Reflections and Resources from Tarheelstate Teacher: 2017
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Roll and Multiply Free Dice Game for Multiplying Whole Numbers

Are your 4th or 5th grade students struggling with multiplying whole numbers and leaving you wracking your brain trying to figure out how to respond? Or, are you realizing that differentiating your multiplication practice is a must because students are all over the place in their mastery?
Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
Well, I've got a "differentiation ready," easy to implement, print and go game for you today that you can use during whole group, math stations, or guided math groups. Your students can play independently or with a partner--or both! You've got a million ways to incorporate this game into your plans!

This game uses a scaffolded and differentiated learning continuum for multiplication that I wish I had understood sooner in my teaching career.

If you read my last blog post, I shared how I see math concepts on a continuum of learning along with 5 differentiated activities to use during your multiplication unit. Here's how I outline the levels of skills for multiplying whole numbers:

Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
We should move students from multiplying 2 digit by 1 digit to 3 digit by 1 digit to 4 digit by 1 digit, then move them to 2 digit by 2 digit and 3 digit by 2 digit. (If you are working with decimals, you can build students up using this same continuum and size of factors.)

Is this continuum obvious? Is this something you already realize? Is this already how you structure your multiplication of whole numbers lessons and student practice AND how you plan for differentiation? If so, I'm impressed! I wish you had been my mentor teacher so you could have guided me to this understanding sooner.

For those of us who did not have this scaffolded continuum handed to us, can you see how this continuum applies to levels of readiness? Not all students are ready at the same time and I'm a big believer in meeting students where they are--FINALLY, by thinking about my curriculum on a leveled continuum, I understand how to meet students where they are.

But, moving on, you're probably here for the multiplication dice game, so let's get to it! I've incorporated this scaffolding into the dice game I'm sharing with you today. If you want the game sent to you, just throw your info into the boxes below.


MATERIALS NEEDED 


YOUR CHOICE OF GAME BOARDS:

Choose from the templates for the area model or the standard algorithm.
Differentiate by assigning students to the leveled game board that matches their ability OR the next level of multiplication that they are trying to master. You have boards for:
  • 2 Digit by 1 Digit
  • 3 Digit by 1 Digit
  • 4 Digit by 1 Digit
  • 2 Digit by 2 Digit
  • 3 Digit by 2 Digit
DICE:

6-sided dice will work for this game, but if you have access to 10-sided dice, students will be able to create multiplication problems with all numerals.

6-sided dice may also be used as a modification for students that need you to limit the challenging multiplication facts for them (since this dice will not require them to multiply by 7, 8, or 9. You can always move them up to the 10-sided dice later)

DECIDE ON THE FORMAT FOR THE GAME:


These “Roll and Multiply” game boards can be used with partners AND as independent practice activities—again and again! Each time you move students to the next level, you can have them play with a partner, then move the game into independent practice.

Students can be given calculators to check their work since there are numerous combinations of multiplication problems that they can create.

INCREASE THE CRITICAL THINKING/ STRATEGY USED IN THE GAMES:

You may set up the game two ways:

1) Students must create the multiplication problem in the order that numbers are rolled on the dice. In this set-up, the winning product will be based on luck.

Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.2) Students decide where to place numerals as they roll them. This will allow students to develop strategies for having the highest product (example—if I roll a nine, I should place it in the highest place value that is available).

When playing with a partner, students can earn points (win the round) by rolling the highest product. The area model template has a place for students to note the winner. For the standard algorithm game boards, you can have them tally their score on a t-chart.

MODIFYING THE GAME EVEN MORE: 


One last way to help students who are really struggling with mastering multiplication (using any model) is to peel back the layers of difficulty even more. These students will benefit from a reduction of the multiplication facts they are expected to recall.
Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.

You can do this for them by setting up their game so that they only multiply by 2’s or 5’s. (I've given you a few of these modified game boards in your download!)

Multiplying by 2's and 5's is a great scaffold because these are the easiest multiplication facts to memorize or count-by on fingers in my opinion.

Students can still roll the dice for the other factor, but by reducing the multiplication facts they must recall, you have freed up some brain space for learning the process of multiplying larger numbers. In your free download, I've included area model and standard algorithm game boards for multiplying 2 digit by 1 digits with just 2's and 5's, but you can write in 2's and 5's on any of the other game boards or multiplication activity you have.

I hope you LOVE using this game in your classroom for multiplication practice and differentiation. You can plan to use the game boards again and again so that you can increase students’ level of mastery and the rigor of the game each time!

Other Differentiated Resources for Multiplication of Whole Numbers that You May Like:

> > > Differentiated Multiplication Assessments and Practice Sheets (3 Levels with 3 Version each--perfect for pre-assessment, small groups, independent practice, review, and post-assessment)
> > > Multiplication Word Problems (in the same set as above)
> > > What's My Error? Error Analysis Task Cards for the Area Model (5 Levels)

This Multiplication Exploration can provide your students with more opportunities for critical thinking about how the factors affect and the magnitude of the products.

