s. We can use that skip counting sequence to solve a problem like 4×5 by skip counting by 5’s four times.

Use the multiplication chart to create arrays.

We can create an array and relate it to an array created with physical objects. Here we see a four by three array. As long as we start the array in the top left corner, the product will be shown in the bottom right. Remember that the more ways we see something, the better!

Times Tables Posters

Bright classroom posters for the multiplication facts

Click Here

Shade known facts on the multiplication chart.

The number of multiplication facts to learn can be overwhelming. But it becomes a lot less overwhelming when students shade the ones they already know. The chart below shows what this might look like once a student has learned the x2, x10, and x5 facts. The number of facts left to learn decreases rapidly (because of the commutative property). When students get to the more difficult facts, there are not many left to learn at all! A mutiplication chart can serve as a good visual for this. I wrote a post about this in more detail which you can view here.

Fill in the missing numbers.

Have your students fill in missing numbers on a multiplication chart to reinforce their knowledge of multiplication patterns.

Free Multiplication Chart

If you’d like to try some of these activities with your students, here are some free multiplication chart printables you can download and use!

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The Best Way to Teach Multiplication Facts: 12 Steps to True Understanding

Shelley Gray — Tue, 12 Jul 2022 20:46:47 +0000

Teaching multiplication is no easy task! Encouraging students to memorize the facts only allows a small percentage of them to be successful. Even then, those good memorizers may not truly understand what multiplication means. Rather than teaching multiplication for memorization, we want to teach it for understanding. Once understanding is built, it’s easier to become automatic with the facts!

If you are teaching multiplication for the first time, or if you’ve taught it before but have students who don’t seem to be grasping it, here are 12 simple steps to teaching multiplication for true understanding.

STEP 1: SUBITIZE TO ENCOURAGE MULTIPLICATIVE REASONING

We can help our students develop multiplicative reasoning long before multiplication is even introduced. Subitizing with ten frames, tally marks, dot patterns, or base ten blocks can help students get a sense of what equal groups looks like. For example, the dice pattern below shows 8 equal groups of 3. We can figure out the total number of dots by adding 3+3+3+3+3+3+3+3 but this is also an opportunity to introduce language such as 8 groups of 3.

See more about subitizing for multiplication HERE or get these Multiplication Subitizing Cards HERE.

STEP 2: CONNECT MULTIPLICATION TO REPEATED ADDITION

Multiplication is a shortcut for addition, and we want our students to be able to see that connection. When we first teach multiplication, students must know that this is not a brand new foreign concept. It is simply an extension of what they already know. This will help multiplication seem less intimidating.

A problem-solving context is an effective way to help students see these connections. The problem below can be solved using addition, but we can also introduce multiplication as a potential method to solve it. Rather than introduce the times symbol immediately, we’ll start with equal groups.

Multiplication should be connected to repeated addition in a way that makes sense for students.

STEP 3: EQUAL GROUPS

Students must understand multiplication as equal groups. If your students have already built some multiplicative reasoning (See Step 1), this will be easier to understand. Provide lots of opportunity for students to work with equal groups in a problem-solving context. This will ensure that these equal groups are a more concrete concept, rather than too abstract.

FREE MULTIPLICATION ACTIVITIES

to help your students master the multiplication facts

Grab them here!

STEP 4: SKIP COUNT

Skip counting is one of the beginning strategies for multiplication. We can skip count using equal groups and then transition to skip counting on a number line.

STEP 5: USE MANIPULATIVES

This step should be used through all of your multiplication teaching, but is so often missed when teachers go directly to multiplication worksheets involving pencils and paper only. Manipulatives provide rich experiences for your students to build their understanding of multiplication, and will ultimately allow more of your students to be successful. Any object can be used for students to create equal groups, such as coins, unifix cubes, base ten blocks, or any other counters you may have in your classroom.

One of my absolute favorite ways to have students represent multiplication is using a rekenrek, which you can read more about HERE.

