The post Successive Blending: A Phoneme Blending Strategy appeared first on Tales from Outside the Classroom.
]]>Successive blending is a great instructional strategy or intervention for those students that can identify the phonemes in a given word, but are unable to successfully blend those sounds into the given word. For students still struggling with letter sounds, successive blending can be implemented by using the sounds that are already known. It’s a great way to dive into word reading with students very much still working on phonemegrapheme correspondence, and phoneme segmentation and blending.
Successive blending is exactly what it sounds like in succession. Readers say the the first sound in the word, followed by the second sound and immediately blend those two sounds together. Then, the third sound is said and is immediately blended with the first two sounds. This process requires less short term memory and is a great strategy for students that struggle with working memory skills.
Here’s an example for reading the word “red” using successive blending:
Successive blending is a strategy that can be incorporated within your existing phonics and phonemic awareness work. Because it’s a decoding strategy, once students are familiar with it, they are able to use it anytime they need to decode an unknown word. But students need repeated practice to build proficiency, as it’s typically used for students that are struggling to blend words successfully. For this reason, it’s also a great tool to explicitly teach and reinforce within your small groups or intervention groups.
My favorite way to intentionally practice it is through a sound and word reading card drill. This routine takes about 5 minutes total, and gives students quick and focused practice on reading a variety of real and nonsense words. I’ve since learned it’s similar to the 3 part drill from OG, but I did this with my intervention students for years before knowing that. My favorite part is that it’s super easy to implement! All you need are letter cards. I have made cards using regular index cards or I’ve also printed ones on my own.
For students that need review in letter sounds, I like to flip through the card deck for a quick practice connecting each sound with each letter. Then I lay the cards out as detailed below to create the stacks for our CVC words. For students that don’t need that sound review, I have the cards ready to be stacked in each of their piles detailed below. Typically, my students that need practice with successive blending are working at the CVC word level so I’ve detailed the steps to include that below. However, I’ve also implemented it with words with blends because many students struggle to add that fourth sound into their blending after spending lengths of time at the CVC level.
C– I like to include “floss rule” letters (FLSZ) here to prevent inadvertent practice with only one letter instead of 2. I include c here to prevent words from ending in it, and we only work on hard c sounds despite the continued vowel. There are even times I eliminate it from our practice so as not to make things more difficult to learn the soft sound later. H, J, K, L, R, V, W, and Y are also always in the first pile either to prevent practicing with letters that create vowel digraphs, or letters that affect the vowel. This also includes two of the letters (v, j) that never end a word in English. I sometimes include Q here so we can practice saying the sounds, but I often eliminate it from practice since it’s not regular.
V– the vowels go here
C– I include g here for hard g practice since that’s the first sound taught.
It seems like a lot to remember, but it becomes pretty intuitive once you’re into it. And if you inadvertently include a letter in the wrong spot, you’ll notice it right away when students go to read it, which makes it easy to adjust. If I’m doing successive blending card drills with CCVC, I also think through where the consonants should go. I include f and s in the first stack, and the t, l, m, n, r in the second stack. Some cards are then eliminated from practice so they’re not practiced as the final sound. I then, at times, have to be intentional with my flips and return some cards back in order to practice blending those sounds.
Once the cards are set up, you’re read to begin. Flip over the cards, blending the sounds as detailed above sound, sound, blend, sound, blend. With card drills, students get exposure with both real and nonsense words. Practicing with nonsense words, which may seem counterintuitive, actually ensures students aren’t just reading words that are stored in their longterm memory. A great routine is to have students identify the word as a real word or nonsense word before continuing on to the next word. When doing card drills, I only change out one card at a time, rather than all 3. You can turn over any amount you’d like.
I made a super quick video tutorial showing how I use letter cards to practice successive blending with words with initial blends.
Successive Blending Slides are digital resources, often in Google Slides and Powerpoint, that walk students through the steps of successive blending. They typically include a picture tool to help students “check their work” or receive feedback. Successive blending slides are designed for independent practice for students working on successive blending in conjunction with systematic phonics instruction. Because they are designed for independent practice, they are great centers options for practice while you’re working with other students.
You can take a closer look at my CVC Successive Blending Slides by clicking on the link. They contain 600 slides! They are broken down into 15 word sets. There is a set for each of the short vowels, and then 3 mixed review sets. In my classroom, I assign a couple sets at a time through Google Classroom. Students work through several sets each time they have it as a center rotation.
Even though these Successive Blending Slides are designed for students’ independent practice, they can also be used during whole class instruction. When students are first being introduced to sounding out and blending CVC words, these slides provide great, whole class interactive practice as you manage each slide from the front of the class!
Students use this decoding strategy only to the point that they need to. Once they can independently blend a new word, there is no need to continue to blend as slowly and explicitly. Once students are working beyond CVCC and CCVC words, they typically no longer need the scaffold of successive blending. Students are then ready to begin tapping/blending the sounds. With that said, some students really benefit from continued practice with successive blending, especially when being presented with new phonics skills.
