multiplication Archives - Shelley Gray

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

The post The Best Way to Teach Multiplication Facts: 12 Steps to True Understanding appeared first on Shelley Gray.

13 Simple and Quick Alternatives to Timed Math Fact Tests (Easy to Implement)

Shelley Gray — Tue, 01 Mar 2022 18:23:09 +0000

Timed tests. Chances are good that those words evoke some sort of emotion in you. For some (students and teachers alike), timed tests bring fear and anxiety. Others may recall the motivation and excitement in trying to beat the clock. While timed tests may have once been the norm for students to learn basic multiplication facts, many teachers are ready to try something new. Is your goal to teach multiplication facts in a way that will benefit all students, rather than only the ones who can be successful with timed tests?

Here are some ideas you can try in your classroom to help students develop automaticity with basic multiplication facts – without the stress of timed tests.

Timed Test Alternatives to Get Kids Moving and Grooving (Kinesthetic Ideas)

Skip Count Ball Toss

Put students in groups of 2-3 (or play as a whole class). Choose a number to skip count by and have students skip count aloud as they pass the ball from one player to the next.

Jumping Jack Facts

Choose a set of facts to recite as students do jumping jacks – “2 times 1 equals 2,” “2 times 2 equals 4,” etc.

Stand Up or Sit Down Products

Say a multiplication fact and have students stand if the product is even or sit if the product is odd. Then say the answer together.

Timed Test Alternatives to Get Kids Speaking and Listening (Auditory Ideas)

Math Talks

Engage students in conversations about how they remember multiplication facts or about different ways they can solve a multiplication problem. If you can do this consistently as a number talk routine – even better!

See more about the slides shown here.

Choral Skip Counting

Count by 2s, 3s, etc. together as a class as a math warm-up.

Roll two dice and skip count by the sum.

Products Out Game

Have the whole class stand in a circle and count from 1 to 50. Choose a number and every time a student says a product of that number, they sit down. The last person standing is the winner. For example, if the number 4 is chosen, the students who say 4, 8, 12, 16, 20, 24, etc. will sit down.

Timed Test Alternatives to Get Kids Seeing and Drawing (Visual Ideas)

Anchor Charts/Multiplication Charts

Hang posters or anchor charts showing vocabulary and multiplication strategies. It can be even more effective if you have students help you make the anchor charts – or if they can make them themselves!

Find these posters HERE.

Manipulatives

Use counters or base ten pieces to make arrays or equal groups.

Drawing Arrays Game

In pairs, have students roll two dice and draw the array on a piece of graph paper. Draw as many arrays as possible until the page is filled. The last one to make an array wins.

How Many Ways?

Have students brainstorm all the possible ways they can think flexibly about a multiplication fact and write their ideas on sticky notes. Have students reflect on the different ideas during a whole-class discussion or number talk.

Timed Test Alternatives to Get Kids Reading and Writing (Linguistic Ideas)

Word Problems and Real Life Situations

Giving students a context for why they are multiplying helps them make sense of the problem and how to solve it. For example, there is a big difference between asking a student to solve 2×3 versus asking them how many socks there are in 3 pairs. Real-Life Math Projects can help students understand where multiplication is used in real life.

Flashcards

The act of creating flashcards is often as important as using the flashcards once they’re finished. Have students create visual flashcards and draw a picture that represents each fact.

Alternatively, use a traditional set of multiplication flashcards, but have students sort them by facts they know and facts they still need to work on.

Multiplication Notebooks

Give students a place to record and reflect on the multiplication strategies they are learning. This can be done in a regular classroom notebook, or in a pre-made booklet like the one shown below.

Find this Multiplication Equation of the Day booklet HERE.

Not every idea will work for every student, but when we give kids the opportunity to learn and practice in many different ways, we allow them to learn in a way that works best for them. When kids understand that there are many different ways to learn and practice multiplication facts, it can relieve the stress and anxiety that so often comes along with timed tests, while boosting number sense and flexibility with numbers.

