The post How I Use Spiral Reviews to Guide my Math Reteaching appeared first on Tales from Outside the Classroom.
]]>I use two different types of spiral reviews in my classroom. Every day for morning work, we do a spiral review page. In the beginning of the year, I spend the first 40ish days reviewing the previous year’s standards during this time. Then, we jump into the current year. During my spiral review, students sometimes see new content. There are some mixed feelings about giving students new content in this way, but I don’t spend a ton of time teaching the unknown skill. We use this opportunity to apply what we know in new ways, and get a quick introduction to the new content. This 15-20 minutes of our day gives ongoing practice with the standards and helps keep vocabulary fresh in students’ minds. I use this time to practice and review. It’s not graded for proficiency. It’s practice. The intention is to give daily practice and reinforcement of the standards. They also could be used as homework or during other independent practice throughout the day. You can find all of my daily math spiral reviews for 1st, 2nd, and 3rd grades in my TpT store. I sell them in sets of 40 pages and include yearlong bundles in both one grade level and mixed grade level sets.
I also use math spiral review assessments to do quick formative reassessments and plan my math reteaching groups. Once we are about halfway through the year, I create a schedule to continue to circle back and reassess content. I choose the highest priority standards as dictated by my state. I choose the standards that most connect to others. They give “more bang for my buck”. I space them out throughout the quarter. This allows me to continue to focus on teaching and supporting my current focus while also supporting our most immediately assessed standards.
I use my 3rd Grade Math Assessments Google Forms to assess all of the standards in the domain in one swoop. Because there are four whole-domain reviews, I can choose to use a couple throughout the year for this purpose. I then use the other two as spiraled practice. From that data, in addition to my original assessment data, I determine which students need reteaching on specific standards. At times, I may also give a specific standard’s assessment if I know I want additional information on something specific. I love that I can get updated data to plan my reteaching in just a few minutes, and that I don’t have to spend a lot of time grading. It allows me to focus my time on planning my math reteaching groups. I also then use the standard specific math assessment to check students’ mastery after reteaching.
A one-time spiral review form isn’t going to detail every missing piece in a student’s puzzle. But, it identifies which students are struggling with a specific standard or unit, or misconceptions that need to be remediated. In the past, I didn’t do the best job going back to skills from the beginning of the year. As the year went on, and I adjusted my math reteaching groups based on our weekly assessment data, our focus was always moving forward. I struggled to go back to earlier concepts in the spirit of continuing to support what my weekly assessment data showed. Once I started utilizing spiral reviews to assess student mastery of previously taught standards, I could easily adjust my groups without spending a lot of extra instructional time I didn’t have.
I want to note that I call these spiral review assessments. I use them as a formative assessment. Unless I’m using them to truly reassess my whole class’s mastery of the standard, I don’t put the grade in the gradebook. I use the assessment to drive my instruction. That’s truly the purpose of assessments, anyway. I also appreciate that it gives students practice on the standards in an ongoing way. It’s just a few minutes for those students that truly don’t need the practice, but it helps to keep the standards fresh in their heads.
My 3rd Grade Math Assessments Google Forms contain two versions of every single standard. Because there’s two, they’re perfect for pre and post teaching. Or for ongoing, spiraled practice. Each domain also has 4 Forms assessing all of the standards in that domain. They’re perfect for ongoing assessments throughout the room to help you tailor your instruction down. You can take a closer look at each of the domain assessments, or the entire year’s set.
Tracking my students’ performance on their math assessments is a critical piece of the puzzle. I track my students’ scores on each skill and standard and provide ongoing support based on our weekly assessment data. I form regular math reteaching groups based on that data. But, as the year goes on, that reteaching also goes forward. My spiral review assessments allows me to ensure I’m focusing on older content.
I track my students’ performance on assessments in a Google Sheet. I like to track it outside of my district’s gradebook system because I can track things standard by standard and get a quick visual of student performance.