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]]>The post Easy Prep 3rd Grade Math Games that Make Learning Fun appeared first on Tales from Outside the Classroom.
]]>Bump is a wellknown partner game that’s typically played on a printed gameboard. You can find many versions out there both with seasonal themes and general ones. When we first went online in 2020, I was looking for ways to continue to work on my students’ fact fluency. Since we typically work on fact fluency through classroom game play, I brainstormed how we could continue those games online. Digital Multiplication Bump came out of that need. I detailed more about it in my Free Digital Multiplication Bump post.
Since then, I’ve continued to use the digital versions in my classroom. Students can play side by side on their device. Or, they can play together by sharing one computer. Part of what I really like about it, is that it gives students a game they can play at home with their families. Since students take home their devices each night, they always have it available to them.
I have 3 different versions available: Multiplication Bump Factors to 6 Freebie, Multiplication Bump Factors to 10, and Multiplication Bump Factors to 12. The free version is great to try out and see how the game works. By focusing on the numbers on a traditional die, students get a lot of exposure with multiplication with factors from 16. The paid versions, however, have intentional practice with the range of factors. This is perfect for working on fact fluency with specific factors throughout the year. A great way to use this version is to play one version per week giving kids repeated practice with a specific factor through game play. This helps to add that fact to students’ longterm memory for easy retrieval later.
5 in a Row is my favorite thing I’ve ever created and I think my students think so too. What started out as a fact fluency game, has turned into much more than that. I’m always working to add versions practicing additional math standards. My students love playing and will literally BEG for us to play when we have a few minutes to fill. My 3rd Grade Math Games Bundle has 9 different sets included with 33 total game versions! Fluency is a component of the game, so the skills included are ones where quick retrieval is beneficial. You can change the speed of the game, however, so it can be played at the speed most beneficial for your students.
5 in a Row is easy to play! You print the gameboards and cut twice to make them into strips. Then, launch the game on Powerpoint. That’s it! It’s so easy to prep! I keep a stack of gameboards printed in my classroom, so we’re ready to play at any time. I always have a variety of skills prepped so we can work on different skills each time we play. This makes it easy to play as a fillin during down time, but I try to play several times a week by carving out time in my math block. Depending on the game version, you can play one game in less than 5 minutes. That includes time for board distribution and checking answers.
The best part of 5 in a Row? The super awesome randomize feature that makes every round you play different! This keeps things exciting for students, and ensures they’re working on a range of content with every game play. You can find out more about 5 in a Row and how it’s played in my blog post. But let’s take a closer look at my 3rd Grade Math Games bundle.
I have 3 different game versions that work on building multiplication & division fact fluency: Multiplication Facts 012, Division Facts 012, and mixed Multiplication and Division. Each version has four different games included so that factors are broken up into manageable chunks. They’re broken down into factors 05, factors 610, factors 010, and factors 012. I always begin playing with Multiplication 05 and build up students’ proficiency and confidence. I then often switch the division because making that transfer can be so difficult for many students. As students become more proficient with their facts, I switch the 610 version. As a third grade teacher, I don’t play the 010 version until the very end of the year.
I have the game versions bundled and discounted. My Multiplication & Division 5 in a Row Game Bundle is available in my TpT shop.
I also have several versions that work on building place value and number sense skills. While we wouldn’t often think of them as fluency activities, we also want students to become fluent with them. The speed component sometimes helps with overthinking. It helps students go with their first thought. At the end of the day, though, it’s another way to give students practice in an engaging setting. The speed can be increased several seconds if students need additional thinking time so that speed isn’t really a component of the game. This helps ensure students don’t get stressed by the time component, but it keeps the game as autoplay without you having to click through.
Place Value to 1,000 5 in a Row practices standard, expanded, word form, and base ten representations with 3digit numbers. 6 different game versions are included with 2 versions of each type: base ten blocks, expanded form, and word form. Play more than one version in a day to practice several skills.
Mental Math to 100 5 in a Row is one of my favorite number sense building games. I’ve used it in 1st through 3rd grades and have found it tough for each of the grades. Students build number sense skills as they skip count the numbers shown to identify the number. This helps build their fluency switching between numeric places, building an understanding between ones, tens, and hundreds. One of the versions includes counting by 25 to help build students’ skills with counting coin values.
Fractions are a foundational 3rd grade skill. I’m always looking for additional ways to work on fractions in engaging ways because my students need lots and lots of practice. I currently have 2 different fractions versions in the 3rd Grade Bundle: Fractions of a Shape and Fractions on a Number Line.
Fractions of a Shape 5 in a Row has students identify the fraction shown by the partitioned and shaded shape. Then, they match it with the fraction on their gameboard. This free version is a great way to try out 5 in a Row in your classroom! It gives you a chance to try it out with a typically somewhat easy skill. Because it’s free, it’s a great game to use to be sure it works well for your classroom systems. You can download Fractions of a Shape 5 in a Row to try it out today.
