Recently, I surveyed more than 20,000 teachers about their biggest challenge in math instruction. One of the most overwhelming responses was that their students don’t know their math facts. I have to agree that a lack of math fact understanding and memorization is an area of concern for me as well. This issue is a not a new trend. Math facts, especially multiplication facts, have been a hot topic since I was in elementary school. I still remember taking “mad minute” tests as a child where we had to solve a certain number of problems in one minute.
We now know that teaching strategies through games and hands-on activities are more beneficial that repetitive drill. But it’s essential that the games and activities you use are intentional and follow a specific framework. To help me stay focused and intentional, I’ve created a series of systematic lessons and activities students can use to memorize and understand multiplication fact practice. You can find those lessons here.
The first step for students is to SEE the different representations of the math facts. For example in multiplication, students sort arrays, repeated addition, and equations. This allows students to begin understanding what the multiplication number sentence means.
After students sort multiplication representations, they should then progress to leveled flashcards. At this point, students aren’t ready for traditional abstract flashcard practice. Instead, students should begin with the set of Build-It flashcards. In this set, students will actually build each multiplication problem. They could use counters or snap cubes for this activity. After students have concrete experience, they can then use pictorial models of each multiplication problem as a flashcard. This pictorial model helps bridge concrete and abstract. Then, in the third set of flashcards, students can try to answer the multiplication problem using an abstract strategy.
Multiplication Strategies Booklet
Students should also have the opportunity to WRITE about the strategies they use to solve each set of multiplication problems. This allows students to internalize their learning. For each set of facts, students describe a strategy they could use to solve a multiplication problem. If I have a student who has already worked their way to automaticity in that set of problems, I ask students to explain to a friend how to use a strategy. Students also represent problems using arrays, repeated addition, grouping models, and a number line.
It’s so important to teach in context, so for each set of facts that students work though, be sure to have them solve AND write multiplication word problems, which is another reason it’s so important to have students write about the strategies they use. For example, if students are working on their four facts they will solve two problems where four is a factor and write two problems where four is a factor.
While I do believe that timed tests can be misused, they can also play a positive role in the classroom. Rather than giving students a certain amount of problems to solve in a set amount of time, I have students solve the entire set of multiplication problems and time how long it took to complete all of the problems. This alleviates the extra stress that comes with a timed test. I also have students graph how long it took to complete the test to encourage metacognition. I staple multiple versions of the set of facts to the timed test graphing sheet to give students four different opportunities to take the test.
To help keep my students organized with each of these activities, I give them color coded bookmarks. The bookmarks show what is expected from students each week. The activities are listed in the order in which they should be completed. As students complete an activity, they check it off on the day it was completed. You can see these activities here!
I did add a few extras at the bottom of each bookmark, because these are things we do weekly, if not daily. I send home a Weekly Multiplication Game with students every Monday. These games only require dice or a set of playing cards, which I provide if students don’t have at home. This isn’t an assignment to be graded. Instead, it’s an opportunity for fun practice.
I also give students who need additional support a Multiplication Fact Booklet that will take them through each multiplication problem for that set of multiplication facts. This gives students the extra support they may need and it solidifies understanding.
Xtra Math is another great practice tool. However, it’s important to keep in mind that it is a tool. Nothing replaces the conceptual activities where students actually work with multiplication facts.
You can read additional posts on multiplication facts here and here. I’d love to hear about what you’ve tried that has been successful!
Setting is one of those reading topics that I love to teach. It’s relatively easy for students to understand, and there is so much great literature that can be tied into upper elementary setting instruction. My greatest challenge in teaching setting is having students use text evidence to support their ideas about the setting of a text. As always, when I require students to support and prove their reasoning, things become much more challenging. This post shares some of my favorite strategies for teaching setting through mentor texts AND ways to encourage students to write thorough responses using text evidence.
Lessons to Teach Setting
The five lessons below are from my 2nd Reading Unit. As always, these texts can be replaced with different texts of your choice, but I highly recommend each of these books. I introduce setting by reading Train to Somewhere by Eve Bunting. This is a historical fiction text based on real events. The setting of the text plays a significant role in the text, and it’s such a heart touching story. In fact, I may get a bit choked up when I read it to my class. This is one of those books that I never skip. Before we read the text, I have students use the cover of the book to make predictions about the setting, which is also great for inferences. Students predict where and when the book takes places, as well as the environment around the events.
Changes in Setting
We then begin to discuss how the setting can change within a story, and how understanding that change is important for our comprehension of the text. To teach this, I like reading An Angel for Solomon Singer. To be perfectly honest, this is a book I did not absolutely want to read, because of the cover. Shame on me. Once I finally forced myself to read it, I was hooked. This is another great text that promotes thought provoking questions and comments. As I read the book, we discuss the changes in the setting and how those changes effect the story. We discuss how this is also true in chapter books, and we discuss chapter books that have substantial changes in setting, such as Holes.
Integrate Informational Texts
I like to incorporate nonfiction texts into my setting instruction. My students love going on a nonfiction setting scavenger hunt, where they find examples of nonfiction texts that take place in a large variety of different settings. I like having students complete this in our school library, because of the large variety of nonfiction books that are available. Plus, the novelty of a reading lesson in a different location is always fun for students. If you have a media specialist, you could even integrate this with library skills.
