Friday, September 10, 2021

What are the SMPs (Standards for Mathematical Practices)?

Raise your hand if you’ve ever had a parent say “Why is math so difficult now?!” or “This isn’t the way I learned math. It’s so complicated and confusing now.” 


Chances are that if you’re an elementary teacher, you’ve definitely heard this or maybe even thought this yourself.


The Common Core Math standards can not effectively be taught without a focus on the Standards for Mathematical Practices (SMPs). Understanding the SMPs will enable you to better be able to shift your teaching practices from a focus on content (the standards) to a focus on application and true understanding. The SMPs are actually the heart and soul of the Common Core Standards.


You might be thinking:


Think of the SMPs as the process which one must take to learn their content standards. In order for students to be truly proficient with their content standard, they must be able to apply, communicate, make connections, and reason about the math content. This differs from how you (or your students’ parents) learned math because back in the day, proficiency was measured by a correct answer or one's ability to carry out a computation (based off of rote steps). 


These practices can’t be learned in a quiet math classroom filled with drill and kill activities/worksheets (think back to when you were in school). This level of thinking must be developed in classrooms filled with thoughtful conversations and hands-on explorations about math concepts. Your ability to ask thought-provoking questions is what will truly be the change in your math classroom.


Let’s take a look at Standards 1-4:


Standard 1: Make Sense of Problems and Persevere in Solving Them


In short, what is expected is exactly what the standard says. Students will be able to understand the problem-solving process and know how to navigate the process from start to finish. They have a variety of strategies and know how to go about solving a problem. Last but not least, students don’t give up at the site of a challenging problem. They have the tools in their “toolbelt” to power through and figure it out on their own. 


How do I get my students to be able to do this?

  • Focus classroom activities and discussions on students’ thinking rather than on the correct answer

  • Do not rely on oversimplified methods to teach concepts, such as keywords (I saw the word altogether so I added).

  • Pose students with problems that push students to apply their understanding of math content and allow them the opportunities to explain their process of solving.

  • Provide students with opportunities to explore complex problems that include multiple approaches to solving. Allow them opportunities to share all of these different approaches. 

  • Praise student efforts, put value on their persistence and process on solving rather than praising the correct answers.

  • Create a supportive and nonthreatening classroom environment where discussions of confusion points are encouraged. Openly discuss these confusion points and include insights on ways to simplify problems and move through confusion. 

  • Acknowledge the efficiency of particular strategies but also celebrate individual, reasonable approaches. 


Standard 2: Reason Abstractly and Quantitatively


Standard 2 addresses the importance of building a strong understanding of numbers. When students are given a problem, they are able to represent the problem using numbers, symbols, and diagrams (abstractions). Students must see the connection between the problem situation and the abstract representation (equations). Once the equation is solved, students should refer back to the context of the problem to evaluate if the answer makes sense. 


How do I get my students to be able to do this?

  • Ask students to identify and describe the data in the problem.
  • Model building appropriate equations to solve problems.

  • Use diagrams to model math situations to make it easier to see what is happening in the problems. Can students draw a diagram to show a word problem for 3 x 5?

  • Frequently ask “what operation makes sense?” or “How should we build an equation to match this problem?”

  • Ask students to write a word problem to go with a given equation.

  • Consistently ask students to explain equations or diagrams, connecting them to the problem scenario (e.g., What does the 6 represent in our equation 6 x 3 = 18?)

  • Ask students to label answers by referring back to the problem to determine what the quantity (solution) represents. 

  • Ask students if the quantity makes sense when referring back to the problem (e.g., Does 3.5174 buses make sense?)

  • Discuss building appropriate equations to solve problems (are there more than one equation that could be used to solve this problem?) 


Standard 3: Construct Viable Arguments and Critique the Reasons of Others


This standard means that students are able to come up with a correct answer and also explain WHY it’s correct. In addition, they’re able to listen to the justification of others, or even look at how a problem may have been solved, and identify any misconceptions or misunderstandings that the person may have had. They are able to communicate their thoughts to others. 


How do I get my students to be able to do this?

  • Don’t just accept an answer from a student, follow up with questions such as “why?” or “How do you know?” 

  • Encourage students to use math vocabulary in their justifications

  • Use probing questions such as “Does that make sense?”, “Why is that true?”, “Does Ronald’s way to solve this problem also work? Why or why not?”

  • Give students the opportunity to listen to their classmates' reasoning. Rather than the teacher asking clarifying questions or correcting a misunderstanding, allow the students to do this. 

  • Create a non-threatening classroom environment where students feel safe to share their arguments and know how to ask clarifying questions, and how to respectfully disagree with others. 