Fractions & Mixed Numbers on a Number Line includes 4 different fractions games. One version includes practice with fractions less than one on a number line. Another includes mixed numbers with fractions larger than 1. Each game has included fractions represented on the number line. It also includes versions with only one fraction represented, upping the complexity of the task.
Roll & Cover is another well known game that’s pretty similar to Bump. If you aren’t familiar with it, it’s pretty simple to prep and play. Students roll 2 dice, or roll one twice, and multiply the numbers together. Then, they cover the product on their gameboard. The first player to cover their board is the winner. Students can play on duplicate versions of the same gameboard, or each student can play with a different set of numbers. The only materials needed are dice and counters. I love easy prep games that build students’ fact fluency with continued play and Multiplication Roll & Cover is great. You can download 10 gameboards for free by filling out the form below. They’ll be sent straight to your inbox!
Roll & Round is a fun partner game that practices rounding to the nearest 100 or rounding to the nearest 1,000. Each partner has a different objective rounding to 0, or to 100/1000. After rolling the dice, players try to create a number that rounds to his/her specific objective. The version that rounds to the nearest 100 only works with two digit numbers, whereas the version that rounds to 1,000 works with three digit numbers.
Roll & Round helps build students’ number sense as students have to reason through which number they should create out of their possibilities. It also helps work on rounding. A number line is included with the middle placement, to help support students that need it.
Roll & Round is ready to play upon printing. Just add a dice, or several, and go! This is great to play on laminated pages, in a sheet protector, or a dryerase sleeve. Download Roll & Round to try it out today!
Left Right Learn is a simple, easy prep game. All you need is a game piece for each player I love to use mini erasers! Students draw a card, solve the fact, and move given the directions on the stated card. It’s a fun way to give students ongoing practice with multiplication facts. I have two different versions. The free one practices facts 05. I love to use this early in the year to give students repetitive practice with these facts. I find that multiplication feels less overwhelming when they feel confident with a bank of facts. We spend a good amount of timing working with facts 05 before transitioning to working with others.
Multiplication Facts 05 Left Right Learn is available for free from my TpT store.
I also have another version that works with Multiplication Facts from 010. 5 different games are included. Because each card practices a range of facts, students get new practice with every play. My favorite part of Left Right Learn is how simple it is to prep. Just print, and cut out the gamecards. Of course, you can also laminate the boards and/or cards. If I print on colored paper, or cardstock, I usually don’t worry about laminating. I like to put the gamecards in a cup or bag and we’re ready to play. You can take a closer look at Multiplication Facts 010 Left Right Learn in my TpT store.
I hope you’ve found some new 3rd grade math games to incorporate into your independent practice. Games are a great way to build student skills in fun and engaging ways.
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]]>The post How to Integrate Algebra with Elementary Students: Equality, Equations, and Discourse appeared first on Tales from Outside the Classroom.
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“How do mathematics educators effectively and meaningfully incorporate algebraic ideas into K–5 curriculum? When elementary teachers are unfamiliar with early algebra, lessons designed and labeled as algebraic may become arithmetic exercises; the algebra then remains hidden from both the teacher and students in the implementation. The result is that the algebra standard is only superficially addressed.” Earnest & Balti
Building strong algebraic thinking comes from continued exploration of math concepts in different formats. Asking for students to explain their strategies when solving, and asking others to share if they did it in a different way, not only builds students’ strategy use, but also their algebraic thinking. By thinking critically about another students’ steps, students evaluate mathematics. Discuss the steps and why they work (or don’t work!). Ask students if another student’s work is correct. Asking students to share their strategies also helps other see that it’s okay, even great, they got to the same answer in a different way, or that they thought of the problem differently. Research shows that students are stronger in mathematics if they can represent a problem in more than one way
I incorporate math discourse throughout our math block, but am very intentional about our discussion during our Word Problem of the Day. It enables us to focus on one problem for 1015 minutes, so we can go deep into the problem discussing the word problem’s context, representations, and student strategy use. Math discourse is powerful and builds deep thinking around concepts. In each of the topics I discuss below, discussion is a critical part!
Interested in these free math talk posters? Click the picture to head to my Word Problem of the Day post to grab them!
Understanding equality is a pivotal part of algebra, but truly all of our mathematics instruction. It is important that students see that the equal sign represents a relationship– that the sides have the same value. Often, students see the equal sign as an indication of something to compute or solve. There are several ways we can present our computational problems that help students build an understanding of equalities.
Have you ever presented your students a seemingly simple equation thinking they’d easily solve it correctly, but they don’t? It can be eyeopening.
9 + 6 = ___ + 5
If you gave your students this problem, how many of them would answer 15 instead of 10? My experience says, a large number – especially if there hasn’t been an investment in building algebraic thinking, or specific work with the equal sign. Every single one of my 3rd graders in one class said 15!
This type of representation can be used with any grade level of students. Very small numbers within 5 can be used with kindergarteners. Equations such as this one can start with first graders. Using manipulatives and models will help students understand how these equations work. And it can be applied with larger numbers, and other operations as well.