If you are sold on differentiating your math instruction based on a leveled continuum, I highly recommend checking out my differentiated assessments and practice sheets. 4th Grade sets are completed for every standard in the curriculum and more 5th grade assessments are on their way.
 Differentiated Math Assessments

You can find the 4th Grade Assessments here in my tpt store or by clicking the photo above.

You can find the 5th Grade Assessments here in my tpt store.



Multiplying Whole Numbers: Ideas for 4th and 5th Grade

Looking for fresh ideas and activities for multiplying whole numbers that might make it more fun and help your 4th or 5th graders master the process of multiplication more quickly?
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
Nearly every group of 4th grade and 5th grade students I've taught have needed me to differentiate and scaffold their learning in order to help them master multiplication of whole numbers.

Over the years, I've learned to envision my standards on a continuum of learning by connecting what I want students to be able to do with lower-level skills that can help them "build up" to the grade-level learning goal. In addition to helping my struggling students master a concept, I like to figure out what would be required of students to go beyond my grade-level standards. I tack these more challenging skills onto my continuum of learning as a stretch for students who work beyond grade level.

I am a big advocate of knowing how your grade level's standards connect to the previous grade level AND the next grade level's standards. I've developed this love of connecting curriculum across grade levels because I'm passionate about differentiation--and this is how I see it being successful--and I've been blessed during my teaching career to loop from 4th to 5th grade where I immediately understood my 5th grade curriculum in relation to the 4th grade "building blocks" I now had to teach.

But I also know that as teachers, sometimes we barely have time to do a deep dive into our own standards, so it can be even more challenging to find the time to figure out how to make appropriate connections within a span of grade levels.

Lucky for you, I love thinking about vertical alignment--the "stepping stones," and the "stretches" that I can use as a road map for differentiation in my classroom. I'm a nerd who's done the work for you!

Here's how I see the continuum of learning for 4th and 5th grade multiplication.
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
In this continuum, you can see that rather than giving students a mix of problems "on grade level" from the start of our multiplication unit, we can give them controlled practice that scaffolds them from 2 by 1 digit to at least 2 by 2 digit for 4th graders and 3 by 3 digit for 5th graders. We also have an idea of how to push students who quickly master the grade level standards.

So, given a continuum for learning to multiply whole numbers that is now concrete and makes common sense to us, how do we proceed with our teaching? Here are some ideas!

1) USE LEVELED ACTIVITIES and GAMES

One of my favorite ways to utilize scaffolding with computation skills is by incorporating dice games. When I discovered the power of 10-sided dice a few years ago, I went crazy designing dice games and activities for my students!
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
We can make sure that the games we have our students play for math practice incorporates the leveled continuum. I like to start by assigning students to the level that matches their ability OR the next level that they are trying to master.
  • For multiplication practice, I've created separate multiplication game boards for 2 by 1, 3 by 1, 4 by 1, 2 by 2, and 3 by 2 digit multiplication just for you! 
  • The game boards include templates for the area model and the standard algorithm. I like to have my students master the area model and introduce the standard algorithm later---I love the area model, but as the numbers get larger, some students have more success with the standard algorithm. I believe both methods are deserving of adequate class time, especially for 5th graders.
Play games like this again and again, increasing the challenge for students each time. You can also have students play games like this with a partner OR independently. I do both and usually make it the games independent once the partner aspect has lost its novelty.

I've written more about this multiplication game here and you can get the "Roll and Multiply" game sent to your email by entering your info below.


2) USE LEVELED ASSESSMENTS

Utilizing leveled continuums, I've developed math assessments and practice sheets that allow you to assess where students are on the spectrum of "building blocks," "goals," and "stretching beyond."

These are perfect for knowing which level your students are at and therefore making it EASY for you to know exactly where to place them in differentiated activities. By pre- and post-assessing with these leveled problems, you can also visibly see how students grow in their mastery of concepts as the unit goes on.

You can find the assessments specific to multiplication here.
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.


3) INCORPORATE ERROR-ANALYSIS PROBLEMS

While your scaffolded games will add an awesome element of fun and differentiation as you help your students learn to multiply whole numbers, you will need additional activities to enrich their learning and make sure that no matter what level of mastery they are on, they can apply their learning of computation to other contexts. 

I LOVE to incorporate error analysis problems as my students learn to use the area model for multiplication. I've found that error analysis can be great for students who are struggling and making common errors, but that it can also provide a challenge for students who have mastered a concept because it makes them think more deeply about the methods we are learning for concepts that came easily to them. Students also enjoy "playing teacher" and trying to figure out what mistakes the "student" has made.
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
In these differentiated error analysis task cards, students identify one error on each card and multiply whole numbers to find the correct product. The task cards come in 5 leveled sets so that you are ready to meet your students where they are. Find the "What's My Error?" multiplication bundle here.