Compare and Contrast
Once students have ample experience with identifying the setting and understanding changes in setting, we begin to compare books with similar settings. To do this, I read parts of Orphan Train Rider: One Boy’s True Story by Andrea Warren. Students compare this text with the fiction text Train to Somewhere. Students work together to create a Venn-diagram that compares and contrasts the setting with the two texts. An added bonus, is that this gives students experience with first hand information, which will come up later in the informational text standards. Students are always captivated by this part of history, because they simply cannot image something like that even existing.
Responding to Literature
Once I feel that my students are ready to progress to applying what they’ve learned through written response, I have students write a reading response essay on the importance of the setting in Follow the Drinking Gourd.This is another book where the setting plays a significant role on the text, and there is a change of setting in the book. As students write, they are required to using quotes and evidence from the text to support their thinking.
The teaching setting with mentor text lessons above can be found in my Reading Unit 2. However, if I ever need an additional lesson to teach setting, I always use Stephanie’s (Teaching in Room 6) cutting up setting lesson. In this lesson, you read students a chapter from a book that has a very descriptive setting. I always use Tuck Everlasting’s first chapter. I type the chapter and print a copy for each student. After reading the chapter, students create a drawing of the setting, but they can only add things that appeared in the chapter. Students cut out the text evidence for each part of their drawing to prove their thinking/drawing. Seriously, this is an amazing lesson!
With the combination of these lessons, I’m typically ready to wrap up setting with a formal assessment and move to our other story elements. A blog post for those is coming soon! If you’d like to learn more about reading workshop, be sure to check out this post!
After students have ample experience working with fractions, developing fraction number sense, and comparing fractions, they will come to the realization that some fractions with different names are the same size. As we work with fractions, I introduce the term equivalent fractions, even though I am not currently teaching equivalent fractions for mastery. It’s important to use UNLABELED fraction pieces for this, actually most, of these fraction lessons. Here are links to the ones I used: circles, squares, and rectangles. You can also find the lessons and printables from this post here.
I don’t initially teach students to multiply the number and denominator by the same number at the very beginning of my equivalent fraction lessons, because that strategy is often meaningless to my students at that point of instruction. To help my students create an understanding of equivalent fractions, I have them use models to find different names for fractions. One way to teach this is to give students outlines of different fractions and have students use their fraction pieces to find as many single fraction names for the region as possible. You can download that lesson below!
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After working with models, I extend this lesson the following day moving from concrete models to picture models by using grid paper and drawing the outline of a region and designated it as one whole. I lightly shade part of the region within the whole and students use different parts of the whole to determine multiple names for the part.
As I transition into more challenging equivalent fraction lessons, I like to have students continue to explore equivalent fractions through literature that moves students into problem solving situations. I prefer using real literature for this, but everything I found was a bit too young for my students and focused only on the size of fractional parts, rather than fraction equivalencies. I finally took a chance and wrote my own “book”. This was unlike anything I had ever created before, but I have to say that I’m pretty proud of the end result. The book takes students through various situations that require the reader to think about fraction size and equivalent fractions. You can download that book for free here.
At this point in the unit, I have not yet introduced students to a rule for finding equivalent fractions. I use the following lesson to begin transitioning students into discovering that rule. I give students an equation showing equivalent fractions, but one of the numbers is missing. I allow students to use any model or method they want to solve these problems. After the activity is complete, we meet together to look for a patterns and anything else that stands out to students. It’s always so tempted for me to tell students how to solve the problem, but I know that giving students time to explore will benefit them in the long-run.
My goal is for my students to see that if they multiply the top and bottom numbers by the same number, they will generate an equivalent fraction. One way to teach this is through an area model approach. I give students a worksheet with four squares in a row. I have students shade in the same fraction in each square using vertical dividing lines. Then, students slice each square into an equal number of horizontal slices. For each square, students write an equation showing the equivalent fraction. I follow this lesson with a class discussion on the rule for generating equivalent fractions. The discussion is important, because many students will only count the squares without thinking about the connection to multiplication.
Once students have been explicitly taught how to multiply the numerator and denominator by the same number, I continue to have students complete problems solving tasks where they apply their understanding of equivalent fractions. I particularly like this pattern block lesson, where the size of a whole is TWO hexagons. It requires students to change the way they look at the whole, because most students identify one hexagon as a whole.
After teaching equivalent fractions for mastery, I review as needed through some of the games and worksheets in my No Prep Fractions.
Students are expected to compare fractions in third, fourth, and fifth grades. If we spend time developing fraction number sense, the ability to compare fractions is MUCH easier for students. When students solely rely on tricks, I find that there is a lot of opportunities for errors and confusion. One source of confusion is that in students’ experience with numbers, the larger number means more. Students then transfer this concept to fractions, where it is no longer accurate.
I love that the third grade standards focus on comparing fractions with the same numerator and denominator. When students order unit fractions, they will begin to understand that the larger the part, the smaller the number will be. Students typically have no trouble when they compare fractions with the same-size parts. However, when fractions have the same number of parts but different sizes, it is much more challenging. This is when students apply the understanding that the larger the denominator, the smaller the piece. Pictured below are some lessons from my Third Grade Fraction Unit. As with my other math units, I move from concrete, to pictorial, to abstract.