As time goes on, we want students to be able to build relational thinking. We want them to start working with larger numbers, and use their number sense and general math understanding to solve without computing in situations where that’s possible. For example, we want student to be able to solve the following equation.
259 + 63 = 260 + ____
This equation shows the algebraic thinking we want students to be able to perform that’s discussed in the quote. Moving beyond just arithmetic and computation and truly thinking about the numbers, equal sign, and what the equation represents. We want students to be able to quickly and easily identify that 62 is the missing number. The discourse around this representation can help students solidify and expand their algebraic thinking.
One of the easiest ways we can incorporate intentional algebra practice with young students is to include unknowns in any location in an equation and moving the location of the equal sign. By working with various formats of equations, students build an understanding of what each of the numbers represents and the purpose of the equal sign. For example:
_ + 2 = 5
5 = _ + 2
Both equations show an unknown addend. Many students will solve the second equation differently than the first. With a poor understanding of the purpose of the equal sign, students struggle with solving the second example. Even students much older than 1st grade! With continued exposure and dialogue with the various formats of equations and the meaning of the operations, students develop proficiency with both the operations and equality.
Balances are a powerful tool for building students’ algebraic thinking and mathematical understanding. Balances are often first introduced in first grade when trying to build the concepts of inverse operations with addition and subtraction and an understanding of the equal sign. Students often work to identify the unknown addend that balances the equation. Often, however, the balance doesn’t continue in our math classrooms as students get older. This is an easy way presentation that helps students look at and think about things a bit differently than we typically teach. This is especially true when working with all four operations. By presenting the equation as objects in a balance, students can see how the numbers relate to each other and what the operations signify.
My TwoStep Equations Balancing Equations shown here are a great segue between solving onestep equations and twostep word problems. We often jump straight into the word problems for this 3rd grade standard, without enough practice with the computation. These balances show an equal group representation with an unknown factor. Students work to identify the unknown. These are also a great way to intentionally practice writing equations with variables for the unknown. All of the numbers are under 100 because the purpose of these is to build the algebraic thinking behind them not the computation.
Another similar concept is true or false equations with expressions on both sides. The key here is to try and move beyond rote computation. Can students make connections between the numbers to help them answer? Can they use their number sense to identify if something is an equality? For example:
101 + 22 = 100 + 23
We want students to be able to immediately identify that the equation above is true without having to complete the computation, just like with the previous examples above. But, by giving two expressions that need to be computed, we help students see that the equal sign doesn’t mean to compute, but shows the relationship between both expressions. There isn’t a missing number box, or a variable for an unknown. Instead, they’re applying their learning by answering a true/false question.
Be sure to give students examples with inequalities as well! A great next step is identifying what would be needed to make the equation true. I have seen kindergarten students engage in this discussion! Students likely have different responses to that question since there usually several different possibilities of changes. But that’s some of the power of working with inequalities the discussion that’s drawn out from the responses.
My True or False Equivalent Expressions Task Cards work with smaller numbers so they can be easily used with young students but would be good support for older students that struggle with algebraic thinking. With these cards, students must add both sides of the expression to determine if they’re equivalent. They are modeled on a balance to give students exposure with balance scales and to demonstrate that both sides should be equal. As with everything else, the value comes from writing the equations and having the classroom discourse around the models.
Want to grab these? Fill out the form below and they’ll be sent to you straight away!
Another easy way to bring algebra into elementary classrooms intentionally is by having students write expressions and equations for models and word problems. Often, students explain the steps they did when solving and demonstrate their understanding of the context. But a great way to provide support for others that aren’t as successful, and to connect their existing understanding to algebraic thinking is by writing it as an equation. By doing this, students learn that variables represent unknown quantities. They also demonstrate that they understand the context of the word problem and the mathematical concepts behind them. We practice writing equations with each of our daily word problems, and again to match models that are often represented in our textbooks. To read more about the steps in my problem solving routine, I detail it in my 3 Reads Strategy for Problem Solving post.
Students need practice writing equations rather than just solving them to truly build an understanding of what’s being represented and what the equation identifies. For students needing support with writing twostep equations, or understanding the differences between addition and multiplication, my Writing Two Step Equations task cards may be helpful. Students are able to see the difference between equal groups and additional items added.
For older students, my MultiStep Balancing Equations Task Cards are great for building an understanding of the difference between expressions and equations, working with variables, and talking about the operations. With each task card students have to complete computation on each side of the balance before finding the value of the unknown. With each of them in this set, students must identify the missing factor.
Functions include building, representing, and reasoning with relationships between numbers. With functions, students generalize relationships between numbers, represent those relationships, or functions, in multiple ways including expressions, equations, tables and graphs; and reason with those generalizations. Functions are what we think of most as algebra applying a formula to solve.