How do you practice math facts in your classroom? I’d love to hear in the comment section below!

The post 13 Simple and Quick Alternatives to Timed Math Fact Tests (Easy to Implement) appeared first on Shelley Gray.

5 Fun Multiplication Games to Practice the Times Tables

Shelley Gray — Thu, 06 Aug 2020 18:42:11 +0000

Are you looking for a fun way for your students or children to learn the multiplication facts? Games help reinforce math facts in an interactive, engaging way. Here are five fun games your students can play to reinforce multiplication facts and continue to build their fact fluency.

Multiplication UNO

Number of Players – 2+ (ideally 3-5 students)

Just as the name suggests, this game is played with similar rules as UNO but with a regular deck of cards and a multiplication twist!

Each student is dealt 7 cards and the remaining cards are placed in the center. The object of the game is to get rid of all the cards you are dealt. In the remaining deck, one card is flipped over to begin play. Whoever can match the same number or suit that is on the first card may play first. After a student plays their card, they must multiply the number on the previous card and the number on the card they are playing. For example, if an 8 of hearts is the first card laid down to begin play, one student could play an 8 of spades, and multiply 8×8.

Each numbered card is worth its own value. Aces mean ‘multiply by 1’ and are a wild card. Kings, Queens, and Jacks mean ‘multiply by 10’ while Kings also mean ‘draw 2,’ Queens are a reversal card, and Jacks are skip-a-turns. Jokers mean ‘multiply by 100’ and are also a wild card + “Draw 4.”

Have students create a key of these card values and meanings to help them remember the rules while the game is still new.

Multiplication Fact Flip

Number of Players – 2+

This game is an excellent way to practice simple multiplication facts! Begin by removing all of the face cards, Jokers, and Aces so that only the numbered cards 2-10 are left. Next, divide the deck evenly among all players. Choose a target number and write it on a piece of paper nearby or whiteboard. This target number is the number that will be multiplied by each card that students flip.

For example, let’s suppose the target number is 6. Each student will flip over one card from their own personal deck. They will flip a card and multiply that number by 6. Whoever has the largest product takes all the cards. If a player says the wrong product, the other player can make the correction and take the cards.

You could easily set a round limit on this game and whoever has the most cards after a specific number of rounds, wins. Or the game can end when one player runs out of cards.

Spiral Multiplication

Number of Players – 2+

Spiral multiplication does require at least one or two dice (depending on-level of difficulty) as well as individual game pieces in addition to your deck of cards. If you don’t have game pieces, you can easily use colored pencil top erasers or even crayons. If you are looking for a virtual dice option, here is a good one to use.

Have students create their own spiral game board with their deck of cards. They may create the game board in any shape or style similar to a Candyland format or even just a simple Monopoly style that repeats around. Students place their game pieces at whatever card is established as “start.” The first player rolls the die and multiplies the number on the die by whatever number the “start” card is. If the student gets the answer correct, he moves the number of spaces that are shown on the die. For example, if the “start” card is a 5 and the first player rolls a 3, he must answer 15 and then move 3 spaces around the board.

Students will love creating their own game board set-up and it is the perfect opportunity to practice facts!

Zone

Number of Players – 2+

Zone is a strategic game where students have to find two cards with a product that is in the “zone.”

First, each player is dealt 10 cards. The remaining cards are piled in the center. Aces are worth 11, Jacks are 12, Queens are 13, and Kings are 14. The first card in the center deck is flipped over and that number is multiplied by 10. Each player looks at their own decks to find two numbers that are in the same “zone.”

For example, suppose the card that is flipped is a 4. It is multiplied by 10, creating a product of 40. The product zone is now 40-49. Students must look at their own decks to find two cards whose product is in the zone of 40-49. If a player has 2 cards that can be multiplied to create a product in that zone, they can remove those cards from their deck. Whoever runs out of cards first, wins!

Mind Reader (also known as Salute)

Number of Players – 3

Mind Reader specifically requires three players so that one player can act as the “leader” and the other two players are the mind readers. Remove all face cards, Jokers, and Aces and then split the deck in half. The two students playing as the mind readers each take half of the deck.