I’ve created math standards tracking spreadsheets for 1st, 2nd, and 3rd grades. They’re prebuilt with each of the Common Core math standards. However, they’re completely customizable. If your state standards are different, you can tweak the content super simply. You also can add additional skills. For example, do you work on counting coins in 1st grade even though it’s a 2nd grade standard? I always did. There’s space to track it. Work on telling time to the minute in 2nd grade but it’s a 3rd grade standard? I always did. And there’s space to track that too. I’ve designed a ready-to-go tracking tool but I also wanted to be sure you can edit it to meet your needs.
There are two parts to the spreadsheet: the data entry sheets where you record your data and the individual student reports that are AUTOMATICALLY generated! The individual student reports are perfect for data meetings or for sending home to parents. The best part? You don’t have to do anything special. As scores are entered on each assessment, the individual student pages are updated.
This FREE tool also includes an in-depth video tutorial specific to your grade level. Sign up to download your math standards tracking spreadsheet by clicking the image below.
Do you use spiral reviews to help guide your math reteaching groups? I’d love to hear about it in the comments below!
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]]>The post 10 Must Have 3rd Grade Fractions Activities appeared first on Tales from Outside the Classroom.
]]>Please note: all fraction resources featured here focus on fractions of a shape and fractions on a number line. Fractions of a set are not covered. This is intentional as fractions of a set are ratios rather than fractional parts of whole numbers.
Commercially purchased fractions strips are widely available and there’s nothing wrong with using them. However, I’ve found that my students use them without building an understanding of what each piece of the strip represents. They become a cheat sheet, almost, or a crutch. Instead, I have students make their own during our first fractions lesson. I introduce our fractions unit by having students create their own fractions strips and turning them into a reference poster. This one, hands-on lesson lays the foundation for our fractions unit.
During this fraction introduction, students explore sizes of denominators to compare fractions and explore equivalence. Because students create each unit fraction themselves, and use one strip to represent the whole, key foundational concepts to understanding fractions are established. The fraction strips can also be used to represent fractions on a number line by adding the number line below. The reference poster can continue to be used as a tool throughout the rest of the fractions unit. This hands-on fractions introduction lesson will make all the difference in your fractions unit and it’s detailed for you in the linked post!
I rely on the Fractions and Number Lines Apps from the Math Learning Center so often during our fractions unit! These quick tools allow me to display and manipulate circles and rectangles for fractions of a shape, and use number lines to explore fractions less than, equal to, and greater than 1. Both are very customizable so you can use them in a variety of your lessons. Each app is available as a web app you can link to (and link to precreated versions) and is available as an app for Chrome and iOS. I’ll do my best to detail how I use each tool, but spend some time exploring each of them yourself!
The Fractions App gives you a blank slate to begin. Using the toolbar on the bottom, you choose whether to use a rectangle or a circle and then you choose the amount of parts in the shape. Once the shape is displayed on the screen, you can select to have the fraction displayed as you add shading to the parts of the whole. This tool is perfect for giving visual models of fractions of a shape and allowing students to explore fractions. It’s also great for visual models when comparing fractions or determining equivalence. Students can build two shapes of the same size as they work independently. Or, you can use the tool during your lessons.
The Number Lines app allows you to choose the spacing on your line and whether or not you want numbers and fractions displayed. Without numbers, it’s virtually an open number line that can be used for any part of your lesson. If you choose to display the fraction, you can select the denominator up to 12.
The masking tool allows you to display only specific numbers. By clicking on one of the blue boxes, that number will be displayed. The jump tool shows the movement from one hash to the next. The unit fraction for each jump can be turned on or off.
I have only ever used the web version of both of these apps but I find them invaluable during my fractions unit. I also use the number line app during our measurement unit when we’re measuring to the nearest quarter-inch.
I teach my math lesson in two different rotations, allowing me to differentiate my instruction and provide differentiated scaffolding. You can read more detail in my Math Block Structure post. When students are not with me, it’s crucial that they are engaging in high-quality, standards-based practice. I utilize a variety of websites like Moby Max, Freckle, and Khan Academy to give my students ongoing practice at their independent and instructional levels. I also utilize those websites for intentional standards-based practice. But I also use my digital lessons and digital task cards to give students specific standards-based independent practice. This allows me to have a better look at what students complete independently and what they still need support in.