Work with patterns begins in prek and kindergarten. Their work often begins with repeating patterns in shapes. Over time, students should begin to notice patterns with numbers. Beginning in first grade, and continuing through, students should be exploring patterns they notice, such as those on the addition table or multiplication table. Have you ever asked students if the sum of two odd numbers is even or odd? That’s a pattern. It’s also a generalization. Making generalizations helps students understand “rules” of mathematics. Why things work. If we look at 3, 6, 9, 12, one may say that the rule is add 3. That tells us the pattern that we follow to find the next number. But how do I find another number in the pattern without continuing to add 3 to the one before it? I generalize.
Generalizations are a fundamental component of algebra. To generalize, one must first understand the relationship between and among quantities. Reasoning with those relationships is making generalizations. One of the first generalizations we often explore with students is the commutative property of addition. Through exploration, students are typically able to understand it on their own.
Let’s go back to the example above. If I want to find the 50th number in the pattern, I can generalize that by multiplying the number in the pattern by 3 will allow me to find the 50th number. The generalization is that if n stands for the numbered place in the pattern, and I multiply it by 3, or n x 3, I will find the answer.
We call these so many different names. I’ve seen them as input/output tables. I’ve shared Function Machines printables. But at the end of the day, they all have the same focus: helping students understand that a function is when an action is applied to a number resulting in a new one. Functions are patterns linear patterns. When solving, students likely are identifying a pattern to help them solve.
“If a horse has 4 legs, how many legs do 8 horses have” would be an example of a function. These Input/Output Tables Task Cards give students the rule, or the equation, they have to follow to complete the rest of the table. This can easily just become a computational activity. Connecting them to the horse example given here helps students see the realworld relevance of the table and how it can be a helpful tool for them.
With input/output tables, it’s important that the input figures aren’t sequential. Students will often quickly identify the pattern and continue it going down the output side, continuing the pattern without generalizing. It takes away the algebraic component. While it’s natural that this is where many elementary students will begin, it’s important that we get them to identify the recursive pattern how we move from input to output the generalization. By changing the numbers by skipping ahead, or working with larger numbers, students have to identify the pattern in order to identify the output. This is much harder work than just continuing the pattern and students will need a lot of support with it.
These TwoStep Input/Output Task Cards have students identify the rule that’s presented. These are SO TOUGH! As students practice with them and build their number sense and algebraic thinking, they become easier. I use these with my 3rd graders and it’s a great challenge for them. As older students work with linear equations, these task cards are great practice for them as they work to not only understand but also write them.
Each of the task cards shown here as examples, are just that examples. Each of these concepts can be easily incorporated into the work you are already doing! My Accessing Algebra line is designed for the middle and upper elementary grades. These print and go task cards help you integrate algebraic concepts into your every day instruction with very little prepwork. You can see my entire Accessing Algebra line in my shop.
Finally, math should be taught with a focus on understanding, not as a set of procedures. Our presentation and ongoing instruction throughout the year helps to build algebraic thinking. Over time, students become used to looking for patterns, generalizations, and structures. Ask questions like: “Is this always true? How do you know? How can you represent that? Did someone solve that differently? Can it be explained in a different way?” Questions like this help students move away from specific arithmetic examples and into generalizations. We can connect algebra to our arithmetic to help develop more proficient math students that are ready for algebra success.
For more on integrating algebra with elementary students, Project LEAP and the book Connecting Arithmetic to Algebra (affiliate link). You may also enjoy the quick read Instructional Strategies for Teaching Algebra in Elementary School: Findings from a ResearchPractice Collaboration by Earnest & Balti
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]]>The post Multiplication and Division Word Problem Types appeared first on Tales from Outside the Classroom.
]]>This post takes an indepth look at each of the multiplication & division word problem types. I also give some helpful links at the bottom that discuss Cognitively Guided Instruction, or CGI problem types. They use slightly different vocabulary than the CCSS but are the same set of skills. An important note when I talk about teaching the multiplication & division word problem types explicitly, I don’t mean that they’re only practiced during a specific unit, or that we teach specific keywords for each problem type. Students need to read the problem and understand the context. Recognizing the problem type can support that work, but it’s not focused on keywords. I also do a daily word problem outside of our focused unit work. I firmly believe in spiraling the standards in word problems so students have to focus on context to solve. For more support with problem solving, check out my Why Your Students Struggle with Word Problems, and What You Can Do About It post.
An important note before we beginthroughout our exploration of both operations, we often return back to the total. We identify in our first lesson that multiplication allows us to find the total number of objects arranged in equal groups. When we begin exploring division, we know the total number of objects we have and have to find the unknown in connection with groups. Throughout our work, with arrays, area, and equal groups, we continue to come back to the concept of total to help students identify the operation needed. It is through identifying the total as known or unknown that students will truly understand the multiplication and division operations. As you will see, that’s a focus with each of the multiplication and division word problem types.
In my Introducing Multiplication and an Working with Division posts I walk through my handson, engaging lessons I use to introduce each operation. When introducing both operations, we focus on equal group arrangements. It’s crucial for students to understand that multiplication and division works with equal groups so it makes sense to begin here. When we first start working with multiplication and division word problems, I ask students to identify the items that are arranged in groups, and identify what that group looks like. For example, the group might be a box or a bag. Those objects could also just be objects in other scenarios. So, identifying that an object is grouped within something helps students to understand the word problem and that an equal group scenario is present.