STEP 6: USE ARRAYS

Arrays are one of the most under-utilized tools for teaching multiplication.

We can use arrays to show students how different facts are connected. For example, the image below shows how 3×4 and 4×4 are connected. 4×4 is simply one more group of 4! Arrays can be built with physical objects (concrete) and then also drawn to represent that physical formation (representational).

STEP 7: TEACH THE COMMUTATIVE PROPERTY

The number of multiplication facts students need to learn can be overwhelming, but it helps to understand the commutative property! When students understand that the product of 3×4 is the same as 4×3, it considerably decreases the number of facts we need to remember! Arrays are one of the best ways to show students the commutative property. Here we can see that when this 3 by 4 array is rotated, it becomes a 4 by 3 array!

STEP 8: MAKE MULTIPLICATION RELEVANT

Multiplication is not one of those concepts that students are never going to use – rather, multiplication will be used all the time in real life. By incorporating real-life scenarios, we can make multiplication relevant and more interesting to students. Real-world problem solving also helps students develop a more conceptual understanding because they can visualize what the multiplication problem really means. How can we do this? We can introduce problems, rather than simple expressions. We can talk about what the problem means. We can also use project-based learning that helps students make those real-life connections.

STEP 9: HELP STUDENTS MAKE CONNECTIONS

Learning multiplication is so much easier when students realize the facts are connected and related to one another. 4×6 and 8×6 do not have to be understood as completely unrelated facts. Rather, 8×6 is simply the double of 4×6! This becomes apparent when we use pictures or visual models. Look at the arrays below. This makes it clear that if we double 4 groups of 6 (24) then we get 8 groups of 6 (48).

These connections are EMPOWERING for students, because it means that they can literally solve anything!

STEP 10: TEACH THE FACTS IN A STRATEGIC ORDER

When I first started teaching multiplication, I taught the facts in regular numerical order. Little did I know, this was completely WRONG! I was making multiplication more difficult than it had to be for my students. When you teach in a strategic order that makes practical sense, it helps students make connections between sets of facts. I recommend the following order of teaching:

x10

square facts (ex. 3×3, 4×4, 5×5, etc)

STEP 11: TALK ABOUT MULTIPLICATION!

It’s important for students to see that there are many different ways to think about and solve problems. Often math is thought of as a black or white, right or wrong subject. But it can be fascinating to see that it’s actually a flexible subject that allows us to think in different ways! One of the best ways to give your students the opportunity to practice flexibility is by having them participate in number talks or math talks.

Through listening and sharing, students are exposed to different ways of thinking, strategizing, and reasoning. This is powerful.

Number talks can feel intimidating for teachers because can feel like you are not prepared enough. But that’s the beauty of it. The role of the teacher is to listen – listen to how students think, listen to how they explain, and listen to how they strategize.

We can learn so much by simply listening.

Here’s an example of a math talk you might have with your students. Think of all the opportunities for rich discussion with this slide. We can see how we double and then double again. We can see how 10×4 is half of 20×4. We can see how 20×4 is 4 times greater than 5×4. We can see that 20×4 has the same product as 10×8.

To get started with a math talk, simply draw a multiplication picture on the board and see where the conversation takes you! Or find out more about these Math Conversations slides, ready-made for the entire year HERE.

STEP 12: REINFORCE MULTIPLICATION ALL YEAR LONG

Multiplication is not just a “unit” that you teach and then move on to other things. Multiplication is an essential operation that is important to your students’ success in future grades. It is highly relevant to their real life and will be used in any job they have. Because of its importance to your students’ future success, multiplication (and the other basic operations) must be reinforced all year long.

This can be done by having a Math Facts center during your daily station time where students work on math fact understanding and fluency.

Here are some free math activities for your math facts center to get you started.

Regular reinforcement can also be done by playing games to practice math fact recall and by spiralling the curriculum and returning to those key concepts repeatedly.