After we’ve spent a couple days working through the standard together, I assign my digital lesson. The digital lesson walks through the skill from concrete representations to more abstract concepts like word problems. Students read lesson information, explore content specific vocabulary, and apply their learning to word problems. These digital lessons reinforce the same content I’m teaching within my instruction.
On another day, students complete digital task cards on the standard. The task cards give students independent practice of the skill in its most typical formats. As a teacher, I love that I can quickly assess students’ understanding of the skill by spending just a quick minute going through their work.
I typically do not assess my students’ mastery of the standard until a full week after I taught it- in short, the Friday following the week of instruction. This allows me to continue to support and reteach those students that need additional practice. It’s also during this second week that I send homework on this particular skill. I like to send homework when students should be able to complete the work relatively independently. To guide my support during this second week, I give my Google Forms quiz at the end of the first week- often on the same day I assign the task cards. Because most of the form is self-grading, I can spend my time planning my reteaching instruction for the following week.
Each of these 3 components are available in my Digital Fractions Resources. The bundle includes units for each of the fractions skills and standards: understanding fractions and unit fractions, fractions on a number line, fractions greater than one (sometimes referred to as improper fractions), whole numbers as fractions, comparing fractions, and equivalent fractions. The bundle is broken into 3 files based on the standards. You can check it out by clicking the image below.
Throughout the year, I spiral back to standards to continue to check in on students’ mastery. I’ve found that after we’ve moved on from a skill, some students forget some things without ongoing exposure. There’s also those kids that don’t master it the first time that need continued instruction and practice. I use my 3rd Grade Fractions Assessments in Google Forms as both a formative assessment tool and as continued practice throughout the year. I love to assign these on e-learning days (we have several scheduled throughout the year and then also for snow days). It doesn’t take students very long, they get immediate feedback, and it’s easy for me to quickly grade the open-ended portions. I can then use the results to form reteaching groups.
My 3rd Grade Fractions Assessments include two Google Forms for each standard- perfect for pre and post assessments or as an assessment or spiraled practice later in the year. It also includes 4 Google Forms that review all of the fractions standards on each Form. These are the versions I use most often for spiral review practice.
With versions for each fractions skill and standard, and for spiral review, these Google Forms assessments are my go-to’s throughout the year!
5 in a Row is a fun, fast paced game that students literally BEG to play! In this free Fractions of a Shape game, students identify the fraction represented in the given shape and match it on their game boards. You can adjust the timing of the game to give students more or less time to play. 5 in a Row keeps kids engaged with its speed. Because it’s self-running, you have a quick second to check an email or manage the paper stack on your desk. To play, all you need is Powerpoint! Students play on printed gameboards (you choose to laminate and reuse or not). You launch the slideshow, click a button to randomize the slides, and push start. That’s it! you can download my free Fractions of a Shape 5 in a Row by clicking the image below.
You may also be interested in my Fractions & Mixed Numbers on a Number Line 5 in a Row! 4 different versions are included to provide and remove scaffolding.
If you aren’t familiar with Arcademics.com, formerly known as Arcademic Skill Builders, you should take a few minutes to explore it! They offer individual and group based online games for a variety of skills. Pizza Pandas is a fun, fast paced game that has students matching fractions into pizza representations of fractions of a shape. This would be a fun and engaging game to add to your small groups since students could play against each other live.
NUMBEROCK has a multitude of math songs available for a variety of grade levels and math standards. There are several videos that would work well with your fractions unit, but my personal favorite fractions resource is their Fractions on a Number Line song. It’s catchy and my students love singing it as they work with fractions on a number line. You can watch Fractions on a Number Line, and so many of their other videos, on their YouTube channel. They also have the video hosted on Vimeo for easy sharing, along with lyrics and other helpful information, on the NUMBEROCK site.
I love to use task cards in my classroom. One of my favorite ways is Musical Solve. I put task cards up around the room, put on some fun music, and have the kids walk from card to card. I put extras up in the room so there’s typically a buffer if a kid stops at one they’ve already done before. I’ve also seen people do this on the kids’ desks but I usually use spaces around the room or just a desk corner. In all of my 3rd grade Mustache You Task Cards, I include 36 cards. This allows for larger class sizes while still giving a few cards that are available to be done whole group. These 3.NF.1 Fractions of a Shape Task Cards are free in my TpT store. Just click to head over and download them!