The mind readers take 1 card off the top of their deck and hold it next to their forehead for everyone else to see except for themselves. Because the leader can see both cards, she multiplies the numbers and says the product out loud. The mind readers must decide what number they are holding, based on knowing the product and the other mind reader’s card.

For example, suppose that the leader says, “42.” If one mind reader can see that the other mind reader is holding a 6, she knows that her card has to be a 7. Have students rotate duties so that each one is able to play the leader, as well as mind readers!

FREE MULTIPLICATION ACTIVITIES

TO HELP YOUR STUDENTS MASTER THE MULTIPLICATION FACTS

Grab them here!

The post 5 Fun Multiplication Games to Practice the Times Tables appeared first on Shelley Gray.

How to Use Halving and Doubling for Multiplication

Shelley Gray — Tue, 23 Jun 2020 19:24:39 +0000

The halving and doubling strategy for multiplication is one of the most fascinating multiplication strategies. The best part is that it actually IS a strategy – not a trick.

First, let’s take a look at the halving and doubling strategy in action.

To use halving and doubling, you simply half one of the factors and double the other. Take this example. To solve 25×16, we could double the 25 to make 50 and then half the 16 to make 8. Suddenly this problem becomes much easier to solve!

We could actually take this one step further if we wanted to, by doubling the 50 to make 100 and halving the 8 to make 4. Now we are left with 100×4. So, the product of 25 and 16 is 400.

CONCEPTUAL UNDERSTANDING

It’s essential to know WHY strategies work. Let’s take a look at exactly why the halving and doubling strategy works. It’s easiest to see this in an array.

Here we have a 4×5 array.

Suppose we divide the number of rows in half and we rearrange them like this:

Do we still have the same number of objects? Yes! They are just arranged differently. Now we have a 2×10 array. All we did was half the number of rows and double the number of objects in each row.

Try this yourself with 3×8!

DOES IT ALWAYS WORK?

Halving and doubling will always work, but there are some situations that are better suited to it than others. For example, suppose you have 17×15. Technically we could half the 17 to make 8.5 and double the 15 to make 30. However, this does not make the problem easier to solve, and there are other strategies that would be more effective in solving 17×15.

USING DOUBLING AND HALVING

Doubling and halving works best when one of the factors is even, and when the other factor is a number like 5, 10, 25, or 50. For example, doubling and halving would be an efficient strategy for:

50×18
120×5
25×20

TEACHING DOUBLING AND HALVING

Doubling and halving is a fantastic strategy for your students to work with. You can begin modeling doubling and halving with basic facts like 5×6. However, your students must understand WHY it works. It is not enough to simply tell your students that they can double one factor and half the other. The ability to visualize is key to conceptual understanding. This will be best done with arrays, so be sure to include lots of array practice as students build their understanding of this strategy.

Here are some other considerations to make as you teach doubling and halving:

Allow students to discover this strategy on their own through activities with arrays. You might have students build a 5×6 array, and then a 10×3 array and ask, “What do you notice?” Then build a 4×7 array and a 2×14 array and ask the same question. Encourage students to look for relationships and connections.
Implement math investigations where you ask pairs of students to investigate questions like:

- Do doubling and halving always work? Prove it!
- For which types of problems does doubling and halving work best?
- What kinds of problems are NOT very well suited to doubling and halving?

RESOURCES TO HELP

See this blog post in video format here.

This next video is intended for upper elementary students and explains the doubling and halving strategy. This can be used as an introduction.

PIN IT FOR LATER

The post How to Use Halving and Doubling for Multiplication appeared first on Shelley Gray.

Top Reasons Why Arrays Are Essential for Teaching Multiplication

Shelley Gray — Tue, 24 Mar 2020 13:44:02 +0000

What is an array? Why should we use arrays? An array is a way of arranging objects in groups or columns. In math, we generally see arrays with rows and columns of dots, like this: However, arrays appear in real life too! Take a look at these pictures below:

Why are they useful?