I hope this article helps to empower you to teach multiplication for true understanding, rather than for memorization only. Although it may seem complex, you make a life-changing difference for your students by making small changes and beginning to implement the suggestions above.

If you’d like a completely done-for-you system for teaching multiplication, check out The Multiplication Station, used by tens of thousands of teachers. Or grab a free sample of it here!

Fun Multiplication Games for 3rd and 4th Grade (help them master the facts)

How can you make learning multiplication fun while also allowing your students to master the multiplication facts? WITH GAMES! Multiplication games are an effective way

Here’s A Fun Multiplication Math Game Your Students Will Love

Once your students learn the multiplication facts, it’s important to continue to reinforce them. But this can be easier said than done when you have

What’s the Multiplication Area Model and How Do You Teach it? Comprehensive Guide

The area model is a strategy for multi-digit multiplication, allowing students to build conceptual understanding before transitioning to the traditional algorithm. But there is more

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25 Fun End of the Year Classroom Activities

Shelley Gray — Sun, 15 May 2022 01:22:19 +0000

As the end of the school year approaches, it can be more and more difficult to keep your students engaged in and excited about learning. It’s a chaotic time! You’ve got a million things to do and not much time to do it! But I know that you STILL want to make sure that these days are memorable for your students. Luckily, there are tons of different, fun ways to keep your students learning right until the last day of school! Here are 25 end-of-the-year classroom activities to make the year-end memorable for both you AND your students.

1: Do passion projects. Have students choose a topic that they are passionate about. This can be ANYTHING – soccer, dogs, the environment, or fashion. Have students decide on a topic and guiding questions, and then complete research. Then have students create a PowerPoint presentation, poster, or lapbook in order to present their information.

2: Create a memory book. Reflecting on all the things that have happened over the year is sure to bring pride and laughter to your students. This memory book is created lapbook style, allowing your students to make their books unique.

3: Try a room transformation. Bring a small tent, some checkered tablecloths, and flashlights, and you’ve got yourself a fun camping-themed room transformation! Use this free math project to align your curriculum with the camping theme!

4: Have a bake sale! Have students bring in baking to sell to raise money for a local charity. Use this as an opportunity to work with money in a real-life setting.

5: Do a “Meet the Teacher” day when next year’s class comes to meet the teacher and do an activity together.

6: Have the students write a letter to the upcoming students. Have them include their favorite part of the year as well as tips to be successful.

7: Plan a picnic lunch! Take your class outside for a special picnic.

8: Hand out classroom awards! Use PowerPoint to make your own awards to suit the students in your class, or try these pre-made classroom awards that focus on positive character traits like optimism, curiosity, persistence, leadership, and kindness!

9: Have a pizza party and let students make their own personal pizzas! Add an ELA and Math component by writing about “How to Make a Pizza” and incorporating fractions. This Pizza Place Math Project might also come in handy!

10: Create a time capsule to open when your class graduates! Include a “Letter to My Future Self” as well as any memorable items from the year. Have students write down memories to include as well.

11: Pass a ‘Graffiti Page’ for each student around the room; all kids write a compliment for each of their classmates. Your students will love reading all the compliments when they get their own graffiti page back!

12: Try an Escape Room! Escape rooms are fun for any time of the year, but are especially wonderful for keeping your students engaged in those last days of school. This Trapped in the School for Summer Escape Room will have students jumping with excitement as they try to overcome the obstacles and get out of the school! See my best tips for doing an escape room with your class here.

13: Have a Writer’s Workshop celebration! Put out all the books your students have written over the year and give them time to read each other’s books. Hand out hot chocolate as they read to make it extra special!

14: Write thank you notes to someone in the school. This could be another teacher, the custodian, the principal, or anyone else who has made an impact on your students over the year!

15. Play games! Salute, Knock off the Clock, and High Low are just a few examples of fun games you can play with minimal prep and materials. Multiplication Bump is another fun one your students will love!