I also have Fractions on a Number Line task cards. It includes 3 sets: 1) identifying the fraction given on a number line; 2) partitioning a number line and locating the fraction; 3) fractions greater than 1 on a number line. Throughout the sets, students will also have practice working with whole numbers as fractions. As with my Fractions of a Shape task cards, each of the sets has 36 cards making it perfect for practice throughout several days, or as both a whole group guided practice and independent practice activity. You can get my Fractions on a Number Line Task Cards by clicking the image below.
Find is a powerful formative assessment tool during your fractions unit. And, it’s quick and easy to implement. Give students an open number line with one given fraction. Ask them to find another. What that other fraction is, however, is where the power of Find comes in. The number lines aren’t partitioned so students have to reason through where the fraction should go. The difficultly of Find can be adjusted based on where you are in your unit: identifying fractions on a number line, or when working with mixed numbers and/or fractions greater than one. Fractions on a Number Line is one of the hardest part of our fractions unit in 3rd grade, and Find really helps me hone in on where students need support. It also gives you an indication of their number sense. To take things a step further, ask students to explain their reasoning on either the bottom or the back of the task card. You’ll get valuable information on their thinking which will help you adjust your instruction as you teach.
You can download a set of 10 pages of Find Task Cards for free by filling out the form below. The task cards will be sent after you confirm your email.
These 3rd grade fractions resources help my students master fractions each year. Use any of these fraction activities in your classroom? I’d love to hear what you like best in the comments!
The post 10 Must Have 3rd Grade Fractions Activities appeared first on Tales from Outside the Classroom.
]]>The post Christmas Distributive Property Project appeared first on Tales from Outside the Classroom.
]]>These Distributive Property Trees, or Distribu-trees as I called them, have 3 different parts: the trunk to show the expression to be solved, the body to show the decomposition of the expression into smaller parts, and the star for the product. Because we’re still very much practicing this concept, I had students do their work on dry erase boards first. This way, I could do any on-the-spot reteaching I needed.
I gave students several choices. They chose the expression they were going to solve within parameters. They also were able to decide how many components would be in their equations. In the future, I would remove that choice for students. That was where my students had the most difficulty. It’s too complex of a skill, that they have not yet mastered, to add that variable. Next time, I’ll stick with 3 parts as that’s what I have for the blacklines.
Though, despite some of that difficulty, I absolutely love the way the trees turned out in the end. It was easy to scaffold for those students that needed additional supports. I also love that it was super meaningful for what we’re studying right now, and provided a way to practice what we’ve learned while bringing in some fun and Christmas decorations.
If you’re looking for your own Christmas Distributive Property craftivity or project, you can download my Distribu-trees project by filling out the form below. It will be emailed to you immediately after email confirmation. It’s a fun math Christmas project for December!
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]]>The post 2022 Calendars for the Classroom appeared first on Tales from Outside the Classroom.
]]>Each year, I give my students the opportunity to have special, personalized parent gifts. I have done various projects throughout the years and am always looking for new ideas, and circling back to older ones. Several years back I started these printable calendars as gifts and I’ve done it every year since. The gift version of the file includes bubbled letters for the month so students can decorate each month. Students also decorate the cover, and then include a personally created image for the back of each month that gets displayed while hanging. I love the affordability of this parent Christmas gift- I print on white cardstock, and bind using the machine at school. I usually get these set up for students to work on all throughout the last week of school before break. As students have a few minutes, they can work on decorating their calendars. I give specific holidays to hand-write and we talk about what might be a good picture to create on the back of each one. Click here to download the specific file for the 2022 Calendars for Parent Gifts. My Art Inspired Christmas Parent Gifts and December in our Classroom posts have other ideas for Christmas gifts.
There are so many different ways you can use printable calendars in the classroom. These simple, open-ended calendars are perfect for both teachers and students. I’ve used these in a variety of ways over the years. You can download my 2022 Printable Calendars and keep reading to see how I use them in the classroom!