Arrays allow us to see a visual representation of repeated addition or multiplication. For example, in the egg carton above, we see 2 rows of 5. We can think of this as 5+5 or 2×5. In the muffin tin, we see 3 groups of 4. We can think of this as 4+4+4 or 3×4. Arrays also help us see that the order of the factors doesn’t matter when solving a multiplication problem. For example, 3×8 will have the same product as 8×3. To visualize this, we can have our students rotate the arrays. The picture below shows a 4×5 array that has been rotated to show 5×4. This shows us that there are the same number of objects in 5 rows of 4 as there are in 4 rows of 5.

When should they be used?

Arrays can be used for addition in the early grades. Students might use blocks, counters, or bingo chips to create arrays. Then a repeated addition sentence can be created. For example, 6 rows of 3 can be written as 3+3+3+3+3+3=18. Arrays are essential as a tool for multiplication. We can begin by making equal groups using blocks or counters. Then we can arrange those objects into an array.

Tips for Using Arrays To Teach Multiplication Concepts:

Have students work with rotating the array to show the commutative property of multiplication (the order of the factors doesn’t change the product). For example, a 4 by 3 array has the same number of objects as a 3 by 4 array.
Have students show equal groups using an array. For example, a 4 by 3 array represents 4 groups of 3. This can be written like 4×3.
Have students break up the array to show the distributive property. For example, a 4×5 array can be broken up into a 3×5 piece and a 1×5 piece. This proves that 4×5 is equal to (3×5)+(1×5).
We know that our students move through three stages in terms of number – concrete, representational, and finally abstract. Use arrays as the “concrete” part. Then have students represent the array in a drawing (representational). Lastly, have students write an equation to represent the array (abstract). Remember that lots of practice in the concrete and representational stages will help once we expect students to work in the abstract stage!

How do you use arrays in your classroom? I’d love to hear in the comments below!

FREE MULTIPLICATION ACTIVITIES

to help your students master the multiplication facts

Get them here!

The post Top Reasons Why Arrays Are Essential for Teaching Multiplication appeared first on Shelley Gray.

Two Effective Ways to Make the Multiplication Facts Concrete

Shelley Gray — Wed, 23 Oct 2019 21:22:32 +0000

Are you guilty of moving too quickly through concrete models of multiplication in order to get to the abstract quicker? Most of us are. We know the end result that we want to achieve, and we sometimes skip the experiences that feel unrelated to the final goal.

The CRA (Concrete-Representational-Abstract) Model is an instructional model where we move through stages of teaching/learning. In this post we will consider this model in terms of basic multiplication facts.

In the concrete stage, we work with manipulatives and objects in order to develop an understanding of what multiplication really means. For example, we might use a rekenrek to show 4 groups of 5 or similarly 4 paper plates with 5 snap cubes on each.

In the representational stage, we represent this understanding in pictures. For example, we can use pictures of a rekenrek to show 4 groups of 5, or ten frames to show it another way.

In the abstract stage, we move to numbers and equations. This is where we will write 4×5 and expect students to understand that this means 4 groups of 5. Remember that this is the final stage and should not be our first step in teaching multiplication.

MAKING MULTIPLICATION CONCRETE

The concrete stage is an ESSENTIAL piece. This is not something that we reserve only for students who need interventions. This is an experience that ALL of our students will benefit from. Why? Because the concrete stage is where number sense is built and connections are made. Connections are often the missing piece for our students (think of the student who knows what 5×5 is but doesn’t know how to use that to figure out 6×5).

I encourage you to allow your students the opportunity to spend a lot of time in the concrete stage. This time will strengthen their conceptual understanding of multiplication. Later when you focus on the facts, this time will pay off.

Here are two important ways to make multiplication concrete.