4) INCORPORATE REAL-WORLD WORD PROBLEMS

I incorporate multi-step, "real-world relevant" word problems into all of my math concepts. This is typically how students are expected to apply and show their learning on our state test, so I want them to get comfortable with word problems from the start.
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
In my differentiated math resources, I've included real-world word problem sets that students can relate to. The 4th grade differentiated multiplication word problem sheets contain three versions of leveled word problems with 6 problems each that align with the continuum of multiplication.

5) USE THE MULTIPLICATION CONTINUUM WHEN TEACHING OTHER CONCEPTS

Going forward, I am sure to incorporate these levels for multiplication into other parts of my math content as the year goes on. If your students struggle with multiplication and division now, they may struggle with converting measurements later in the year, for example. 
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
However, if you use your measurement unit as an opportunity to continue moving them along the continuum of mastery (by starting out with 2 by 1, 3 by 1, and 4 by 1 conversion problems and then moving to 2 by 2 and 3 by 2 problems), you will give your students the opportunity to understand measurement concepts at their comfort level. (If you want the resources for differentiation already put together for you, you can find the 4th Grade Measurement Assessments and Practice sheets right here.)

What's the point? Why plan your math teaching like this?

I believe that students who are struggling to master a concept deserve controlled practice to help them achieve mastery of a concept. We need to be the experts who know how to scaffold students' learning.
Need ideas and activities for teaching multiplying whole numbers to your 4th and 5th graders? If you want to infuse your classroom with differentiated activities, this post is a must read with at least 5 ideas for differentiating your multiplication practice and student assignments. Read on for a look at the 4th and 5th grade leveled continuum for multiplication concepts, a free multiplication dice game, and other ideas for differentiation during your multiplication unit.
By understanding math concepts on a continuum of skills, you have an advantage that helps you set up opportunities to scaffold your students to greater mastery of the math concepts you are teaching.

If you are sold on differentiating your math instruction based on a leveled continuum, I highly recommend checking out my differentiated assessments and practice sheets. 4th Grade sets are completed for every standard in the curriculum and more 5th grade assessments are on their way.
 Differentiated Math Assessments

You can find the 4th Grade Assessments here in my tpt store or by clicking the photo above.

You can find the 5th Grade Assessments here in my tpt store.

Love this post and want more like it? 

Well, I'm glad you feel that way!  I am going to continue to break down key math concepts in the 4th and 5th grade curriculum--division and fractions concepts are coming up next. 

Make sure you grab your "Roll and Multiply" Differentiated Dice Game and you will also be notified when I publish a new differentiated math blog post. Happy teaching, passionate differentiator!

Different Approaches to Pre-Assessment in Math

Today I'm sharing some pros and cons for the different ways we pre-assess or pretest students in math. If you are looking for ideas for pre-assessing your students or simply considering if there is a better way for you to implement pre-assessments in your classroom, my blog series on pre-assessment in math should help you make some decisions!

{I'm writing a little mini-series about my love of pre-assessment. If you missed my last post about why we should use pre-assessments in math, even in a test-weary education world, you can click here to go back and read it!}Is there a better way to pre-assess students in math class than what we have traditionally done? Check out 4 ways we pre-assess in math and what I believe is the best way to pre-assess my 4th grade and 5th grade students in math. After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!
Now, while I'm encouraging you to implement pre-assessments into your math plans, I have to admit that it took me a while to perfect my pre-assessment routine.

Believe me, I've done plenty of things not-quite-so-right when it comes to pre-assessing (and assessing) my students in math. In the past, assessment has sometimes occurred as an afterthought and I have fallen into the trap of giving students a test because I needed grades or evidence for report cards.

#I'mnotsayingIamperfect but I'm here to help!

I've administered pre-assessments in math a few different ways, and I've had some time to think about "best practices" for pre-assessing students. As you read my analysis of each of the four ways I've assessed students, you'll be able to see how my beliefs about the purpose of pre-assessments evolved.

Note: Read carefully because I am NOT endorsing all of these options as "the best" ways to assess.

Different Approaches to Pre-Assessment in Math


After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!
1. Pre-test and post-test students with the same summative test for the unit's content.

When grade level teams are moving towards "common formative assessments," this is often how it's done. The team or district creates a summative assessment for the unit and teachers give it at the beginning of the unit to get a measure of "pre-learning" data.

POSITIVES:
You only have to create or find one version of the assessment. You have lots of information on what students know and don't know as you prepare to teach a new unit.

DOWNSIDE:
1. > > > Because you have "lots of information on what students know and don't know as you prepare to teach the unit," you may be overwhelmed by the information you have collected. By pre-assessing students on-grade level topics that they have not yet been taught, you will most likely find that students have deficits on MOST of the content.

With a pre-assessment that is really meant to be used as a summative assessment at the end of a unit, it is hard to know where to begin (wasn't figuring out how to proceed part of the goal of the pre-assessment?) and it can be difficult to sort out students who will really struggle with the content versus students who just have not yet been exposed.