Third Grade Lessons
In fourth grade, students began comparing fractions with unlike numerators or denominators. I begin by having students use one-half as a benchmark number. I ask students to think about whether each number is more or less than a half. I also teach students to think about how far the number is away from one whole. This is great for comparisons with fractions such as 2/3 and 7/8, because students realize that 7/8 is much closer to a whole than 2/3. The lessons below are from my Fourth Grade Fraction Unit.
Fourth Grade Lessons
I begin with a brief review of common numerators and common denominators. I’m careful to never assume my students understand this concept.
In this lesson, I want students to compare fractions by thinking about benchmark numbers.
Students must also understand that a fraction does not say anything about the size of the whole or the size of the parts. The fraction tells us about the relationship between the part and the whole. This means that comparisons can only be made if both fractions are parts of the same whole. I love illustrating this with comparing a fun size candy bar with a HUGE candy bar. A half of one is not the same as a half of the other.
Fourth Grade Lesson
When having students compare fractions, I like to have students draw a representation of the fractions they are comparing. I do this in addition to comparing fractions with models or providing students with an outline of the whole. When I eliminate that support, it forces students to think about the size of the whole. If I always provide the representation, I may not see a student’s misconception on this topic.
My favorite comparing fractions activity was, without a doubt, my Fraction Skittles lesson. Each student received a bag of Skittles and found the fractional part of each color of Skittles. Students then find a partner who has a different denominator and compares the fractional part of each color of fraction. Students repeat the process with a different partner. Finally, students determine which partner has the greatest fractional part of each color.
Fourth Grade Lesson
I will not say that I never teach rules or tricks for comparing fractions, but I try to avoid those rules for as long as I can. I want my students to have the opportunity to think about the relative size of fractions, and these comparison activities help students develop an understanding of fraction size. The task cards shown below are from my Third Grade Fraction Unit.
After I teach the concepts, I give my students plenty of opportunity to practice and review through games and task cards.
Third Grade Task Cards
After I teach my comparing fractions lessons, I offer additional practice and support as needed. I have several different practice pages and games in my No Prep Fractions pack. This is great for review, center games, or extra practice.
I’ve also made a freebie that I think you’ll love. I made a comparing fractions flipbook that offers students support and practice in using these various strategies to compare fractions. You can use the form below to receive your free copy!
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To read more about teaching general fraction concepts, be sure to check this post out! It’s full of great ideas for introducing the concept of fractions to upper elementary students.
Fractions are a critical concept for upper elementary students, and fractions are a topic that often present some difficulty for students. Fortunately, there are MANY ways to make fractions meaningful and fun for students. In this post, I’ll share some of my favorite strategies and resources for teaching fractions to upper elementary students.
When teaching fractions, I always begin by teaching students the concept of fractional parts of the whole. I first model how to identify and make equal parts from a whole and show examples and non-examples of partitioning shapes into equal parts. I place several pieces of chart paper around the room and labeled each piece of paper with halves, thirds, fourths, and fifths. Then, I give my students a large piece of construction paper, and they use the construction paper to cut out different shapes and to partition them into equal pieces to create halves, thirds, etc. Students had to use a variety of shapes, so I didn’t let them cut all squares or even all squares and rectangles. After students partitioned their shapes, they taped the shape to the corresponding piece of chart paper. This allows me to address any misconceptions about equal sized parts.
I then begin teaching the idea of fair shares through sharing tasks written as a word problem. Students initially perform sharing tasks by distributing items one at a time, and when there are leftover pieces, those items must be subdivided. I love watching how different students approach this differently. Some students first share the whole items and distribute the leftovers, and other students slice every piece into equal parts and then distribute the pieces. When I first started teaching third grade, I thought the brownie task would be too difficult for my students, but I was wrong. It’s true that students may not know how to correctly write a fraction, but I can help with that in the task. My real goal was to get my students thinking about equal parts and equal pieces. In the pizza task below, I intentionally include problems where there would be whole pizzas shared, as well as only fractional parts shared, because I don’t want to isolate mixed numbers into a unit of their own. You can find a collection of my third grade lessons here and fourth grade lessons here.
Third Grade Task
Fourth Grade Task
After I feel that my students have an understanding of fair shares, I begin to use models for fractions, with area models, length models, and set models. I like to first introduce area models, and I try to incorporate a wide variety of models. I commonly use circles, grid paper, and pattern blocks. I avoid using prelabeled fraction bars or fraction circles, because I want my students to know that the size of a whole can change and that everything relates back to the whole. When I use a length model, I often use a fraction bar or number line. I do not spend a lot of time working with set models, but when I do I typically use two-color counters. The following fraction model lessons are from my third grade unit’s area model, length model, and set model lessons. I don’t spend quite as much time on this when I’m teaching fourth grade.
Confession: I actually teach these lessons in my classroom, and there is no way I have time to take nice pictures as I teach, so I take my pictures at home. I didn’t have any Skittles for this lesson, so I improvised with M&Ms. I took one for the team and ate the brown ones.
After showing various fraction models, I move to fraction symbols and teach the vocabulary of fractional parts. I explain that the numerator is the counting number that tells how many shares or parts we have. Then I teach that the denominator is what is being counted and/or how many parts it takes to have a whole. To help students generalize this concept, I give students the opportunity to see how different wholes can e designated in the same model. This prevents a given fractional part from being identified with a special shape or color.