MULTIPLICATION  QUOTATIVE DIVISION  PARTITIVE DIVISION  
TOTAL UNKNOWN  # of GROUPS UNKNOWN  # in each GROUP UNKNOWN  
4 x 6 = ? ? ÷ 4 = 6 
? X 6 = 24
24 ÷ ? = 6 
4 x ? = 24 24 ÷ 4 = ? 

Equal Groups  There were 4 bags on the counter. Each bag had 6 apples in it. How many apples were there in all?  There are 24 apples split equally into bags. Each bag has 6 apples in it. How many bags of apples are there?  There are 24 apples split equally into 4 bags. How many apples are in each bag? 
These are the word problems we typically think of with multiplication. It’s an arrangement of items into equal groups to find the total number of items. Identifying that the number of groups and the number of items into each group are known, while the total is unknown, helps students solve these word problems.
When the number of groups are unknown, it is a quotative division problem. Let me clear, I don’t teach my students the term quotative. Rather, I teach them that there are two types of division. When students are able to identify that the total number of objects is known, but the number of groups is unknown, they then know that they are dividing. It’s important that students have lots of practice with both types of division.
When a word problem identifies the total number of items and how the items are arranged, but doesn’t give the number in each group, these are partitive division. Think of it as partitioning. The number of groups is known so the partitions are known. Again, I don’t teach this term with my students, but it’s important that students know that division is presented in two ways.
Once both operations have been introduced and practiced separately, I like to use my Multiplication & Division Scenario Tables Task Cards to practice writing equations and understanding group arrangements in context. I find that removing all of the components of the word problem, and working through just the total and group information, helps students truly understand the operations in connection with equal groups. This helps them then apply their learning within word problems. Students get practice with different ways items can be grouped, which helps them look for and identify grouping relationships in word problems later.
In conjunction with teaching equal group arrangements described above, arrays should also be included. Arrays are how students are first introduced to multiplication in 2nd grade. Students should have background knowledge with rows and columns vocabulary. Arrays are how I connect what we’re learning now, with what they learned before. Therefore, I teach arrays at the same time that I teach equal group arrangements. I correlate rows and the number of groups. I always emphasize that the columns are the same as the number in each row (or the group).
MULTIPLICATION  QUOTATIVE DIVISION  PARTITIVE DIVISION  
TOTAL UNKNOWN  # of GROUPS UNKNOWN  # in each GROUP UNKNOWN  
4 x 6 = ?
? ÷ 4 = 6 
? X 6 = 24
24 ÷ ? = 6 
4 x ? = 24 24 ÷ 4 = ? 

Arrays  There are 4 rows of bags with 6 bags in each row. How many bags are there?
The bags are arranged in 4 rows and 6 columns. How many bags are there? 
There are 24 bags arranged in rows of 6. How many rows of bags are there?
There are 24 bags arranged in 6 columns. How many rows of bags are there? 
There are 24 bags arranged evenly in 4 rows. How many bags are in each row? There are 24 bags arranged evenly in 4 rows. How many columns of bags are there? 
It’s important to note that the CCSS lay out two rigors of array word problems: ones where the items in rows are presented, and those that give the word problem in rows and columns. Through continued exposure and practice, students understand that these are interchangeable. Array word problems are not very common, but are definitely a problem type that students should have exposure and practice with. They also lay the foundation for students to work with our next word problem type: area
Area is a critical component of our multiplication and division work. It’s a major part of 3rd grade math instruction and it’s important that students work with many word problems where they have to recognize area in context and solve. This is especially important to learn how to differentiate between area and perimeter by making connections between arrays and what is known about multiplication and division. Area should be introduced with arrays and connected to an area model. This concrete, visual example helps students connect what they already know (arrays) with their new learning (area). Unit squares are written in the standards to be this bridge. Area models continue on as you work with more the more complex rectilinear figures, and to help students understand the distributive property of multiplication. The CCSS don’t list area problems as their own line, rather, they’re included with arrays. While this certainly makes sense since arrays can be created inside the rectangle, and that’s how area should be introduced, most area word problems don’t use rows or columns when providing side lengths. I think it’s an important distinction to look at area word problems separate from arrays.
SIDE LENGTH UNKNOWN  SIDE LENGTH UNKNOWN  
Area  A rectangle has one side measuring 6 feet and another measuring 4 feet. What is the area of the rectangle?  A rectangle has an area of 24 square feet. If one side is 6 feet long, how long must the perpendicular side be?  A rectangle has an area of 24 square feet. If one side is 6 feet long, how long must the perpendicular side be? 
Solving area problems again connects back to total and known/unknown values. When students are trying to identify the total area of the shape, and are given both side lengths, students need to multiply to find the area.
When students are given the total area of the shape, but need to find a missing side length, they must divide.
Ultimately, if students have a solid understanding of multiplication and division word problems and their connection to total, they will likely be successful with area word problems.