2. > > > A detailed pre-assessment that is as long as your post-assessment may take a huge chunk of class time. If you plan to pre-assess your students this way for each unit, the class time lost may negatively add up and in the end, you may be led to believe that pre-assessing is a waste of your time.

It's not, but I've been there, and I'm glad I now have a better way!

3. > > > I personally don't like using the same pre and post assessment because students have already been exposed to the questions. I often pull out my pre-assessments to have students go back and see that they now understand problems that they didn't understand at the beginning of the unit. For me to feel really good about my students' mastery of a topic, I like to see that they can solve similar (but different) problems on the post test.

MY OPINION: This is not my favorite way to assess students.

This type of pre-assessment is usually based on the current grade-level's standards. As a pre-assessment, it contains concepts and skills that students may have never been exposed to. While you may get a window into students' misconceptions, this pre-assessment approach can lead to a lot of teacher overwhelm and waste a good chunk of class time, especially if you cannot wrap your head around how to move forward with ALL of the data you have collected. A detailed assessment of ALL of the standards for one unit may also take a large chunk of class time (often 1-2 math blocks).

After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!
2. Use a pre-assessment that is similar to the post assessment but contains different questions.

POSITIVES:
Students will not have been exposed to the exact post-test questions before.

DOWNSIDE:
> > > The same as in #1. I find myself overwhelmed and confused about what direction to go in when I have 25 questions on different standards and skills of a math unit for 25 or more students. This "pre-assessment data overwhelm" often leads to just teaching my unit the way I planned to and differentiating based on classroom observations rather than the pre-assessment. (What was the point of the pre-assessment, again?)

MY OPINION: This assessment approach doesn't get me giddy either. If differentiation is one of the main purposes of my pre-assessment, I don't want to have so much data that I don't know where to start.


After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!
3. Use short quizzes focused on targeted skills and concepts for your grade level's standards.

POSITIVES:
With short pre-assessments or quizzes, you are less likely to feel overwhelmed by the data you have collected, and students will be able to show MORE of what they know. Most importantly, you will have specific data on what your students are able to do and not do with your grade-level's standards.

DOWNSIDE:
> > > You will most likely be "pre-assessing" more often. You will have to plan for pre-assessments more strategically and think of your unit in chunks of related concepts.

> > > Assessments based only on grade-level standards do not always give struggling students the opportunity to show growth OR gifted students the opportunity to be challenged. These grade-level-only based assessments may still just having you sorting students into the "doesn't know it yet" and "has mastered it all" groups.

MY OPINION: This assessment approach is a good start. Assessing with short quizzes based on grade-level expectations makes it easier to sort students into "gets it/doesn't get it" groups. It also allows you to address very specific math concepts, rather than feeling overwhelmed that some students have mastered "everything" and others have a #wholelot of deficits that you need to remediate.

After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!
4. Use leveled pre-assessments that are based on a continuum of understanding.

Leveled or "tiered" pre-assessments contain sections of questions based on below-grade level, on-grade level, and beyond-grade level standards. I call these "differentiated math assessments" and I've spent the past year developing leveled math assessments for 4th grade and 5th grade math.

POSITIVES:
Leveled pre-assessments allow you to assess students on a range of skills that you consider "pre-requisite" to grade-level concepts and a "stretch beyond" grade-level expectations.

Leveled pre-asssessments allow you to get a better understanding of the depths of students' knowledge--have they mastered pre-requisite skills, and are they therefore ready to tackle grade-level concepts? Are students struggling with the "building blocks" from previous grade-levels and will therefore need remediation before they are ready to meet your grade-level standards? Do students already know how to solve problems based on your grade-level standards and therefore will be ready to "stretch beyond" your grade-level standards-focused lessons?
 Place Value Rounding Leveled Math Assessments

With data from pre-assessments that contain a continuum of learning objectives, you will be ready to differentiate your lessons, stations, and student assignments right away!

the (not so) DOWNSIDES:
 Differentiated Leveled Pre Assessments for Fractions

> > > You may be (mini) assessing students more often, because you are looking at individual standards. However, you do not have to pre-assess students on every single standard in your unit in order for them to make progress. I suggest pre-assessing students on the skills and standards that are the MOST important and/or those where students are typically on a wide range of mastery (like adding and subtracting fractions, rounding, or subtraction with borrowing).

Take time to pre-assess for a skill a day or two before you plan to teach that lesson and you will find yourself planning differentiated stations or activities to easily meet the range of student needs. (Yay!)

You will be planning your teaching based on student ability and understanding because you have the information you need to know staring right back at you. (That's an UPSIDE!)

> > > Another downside is that in order to take a step back from your grade level's standards, you'll need to figure out the pre-requisite skills from the previous grade levels (or the lower-level building blocks) that make sense to link to your grade-level's math objectives. It can be time consuming to find the connections between grade-levels and if you are trying to incorporate leveled assessments throughout your math units. (No worries! I've done the work for you!)