  • Provide students opportunities to work with error-analysis problems. 


Standard 4: Model with Mathematics


This standard encourages students to create models or visual representations of abstract math ideas. When students create models of problems, they are able to see the problem clearly and then work towards a solution. When you ask students to create math models, you are challenging them to represent their math understanding- to get it out of their heads. The power of this is that as students share their own thinking (Standard 3) and view the models of others (and listen to their thinking) they are able to gain new insights and strengthen their own understanding. 


How do I get my students to be able to do this?

  • Model the use of diagrams and drawings to represent problems

  • Encourage the use of manipulatives

  • Encourage students to create simple diagrams to show problems

  • Encourage students to come up with multiple ways to model a given problem

  • Have students justify why they chose to use a given model

  • Ask students to interpret models of their classmates

  • Have students share out about the models they created and why


I hope that this post was helpful in learning a little about what the practices are and why they are important.


Be sure to come by next week, where I will be sharing the last 4 Standards for Mathematical Practices with you.





Friday, September 3, 2021

How to Set Up Your Emergency Sub Plans

Emergency Sub Plans are a MUST for every classroom teacher. Setting them up is the most daunting task, but once you have them created, you’ll be so grateful for them the day you actually need them. Today I’m here to share some tips and ideas on how to get your plans started!


Set up your Emergency Sub Plan Binder/Folder. 

In this folder, include the following:
  • Class List
  • Daily Class Schedule
  • Your School's Emergency Procedures

  • Contact Info (let the substitute know who to contact for various reasons)

  • Behavior Management System

  • Class Procedures/Routines

  • Ideas for activities that the substitute can do with extra time or early finishers

  • Instructions/Notes for the sub on how to access the appropriate materials to use for the day

  • Extra papers for recording attendance and lunch counts

Preparing Lesson Plans and Student Work

I recommend creating several student work options for each subject that the substitute can choose from. Therefore, it’s probably best to house all of these materials in a filing crate or file box. You’ll also be able to fit your Sub Binder in here as well!


You’ll want to be able to provide your substitute with different work options for each main subject in your daily schedule. To do this, think of work options that students can do throughout the year. Print those worksheets and write up a lesson plan to go along with each worksheet set you’ll be including in your Sub Tub. 



When choosing math assignments, think of different assignments students could use extra practice with throughout the year. Create different lesson plans depending on the time of year and what has been taught. When creating these plans and putting them in your tub, don’t forget to label that folder with the time of year it can be used! 


Bonus Ideas

  • Try to create ELA and Writing lessons focused on a picture book. Have the substitute read the story aloud. Students can fill out graphic organizers, write summaries, or answer comprehension questions about the story that was read. Later, they could write a different ending to the story and draw a picture to go along with it! Don’t forget to also put the book into your Sub Tub! If you're in need of Reading Comprehension Graphic Organizers to use for this purpose, I have them in my TPT store.

  • Utilize your Time for Kids or Scholastic News Articles (if your school purchases them). They work great for having your students read through and completing the assignments/questions.

  • Include an additional lesson plan page or instruction sheet letting your sub know of different activities or games they can do with students if they have extra time in their day. I recommend providing approximated time and corresponding activities.

  • Make it a day and set up plans with your Grade Level Partners!! You can each write plans and search for the materials for the different subject areas, then share with each other. You’ll get the work done so much faster and you’ll both be prepped and ready!


If you’re strapped for time, or can’t handle ANOTHER task for your to-do list, I’ve got you covered if you teach 3rd Grade! Check out my already created Emergency Sub Plans! All you need to do is add your class information and you’re set to go!


What other tips do YOU have for creating Emergency Sub Plans? I’d love to hear them in the comments below!


Friday, August 27, 2021

How to Teach Rounding to 3rd Grades

Hey, there fellow 3rd Grade Teacher Friend!!


Whether you're new to the grade level or just need some extra tips on teaching Gr.3 Math, I'm here to support you with tips, ideas, and resources to best address your Math Standards!

Did you know that most of the math content taught in 3rd grade is brand new concepts for your students? For the first time ever, many students tend to struggle with math because they're learning everything for the first time! I'll be updating this blog frequently to share some tips with you on teaching these tricky math standards!


Before we begin though, I did want to share this important resource with you. Use this as a guide to know what your critical math content is and where you should spend the most of your time and focus on in instruction.


Let’s jump in and talk Rounding: 3.NBT.1.

 

First things first, Rounding is NOT a critical skill for 3rd Grade. I would not spend any longer than 1 week (max) focusing on this skill. Students WILL need to know and understand how to round in the 4th grade (they will round to larger place values).