Third Grade Lesson
It is essential that students understand that the number of equal parts that make up a whole determines the name of the fractional part. This allows students to realize that when they know the type of part they are counting, they know when they get to one whole. Students should learn to think of counting fractional parts the same way they would any other time one-sixths, two-sixths, three-sixths, etc. As students learn to conceptualize fractions, they do not need to arrange pieces into one whole to determine if their fractional part is more or less than a whole. I make a point of NOT telling students that if the numerator was larger than the denominator the fraction was larger than a whole, because I wanted students to discover that on their own to make it meaningful, rather than a rule.
Fourth Grade Lesson
Once students have counted fractional parts beyond a whole, they already know how to write an improper fraction. I do teach students how to write a mixed number, but I don’t teach students the rule for converting mixed numbers to fractions. To allow students to discover this on their own, I give students a task where they are given a mixed number or an improper fraction and students write the fraction in a different form and explain their answer with pictures and words.
Fourth Grade Lesson
As I move through our fraction unit, I try to instill number sense where students have an general idea of how big a particular fraction is. I teach students than an importance benchmark fraction is one-half. This number sense will later help students as they begin to compare and compute with fractions.
Fourth Grade Lesson
These concepts and lessons are what allow students to work efficiently with fractions and more advanced math concepts. Even though some of these concepts are not stated in my standards or assumed that students have mastered the concepts from previous years, I always begin my faction until by helping students build a strong understanding of the concept of fractions. After I have taught my introductory lessons, I follow the concepts with extended opportunities for practice.
The pages below are examples of extra practice that I give students on an as-needed basis. These are all from my No Prep Fractions pack.
I have a whole blog series on fractions ready to go! Up next is comparing fractions. I think you’re going to love it!
In third, fourth, and fifth grades, there are few math concepts more important for students than multiplication. This builds the foundation of multiple other math topics and concepts. However, many students need additional instruction and remediation during and/or after their multiplication unit. This blog post shares ideas that can be used for multiplication remediation or multiplication interventions that can be used with students who need extra support. These are not the same lessons that I teach in my multiplication unit. Instead, these are lessons I teach in addition to the lessons taught within my multiplication unit.
The intervention lessons begin very easy, but they build a conceptual understanding of multiplication that will later help students problem solve and solve word problems with larger numbers. I’ve included each of these as a part of my Math Intervention resource. During this time, I do not focus on the memorization of multiplication facts, because I don’t want to focus too much time on memorization and forfeit understanding. However, at other times I do focus on these facts, and you can read more about that here.
I like to begin by using a game to continue helping students understand the concept of multiplication. In this game, students spin once to determine the number of groups they have and spin again to determine how many are in each group. I have students build the group with manipulatives, draw the groups with a pictorial representation, or use a symbolic representation. With each turn, I make sure students understand the difference between the number of groups and how many are in each group.
It’s also important to show students models of multiplication problems and have students determine which multiplication fact the model shows. I do this through manipulatives and pictorial representations. This time spent working with equal groups will allow student to understand the meaning of multiplication.
When teaching about the meaning of multiplication, it is also necessary to spend a considerable amount of time teaching students how to correctly create and read arrays. I’ve found that many students try to create a top row and a left column, but they leave all the middle pieces, which shows yet another misconception. After students have an understanding of arrays, we work to build all of the arrays possible for numbers 1-24. This will be a great lesson to refer to when teaching about prime and composite numbers. A solid understanding of arrays will also be a tremendous help for students when they begin to use the distributive property to solve larger multiplication problems.
Another activity that allows students to see patterns within multiplication is to have students place counters on a number line to show the multiples of different numbers. Ask students to predict what other numbers would be marked if the skip-counting continued. Ex: “When skip-counting by twos, will the number 127 have a peg? You can also have students mark two sets of multiples on the same number line, for example, multiples of three and six. Some numbers will have two counters on them.
It’s also important to give students the opportunity to work with a multiplication table. Have students use the grid paper to build and cut out all the possible arrays for 12 and write the multiplication equation inside the array. Have students place the 4×3 array on the chart so that the upper-left corner of the rectangle lies on the upper-left corner of the chart. Students should hold the rectangle in place as they count the squares. Then have students lift the lower-right corner of the rectangle to show the product 12.
As students work with grid paper and multiplication tables, they will begin to see how multiplication problems can be broken into smaller problems. A great way to reinforce this is to give students a multiplication expression such as 6×8 as an array on grid paper and have students find all of the different ways to make a single slice through the rectangle. For each slice, have students write an equation. For example, students would write 4×6=4×3+4×3.
At this point, students are typically ready for more challenging multiplication concepts, so I then begin to teach students to multiply by tens and eventually multiples of ten. One way to teach multiplying by multiples of ten is through money, so I like to spend time having students multiply using pretend $10 bills. I also teach students to solve multiplication problems that have three factors. I model how to pair two factors and find their product and then multiply again to find the product. I like to model how to multiply using all three possibilities, which allows great multiplication conversations. This is another activity that’s easily turned into a game for students.
