Tuesday, September 21, 2021

What are the SMPs Part 2

Why hello, there teacher friend! I'm back this week to share about the last 4 Standards for Mathematical Practices. If you missed my previous post that included information about the first 4 practice standards, you can find that here.

Let's jump in, shall we?! 

Standard 5: Use appropriate tools strategically

Standard 5 is all about students being able to select the most appropriate mathematical tools to be able to successfully complete a math task. Typically when you hear the term math tools one might think of a ruler, protractor, or calculator right? While that isn’t incorrect, the term math tools have a much broader definition when we’re looking at Standard 5. Tools are anything that can support students to perform a task. This could be concrete materials such as base-ten blocks, connecting cubes, counters, a number line, etc. Calculators, paper and pencil, and mental math are also math tools. 

Often times there is more than one tool that can be used for a task, but some tools are more efficient than others. This standard is all about students choosing the tools that are MOST efficient in solving their math tasks. 

Standard 6: Attend to Precision

This standard in particular is referring to precision in calculations and performance of math tasks as well as precision in communication. 

In math, there are times where estimation works. There are other times when precise calculations are vital (balancing a checking account, ordering window blinds to fit within a frame, calculating hourly pay, etc). Initially, precision may be answers expressed in whole numbers, but as our students get older and progress in their understanding of math, that precision is refined with answers expressed as decimals to the tenths, hundredths, or thousandths. 

In addition, students must also be precise in other math tasks such as constructing graphs, determining the probability of events, using a ruler, measuring angles, etc. As primary students learn about measurement, they may start with lining up cubes to measure an object. They might notice gaps between the cubes whereas their neighbor doesn’t have any gaps and their measurements differ. As students develop their skills, attention is placed on moving the cubes together to eliminate gaps, and in turn, their measurements become more precise. 

When we talk about precision in communication, we expect students to thoroughly describe math ideas, precisely explain how they solve a problem, and give specific examples as they construct their mathematical arguments. In order to do so, students must know the words that express their thoughts. This is where math vocabulary comes into play. 

If a student is explaining that they measured “around it” rather than talking about the perimeter of the figure, this student doesn’t quite have the vocabulary to precisely explain their thinking. 

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

  • Model precise communication by using grade-level appropriate vocabulary.

  • Discuss important math vocabulary and explore the meanings of math words through familiar language, words, pictures, and examples

  • Expect precise communication and ask students to elaborate on ideas, choose specific words, specify units of measure, and explain symbols they use.

  • Orchestrate ongoing experiences for students to talk and write about math. 

  • Require students to label units, quantities, and graphs 

  • Expect students to justify labels (e.g., what area is labeled as square units and volume is labeled as cubic units

  • Model specific and thorough explanations

  • Allow students opportunities to work with partners to come up with explanations 

Standard 7: Look for and make use of structure 

Standard 7 focuses on understanding the structure of mathematics and using this understanding to simplify things! For example, when adding up how much your grocery list will cost, you don’t worry about the order in which you add the items. If your students understand math properties, they know that the order in which numbers are added will never change the total. Another example of this standard in real life is when baking. If you can’t find the ¾ measuring cup, you could simply use the ¼ cup three times because you know it’s the same amount or quantity. 

This standard is where conceptual knowledge is necessary. Students must truly understand how math works to be able to apply properties and see patterns. The goal of this standard is to get students to see the flexibility of numbers, understand properties, and recognize patterns and functions. Below are a few examples of each.

The flexibility of Numbers: This is the understanding that numbers can be broken apart and put together in a variety of ways. Using this understanding can help students to be more efficient in how they choose to solve problems. This also helps students tremendously with mental math. 

6 x 8 is the same as 5 x 8 plus 1 x 8. 6 x 8 is ALSO the same as 6 x 4 + 6 x 4.

53 + 18 could be solved by adding 53 + 20 = 73 - 2 = 71. Here the student understands that it is easier to add 20 to 53 and knows that 18 is 2 less than 20. 

Understanding Properties: Understanding the different properties helps students to be able to solve problems more efficiently. 

If a student was asked to solve the following problem:

The cafeteria had 14 rows of seats and 8 seats in each row. How many people can be seated? 

A student that understands properties can quickly and easily solve this problem in their head. They will immediately break the 14 rows apart into 10 rows and 4 rows. In their head, they would figure out 10 x 8 = 80 and 4 x 8 = 32 and 80 + 32 = 112. This understanding of how distributive property works helps the student simplify the task. 

Recognizing Patterns and Functions: When students are able to truly make sense of math, they can look at the numbers to find patterns. Look at the table below.

1/2 = .5

1/3 = .33

1/5 = .20

1/4 = .25

1/6 = .167

1/10 = .10

1/8 = .125

1/12 = .083

1/20 = .05

1/16 = .0625

1/24 = .0467

1/40 = .025

In this table, we see that as the fractions are being halved, their decimal equivalent is also halved. Using this knowledge students can solve other types of problems. 

For example, if you don’t know the decimal representation for 3/8 but we know that 1/4 is .25 and that 1/8 is half of that or .125, you could triple .125 to find that 3/8 equals .375

Standard 8: Look for and express regularity in repeated reasoning. 

Standard 8 is all about students seeing and finding patterns and repetition in what they are doing in math. By recognizing the repetition, students are then able to develop shortcuts- like algorithms or formulas to make tasks easier. 

In Kindergarten students notice repetition in the counting sequence, always following a 1 to 9 sequence. Once they recognize this, they are then able to continue their counting with “twenty-one, twenty-two, twenty-three….thirty-one, thirty-two, thirty-three….forty-one, forty-two, forty-three…..”. 

Standard 8 is where you as a teacher help your students to discover patterns and make sense of them to gain a deeper understanding of math as opposed to just telling them. Letting students discover on their own will make the learning stick.

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

  • Set up learning opportunities for students to gather data and observe repetitions to find shortcuts.

  • Ask students to explain shortcuts

  • Frequently ask “What do you notice?” “Do you see any patterns?” “Have we seen this before?”

  • Pose problems that draw attention to repetition

  • Ask students to think about how new problems are like previously solved problems

  • Ask students to use familiar problems as a way to decide on an appropriate strategy

I truly hope that these blog posts helped you to gain a better understanding of what the SMPs are as well as how incoporating
these math practices play a critical role in getting your students to achieve true proficiency with the Common Core Math Standards.

If you're interested in learning more, this is a wonderful book that has many examples of each Practice Standard across various grade bands.

If you'd like to save this post to view later, you can hover over the main image at the top of this post to save to your Pinterest board!

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.

Head on over to this post to learn about the last 4 Standards for Mathematical Practices.

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!