Now, I want you to forget about all prior ways of teaching rounding you may have used in the past. 


  • Rounding Mountain

  • The Roller Coaster

  • Any cute songs or poems about “5 or more raise the score…” or “underling the digit you’re rounding to, look next door”


ALL OF IT! 



What is Rounding?

Engage in discussion with students about what it means to round. They must understand that rounding means estimating a number's value by finding the nearest ten or hundred.


Then, you'll want to talk about instances when a student might use rounding.


Before Teaching:

Before teaching, make sure that students can skip count by 10s. Continue to skip count well into the hundreds so that students can see/hear the patterns (110, 120, 130, 140…..210, 220, 230, 240, etc). 


The Simplest Way to Teach Rounding:

Number lines are the best way for students to visually see and understand what a number will round to. 





I’ve created this number line that can be used for Rounding to the Nearest 10 and 100. Before teaching, all you need to do is print a double-sided copy for each student and place them in a sheet protector. Each child will have their own to work from. They can simply use an expo marker to practice and then erase.


  1. Ask students what two 10s the number is in between. Label it on the number line.

  2. Ask students what the halfway point between those two 10s is. 

  3. Ask students where the number they are rounding falls on the number line? Is it before or after the midway point? Plot it.

  4. Students can then visually see which 10 the number is closest to. 



You would follow this same procedure for rounding to the nearest 100. 


This method is so simple, yet so effective! Have kids hold their “boards” up so that you can do a quick scan around the room to check for accuracy. The best thing about this strategy is that eventually, students will begin to visualize that number line in their heads and will no longer need to draw it out! 


Guided Practice

Rounding is so easy because you can literally throw out ANY number for students to practice with. BUT, if you want something consistent and all the answers figured out for you, I’ve got a set of Rounding Task Cards for you available in print form OR a Digital Google Form (best thing about this is that it self grades for you!) If you want to save 10%, you can pick up both items in this bundle.




I also have these Quick Check Formative Assessments in my store for use with ALL of your Grade 3 NBT Standards.

For more tips, tricks, ideas and FREEBIES specifically geared towards 3rd Grade - be sure to subscribe to my exclusive 3rd Grade Teacher Email List! 


Unit next time! Aloha,

Sunday, July 25, 2021

Cut Back on Grading and Paper Clutter NOW!

If you've got stacks of ungraded papers piling up (or shoved in drawers), this post is for you!


Let’s be real, you have enough on your plate and don’t need to be grading unnecessary amounts of stuff. It’s time to think about what really matters and let’s get rid of some of that paper clutter AND grading.


Tip #1: Stop assigning tons of homework

Re-assess what you are currently assigning for homework. Ask yourself these questions:


1. What is the purpose of this assignment?

2. Is the purpose of this assignment being met?


When I first started teaching, I viewed homework as an opportunity for students to get the extra practice and support needed to gain mastery. When I reflected on the questions above, I realized that the students needing the most support were the most were very ones NOT DOING THEIR HOMEWORK!


It was a constant battle chasing down assignments (and trying to keep track of who did or did not do each assignment).


When I truly thought about it, most of my homework assignments weren’t even truly serving the main purpose. So, I stopped.



I stopped assigning math homework (because parents tried to undo what I was teaching anyway) and stopped any type of spelling homework (because I didn’t want my students memorizing words).


Instead, I only assigned quick and easy assignments that truly supported my students’ learning. It was something I knew they could do independently (which is what I wanted). 


You can read about my nightly homework routine here. The type of assignments that I did assign, for the most part, I was able to do a quick spot check, mark my grade book, give it a star then return it back to students. 


Tip #2: Use Task Cards

I love task cards because you’re able to provide your students with LOTS of practice and you only use up 1 sheet of paper!


Teaching math using the math workshop approach allows you to differentiate work, differentiate instruction, and provide lots of practice with little paper clutter.


One of my stations would be ‘hands on’ where my students would be doing a scavenger hunt around the room solving task cards. Since my rotation blocks were short, they would work on completing that 1 set of task cards throughout the week. I would also typically assign 1 worksheet to check up on how students’ understood the small group lesson for the day. 


For the entire math block, I would only be collecting 1 piece of paper for every student (and the task card sheet at the end of the week). 


For more ideas on how to use task cards in the classroom, you might enjoy this post.


Tip #3: Grade Right Away!

My last tip is to grade whatever assignments you need to right away! This one probably seems like a no-brainer, but might be one of the most difficult because you'll need to get yourself into the HABIT of doing this.