1. Ten frames

To use ten frames as a concrete experience, we need to ensure that students are able to manipulate and work with their hands. This set of magnetic ten frame manipulatives works well to build concrete understanding. Notice that here we are showing 2 groups of 5. Because students have used ten frames in previous grades, they know just by glancing at it that there are two groups of 5. In this stage we’ll try to move students from additive reasoning (5+5=10) to multiplicative reasoning (2 groups of 5 makes 10). For an inexpensive option, use masking tape to make a ten frame on a table or the floor, and bingo chips as the objects.

Later when we begin working with ten frames in the representational stage (as shown below), students will make connections based on how they used the hands-on ten frames. The subitizing cards below show two different representations of 4 groups of 5. These work great as “quick looks” where we show the cards for only a second or two and expect students to use strategies to figure out how many dots, rather than counting.

2. Rekenreks

When I was in the classroom, I had a few rekenreks that sat on my shelf collecting dust, because I really did not know how to use them properly. Ahhhh! If I would have only known then what I know now! Rekenreks are an AMAZING tool for building number sense! When you use a rekenrek, keep the white to the right side, and move beads over to the left side as needed. For example, this shows 4 groups of 3.

Notice anything with this close-up? Using a rekenrek gives your students their first experiences with arrays. This is going to enable them to make connections later on! Connections are a primary goal and are the missing puzzle piece for many students.

Later when we begin making multiplication representational, we can represent concrete rekenrek models in pictures. Again, notice the array in the representational picture. The card shown in the picture below can also be used as a “quick look” subitizing activity.

Fancy or expensive manipulatives are not essential to build understanding. You can easily use paper plates and small blocks to create concrete multiplication experiences.

BIG IDEA

When we give students lots of experiences with concrete and representational models, they will build an excellent conceptual understanding of multiplication as equal groups. This conceptual understanding is what will enable them to make essential connections later on. We do not need to introduce the “times” symbol until an excellent conceptual understanding has been established. This can be reserved for the abstract stage.

KEEP IT CONCRETE

Often when we do begin with concrete experiences, we tend to move on from them very quickly. Remember that even when you move your students on to the other stages, they can still benefit from being offered concrete experiences. When we can incorporate all three stages (concrete, representational, and abstract) into our teaching, our students get to see multiplication at the stage they are at. The more ways that we can assist our students in making their own connections, the better.

HELPFUL LINKS

Here are the links to the resources shown in this blog post. For full transparency, the Amazon links are affiliate links, meaning that if you order using this link, I will receive a very small commission. The subitizing cards can be found in my TpT store using the link down below.

MAGNETIC TEN FRAMES

REKENREKS

SUBITIZING CARDS

FREE MULTIPLICATION ACTIVITIES

to help your students master the multiplication facts

Click Here

The post Two Effective Ways to Make the Multiplication Facts Concrete appeared first on Shelley Gray.

Four Ways to Represent Multiplication

Shelley Gray — Tue, 27 Mar 2018 19:30:20 +0000

When it comes to teaching multiplication, it can be tricky to know how to approach it in your classroom. Often we teach multiplication using the “equal groups” idea and leave it at that. But it is important to teach multiplication using different approaches and strategies so students understand it in many different ways.

Here are four ways to teach multiplication in your classroom. Make sure that these are all included in your instruction so that your students are able to visualize multiplication in different ways while they learn what it really means. Once students REALLY understand multiplication, you’ll be able to move away from these approaches and focus more on multiplication fact mastery.

REPRESENT MULTIPLICATION USING ARRAYS

An array is a group of objects that is arranged into rows and columns. This group of objects can be used to represent a multiplication equation by multiplying the number of rows by the number of columns. For example, the array below shows 6 rows and 7 columns. This represents the multiplication equation 6×7 or 7×6. Altogether there are 42 objects in this array.

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

Ask students to identify the equation represented by an array, as well as draw arrays to represent multiplication equations.

SKIP COUNTING TO REPRESENT MULTIPLICATION

Skip-counting is generally an introductory activity for multiplication. Students can use a number line, or a simple skip-counting sequence to figure out the product of an equation. For example, to figure out the product of 5 and 4, we can skip-count 4 groups of 5 – 5, 10, 15, 20 or 5 groups of 4 – 4, 8, 12, 16, 20.