The most complex multiplication and division word problem types are comparison word problems, in my opinion. Just as they are in addition & subtraction, the way these problems are structured, cause them to be more complex than the others. For these, it’s important to look at each of the different problem types and digest what’s being given. I use a 3 Reads Routine when working through word problems, and these problems always bring the greatest discussion as students grapple with the information that’s presented.
COMPARISON UNKNOWN  CONSTANT UNKNOWN  
Compare  The small bag of apples costs $4. The box of apples costs 6 times as much. How much does the box of apples cost?  The small bag of apples costs $4. The box of apples costs $24. How many times as much does the box cost compared to the bag of apples? 
A box of apples costs $24 and is 6 times as much as the cost of the small bag of apples. How much does the small bag cost? 
The multiplication and partitive division (constant unknown) examples have very similar wording since they both have the comparison statement: “6 times as much”. This is a description of the relationship between two groupsthe total, and the comparison group. The quotative (comparison) example is worded differently since the unknown is the comparison relationship: “How many times as much does”
The key to understanding multiplicative comparison problems is that the comparison is the repeating groups, whereas the constant is the group size.
In a multiplication word problem, you are told the amount in the comparison group, 6, and the constant, 4. Each bag of apples is $4, so if it’s 6 times as much, it’s the same as having 6 of the bags. Thus, 4 x 6.
In a (partitive) division word problem, you are given the total number (the cost of the box of apples). Once you partition, or divide, that cost into 6 equal groups, you are able to identify the cost of one of those groups, which is the same as the cost of the small bag of apples, and that is the same as the number of ducks.
In a (quotative) division word problem, you are given the constant, the cost of the small bag, along with the cost of the box of apples. The unknown is the relationship between them. With these word problems, the wording of the question can often throw students off.
Once students are able to decompose the word problem to identify the total, and the comparison, they’re able to connect that to what they already know about multiplication and division to help them when solving. Teaching students to closely read the word problem is key. To read more about my 3 Reads Routine you can click the image below.
Looking for additional resources? You can download my Multiplication & Division Word Problem Types reference sheet and use it to help identify and write the different word problem types for classroom practice.
Want additional multiplication & division word problem practice? I have a FREE Multiplication & Division Word Problem Task Cards set. Each of the multiplication & division word problem types discussed here are practiced during the 24 task card set. This is great practice for later in the year to ensure students have ample practice with each type. It would even be a great tool to help students discuss the different problem types and how they’re presented. To download the Multiplication & Division Word Problem Type Task Cards, just fill out the form below and they’ll be sent straight to your email.
You might also find the following links helpful.
Partitive & Quotative Division from SFUSD
CGI Resources from LAUSD
Multiplication & Division Word Problems from ND Counts
Two Ways of Thinking of Division from Langford Math
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]]>Morning meeting is traditionally done right at the start of the day. In reality, it doesn’t always happen that way, but, for me, I like starting the day off on a positive, calm note. Most years, we do our morning meeting after our morning work since I’ve often had students trickling in. I want to ensure each student is present in our meeting, as much as in my control. We all have different routines in our day, so find the time that works best for you.
I call students down to the rug that’s central for our instruction. I like to have the rug as our home for meeting and for most whole group instruction. Us sitting together, in a much smaller space, just helps with the closeknit feel I’m looking for. I have my students sit around the rug, forming a large, often misshapen, oval. This makes it possible for students to easily make eye contact with each other. It also makes it easier for students to realize that their attention should be on the speaker, and not with me. I also like to give my students assigned spots for morning meeting. I find that this makes our movement quicker. It also allows me to create some key student partnerships. If I have a student that doesn’t seem to be building relationships as easily, I can put them with a student I think would mesh well with them. Or. I can put students that need some visual reminders in key locations around the oval.
There are 4 components to the traditional morning meeting: Morning message, greeting, activity, and share. Some programs may vary from these 3 routines slightly, but these tend to be the most common.
The first part of our morning meeting is the morning message. I use my Daily Schedule & Morning Message to display our day’s schedule, our student of the day, and the morning message. Our morning message gives students a look at our day and what they can expect. I let them know key changes in our regular routine. I also use this time to give praise for yesterday, or something I’m hoping to reinforce today.
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The next morning meeting component is the greeting. The purpose of the greeting is to make every student feel acknowledged and welcomed into the classroom. Each student is greeted by at least one other person in the classroom. The greetings we use change throughout the year. We start out with a simple Good Morning, Name. I also try to incorporate “hello” in other languages, especially those native to my students and their families and others I think it’s great for them to know. These are the versions of hello I typically use in my classroom:
Spanish: Hola!
French: Bonjour!
German: Guten tag
Japanese: Konnichiwa
Hawaiian: Aloha
I would encourage you to incorporate languages important to your students and their families. You can ask students to be expert pronunciation guides, or utilize Google or Alexa to help support you. Even if your pronunciation isn’t spot on, students will appreciate the attempts to make their home language feel present in the classroom.