In another lesson, students reverse what they learned and turn 2-factor problems into 3-factor problems. To teach this, show students the problem 4×30 and model how to solve as 4x3x10. Ask students to explain why they think you chose to save 10 for last. Repeat with 4×300. Ask students why factor they could save for last. This is a skill that will be a tremendous help for students when they begin to solve more challenging math problems.
I then like to teach students how to use the distributive property to solve 2-digit multiplication problems with an array. Eventually, students will solve these problems using an area model, so I slowly scaffold away, by fading, the interior squares in the array. As the squares fade, students grow less dependent on the model.
To move students toward larger multiplication problems, present students with a 3-digit by one-digit problem such as 4×384. Ask students if it would make sense to literally draw an array with 4 rows of 384. Since we know that would take too long, ask students what their other options are. Guide students into understanding they can draw the outline of the array and break it into parts. Model how to break apart 384 into 300+80+4 and how to multiply each part by 4. Repeat this process until you feel that students are comfortable breaking apart the numbers.
I like to have students begin 2-digit by 2-digit multiplication by multiplying multiples of ten, and then I move students into using grid paper to create area models for solving these multiplication problems. Since this is often challenging for students, I like to incorporate base-ten blocks into my instruction. This helps eliminate misconceptions and common errors.
Toward the end of my multiplication remediation lessons, I teach students how to solve problems with partial product and/or the algorithm. I like to have students complete two problems together, complete two more through guided practice, and then complete two independently. This allows me to see where to progress from that day’s lesson.
Each of the lessons in this post are a small part of my Upper Elementary Math Intervention resource. It has been such a game-changer for me! I did want to add that each lesson includes a very brief exit slip that allows you to monitor and track student progress.
You can read more about the organization and implementation of math interventions here. Please let me know if you have any questions!
Multi-step or multi-part word problems has to be one of the, if the THE, most challenging topics of the year. These types of problems difficult for my students to master, and it’s not something quick or easy to teach. I’ve found the saving a multi-step word problem unit for the very end of the year or right before testing is the least efficient way to teach this tricky skill. Instead, students need multi-step word problem instruction embedded in the curriculum throughout the year. As with most challenging concepts, students need time and practice in order to be proficient with these problems. This post shares some of my favorite ways to teach and practice multi-step and multi-part word problems.
Before students can begin mastering multi-step word problems, they need to learn how to solve single-step word problems. When students are present with a word problem, they tend to rush to solve the problem, without thinking about the meaning of the content. In fact, I proved this to my students with this little exercise.
As you can see, there is no solution to the problem, but I have seen many excellent math students “solve” the problem. My hands-down favorite way to prevent this is through numberless word problems. In fact, I recently wrote an entire blog post dedicated to numberless word problems. You can find that post here. In a nutshell, with numberless word problems, all numbers are removed temporarily while students process what the situation is and determine what information is needed to solve the problem. Then, numbers are gradually revealed until a solution is reached. Numberless word problems are a great way to help students notice the relationships in problem situations before being presented with a number.
I don’t have any catchy acronyms, such as CUBES, for teaching the steps of solving multi-step problems. This isn’t because I don’t like that strategy, but my brain likes breaking things down into detailed steps.
I like detailed steps, because they help guide students through the process of solving multi-step and multi-part problems. It also helps me as I verbally model the steps to solving a multi-part problem. I have a tendency to skip or combine steps, so this helps me break things down into more manageable pieces for students. I’ve found that the more students apply these steps, the more they will internalize the steps and the anchor charts and posters become no longer necessary. You can download the handout with step-by-step directions here.
Multiple representations are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, concrete models, and manipulatives.
When I first learned about multiple representations, I was quite frustrated, because I knew it was completely unrealistic for students to solve every word problem they encounter with multiple representations. There simply isn’t enough time during the day. I quickly realized that it is not necessary for students to use this for each and every word problem they solve. However, I do like to have students use this strategy a couple times a week. We often complete one together for guided practice and then I incorporate another opportunity for practice in our centers.
I’ve found that students need the most modeling and scaffolding with the written response portion, as they typically want to write the shortest and most concise answer possible. To prevent this I require students to restate the question, which helps students focus on what the question is asking. I then encourage my students to label their numbers. Rather than writing I added 10+35, they would write I added ten forks with 35 spoons. I also highly encourage students to incorporate proper math vocabulary.
I love using this graphic organizer with any set of task cards. Since not all problems lend themselves to all types of representations, I only require students to use words and equations for two of their representations. I allow students to select the other two representations they think work best with that particular problem.
Once I feel like my students are proficient with general word problems and multiple representations, I begin to focus more on multi-part word problems. I love using foldables that my students can add to their math notebooks to provide students with a little extra scaffolding. Yes, it probably would be faster for my students to skip this step, but like that the flaps force students to slow down and to think about the process of solving a multi-step word problem. Step one is where students highlight the different parts of the problem, and that is on the part of the foldable that is not cut.
We do a few of these together for guided practice, and then I have students work on their own. I slowly begin to remove the scaffolding until students are solving multi-step word problems independently. This can be completed through centers, in students’ math notebooks, or as a part of students’ math warm-up.
It’s certainly not enough to introduce and practice multi-step word problems. This is one of those skills that will need to be practiced throughout the entire school year. As I have my students practice, I’m careful not to assign problems with operations or size of numbers that I have not yet introduced. I don’t want my students stumped because of content I have yet to teach.