FREE MULTIPLICATION ACTIVITIES

to help your students master the multiplication facts

Get them here!

REPEATED ADDITION

When we teach multiplication, we want our students to understand that it can be used as a shortcut to addition. For example, to figure out the problem below, we could add 8+8+8+8+8 to make 40 and get the correct answer for this problem. However, it is much faster to multiply 5×8 to make 40 instead.

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

We can ask our students to look at a repeated addition equation and identify the multiplication equation that is represented.

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

PICTURE REPRESENTATIONS/EQUAL GROUPS

Equal groups are a great way to introduce multiplication. The idea of equal groups can be understood more when introduced with a picture. This task card shows the equation 6×8 represented in an “equal groups” picture. Be sure to have your students draw picture representations that make sense to them, as well as identify the equation represented by a picture.

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

NEXT STEPS

Create a multiplication anchor chart like the one shown here to post in your classroom:

Read more about multiplication fact strategies HERE.
Use Basic Multiplication Task Cards to reinforce each set of facts using the approaches shown in this post. Find the full package HERE or a free sample HERE.
Implement basic multiplication into your daily practice to ensure that it is being continually reinforced. Find the full Basic Multiplication Equation of the Day package HER E or a free sample HERE.

The post Four Ways to Represent Multiplication appeared first on Shelley Gray.

Free Set of Multiplication Task Cards

Shelley Gray — Mon, 26 Mar 2018 20:31:13 +0000

I’ve heard over and over again that the average curriculum just does not include the types of resources that you need in order to really support your teaching. With regards to multiplication, the chances are good that the resources that you currently have access to do not properly support conceptual learning or strategic thinking.

It is so important that each set of multiplication facts is reinforced in a variety of ways, including problem-solving, finding missing unknowns, skip-counting, making groups, arrays, and picture representations. We want our students to REALLY understand each set of multiplication facts so that mastery becomes accessible.

This is why I recently created these Multiplication Task Card sets. With 24 task cards in each of the 17 sets, the basic multiplication facts are reinforced in a wide variety of ways.

If you are currently using The Multiplication Station in your classroom, these task cards are a fantastic way to support your students! Make the task cards available at the end of each level for students to practice before their oral test, or as extra support for students who still need a bit of help mastering the facts after a level.

I’d love to give you a free set of task cards! Sign up HERE and I’ll send you the Multiplication by Two Task Cards right to your inbox.

Want to tackle all of the basic multiplication facts in your classroom?

GET THE FULL MULTIPLICATION TASK CARDS BUNDLE HERE.

Next Steps:

Ready to get serious about teaching multiplication in a strategic way? Read more about effective strategies for teaching basic multiplication HERE.

The post Free Set of Multiplication Task Cards appeared first on Shelley Gray.

Teaching Basic Multiplication | A Round Up of Ideas, Tips, and Resources

Shelley Gray — Thu, 15 Feb 2018 18:03:15 +0000

Teaching basic multiplication is a daunting task. But it doesn’t have to be! I would love to help you ensure success for every student in your classroom this year. My website is full of ideas, resources, and strategies for teaching multiplication, but I wanted to provide you with a way to easily find all things multiplication in one, easy-to-navigate place. Below I have included links to helpful blog posts, resources, and Pinterest boards for all things multiplication. Enjoy!

PINTEREST BOARDS

I love Pinterest as a visual way to easily organize ideas. On my Multiplication and Division Pinterest board, you’ll find a wealth of ideas from a variety of sources around the web! Be sure to follow my boards, as I am constantly pinning fresh new teaching ideas!

BLOG POSTS

Over the years I’ve written a lot of different blog posts about multiplication tips and strategies. Click on any one below to visit!