Another aspect of our greeting is often a handshake or a high five. I like to do the handshake so we can talk about the norms of handshakes and practice making eye contact while shaking hands. Of course, there’s many other ways to incorporate a greeting into your morning meeting. You can do a different one every day, or have a large repertoire you spiral through.
Looking for more morning meeting greeting ideas? I have 15 Morning Meeting Greetings in one easy to use, black and white download. Fill out the form below to have it sent to you straight away.
A group activity of some sort is often included, especially if you’re following a specific morning meeting format from a specific program. This tends to be the aspect that I struggle to fit in most days. Our day is so crunched for time. And while I believe in the power of morning meeting, I just struggle to find more time to include team building activities. I do try and incorporate them some at the beginning of the year, when we’re really trying to build relationships with each other. I also try to utilize days before and after breaks or field trip days, where are schedule is already awry, to incorporate activities.
The last component of most morning meetings is the share. Like everything else, it can look many different ways. It’s an opportunity for students to share with others. If we have time, often at the beginning of the year, or when our schedule is otherwise interrupted, I incorporate a more broad share. Some programs call this sharing the “news”. I also try to include this on Mondays so students can share about their weekends if they would like. I call it just “share” and students can share anything they would like. This is when I also allow my students to optout and they can pass when it’s their turn.
Most days, our morning meeting wrap up is our Question of the Day. I first started implementing Question of the Day as my share routine with my Kicking off a Great Year unit. I use the scaffolded question cards to introduce restating the question with our acronym PQA (Put the Question in the Answer) alongside our student interviews. You can see more about this in my post Ideas to Teach Students to Restate the Question. We do a few cards whole group, and then I split students up into small groups to read and respond to cards as they get to know each other. This is also when I introduce expectations around someone else speaking.
After we use the scaffolded question cards in small groups, I choose a card a day to do during morning meeting. Sometimes we even do a couple once students have become pretty quick with it. Students read aloud the question on the card and respond in a complete sentence while restating the question in their answer. If I’m teaching first grade, I use the scaffolded cards for several weeks. But, most of my time has been in third grade and I’m able to move to the nonscaffolded cards pretty quickly.
Once I started implementing this routine, it became abundantly clear that our morning meeting was the perfect place to practice restating the question. Before students should be expected to use it in their writing, they have to be able to do it orally. By establishing the expectation during morning meeting that students answer every question in complete sentences with a restatement of the question, it becomes much more seamless during the rest of the day. Students also build so many other oral language skills during this time as well. They work to answer different types of questions, give answers in compound and complex sentences, and generate complete thoughts.
This year, in addition to using the question cards from Kicking Off a Great Year, I’m also going to implement a digital Question of the Day.
Question of the Day is just that: a daily question prompt. It’s designed with morning meeting in mind. Students are given a question to respond to in a complete sentence. At the beginning of the year, the questions focus on getting to know students. They answer questions about themselves, their families, and their likes and dislikes. It’s designed for students as young as first grade, but can easily be used with 3rd and 4th graders!
A variety of question types are included to give students practice answering different types of questions and restating the question in different ways. When a new question type is given, students are given response frames for several days. After, the support is removed and students are expected to generate the complete sentence independently. With my third graders, I will likely move away from scaffolded questions pretty quickly in the year, as long as my students demonstrate their readiness. I find that at the beginning of the year, my third graders always struggle with this routine because the expectation hasn’t been there, previously. After a few weeks, it becomes second nature to them. I intentionally built the questions to begin with simple sentence responses, and to longer responses requiring details and/or justification. Students get specific practice with and and because.
Question of the Day is provided in 3 formats: Powerpoint, Google Slides, and a PDF. My hope is that this enables anyone to use it regardless of the digital compatibility with your device.
200 different questions are included, along with an editable template in Powerpoint and Slides. With 200 given prompts, there are extras included for you to swap things out if you’d like. Have a special program and want to incorporate it? The editable template makes it easy to create your own!
“What are two things you saw at the museum yesterday?”
“Name two animals you saw at the zoo.”
These are just two examples of questions you might use as your Question of the Day to connect with a special event. The power Once students understand the expectations around Question of the Day, it’s easy to incorporate different opportunities with it. Rather than having each individual student share orally for the whole class, students can share privately with a partner with a few sharing aloud. Or, students can be broken up into groups to each share with just a few key students sharing orally.
It’s also easy to incorporate written responses with morning meeting Question of the Day. Students can write sentences on their dry erase board, a PostIt, or index cards. With the sentence frames displayed, students are then just responsible for encoding the words specific to their response. This is perfect written practice for young students to apply what they’ve been learning. It can be incorporated during morning meeting time, or even as a precursor during morning work. Obviously, adding the writing component can extend the time needed, so I would pick and choose when to include it. With that said, it’s valuable practice to apply what’s been rehearsed with a partner orally into writing and is exceptional practice for young students.
Take a closer look at my Question of the Day unit in my TpT store.
Have questions about morning meeting or question of the day? Leave them in a comment below!
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