In addition to task cards and assignments that specifically review multi-part word problems. I also like to have students regularly complete a spiral review assignment, where multi-part word problems are a part of that review. Each week I give students one multiple choice spiral review, and toward the beginning of the year, the multi-step word problem gets them every time. After ample instruction and practice, they begin to say that those are the easiest problem on the page.
I hope these ideas and strategies are helpful for you and your students. I’d love to know any additional tips you have for teaching this tricky skill.
Reading assessments can have a tremendous impact on the upper elementary classroom. However, it’s imperative to understand what assessments we’re giving and the purpose of those assessments. Otherwise, we fall into the trap of over-assessing, which is when we assess for the sake of assessing. This post shares some of the most common forms of reading assessments and how to use those assessments to support your students.
Screening assessments are given to all students at the start of the school year to determine which students are at risk. These assessments are not used to diagnose specific skill gaps. Instead, they help to identify students who need diagnostic assessments. These assessments should be relatively fast to administer and not use up a great deal of instructional time. Examples of screening assessments are DIBELS or Aimsweb. Once students reach fourth and fifth grades, many schools use a students’ previous years state test score as a screener, rather than administering a universal screening. When giving a screening assessment, it is important to remember that we should not tailor our instruction to these screening assessments in hopes of raising our students reading ability. Instead, we must work to raise our students’ reading ability, which will reflect in subsequent screenings.
Diagnostic assessments are used to assess specific components of reading such as phonemic awareness, phonics skills, and fluency. The results of diagnostic assessments help shape reading instruction and intervention plans. Not all students need this kind of in-depth reading assessment, as this most important for struggling readers. However, a diagnostic assessment is critical for our at-risk readers, because we must find the root of their struggle, so we can pinpoint our instruction to what the student needs. I typically use my students’ screening scores to determine where to begin with diagnostic assessments.
Phonemic awareness is the very foundation of reading. It is a subset of phonological awareness in which students are able to hear, identify and manipulate phonemes. I love using Literary Resources screener for a phonemic awareness diagnostic assessment for upper elementary students. You can download the assessment here.
Phonics involves the relationship between sounds and their spellings. The goal of phonics instruction is to teach students the most common sound-spelling relationships so that they can decode words. This decoding ability is a crucial element in reading success. I like using Scholastic’s Core Phonics Survey for my phonics diagnostic assessment, and you can download that here.
Sight words are also called also called high frequency sight words, are commonly used words that young children are encouraged to memorize as a whole by sight, so that they can automatically recognize these words in print within three seconds without having to use any strategies to decode. You can download a free sight word screener here.
Fluency is the ability to read a text accurately, quickly, and with expression. Reading fluency is important because it provides a bridge between word recognition and comprehension. If a student does not show any areas of weakness in phonemic awareness, phonics, or sight words then I target fluency for their intervention. However, I do not make fluency my primary goal if the other elements of reading are an area of weakness. However, through targeted instruction, students’ fluency will grow and can later become an area of focus. You can read more about my fluency interventions and assessments here.
It is easy to find phonetic and fluency assessments, but it is more challenging to find vocabulary and comprehension assessments that can serve as a diagnostic assessment. Vocabulary and comprehension are multidimensional and context dependent, so they do not lend themselves to simplistic, singular assessment. I’ve always used DRA (Developmental Reading Assessment) for a comprehension diagnostic assessment, which is a long test to administer, but I appreciate the information I gain from the assessment.
Progress monitoring assessments measure a student’s overall progress toward acquiring specific reading skills that have been taught. These tests are typically administered frequently or on a weekly basis. These assessments are given to monitor students’ progress on a particular skill or concept a student is currently focusing on. For instance, if I have a student focusing on improving reading fluency, I give that student a brief fluency check each week to ensure the students’ fluency growth. Teachers may also use progress monitoring assessments to observe their students’ progress on the standards that are currently being taught. For example if I am teaching point of view, I may give a brief point of view assessment a few days that week to be certain my students are learning the content. If I see that students are struggling with the concept, I will reteach and meet with students in reading groups as necessary. I often use a Daily Reading Comprehension check is a comprehension progress monitoring tool.
I do not record grades for progress monitoring assessments, as I want students to have the opportunity to practice working on a particular standard with useful feedback before they are formally assessed on that standard.
After I teach a reading standard and give students multiple opportunities to practice that particular skill or strategy, I give students a standards mastery assessment. This type of assessment may be called a variety of different names, but ultimately this is the assessment students complete to show their understanding or mastery of a particular reading topic or skill. I do assign grades for these assessments. I like to give students an assessment for each standard, and I know that other teachers assign assessments for each unit of a reading series, or a weekly assessment that covers multiple standards. What type of standards mastery assessment you give, will depend on your needs and your district’s requirements.
Since I assess each reading standard, I’ve created my own standards based reading assessments. One version of the assessments is an open-ended assessment that can be used with any text. There is also a brief one-page assessment with a short reading passage and questions. I’ve also included a more thorough assessment, where the text is a bit lengthier, two pages, and then there is a page of questions. In that assessment, there are two multiple choice questions, two short answer questions, and one essay question. The essay question is perfect constructed response practice.