Effective Strategies for Teaching the Basic Multiplication Facts

Free Guide: A Suggested Order for Teaching the Basic Multiplication Facts

8 Ways to Use Multiplication Flashcards in your Classroom (with Free Printables)

5 Reasons That Your Students Aren’t Mastering the Basic Multiplication Facts (and what you can do about it)

Free Poster for the 9’s Multiplication Trick

How to Teach the 12’s Multiplication Facts

How to Teach the 11’s Multiplication Facts

How to Teach the 10’s Multiplication Facts

How to Teach the 9’s Multiplication Facts

How to Teach the 6’s, 7’s, and 8’s Multiplication Facts

How to Teach the 5’s Multiplication Facts

How to Teach the 4’s Multiplication Facts

How To Teach the 3’s Multiplication Facts

RESOURCES

I love helping teachers teach multiplication! An effective approach can be such a game-changer for your classroom!

The Multiplication Station

Of any of my multiplication resources, The Multiplication Station has touched the most students – tens of thousands of students around the world. It utilizes all of the most effective ways to teach multiplication, and incorporates those into one, self-contained station that students work on independently, at their own pace. I won’t spend too much time talking about all of the benefits that you will see when you start using this resource, but I encourage you to read through the comments from the thousands of teachers who have used this resource HERE.

Other Multiplication Resources

See my entire selection of multiplication teaching resources here

Multiplication Equation of the Day: Basic Multiplication Facts Booklet

Task Cards for Basic Multiplication: The Big Bundle

Fact Family Array Task Cards: Multiplication and Division with Arrays

Multiplication Arrays Task Cards

Basic Multiplication Problem Solving Task Cards

Multiplication or Division? Problem Solving Task Cards

Multiplication Facts and Strategies Mini-Book

Get Up and Move: Basic Multiplication Gallery Walk

Get Up and Move: Introductory Multiplication Gallery Walk

Multiplication Strategy Posters for 0-12 Times Tables

Basic Multiplication Facts Flashcards: Flashcards for Basic Multiplication Facts

Springtime Multiplication Math Stations (also great for home math bags)

The Math Choice Board (includes a variety of math topics and tasks)

FREE: Quick Tasks for Multiplication Flash Cards

FREE: The 9’s Trick for Multiplication Poster

The post Teaching Basic Multiplication | A Round Up of Ideas, Tips, and Resources appeared first on Shelley Gray.

Free Guide: A Suggested Order of Teaching for the Basic Multiplication Facts

Shelley Gray — Thu, 15 Feb 2018 16:31:50 +0000

Multiplication facts can be intimidating for both students and teacher. Luckily, there are strategies that we can use to help us teach the multiplication facts more effectively so that every student can be successful.

The main mindset shift that we must make is that we are not simply teaching students to memorize the facts, but rather we are teaching students how to think about multiplication. We must take a strategic approach to our teaching that emphasizes conceptual understanding first. Fact fluency will be a bi-product of excellent understanding.

One thing that we can do is teach strategies that make multiplication easier to understand. Although quick recall is a goal, we want our students to have effective, efficient strategies that will enable them to use what they know for many other multiplication situations. Read more about effective strategies for multiplication HERE.

We can also teach the facts in a strategic order. When I first started teaching multiplication, I taught the facts in regular numerical order – the 1’s, then the 2’s, then the 3’s, etc. This is a mistake!

Instead, we want to teach the easiest facts first, and leave the hard ones til last. Why? Simple! Because when we teach like this, we give students a strong foundation early on, enabling them to derive facts easily. This way of teaching also results in high motivation, as students can see their progress and how rapidly they are learning their facts.

This free guide will explain a suggested order of teaching the basic multiplication facts. This will result in maximum confidence, motivation, and success. Just click on the image below to begin downloading.

Looking for even more support? Implement all of these ideas easily using The Multiplication Station.

The post Free Guide: A Suggested Order of Teaching for the Basic Multiplication Facts appeared first on Shelley Gray.

8 Ways To Use Multiplication Flashcards In Your Classroom (with free printables)

Shelley Gray — Wed, 14 Feb 2018 18:41:10 +0000

Looking for a way to take that old set of multiplication facts flash cards and make them new again? Here are 8 simple tasks that your students can perform with a set of multiplication task cards. Free printables are included!