16. Have a ‘secret’ Random Acts of Kindness Day. Without telling anyone that they’re doing it, have your students do random acts of kindness like holding doors open, giving compliments, etc. throughout the day. At the end of the day, have a conversation about how it felt.

17. Invite a local animal shelter to the classroom to talk about what they do and how you can help. There’s no denying that kids love animals, and I’ve heard from a lot of teachers who have had great success with a talk from a local animal shelter after completing this Run a Pet Shelter Math Project.

18. Hand out End of the Year Activity Books to use as early finisher activities, Friday Fun activities, or just in those times between special events at the end of the year. This activity book includes fun activities like jokes, acrostic poetry, math squares, word search, crossword, code cracking, and more!

19. Reinforce growth mindset. When reflecting on the year, don’t just limit it to favorite activities and memorable experiences. Be sure to reflect on how students grew over the year. What did we get better at? What obstacles did we overcome? What did we accomplish as a group?

20. Do a book project. Have students choose the best book they read this year, and use it to create a diorama. Students can do a book talk and present their diorama to the class. Have other students leave a positive comment for each presenter.

21. Do an A-Z Autobiography, where students write something about themselves for each letter of the alphabet. Get a free template for this activity HERE.

22. Make ice cream sundaes! Here’s another great opportunity for a How-To writing piece. If you’d like to incorporate math as well, try this Run an Ice Cream Shop Fraction Project.

23. Get some fresh air! The end of the year is the perfect time to take your students outside to read, have an outdoor class, or even plan an outdoor scavenger hunt! Being outside feels like a “treat” on a beautiful day!

24. Have a snowball fight! Have each student write their favorite memory from the year on a piece of paper, and then crumple it up into a ball. Split the students into two groups, and position the groups at opposite sides of the classroom. Then (when you say “Go!”) have students throw their snowball to the other side. A student should pick it up, read it, and then crumple it up again and throw it for another student to read. This can also be used to review content for any subject!

25. Have a board game afternoon! Have students bring in their favorite board games, and spend the afternoon playing them!

Have ideas to add? Leave them in the comments below!

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Need a Fun Math Game to Use For Warm-Ups? Try Knock off the Clock!

Shelley Gray — Wed, 20 Apr 2022 17:15:28 +0000

Knock off the Clock is a fun, fast-paced math game that can be used for addition, subtraction, multiplication, or division. If you are playing with younger children, use addition and subtraction only. Older students can use any operation.

Here's How to Play This Fun Math Game

Have each student draw a clock on their paper, with the numbers 1-12 labelled as shown here.

Are your early finishers engaged? Get a 2-week free sample of the Early Finisher Board here.

Yes, please!

Students roll two dice and add, subtract, multiply, or divide them. They write the full equation on their paper and then cross the answer off of their clock, “knocking” out one of the numbers.

Play continues until all the numbers have been “knocked off the clock.”

If you are playing in pairs rather than individually, students compete to see who can be the first one to knock all the numbers off their clock.

Here’s a video so you can see this game in action.

Knock off the Clock is a fun game to play as a math warm-up, or if you have five minutes left in class and want to use it effectively.

Using Math Games with Older Students

Even if you teach older students, try playing simple games like this every once in awhile! You might think they are past it, but don’t underestimate the power of having fun in math class. And who couldn’t use a bit of fact fluency practice?!

Looking for other fun math game ideas for your classroom? Salute was always a class favorite in my Grade 3-4 class, and I know your students will love it too! Find the full game instructions HERE.

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Help Your Students Easily Master the Times Tables with This One Simple Strategy

Shelley Gray — Tue, 05 Oct 2021 16:17:52 +0000

Hands up if you’ve ever seen a student completely defeated over learning the multiplication facts. Do your students view multiplication as

boring?

un-interesting?

difficult?

impossible?

What if I told you that you can help your students easily master the times tables using this one game-changing strategy that will make multiplication fun, interesting, and meaningful!

Focusing on the connections and relationships between facts will transform how your students understand multiplication. But so often this is left out of multiplication instruction.