> > > Another downside is that in order to challenge students who are advanced and have mastered most of your grade level's standards, you will need to come up with ideas for what it takes to "stretch" those students beyond your grade level's standards. What kinds of problems could they solve if they were working a step above those grade level standards? Sometimes you can easily find a direct correlation to your grade level standards in the next grade level's standards, but sometimes you have to get creative on how to up the ante on the learning objective for your gifted students. (Again, I've done that work for you too!)



> > > Because you have the information (darn it, ha ha!), you'll need to gather the resources and figure out how to extend the standards for students who already demonstrate mastery and remediate students who don't have pre-requisite knowledge. (Hopefully, your EC and Gifted teachers can jump in to help here, but I've also given ample resources within my leveled assessments that you can use to differentiate for a wide range of students.)

MY OPINION: This is my favorite way to assess students. I love giving students the opportunity to show mastery of pre-requisite skills before expecting them to try grade-level problems. I also like that students who are advanced and can already complete math problems on grade-level have the opportunity to be challenged by higher-level questions and see that they too have new things to learn in our upcoming unit.

I challenge you to use leveled pre-assessments in math as an opportunity to become an "assessment junkie" + "growth-mindset enthusiast" this school year.

Do you need leveled pre-assessments for your 4th or 5th graders that are based on a continuum of standards and skills?

I've created assessments containing three levels of mastery called building blocks, goals, and stretching beyond.

The assessment sets contain 3 versions for each standard so that you can pre-assess, assign practice or small group work, quiz, and post-assess with ease. You'll be able to easily see growth by comparing students' pre- and post- data as the assessments contain identical formats and number of problems.

Best of all, your STUDENTS will be able to examine their growth and realize that they are LEARNING and MASTERING math concepts. You'll be able to encourage growth mindsets within all of your math units!
 Differentiated Math Assessments

You can find the 4th Grade Assessments here in my tpt store or by clicking the photo above.

You can find the 5th Grade Assessments here in my tpt store.

Is there a better way to pre-assess students in math class than what we have traditionally done? Check out 4 ways we pre-assess in math and what I believe is the best way to pre-assess my 4th grade and 5th grade students in math. After reading the pros and cons for these 4 kinds of preassessments, you'll be ready to implement your pre-assessments with more strategy and less data-overwhelm! You won't want to miss MY FAVORITE way of pre-assessing 4th grade and 5th grade students in math!!

Why Teachers Should Use Pre-Assessments in Math

Do assessments play an important role in your math classroom? Are you an "assessment junkie"? Do you thrive on pretesting and post-testing your students to chart their growth in learning over time?

Or, do you find that assessment (yes, even in math!) is an after-thought? Is your post-unit test simply "the way we know that a unit is over"? Are math tests something you remember to incorporate when the quarter is almost over and you have to give students' grades? (I've been there!)

Or, maybe you (like myself and other educators) are concerned that students are already OVER TESTED and therefore you don't want to incorporate more testing into their lives?

And, maybe (also like my young teacher self) you don't always think you need to assess students in math because you WORK WITH THEM EVERY SINGLE DAY and you can literally spell out what they are able to do and what they are struggling with in your sleep? Does assessing in math often feel like you are wasting a class period where you could be moving on to something else? (I've been there, too, how about you?!?)
Why should you make time for pre-assessing students in math? What are the benefits of formative assessments for students? I believe pre-assessments allow us to encourage students to have a growth mindset. Find out 7 reasons why I believe pre-assessments in math are crucial if teachers want to be differentiation fanatics! 4th and 5th grade teachers, this post is for you!
Whether you teach through a math workshop, guided math, whole group lessons, or small groups and math stations, I believe that pre-assessments are an important component of your instructional plan for math and that they are key to helping your students develop a strong growth-mindset and positive "math-i-tude."

So, let's spend today considering what pre-assessments are, their many purposes, and why you should consider including more pre-assessment opportunities into your math class.

Why should you make time for pre-assessing students in math? What are the benefits of formative assessments for students? I believe pre-assessments allow us to encourage students to have a growth mindset. Find out 7 reasons why I believe pre-assessments in math are crucial if teachers want to be differentiation fanatics! 4th and 5th grade teachers, this post is for you! First, let's review our college pre-service days.

Recall that formative assessments are formal and informal assessment opportunities that are used to modify (form and inform) the learning sequence.

> > > Formative assessments allow you to gauge students' knowledge and adjust course during the unit so that students can be more successful.

> > > Formative assessments provide ongoing feedback to you as the teacher (How's your teaching going? How are your students attaining the information?) and to the students ("What more do I need to learn? How well am I understanding what I am being taught?")

Summative assessments happen at the end of a learning sequence. Most state tests are summative, but teachers typically incorporate summative assessments at the end of a unit. The information may or may not be used to proceed with new lessons.

What is a pre-assessment?

A pre-assessment is an opportunity to collect information about student knowledge prior to starting a new unit or subtopic in your curriculum.

