Math Lesson Structure

The Ultimate Math Lesson Structure

How many math "best practices" have you heard of in your teaching career? I know I've encountered at least 100 effective strategies for teaching math and I'm only in my 6th year (5 if you don't count that awful year I spent teaching 1st grade reading). There's centers, problem of the day, fact fluency, guided practice, independent practice, exit tickets, checking for understanding, giving feedback to individual students during the lesson, small group instruction, technology, writing in math, assessments, reteaching unmastered skills, number strings and the list goes on and on (and then some). If you're like me, you're probably thinking that it is impossible to do them all and still teach all of the grade level standards before the school year ends. Although that may be true, there is a way to consistently push rigor while still incorporating some of the other components of effective math instruction on a daily basis.

Homework Check

Implementing a daily homework check structure into your lessons may not seem like the highest leverage use of time but it has some great benefits. Not only does checking homework increase accountability for students but it is also an opportunity for closing gaps in understanding. Give students 3-5 minutes to check their answers against a key and allow them of fix incorrect problems for credit until the timer goes off. Most of the time, students can find their own error(s) this gives them space to take ownership of their work accuracy. As they are checking their homework independently, the teacher(s) should circulate and check in with each student. Use this time to record the names of scholars with incomplete or missing homework for grading purposes. Also, be sure to touch base with the students that are not completing homework; this can be an opportunity for a great teachable moment related to college and career readiness for the upper grades.

I've been using this homework resource from The Clutter-Free Classroom for a few years now and it has made my life so much easier. I just print the answer-keys included in the bundle for my students and they're all set to check on their own.

Math Facts

Math facts is the space where students build automaticity with numbers. While it is normal for some students to rely on various counting strategies, at some point they should be able to recall certain math facts from memory. The more facts they remember, the more brain space they have for tackling H-level (hard as heck) problems. Give students 1 minute to complete 25 math facts that you want to focus on. Keep the same math fact focus for at least a week (more than a week is also okay) to promote muscle memory. 

I created these Multiplication Facts Worksheets formatted on GoogleSlides that are great for hybrid learning  for my math facts. These worksheets are great for both in-person and virtual teaching!

 

Skill Fluency

The skill fluency portion of the lesson is where the re-teaching happens. This is where you build procedural fluency of previously taught math computation skills that scholars are still struggling with. This is not the place discussing new learning in depth. Start by having students analyze a work sample and facilitate a quick discussions about the work. Then present a Criteria for Success (CFS) and release your students to practice the skill for about 5 minutes. Skill fluency should take no longer than 7-10 minutes total.

I get my practice pages from this RTI progress monitoring resource by Mandy Neal. She includes at least 10 practice pages for each skill at different levels of rigor. It really comes in handy when your students need practice with same skill more than once.

Problem Solving Task

The Problem Solving Task (PST) is my absolute favorite part of the lesson! This is where the new learning takes place. Students are given a problem (typically a word problem) that is a little bit beyond what they already know and are prompted to try it independently. I usually start by reading and annotating the problem as a class so that each scholar understands what the problem is asking. As students are working independently for about 4 minutes, the teacher should circulate and looks for scholar work samples that are going to drive the class discussion.

The PST discussion is where the magic happens! "Show call" (display under a doc cam) 2-3 samples of scholar work with various strategies that you want to highlight and ask synthesizing questions about the work. This questioning will allow for students to do the heavy lifting by articulating what they see and whether or not they agree or disagree with the strategy. The last work sample of the show call should be contain the strategy that you want to focus on for practice. You may have to make your own work sample if you don't anticipate that students will produce the strategy that you want to focus on. After your class discusses the last work sample, allow your students to come up with a "key point" (the "how" of the learning objective) as a class. This allows them to feel a sense of ownership of their learning.

The PST should take no longer than 20 minutes for both the work time and discussion. I usually create my own problem solving tasks and will make them available in TPT store shortly.

Guided Practice

Guided Practice is where your students are seeing the new strategy for the first time. I usually start with an interactive modeling/think aloud of the skill and give students a thinking task as they observe.   Usually the thinking task is, "what are the steps that I did to solve this problem?" After I call on a student to attempt to list all of the steps, I present the CFS for the skill and release them to independent practice.