In this article I’m going to tell you exactly what you can do in your classroom to help students begin forming the connections and relationships that are so important for true fact fluency and understanding.

This will give kids the “a-ha” moments and the ability to solve ANY fact – even if it hasn’t been “memorized.” When students understand that multiplication facts are all related – that they can use one fact to help them solve another – the thought of learning the times tables suddenly becomes much less intimidating.

Here are three simple tips for how you can help your students easily master the times tables by focusing on connections and relationships between multiplication facts.

Tip #1: Incorporate Concepts Like Doubles and Halves

Our students need to understand how facts like 3×5 and 6×5 are connected. Or how facts like 10×2 and 5×2 are connected. This concept of doubles and halves can be made visual with an array. When students can look at an array and actually SEE what the facts mean, it becomes easy to visualize 5×2 as half of 10×2.

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I go more into detail on this concept in this free guide – Three Reasons Your Students Aren’t Mastering The Multiplication Facts (and what you can do about it). Students must understand that multiplication facts aren’t isolated pieces of information they need to memorize in a meaningless way. Facts are related and connected, and we can use this knowledge to master the times tables…without having to memorize! When we understand connections, we can literally solve anything!

Imagine how understanding doubles and halves can help when we get past basic facts? What about solving something like 35×7? We could do this quickly in our heads when we understand that it will be half of 70×7. Or how about 25×12? This understanding of doubles and halves can help us solve this by first thinking of 50×12, then simply halving the product.

Tip #2: Treat Sets of Facts as Related to One Another (Not as Isolated Pieces of Information)

When we help students see that sets of facts are related, suddenly multiplication gets a lot more fun. We don’t HAVE to memorize the facts – all we have to do is understand them!

This activity from The Multiplication Station shows how we can help students make a visual connection between the 10’s and 9’s facts. We don’t have to memorize all the 9’s facts! All we have to do is understand how they are related to the 10’s facts! It is this understanding that will enable students to easily solve a fact like 9×25 without resorting to traditional long multiplication or a calculator.

We can help students master the 9’s times tables simply by helping them understand the connection to the 10’s facts.

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A post shared by Shelley Gray (@shelleygrayteaching)

Here’s another example, using the x2, x4, and x8 facts. Here we can see that these facts are all related. Using the first example on this page, let’s take a look at all the connections we see! 2×10 is half of 4×10. 4×10 is the double of 2×10. 4×10 is half of 8×10. The product of 8×10 is four times the product of 2×10. And it goes on and on. These connections are powerful.

I encourage you to have your students work with manipulatives to help visualize these connections. Sometimes we make the mistake of thinking our students are “past” manipulatives when they get to Grade 3 or 4 but this couldn’t be further from the truth. Using objects that students can move and manipulate will help them solidify these connections and truly SEE them.

Tip #3: Use Arrays

As you may have noticed, I love using arrays for multiplication. I believe that arrays are THE most powerful way to visualize multiplication. They are NOT simply for introducing multiplication. Arrays are for exploring relationships and connections between facts.

So many students don’t see arrays in their minds when they think about what multiplication means.

To help students begin visualizing arrays, we can use simple tools like a rekenrek. These pictures show how we can build an array to show 3×5 (or 3 rows of 5), and then simply rotate the rekenrek to show that 5×3 (or 5 rows of 3) has the same product (the commutative property). This is a fantastic way to make multiplication concrete.

In this activity from the Design a Playground Math Project, students are using arrays in a representational way, and then connecting that to abstract thinking when they write the facts. Again, we are reinforcing the commutative property and the relationship between facts like 2×8 and 8×2.

Connections have the power to change the game for your students when it comes to multiplication and learning the times tables. If you are having trouble getting started with connection-making, begin with these simple steps.

Use manipulatives to form an array. Ask, “What can we add to this array to form a new fact?”
Always help students make connections in the concrete and representational phase, not in the abstract. They need to SEE the connections in order to understand them. We can’t expect just to show students two written equations and have them understand the connections at a conceptual level.