Since the word "assessment" (test or quiz) leaves a sour taste in most of our mouths, you can call your pre-assessments a "show what you know" or find some other fancy way to name them that communicates the {positive} purpose of pre-assessment tasks to students. 

When should you pre-assess?

> > > As a recommendation, I believe that the best pre-assessments in math occur on day 2 or 3 of a new unit. I like to engage students in an inquiry-based activity that helps them tap into prior knowledge before I give them a pre-assessment "cold-turkey."

This also gives YOU a better measure of their TRUE understanding as you tap into their memory of what they have learned in the past.

What is the purpose of a pre-assessment?

The ultimate reason that I am {now} a fan of pre-assessments in math is because I'm a differentiation junkie. I absolutely, positively cannot imagine running my math class without naturally differentiating for my students. I see math concepts on a continuum of skills (like a staircase) and based on my students' classwork, I know where they fall on that continuum.

Formal and informal math assessments are my silver-bullet to knowing where to go with my differentiated instruction plan.

Not only can a pre-assessment help teachers know what students already know and which areas of an upcoming unit they will need more support in, pre-assessments can serve other important purposes, too:
    Why should you make time for pre-assessing students in math? What are the benefits of formative assessments for students? I believe pre-assessments allow us to encourage students to have a growth mindset. Find out 7 reasons why I believe pre-assessments in math are crucial if teachers want to be differentiation fanatics! 4th and 5th grade teachers, this post is for you!
  1. Pre-assessments can encourage students to have a growth mindset. Students can see what they already know and although they may not know how to do many things on a pre-assessment, as you get into your unit, students will have many "light bulb" moments and feel themselves growing in knowledge and confidence. HAVING A MEASURE OF STUDENTS' UNDERSTANDING OF A TOPIC PRIOR TO IT BEING TAUGHT PROVIDES THEM WITH EVIDENCE OF THEIR GROWTH.
  2. Pre-assessments PRIME students for learning. Back to those light bulb moments...Students will remember the kinds of problems they tried to solve on the pre-assessment. As they experience classroom lessons and activities, they will realize that something they once did not understand is now something that they know how to do #growthmindset. You can even use some of the exact problems from your pre-assessments as "bell-ringers" at the start of your lessons. Ask students to explain how they solved the problem or how they know they are correct to increase the critical thinking for students who already knew how to solve the problem. Tell the class that by the end of the lesson (or week for some of those skills that take longer to master), everyone will understand how to solve those kinds of problems.
  3. Pre-assessment data can be used to show that you are meeting students' needs. Do you ever need more evidence that your students are meeting their learning targets? Or that your struggling students (while they may not be mastering all of your math concepts) have grown in their understanding of math concepts? If you have pre and post data, you will be ready to show that your students are making growth.
  4. To add on to #3, pre and post assessment data for individual students is impressive! I keep copies of the math assessments my students complete during the first quarter so that I can pull them out during our first parent conferences. Do you have some parents who stress out about their children learning math? or others who stress you out because they are concerned that their child never gets challenging math work? BOOM! When you use differentiated math assessments that contain levels or tiers of questions and can share pretest and post test data with parents, they can see where their student started out at the beginning of a unit and the level of mastery their child was able to achieve at the end of the unit. (Really, who can disagree with concrete data and proof of growth?)
  5. Pre-Assessment information can help you differentiate your plans by showing you which students can handle a compacted curriculum and which students have gaps and will need remediation. How many of your students are dying inside as you (once again) go over the number of inches in a foot? Don't they deserve to be working on a math concept that challenges them and allows them to take their learning deeper? 
  6. Pre-assessments can help you pace your unit and lessons. Were you planning to spend a week on rounding because students in the past have always struggled with the concept? A few years ago, my 4th graders surprised me when I did my rounding pre-assessment. They already had a deep mastery of rounding; based on my tiered math assessment, most students could already go above the grade-level standards. I was also able to see where the processes broke down for some students as the numbers increased in size.
  7. Pre-assessments help bring students' misconceptions to the surface. In my math class, misconceptions (and the kinds of mistakes students make) are golden! I love to use excerpts of their explanations for problems in bell ringers and have them "talk back" to the explanation, revise it, and explain more. I've even designed entire lessons and activities around addressing the misconceptions students show in their pre-assessments. If you see something you don't want to forget, I suggest snapping a picture of it with your phone. You can easily use their words to create a bell ringer--just change the student name to a fake name and ask students to respond to their thinking.  
Why should you make time for pre-assessing students in math? What are the benefits of formative assessments for students? I believe pre-assessments allow us to encourage students to have a growth mindset. Find out 7 reasons why I believe pre-assessments in math are crucial if teachers want to be differentiation fanatics! 4th and 5th grade teachers, this post is for you!
In her article titled Deciding to Teach them All, Carol Ann Tomlinson says that teachers should become "assessment junkies." She believes that assessment should be "an ongoing process, conducted in flexible but distinct stages, and it should maximize opportunities for each student to open the widest possible window on his or her learning."