There are two different types of reading foundational skills assessments. One of the assessments is a more traditional assessment. However, some of the foundation standards are better assessed through a rubric, so those standards are assessed through a rubric. I’ve also created a rubric for the listening and speaking standards.
These are the dreaded high stakes assessments that are given to all students. These assessments measure students’ skills against grade-level expectations. There are two main types of outcome assessments: norm referenced and criterion referenced. Norm-referenced tests report whether students performed better or worse than an average student, which is determined by comparing scores against the performance results of a statistically selected group of students the same age or grade level, who have already taken the exam.Criterion-referenced assessments are designed to measure student performance against a predetermined criteria.
I typically do not receive my students’ outcome assessment results until the very end of the school year, so I am limited in what I use that data for. I do use it as part of my professional reflection, but I do keep in mind that these assessments are just a small snapshot of my students’ progress.
Does anyone else feel that government has to be one of the most difficult social studies units to teach? It is such an abstract topic that students have a difficult time making connections to all of the concepts, and the vocabulary is very difficult for upper elementary students. Fortunately, there are many ways to make this unit meaningful AND fun for students, so hopefully you will get a few good ideas from this post.
My students always enjoy a good simulation, and I find that simulations tie in perfectly to social studies. When I teach government, I use a direct democracy and representative democracy simulation to engage my students. It’s such a fun way to make a difficult concept concrete and meaningful. In this simulation, students on vote on the best way to spend money on a new playground in a direct democracy and then they vote on a student council representative in a representative democracy. Students have to decide which representative best reflects their own opinions, and they see that there may not always be a perfect fit. The simulation is a part of my American Government Unit.
I love integrating social studies and science units with reading and writing, and it’s a great way to present new content to students. I’ve created a Government Close Reading packet that I incorporate this into my social studies lessons, rather than my reading lessons. I only focus on one passage a week, so it doesn’t take us too much time to complete. Here’s a glimpse at how I use the close reading passages:
Monday: We read the passage together. Students wrote notes and asked questions on the passage.
Tuesday: Students answered the first read questions and cited the text evidence they used.
Wednesday: Students reread the passage and highlighted key words and circled any words they couldn’t read or didn’t know the meaning of.
Thursday: Students reread the passage and answered the second read questions.
Friday: Students answered the third read question.
I think Wednesday was my favorite day, because it was so enlightening for me to see what words my students circled. There were words that I expected my students to circle, but there were also words circled that really surprised me. It’s important for me to have leveled reading passages, because this allows me to differentiate for my students. I’ve written each passage on three different reading levels.
I’ve also written three sets of questions for each passage. The first set of questions requires students to answer explicit questions using information from the text. I always have my students underline the answer in the passage.
On the second set of questions, students focus on vocabulary and nonfiction text features. This is also where students think about main idea and author’s purpose which are always challenging skills for students.
The third set of questions is where students apply informational writing strategies with a constructed response question. In this activity, students must use text evidence to support their answers.
The topics included in the reading passages are:
levels of government
branches of government
rights and responsibilities
I often start my government unit by teaching about the three levels of government. I made a little PowerPoint presentation that explained the three levels of government in student friendly terms. You can download a copy of the PowerPoint presentation here.
I think movies are even more engaging that PowerPoints, so I use them as often as I can. I’m a huge fan of BrainPop, because I love the quality of the videos and the huge selection of topics and follow-up options. I also like that they’re short and sweet and hold my students’ attention.
I like to use several different graphic organizers for teaching levels of government and branches of American government. I use interactive notes, and a couple cut and paste activities where students sort the branches and levels of government, flow charts, and more!. I find that the graphic organizers help students organize their thoughts as they read material on government, and they help keep my students focused. The graphic organizers below are part of my American Government Unit.
As I present new content and students learn about different aspects of American government, students add entries to their social studies interactive notebooks. This is such a wonderful tool that allows students to take focused notes in an engaging and purposeful way. I have students add to their interactive notebooks on the day after I introduce a new topic. I like to give students an opportunity to explore and process the new information the previous day, because these are challenging concepts. You can find my Social Studies Interactive Notebook here.
In one entry, students create a levels of government bulls-eye or circle map, where students describe the responsibilities of each level of government (federal, state, and local).
My favorite government interactive notebook entry is where students create a literal tree for the branches of government. A tree trunk is divided into three parts, and students glue the correct leaves to each branch of the tree.
I tried to include a huge range of activities and options to meet as many teachers’ and students’ needs as possible.
I also like to have my students complete variety of sorts when teaching about government. I created a levels of government sort and a branches of government sort. The government sorts are a great assessment, because it requires students to apply what they’ve learned about government. I have student cut out the pieces of the sort and glue them on construction paper, because it gives students plenty of extra room. to glue down the cards. Of course, you could run these off on card stock and not require students to glue down the cards and physically sort the cards. Both sorts are included in my American Government Unit.
I also incorporate task cards into my government instruction, because I don’t know if I can ever provide enough review for my students! We enjoying playing Scoot with our government task cards. You can download the task card here.