Reading logs can result in mixed feelings. I’ve found, for many of my students, they need some sort of accountability for their independent reading. This printable calendars allows me to have students record their reading in a quick and easy way. They just leave the calendar in their daily binder so it’s easy to access each day. Students can track how many pages of their book they have read. They can just put the title. Of course, it could also be sent home as a reading log for students to track their evening reading. I keep it simple so it doesn’t feel cumbersome. You are able to use this however would work best for you and your students.
It can be difficult to track classroom interventions, especially when they’re fluid groups. I’m often pulling quick groups for 5-10 minute small group lessons on specific skills and it can be difficult to record which students received the intervention on specific days due to absences. I like to keep several copies of these calendars for daily recording. I use these calendars to record the students’ name, what we worked on and for how long, and any necessary progress monitoring data based on that group work. I keep each student’s calendar in a binder at my small group table and then I have it available for recording our official interventions. It takes me 30 seconds per student and then just a few minutes to compile the specifics for our formal intervention meeting. I also love that I can have a quick visual on which students I’ve met with each week and which ones I need to meet with next. I can glance and see who has empty spaces that week to help me prioritize my time.
These printable calendars are perfect for individual goal tracking as they’re open ended and students can record any goal you agree upon. Student goal setting can build motivation and investment, and these calendars are easy for any classroom goal with students. Some ideas for goals to track would be independent reading, practicing math facts, and working on a computerized tier 2 program.
If you have a lot of events at your school, or have a different focus each week (like a preschool or thematic learning), these calendars would be helpful to give parents a look at what’s coming up. The editable 2022 calendars are perfect for this! Open with Adobe Reader, edit as you need, then print and send home! Include special events, test dates, guest classroom readers, and more!
You can download my 2022 Printable Calendars to use them right away or download the Editable 2022 Calendars. I hope you find them useful in your classroom! I’d love to hear in the comments how you plan to use them!
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]]>The post Addition & Subtraction Word Problem Types appeared first on Tales from Outside the Classroom.
]]>This post takes an in-depth look at each of the addition & subtraction word problem types. I also give some helpful links at the bottom that discuss Cognitively Guided Instruction, or CGI problem types. They use slightly different vocabulary than the CCSS but are the same set of skills. An important note- when I talk about teaching the addition & subtraction word problem types explicitly, I don’t mean that they’re only practiced during a specific unit, or that we teach specific keywords for each problem type. Students need to read the problem and understand the context. Recognizing the problem type can support that work, but it’s not focused on keywords. I also do a daily word problem outside of our focused unit work. I firmly believe in spiraling the standards in word problems so students have to focus on context to solve. For more support with problem solving, check out my Why Your Students Struggle with Word Problems, and What You Can Do About It post.
Probably the most common addition and subtraction type in most teachers minds is part part whole. We use number bonds and bar models to model and represent part/whole relationships. We model addition as two sets of objects coming together. We introduce subtraction as separating our total number of objects into smaller parts. And it’s the foundation for future work with fractions and multiplication and division. Part-part-whole is such a critical concept for our students’ mathematical understanding. It’s important that we connect this work to our language in word problems. Many word problems can be thought of as part-part-whole scenarios (even many in the start-change-end types described next).
TOTAL UNKNOWN | PART UNKNOWN | BOTH PARTS UNKNOWN | |
There were 5 bluebirds and 3 cardinals in the tree. How many birds are there in all?
5 + 3 = 8 |
There are 8 birds in the tree. 5 are bluebirds and the rest are cardinals. How many cardinals are there?
8 – 5 = ? |
There are 8 birds in the tree. Some are bluebirds and some are cardinals. How many of each kind of bird could there be? ? + ? = 8 |
Total unknown problems are typical addition problems. There are two sets that come together. Often, these are not the same exact subject. For example, it could be red apples and green apples coming together. Or cats and dogs. When it’s the same object, it’s often, but not always, a start-change-end scenario because the change is those two sets joining. The word problem below demonstrates a total unknown that has the same subject- people.
Part unknown problems are subtraction. We know the total number of items, but we don’t know the number in one of the sets. Through our work with part unknown problems, we reinforce the inverse relationship between addition and subtraction. We can write the similar equation 5 + ? = 8 to connect the two operations. It’s important to work with unknowns in any position and part unknown problems are where I like to spend some work on inverse operations and fact families.