Wow! That's a tall order, but I sure am in love with the idea of becoming an "assessment junkie." If we as teachers also aspire to become "growth mindset enthusiasts," then we will be assessment junkies for all the right reasons!

As you consider adding more pre-assessment opportunities to your math routines, I'd ask you to know which of the purposes above you most want to target--then, I'd also like for you to be ready to explain pre-assessments to your students in a positive way. I tell my students, "This helps me know how to plan our math activities and stations. I don't want to keep teaching something that you already know how to do, and I also don't want to assume you already know something that you don't yet know well."

This explanation works perfectly at the beginning of the year when you are truly getting to know your students--then, it just becomes second nature for them to give a pre-assessment a good try as the year goes on because they see how you use them to plan for their learning AND they come to know that their own growth in understanding is on it's way!

Do you need pre-assessments for your 4th or 5th graders?

I've created assessments that assess students on three levels of mastery--building blocks, goals, and stretching beyond.

The assessment sets contain 3 versions for each standard so that you can pre-assess, assign practice or small group work, quiz, and post-assess with ease. You'll be able to easily compare pre- and post- data on your students' understanding as the assessments contain identical formats and number of problems.

Best of all, your STUDENTS will be able to examine their growth and realize that they are LEARNING and MASTERING math concepts. You'll be able to encourage growth mindsets with all of your math units!
 Differentiated Math Assessments

You can find the 4th Grade Assessments here in my tpt store or by clicking the photo above.

You can find the 5th Grade Assessments here in my tpt store.


"Must Have" Math Manipulatives for Upper Elementary

Today I'm sharing my love of math manipulatives with you. Having a variety of math manipulatives "at the ready" in my classroom is critical for inspiring ideas for hands-on math games and activities. Different manipulatives give me the opportunity to design games and lessons at different levels for scaffolding and differentiation that helps students build on their understanding of a concept.
What math manipulatives could you be incorporating more of into your 4th grade or 5th grade classroom? I've got 6 math tools and manipulative ideas that I love to use when teaching math with my upper elementary students. Manipulatives are awesome for math activities, math lessons, and hands on math games and for increasing engagement in your math lessons!
For many of these manipulatives, it was when I had a class set that I considered them a "game-changer" for my math instruction. (Doesn't it STINK when having access to materials holds you back from doing awesome things in your classroom?!?) With class sets, I found that I could implement ideas with manipulatives without worrying about having enough materials. I could introduce games and activities during whole group instruction and later move them into stations or use them when students finished assignments later in the week.

A few years ago, I was lucky enough to land in a classroom that had access to tons of math manipulatives. Seriously, I spent the entire summer cleaning out that classroom and organizing #allthethings. For some of the math manipulatives I had available, I was truly unaware of their benefits in a 4th or 5th grade classroom.

However, having access to these materials (many in quantities great enough for each student to have their own materials) truly opened my mind to many of the ways I could incorporate them into my math lessons.

I keep many of these manipulatives available to grab at a second's notice when I'm working with students on different concepts.  The more you use these manipulatives in your classroom, the more you will find yourself being prepared for "on the fly" differentiation that helps students "see" concepts versus just showing them again and again with pencil and paper.

Note: Some of the links in this post are affiliate links. This means that I am a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com. Read my full disclosure here.

If you do not have access to some of the manipulatives I share in this post, I would really encourage you to get class sets of what you can afford (beg your principal?!) and at least purchase one set for yourself to play with to design games and activities. Ask around the school and perhaps you can borrow what you need for a while.

Let's get to the fun stuff:

1) Base 10 Blocks

I love having enough base-10 blocks at my disposal for students to use. I use base-10 blocks during whole number operations units (place value, comparing numbers, adding and subtracting, etc) but I also bring them out again during fractions and decimal units. Instead of the 100's block being 100, it is now our "whole." Using "10 sticks" and ones cubes, students develop better understanding of tenths and hundredths. I've also seen lessons using these for multiplication, area, and the area model.

Do 4th graders really need to "play" with base-10 blocks? Yes, I think they do! One way we "played" with base 10 blocks at the beginning of the year was with our "Place Value Houses" activity.

2) Dice (in many varieties!)

#fortheloveofdice!!!!!! Dice come in so many shapes and sizes, I truly did not know all of the variety until I came across different ones in my new classroom.


The standard 6-sided dice are great for games, but 10 sided dice are a game changer for easy differentiation.

I've now got dice that range 1-20fractions dice, and dice with the four operations, equals, and a comparison sign.

I also found place value dice on amazon that have one dice each for "ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, tenths, hundredths, and thousandths. Each die is ten-sided so students can generate every possible number between 0 and 9,999,999.999."
 Place Value Dice from hundredths to millions

(WOW oh WOW!). Seriously. A class set of these are a a game-changer for my place value, expanded form, standard form, comparing numbers, and value of the digits lessons. To differentiate, I can just have students who need to start small remove the dice for larger numbers and decimals. I just added those to my cart and can't wait to play around with them!

Have any favorite dice of your own? Let me know in the comments! 