I think my favorite government review activity is the government review fortune teller. I’ve heard some people call them Cootie Catchers, but we always called them fortune tellers when I was in school (100 years ago). There are three different versions of the review game, and my students LOVE playing with them! These fortune tellers are also in my
Math fluency plays a critical role in the upper elementary classroom, and I hope to share some of my favorite strategies with you. No matter what state your teach in, more than likely math fluency is mentioned somewhere in your standards. However, before beginning a blog post on math fact fluency, it’s essential to fully understand what exactly is math fluency. According to the National Council of Teachers of Mathematics,
That’s a lot to take in! As a new teacher, I always viewed fluency in math as solely the memorization of math facts, but over the years I’ve learned that it’s so much more. (Don’t worry-this isn’t going to be a don’t teach students math facts post! We’ll get to that soon!)
Math fluency is more than memorizing math facts or procedures. Conceptual understanding is an essential foundation for math, but procedural knowledge is important as well. All students need to have a deep and flexible knowledge of a variety of procedures, along with an ability to determine which procedures or strategies are appropriate for use in particular situations. Effective math instruction provides experiences that help students connect procedures with concepts and provides students with opportunities to practice the strategies.
Math facts are a small, but important, part of math and they are best learned through the use of numbers in different ways and situations. When students focus on memorizing math facts, they often memorize facts without number sense. As we teach math facts, we must remember that some students will be slower when memorizing their facts, but they still have great math potential. We must prevent students who don’t memorize math facts well from feeling that they can never be successful with math.
Fluency should not require rote memorization. Instead, students should either have a fact meaningfully memorized or be able to produce that fact through a highly efficient strategy. A student has mastered a math fact if they can produce an answer within three seconds, through either recall or an efficient strategy. When giving any type of timed test, digital or written, I do allow extra time for the act of recording the number. Some students can recall the math fact within three seconds, but they are not physically able to record the number within that time frame.
I want math facts to be effortless for my students, so their focus and energy can be geared toward problem solving and upper level math concepts, rather than basic computation. The remainder of this blog post shares some of my ideas and strategies for teach math facts along with developing number sense.
I do not teach a multiplication facts unit, but I do teach a unit on the concept of multiplication and multiplication strategies, and you can see some of those instructional lessons here. I begin with a grouping model, where students build models of groups with a certain number in each group. I also spend a great deal of time teaching arrays and repeated addition, and a little time teaching multiplication on a number line. I use a lot of the practice from my No Prep Multiplication pack. I use these for extra practice, because this is building students’ multiplicative number sense, which will allow students to begin learning their multiplication facts.
I also incorporate multiplication practice into our math centers each week, and I always have at least two centers where students play different multiplication games. Most of my games include a built in spinner or dice. If I’m trying to save paper and copies (which is always), I like to laminate the paper and let students use counters rather than coloring in boxes. This allows me to reuse the same forms again and again. All of my games below are from my No Prep Multiplication pack.
I also send home one of my Weekly Multiplication Games for homework, which have been a huge success with my students and their parents. This is not homework in a traditional sense, as there is no worksheet or assignment to complete. Instead, I send home a new multiplication game each week. The only special materials needed are dice and a deck of playing cards, which are both extremely inexpensive. At first I was worried that this would be a waste of my time, but I soon found that students WANTED to play these games!
As I mentioned above, the best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense. I love using my Multiplication Fact Booklets for additional practice. As students work through their booklets, they gain a conceptual understanding of each multiplication fact. They are able to solve the fact with multiple strategies, as well as begin to observe patterns and develop a mathematical vocabulary.
Math fact flash cards have been around since I was in school, and I’ve created a set of flash cards with a twist. Rather than giving students a multiplication number sentence, these flash cards show students a multiplicative set, where students try to automatically see how many groups there are, how many are in each group, and the total number of dots. I love using these multiplication subitizing flash cards to foster multiplicative reasoning and automaticity. These help students take multiplication understanding from concrete to abstract. You can download these cards here.
I love Xtra Math because it’s free, it progresses students through multiplication acts in a logical order, and because students type in the answer regardless of how long it takes them to solve the multiplication problem. I also like that I can adjust what programs my students are working on. I’ve shared a clip from my account to show how varied students’ programs can be. For example, some students are still working on multiplication facts with a six second time limit, some are working on multiplication facts with a three second time limit, and some are on division facts with a six second time limit, and some on division with a three second time limit. I can see when my students practice, and I can observe their growth over time. I only use this as a tool. I do not use it for my multiplication instruction.
I love celebrating students’ growth and learning, and to celebrate learning multiplication facts students have an ice cream sundae party. Students earn spoons, bowls, ice cream, and toppings as they learn each set of multiplication facts. I always have to explain that no one is HAS to get a topping they don’t like, and that I’ll have an alternative (sorbet or something else) for those who can’t have dairy. I send the letter below home, and students can use it as a reference of what topping they are working toward. I also have an alternative version of the letter that is better suited for Xtra Math. This is a bit more equitable for students, since you can control the settings on Xtra Math and differentiate as needed. This will allow you to push students who need a little extra nudge, and give some students a little extra time. You can download this version here.
I also printed a little coloring activity where students can color in parts of their ice cream sundae as they master each set of facts. I typically have several parent volunteers for the multiplication sundae party, and one of the challenges I’ve had, was that parents didn’t know who got what topping. To help with this, I made a multiplication sundae punch card. I’ll let students punch the corresponding square when they pass a set of multiplication facts. Students will use this as their ticket to the party. You can download the punch card here.
Hopefully, this post will leave you with a few new ideas for teaching math facts with number sense.