Both Parts unknown problems are less common. They are scenarios with multiple solutions. Students know the total number of items and they give a possible arrangement for how those items are broken up. Both parts unknown scenarios are my favorite way to introduce the unknowns to the right of the equal sign 8 = ? + ?. This helps students to know they don’t just solve from left to right and what the equals sign means.
For more information on Part Part Whole, I have an in-depth blog post that shows the hands on strategies I use to introduce and practice part/whole relationships.
While part-part-whole is the most common addition & subtraction problem type in many teacher’s minds, it’s probably not the most common in story problems. In real-world scenarios, addition and subtraction is most often demonstrated through start-change-result. In start change result scenarios, something joins or leaves the others. These are the problem types where someone got more of something, or something broke. If we’re not intentional with our word problems, we tend to default to “result unknown” problems. These problem types often have questions such as “how many are left?” and “how many are there now?”. The action has already happened.
I use the term “end” instead of “result” because “end” is the opposite of “start” and I think think students have a clearer understanding than with result. It’s also the same language I use with elapsed time problems in 3rd grade and I like to keep my language as consistent as possible.
The table below gives examples for each of the 6 start change end problem types. They’re pretty straightforward so I’m not going to explain each one in depth. Whether it’s addition or subtraction, the language indicates the location of the unknown: the subjects at the start, the subjects that changed, or the subjects at the end.
START UNKNOWN | CHANGE UNKNOWN | END UNKNOWN | |
Addition |
Some birds were in the tree. 3 more birds flew on the branch and now there are 8 birds in the tree. How many birds were in the tree to begin?
? + 3 = 8 |
5 birds were in the tree. Some birds flew on the branch and now there are 8 birds in the tree. How many birds had flown onto the branch?
5 + ? = 8 |
5 birds were in the tree. 3 birds flow on the branch. How many birds are on the tree now?
5 + 3 = ? |
Subtraction | Some birds were in the tree. 3 birds flew away and now there are 8 birds in the tree. How many birds were in the tree to begin?
? – 3 = 8 |
11 birds were in the tree. Some birds flew away and now there are 8 birds in the tree. How many birds flew away?
11 – ? = 8 |
11 birds were in the tree. 3 birds flew away. How many birds are on the tree now? 11 – 3 = ? |
It’s important that we give students practice with unknowns in all positions. It is through these start-change-end problem types that students see that they can be asked to identify how many of something there was in the beginning. Or, what the change/action was. With start-change-end problems students get to build their understanding of unknowns being in all positions, and build their competence with addition and subtraction being inverse operations. Through unknowns in any location, students model and solve using the inverse operation.
If start-change-end is a new concept for you, I give you tools and strategies in an in-depth post on teaching Start Change End.
Comparisons are the most complex word problems for students. They aren’t naturally what we think of when we think of the operations. For this reason, we need to teach them and practice them. A lot!
DIFFERENCE UNKNOWN | BIGGER UNKNOWN | SMALLER UNKNOWN | |
Compare | How many more?
Sara has 3 birds. Raina has 5 birds. How many more birds does Raina have than Sara? How many fewer? Sara has 3 birds. Raina has 5 birds. How many fewer birds does Sara have than Raina? 5 – 3 = ? 3 + ? = 5 |
More
Sara has 3 birds. Raina has 2 more birds than Sara. How many birds does Raina have? Fewer Sara has 3 birds. She has 2 fewer birds than Raina. How many birds does Raina have? 3 + 2 = ? ? – 2 = 3 |
More Raina has 5 birds. She has 2 more birds than Sara. How many birds does Sara have? Fewer Raina has 5 birds. Sara has 2 fewer birds than Raina. How many birds does Sara have? 5 – 2 = ? 2 + ? = 5 |
Difference Unknown problems are typically solved with subtraction. Regardless of the question being how many more or how many fewer, the question wants to know the amount between them. The word “more” can throw students off here because they want to add. You can use the addition equation to demonstrate it as presented, but ultimately subtraction is the easiest way to solve it. My favorite way to model these problems is on a number line because I can demonstrate both question types by counting forwards or backwards.