The resources mentioned in this blog post are linked below:

FREE MULTIPLICATION ACTIVITIES

to help your students master the multiplication facts

Get them here.

The post Help Your Students Easily Master the Times Tables with This One Simple Strategy appeared first on Shelley Gray.

Math Conversations – Math Prompts for Number Talks or Math Talks

Shelley Gray — Wed, 02 Dec 2020 18:39:34 +0000

Is there anything better than hearing kids talk about math? And not only talk…but think – REALLY think. Sometimes we get into a rut with teaching math, where we focus only on getting answers. But what if we focused less on getting answers and more on thinking flexibly and making connections? Would math suddenly get more interesting? More relevant? More fun? A daily math conversation routine is one of the most powerful practices you can have in your classroom.

What are Math Conversations?

Math Conversations are prompts intended for whole-class discussion to get your students thinking flexibly about math. So often math is taught as a subject with right answers. But it’s more than that! Math should be flexible and strategic!

The goal of Math Conversations is to get you and your students talking about math. When kids get the opportunity to share strategies, consider others’ thinking, and justify their own thinking, they can make connections that build their understanding. The secret is to use questions and prompts that don’t only have one correct answer. Tasks like this allow students to use what they know and think in their own ways.

Tips for Getting Started With Math Conversations

Here are some tips for using Math Conversations in your classroom:

Allow adequate thinking time.

Some students will have an answer right away, while some may take longer. It’s important that all students have a chance to think. Many teachers have students put a thumb to their chest when they have an answer (instead of raising hands) so that students who are thinking feel less rushed. See more about the thumb to chest on this post about number talks.

Record students’ thinking as they share and discuss.

When you choose a couple of students to share their thinking, be sure to record it as they explain. This makes the thinking “visual” for other students and will help them form connections and understanding.

Be patient

Expect that it will take time for students to become comfortable with disagreeing with one another and justifying their answers. Speaking up and voicing an opinion can feel scary for some students, and it may take time. Cultivate an atmosphere where disagreements are not only okay but they are valued because it means that learning is taking place! Encourage students to use prompts like the ones shown below while they are getting comfortable with speaking up.

The Importance of Making Mistakes

Another important part of math conversations is understanding that mistakes are not bad! Mistakes mean that learning is taking place. In her book, Mathematical Mindsets, and also in this article which I highly recommend reading, Jo Boaler discusses the importance of mistakes and making them a celebrated part of math.

As you get started with your math conversation routine, I wanted to share an activity that I read about in Mathematical Mindsets called “Favorite Mistakes.” This is a great addition to a math talk where you have several students sharing their thinking. Favorite Mistakes is an activity where teachers share their favorite mistakes that students have made. Boaler states these should be “conceptual mistakes, not numerical errors. Teachers can then share the mistakes with the class and launch a class discussion about where the mistake came from and why it is a mistake. This is also a good time to reinforce important messages – that when the student made this mistake it was good, because they were in a state of cognitive struggle and their brain was sparking and growing.” (Mathematical Mindsets, page 17)

Let’s take a look at how this might look for the prompt shown here. Suppose a student offers this answer: “I can use 17-7 to solve 17-8. I’ll figure out 17-7 which is 10, then add one more to make 11.” This is a conceptual mistake because the student knew she could use the connection between 17-7 and 17-8 to solve the problem. But she should have subtracted one to make 9 rather than add one to make 11. You might say, “I see what you were doing there! This is an excellent mistake because you knew you could use the connection between 17-7 and 17-8, but let’s draw a picture to help us understand where you went wrong.”

Can you imagine how your math class might change if mistakes were celebrated?

Ready to get started?

Math Conversations are a digital resource with NO PREP required. Simply bring up the slide for the day and you are ready to go! Find all Math Conversations packages using the links below:

Math Conversations for First Grade

Math Conversations for Second Grade

Math Conversations for Third Grade

Math Conversations for Fourth Grade

Math Conversations for Fifth Grade

Or, if you’d like to try a free sample first, simply sign up here and I’ll deliver it right to your inbox!