3) "Play" Money (especially dimes and pennies)


So, true story. When I switched schools, the classroom I took over was full of play money. Dimes, pennies, nickels, all over the place. I could not for the LIFE OF ME figure out why a 4th grade classroom had "play" money. Money is a lower-grades standard, right?

Well, when we got to our fractions and decimals units, I had students using bags of money A LOT. This is one of the {very important} manipulatives that I would keep close by during my decimal lessons. When students made mistakes like "1/100 > 1/10," I would bring them a bag of money and ask them, "Which coin is 1/100 of a dollar? Which coin is 1/10 of a dollar? Which coin has a greater value?"

When students compared decimals (.08 compared to .3) and chose the wrong number, I'd have them represent each decimal with money, discuss the value of the monetary representation, and then explain how they knew which decimal number was larger. By bringing out the money, I was able to continuously address misconceptions and help students develop their concept of decimals. This, combined with our classroom lessons continuously reinforced their understanding of decimals.

4) Fraction Sets

Okay, I already told you I was lucky at my school, but in this case, I felt SUPER spoiled. I was able to request a CLASS SET of plastic fraction circles. The realllly good fraction set is the one that has a plastic container to put the pieces in. These were in short supply when I purchased mine, so I had to supplement with the fraction sets that just come in a plastic bag.


(I've read some research about having students create their own representations of fractions with paper, and I'm not going to debate the value of that, but I will say, no one can really contest the benefits of having ready-made fraction manipulatives that students are able to get their hands on again and again to bring fraction concepts to life during math lessons. Manipulatives in the hands of a good teacher are never bad, in my opinion. And, ready made manipulatives are better than using NO manipulatives at all, seriously.)

With my 4th graders, nearly every lesson at the beginning of our fractions unit started with me prompting them to do something with their fractions sets. (I recommend giving each student a ziploc bag, having them write their name on it, and giving them the same set of manipulatives each time you use them. This way, their mess is their mess and if they lose pieces (cringe), they have to be the one to deal with not having what they need).

Some examples of prompts to have them do (based on your lesson objective):
-create all of the equivalent fractions you can
-make 1 whole all the ways you are able to
-find all the ways you can to make 1/2 (3/4, 2/3, etc).
-make 7/8 as many ways as you can (to work on decomposing fractions)
-using fraction models and words, explain why 2/3 + 2/3 ≠ 4/6

Note: I prompt with these directions on the smart board and students record their answers in their math journals.

5) Decks of Cards

Decks of cards can be used for so many activities! The range of digits from 1-10 (making an Ace a 1) make them perfect for place value lessons, comparing whole numbers, multiplication or division war, and more! You can remove the face cards or make them "wild cards" where students can choose the number they'd like to use. Whip up a quick playing mat OR let students draw on their desks with Expo markers for even more excitement.

Playing cards would be a PERFECT thing to add to your back to school supply list to easily get your class sets, or grab them at the dollar store (if you are Type A and would want all of them to be of the same quality!) I'm game for shopping around and finding 25 different and CUTE decks of cards so that we can keep them all separate.

One of my most favorite ways to incorporate playing cards into my fractions unit was when we played a comparing fractions card game. As we were playing, I figured out different ways to scaffold and help my students increasingly develop their ability to compare more challenging fractions. (You can check out all the rounds I used for the game in this blog post.)


6) Dominoes

I haven't incorporated dominoes a lot into my math activities, but THEY LOOK LIKE FRACTIONS, so what am I waiting for? Perhaps it's because I've never had a class set of dominoes, but I want to grab some so that I can play around and come up with new ideas.

This domino set looks awesome. It contains 15 sets in 6 different colors. This is another item you can grab at the dollar store too! And don't even get me started on the domino sets designed specifically for math activities--fraction dominoes, polygon dominoes (I have something similar to this)! Students can even make their own Domino activities! The possibilities are endless!

Have you read this post and still feel unsure of how to really use math manipulatives in your math classroom? 

What math manipulatives could you be incorporating more of into your 4th grade or 5th grade classroom? I've got 6 math tools and manipulative ideas that I love to use when teaching math with my upper elementary students. Manipulatives are awesome for math activities, math lessons, and hands on math games and for increasing engagement in your math lessons!I didn't give you a ton of ideas in this blog post...I am just getting started and plan to share more ideas for using these manipulatives for different concepts...but,

My advice: Don't wait until you "know" how you will use these manipulatives to get your hands on them. Start collecting and buying to build yourself class sets of these tools for math (if you are not lucky enough to have them given to you or purchased by your school). Many of the ways I figured out to use these manipulatives in my lessons only happened because I had ACCESS to them.

Pinterest is also a great tool to use when trying to come up with ideas! Search for ideas on the topics you are covering and I just know you will find some way to engage your students in a more hands-on math block!

I know there are other math manipulatives that some teachers would consider crucial, but these are my favorite 6. What other manipulatives should I add to my upper elementary toolbox?


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