The Bigger Unknown and Smaller Unknown questions are where things get a bit more complicated. For me, as with any problem, I ask students to start by focusing on the unknown in the question. With these problems, I think it’s best to work on them together because they can be easily confused.
In my Addition & Subtraction Word Problem Type Posters I combine by known information. In both situations above, we’re told that someone has more and they both have the same question. By focusing on what “more” indicates, we’re showing students the differences in question types, and the subtly between the two. You can download my Addition & Subtraction Word Problem Type Posters by signing up below.
Bigger Unknown problems in the table both have the question, “How many birds does Raina have?”. Due to the table placement, we understand that Raina has more birds than Sara. But let’s take a closer look at the problems.
Sara has 3 birds. Raina has 2 more birds than Sara. How many birds does Raina have?
In this problem, it tells us that Raina has more than Sara. This is a pretty easy addition problem adding Sara’s number plus the number more- the comparison- to find Raina’s total.
Sara has 3 birds. She has 2 fewer birds than Raina. How many birds does Raina have?
This problem is not as straightforward. It tells us that Raina has more by telling us that Sara’s 3 is 2 fewer than Raina’s. When students see “fewer” they want to subtract but the bigger number is unknown. We can model that subtraction equation as the unknown – 2 gives us Sara’s 3.
Smaller Unknown problems both ask how many Sara has in the table since Sara has the smaller amount. Again, let’s take a closer look at the problems.
Raina has 5 birds. She has 2 more birds than Sara. How many birds does Sara have?
In this problem, the word “more” can make students feel like they need to add. But subtraction is the better operation. If Raina has 2 more than Sara, we can subtract 2 from Sara’s to Raina’s. Or, as addition, Sara’s + 2 = Raina’s 5.
Raina has 5 birds. Sara has 2 fewer than Raina. How many birds does Sara have?
This problem is more straightforward than the last. Sara has 2 less than Raina so students will naturally subtract.
For these scenarios, I find it most helpful to start with the question. The unknown. If I need to know how many birds Sara has, I keep that in mind as I go back to the word problem a second time and restate it. Raina’s 5 is 2 more than Sara’s. Sara has 2 less than Raina’s 5. By starting with the unknown I’m solving for, I can better understand what the question is asking me to do by connecting it to the known.
I teach my students to read each word problem twice. The first time is to get a general understanding and focus on the question. The second time is to take the information that’s given and connect it to the question. I call it “Being a Problem Solving Ninja”. I explain each of the steps in my problem solving process in my Teach Students to be Problem Solving Ninjas post. I also have free posters you can use to teach students these steps focused on understanding the context.
I have posters for each of the addition & subtraction word problem types. You can use these as part of an anchor chart as you write your own word problems together for each problem type. You can display them as you introduce them. You can print several to a page and give students their own individual ones as reference.
I also have a Addition & Subtraction Word Problem Types Reference Sheet for you. This one-page printable is a nice reference sheet for you to keep at your side. Or, students can keep a copy in their math reference folder if you have one. The word problems included are the same as what’s on this site, and not the ones on the posters linked above.
Complete the form below to sign up to receive my Addition & Subtraction Word Problem Type posters.
I also have Addition & Subtraction Word Problem Types Digital Task Cards. They are organized by word problem type and practice addition and subtraction within 20. The Part-Part-Whole and Start-Change-End sets both have specific practice differentiating between them where students match the unknown and given equation to the given scenarios.
Each of the sets give students specific practice on each of the addition & subtraction word problem types. Students use the built-in tools to write equations with variables or symbols for the unknowns. After writing the equation, students use the manipulatives to model the problem on a number line and tens frames. The format allows students to practice several of the Standards for Mathematical Practice as they model and solve the problem, and check their work.
In addition to part-part-whole, start-change-end, and comparison problem types, there’s also an Adding 3 Numbers Word Problems set. This set is presented in part/whole, or part-part-part-whole scenarios. The set is free and can be downloaded from my TpT store by clicking the cover below.
I hope this post has given you ideas and resources for teaching each addition & subtraction word problem type with your students. The more practice and exposure students get, the more successful they will be.
For more reading on CGI Word Problem Types, this post from Langford Math is quite detailed and this wiki has a bunch of sample word problems.
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