Find some time during recess, at lunch, or after school. Make it a rule to yourself that while you're grading, you won't get distracted by anything (no scrolling social media or checking emails).


Not letting the grading pile up will be a tremendous help later. Plus, grading along the way will provide you with valuable information about what your students know and/or need extra support with. 



Tip #4: Create a System for Grading

Grading multi-page reading assessments used to take forever, until I came up with a system! Grading 1 page at a time for all students makes the grading 10x faster (this is especially easy with multiple-choice questions).


I then write how many points the student earned on the bottom right-hand corner of the page. That way, when I’m done, I can add up all the points then record them on the front of the assessment. 


Until next time!
Aloha,

Sunday, July 18, 2021

Using the CPA Approach to Teach Math

Do your students struggle to retain the concepts that you are teaching? Do you often find yourself asking "Why don't my kids get it?!".


If this sounds like you and your students, this post is exactly what you need to transform your math instruction!


What is the CPA Approach? 

The CPA Approach was created by psychologist Jerome Bruner and stands for concrete, pictorial, and abstract learning. Jerome Bruner proposed this approach as a means of scaffolding learning. The CPA Approach builds on a child's existing knowledge by introducing abstract concepts in a concrete and tangible way. It’s learning that transitions from concrete materials, to pictorial representations, to abstract symbols and problems.

Concrete: Using physical objects to solve math problems. This is a ‘hands-on' approach using real objects and it is the basis for understanding math concepts. 


Pictorial: Using drawings to solve math problems. It is sometimes referred to as the “seeing” stage. 


Abstract: Solving math problems using only numbers. It is sometimes called the “symbolic” stage. 


Why should I use the CPA Approach? 

Math is abstract and can be confusing for students! That's why providing concrete learning is so important in teaching elementary math. By using concrete materials students are able to ‘see’  the math, and make sense of what is happening. The CPA Approach makes learning math accessible to all students, including those with math learning disabilities. 


There is a common misconception that older students do not need to use manipulatives and that they are just for the younger grades. However, concrete learning is equally important with older learners as it is with younger learners! ALL students benefit from learning math concepts in a concrete way, as opposed to just memorizing a procedure. 

 

Concrete Learning

One benefit of concrete learning is it promotes discussion, which allows students to talk through and explain math concepts. As students work through math problems using manipulatives, teachers are able to observe and gain a greater understanding of misconceptions and to analyze students' depth of understanding. 

 

In the 3rd Grade, many of the math standards are NEW to our students. It’s their first experience with these concepts and they have a difficult time jumping into the math workbooks because the math is so abstract. Over the years, I have found that when I’ve used manipulatives to let students truly understand what they were doing and make connections, this helps them learn the standards the best. 

 

Pictorial Learning

Once students feel confident in concrete learning they can move to pictorial learning. Pictorial learning involves drawing pictorial representations or sketches. Students are no longer using the manipulatives but still are supported by the drawing. 


Some teachers choose to skip over this step, but it is an important bridge between concrete learning and abstract learning. Without this step, students can find visualizing a problem very difficult. 


Abstract Learning

Once students have grasped an understanding of the concept through concrete materials and pictorial representations they can progress to abstract learning. In this stage, students are using numbers to solve problems. 


Although the CPA Approach has three distinct stages, teachers should be using all stages within one lesson. This allows students to make strong links between each stage. 


Applying the CPA Approach

One of the greatest struggles I hear that other 3rd grade teachers have is with problem-solving. Using the CPA Approach to teaching students how to problem-solve will be a game-changer. Let me walk you through some examples of what that might look like.


Concrete: Have a discussion with students about what it means to add. When students explain that it means putting two amounts of something together and getting a new total or amount, ask them how they might show that using unfix cubes. Go through several examples of having students add (you can give word problems) and have them demonstrate it with their unifix cubes.


Pictorial: Now make the connection for students of what a pictorial representation would look like. Draw out what you see in front of you. Ask students if that picture represents what they have in front of them.


I usually ask students how I might show a larger number. Would I draw each individual unifix cube? No! That's when you transition that understanding they just built to bar model drawings.


Abstract: Now that students have been walked through this process, they can see that this bar model drawing now represents an addition problem or equation. They should be able to determine equations by looking at different bar model drawings.


I go through this process with all 4 operations. Getting students to truly grasp what it means to add, subtract, multiply and divide helps them to be able to solve problems. When they read word problems, they are able to draw a pictorial representation and from that, can determine what equation (what operation to use) without relying on keywords.


What do you think of the CPA Approach? What questions do you still have? Leave them for me in the comments below and I'm happy to answer them for you!