Don’t have a set of Multiplication Flashcards yet? Grab a set here!

1. Reinforce the commutative property by having students write a related multiplication fact for each flashcard.

2. Order the flashcards from highest to lowest product, or vice versa.

3. Use each multiplication fact to write a multiplication/division fact family.

4. Draw an array to represent each multiplication fact.

5. Write a story problem for each multiplication equation.

6. Increase metacognition by sorting into “facts that I know” and “facts that I don’t know.”

7. Sort the flashcards into even and odd products.

8. Represent each multiplication equation with a picture.

FREE PRINTABLES

Grab these Flash Card Task Cards for FREE here! I mounted mine on colored paper before laminating for an extra pop of color.

NEED THE FLASHCARDS?

Grab them here!

I would love to help you get really strategic with multiplication this year! Whether it’s implementing a strategic order of teaching the facts that will result in maximum retention and confidence, or using mental math strategies that really work, let’s put a plan into action!

OTHER RESOURCES FOR MASTERY OF MULTIPLICATION FACTS

The Multiplication Station: a complete program for multiplication fact mastery

Task Cards for Multiplication and other Operations

All Multiplication Resources

The post 8 Ways To Use Multiplication Flashcards In Your Classroom (with free printables) appeared first on Shelley Gray.

multiplication Archives - Shelley Gray

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

13 Simple and Quick Alternatives to Timed Math Fact Tests (Easy to Implement)

Timed Test Alternatives to Get Kids Moving and Grooving (Kinesthetic Ideas)

Skip Count Ball Toss

Jumping Jack Facts

Stand Up or Sit Down Products

Timed Test Alternatives to Get Kids Speaking and Listening (Auditory Ideas)

Math Talks

Choral Skip Counting

Products Out Game

Timed Test Alternatives to Get Kids Seeing and Drawing (Visual Ideas)

Anchor Charts/Multiplication Charts

Manipulatives

Drawing Arrays Game

How Many Ways?

Timed Test Alternatives to Get Kids Reading and Writing (Linguistic Ideas)

Word Problems and Real Life Situations

Flashcards

Multiplication Notebooks

5 Fun Multiplication Games to Practice the Times Tables

Table of Contents

Multiplication UNO

Multiplication Fact Flip

Spiral Multiplication

Zone

Mind Reader (also known as Salute)

FREE MULTIPLICATION ACTIVITIES

How to Use Halving and Doubling for Multiplication

CONCEPTUAL UNDERSTANDING

DOES IT ALWAYS WORK?

USING DOUBLING AND HALVING

TEACHING DOUBLING AND HALVING

RESOURCES TO HELP

PIN IT FOR LATER

Top Reasons Why Arrays Are Essential for Teaching Multiplication

Why are they useful?

When should they be used?

Tips for Using Arrays To Teach Multiplication Concepts:

FREE MULTIPLICATION ACTIVITIES

Two Effective Ways to Make the Multiplication Facts Concrete

MAKING MULTIPLICATION CONCRETE

1. Ten frames

2. Rekenreks

FREE MULTIPLICATION ACTIVITIES

Four Ways to Represent Multiplication

REPRESENT MULTIPLICATION USING ARRAYS

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

SKIP COUNTING TO REPRESENT MULTIPLICATION

FREE MULTIPLICATION ACTIVITIES

REPEATED ADDITION

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

PICTURE REPRESENTATIONS/EQUAL GROUPS

FIND THIS TASK CARD IN THE BASIC MULTIPLICATION TASK CARD BUNDLE HERE.

NEXT STEPS

Free Set of Multiplication Task Cards

Teaching Basic Multiplication | A Round Up of Ideas, Tips, and Resources

Free Guide: A Suggested Order of Teaching for the Basic Multiplication Facts

8 Ways To Use Multiplication Flashcards In Your Classroom (with free printables)