The post Math Conversations – Math Prompts for Number Talks or Math Talks appeared first on Shelley Gray.

Free Daily Journal Template for Use with Google Drive

Shelley Gray — Tue, 31 Mar 2020 15:35:57 +0000

Journal writing is a great way to get your students writing about things that matter to them. This free daily journal template is created with Google Slides, making it compatible with Google Drive/Google Classroom.

Download this journal template for free on Teachers Pay Teachers HERE.

Looking for other digital resources? See them all HERE or browse a couple of them below.

PIN FOR LATER

The post Free Daily Journal Template for Use with Google Drive appeared first on Shelley Gray.

Supports for At Home Learning: Grades 2-5

Shelley Gray — Sat, 14 Mar 2020 16:31:07 +0000

The great part about difficult times is seeing people come together, and the teacher community is no exception. While teachers around the world are facing the daunting task of planning weeks of at-home activities for their students, the teacher-author community has responded.

Below is a collection of links where you will find at-home learning activities for Grades 2-5 students. We hope this can be a small help during this difficult time.

Take care and stay healthy!

The post Supports for At Home Learning: Grades 2-5 appeared first on Shelley Gray.

Other Archives - Shelley Gray

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Simple Tips for Getting Started Subitizing with Dot Talks

Begin with visuals that seem “too easy.”

Consider leaving images on the screen before getting into Quick Looks

Use Dot Talks as a way to ease into number talks.

About the Dot Talks Subitizing Routine

Three Fun Math Games Your Students Will Love

Do You Need Help With Number Talks? Here’s The Quick Start Guide.

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5 Fun Ways to Use a Multiplication Chart

Cut it up to create a puzzle.

Find patterns.

Use the multiplication chart to create arrays.

Times Tables Posters

Shade known facts on the multiplication chart.

Fill in the missing numbers.

Free Multiplication Chart

The Best Way to Teach Multiplication Facts: 12 Steps to True Understanding

STEP 1: SUBITIZE TO ENCOURAGE MULTIPLICATIVE REASONING

STEP 2: CONNECT MULTIPLICATION TO REPEATED ADDITION

STEP 3: EQUAL GROUPS

FREE MULTIPLICATION ACTIVITIES

STEP 4: SKIP COUNT

STEP 5: USE MANIPULATIVES

STEP 6: USE ARRAYS

STEP 8: MAKE MULTIPLICATION RELEVANT

STEP 9: HELP STUDENTS MAKE CONNECTIONS

STEP 10: TEACH THE FACTS IN A STRATEGIC ORDER

STEP 11: TALK ABOUT MULTIPLICATION!

STEP 12: REINFORCE MULTIPLICATION ALL YEAR LONG

Fun Multiplication Games for 3rd and 4th Grade (help them master the facts)

Here’s A Fun Multiplication Math Game Your Students Will Love

What’s the Multiplication Area Model and How Do You Teach it? Comprehensive Guide

25 Fun End of the Year Classroom Activities

Need a Fun Math Game to Use For Warm-Ups? Try Knock off the Clock!

Here's How to Play This Fun Math Game

Are your early finishers engaged? Get a 2-week free sample of the Early Finisher Board here.

Using Math Games with Older Students

Help Your Students Easily Master the Times Tables with This One Simple Strategy

FREE MULTIPLICATION ACTIVITIES

Math Conversations – Math Prompts for Number Talks or Math Talks

What are Math Conversations?

Tips for Getting Started With Math Conversations

Allow adequate thinking time.

Record students’ thinking as they share and discuss.

Be patient

The Importance of Making Mistakes

Other Sample Slides From Math Conversations

Ready to get started?

Free Daily Journal Template for Use with Google Drive

PIN FOR LATER

Supports for At Home Learning: Grades 2-5