I usually do guided practice problem in a math journal/interactive notebook structure. This should not exceed 10-15 minutes. Check out my UPESC and Bar Models interactive notebooks if you want to build problem solving skills in your classroom. Other skills and standards will be available in my TPT store shortly.

Independent Practice & Exit Tickets

After students get some practice with the teacher and/or partners, they should have some time to practice the skill indecently and receive feedback on their progress. Use the CFS to give bite-sized feedback so that you don't spend too much time with just one scholar. It is very important that each students gets a chance to receive feedback from you so that they are not practicing the wrong thing for too long. If you notice a trend (more than 3 students are making the same mistake), they pull the team back as a whole to stamp the error and highlight the part of the CFS that they should focus on to avoid that mistake then release them back to work. After practicing for about 10 minutes, give your students an exit ticket. This is a final product of the day's learning that students complete independently without feedback. The teacher should collect and grade the exit ticket and use the data to inform instruction. Try to have exit tickets graded and handed back to students within 2 days with an exemplar attached. The immediate feedback helps to promote the quality of student work as they progress through the unit.

Other Components

Due to my math block being so short (only 60 minutes) I have to find creative ways to incorporate some of the other components of math. Once a week, we have a Centers & Math Workshop Day where students get to work with different centers while my co-teacher and I give small group intervention for tier 2 and 3 scholars. I use Jennifer Findlay's math centers and my students love them! 

One of the centers is a technology station where one table gets to work on the I-Ready math program. I-Ready has been a great way for my students to get tailored instruction at their level! 

On Friday's my students get a weekly quiz with a mixture of past and present skill focuses. I use the data from these quizzes to inform my skill fluency reteach lessons for the next week. After the quiz, I use the remainder of the block to do some of the other math best practices such as number strings, problem of the day, or any other structures that promote student achievement. While I am flexible with this use of time for the whole group, my co-teacher uses this space as another opportunity for small group instruction with our struggling scholars.

This lesson structure has been a sure fire way to promote student achievement by pushing rigor and conceptual understanding as students learn new skills as well as building procedural fluency throughout the year. If you are looking to revamp your math instruction, try using this structure to inform your planning an let me know how it works for you! By the way, don't forget to make a hot cup of coffee as you plan!

Problem Solving Using UPESC

When I first started teaching, I struggled to find a way to help my students with their problem solving skills in a way that was rigorous yet consistent. I often found myself blaming my students' low reasoning skills on their lack of reading comprehension but I soon found this thinking to be extremely false. As the years went on and my delivery of instruction improved due to professional development, I finally feel that I am at a place where I am confident in my ability to help my students develop their problem skills.

First you want to give students a consistent process for solving word problems. My students use the acronym UPESC which stands for Understand, Plan, Estimate, Solve and Check.

Understand- To understand the problem, I teach my students to read and annotate word problems by circling important numbers with the units, underlining key information (important information without numbers) and labeling the important information. To keep my students from randomly circling and underlining, I try to stress that anything that is circled/underlined should have a specific smart note on why that information is important. Without naming this stipulation, it is almost guaranteed that students will underline the entire problem and circle every single number that they see without trying to fully understand what is being asked. The two questions that help the most during this process are: what do we have? and, what do we need to find?

Plan- During the planning process, students should use their annotations to help them choose the operation. Visual models definitely help students choose the appropriate operation by forcing them to represent the situation of the problem. My students use bar models as their visual representations and with consistent practice and feedback, choosing the appropriate operation becomes a breeze even for my students with the most gaps in their reasoning ability. Once students have shown mastery of choosing the appropriate operation on a consistent basis, I allow them to simply list the steps for solving.

Estimate- There are several estimation strategies that I teach my students to choose from throughout the course of the school year, the strategy that they use depends on the problem. The most common strategy that students can use to estimate is rounding. When dealing with fractions students can use benchmarking or their understanding of relative magnitude to help them estimate their final answer. The purpose of this component is to help students gauge the range of their final answer so that they can readily recognize when they have made a mistake after solving. There are countless occurrences where my students were able to avoid silly mistakes based on estimating their answer before hand.

Solve- Once students fully understand the problem and have a clear plan of execution, they can solve but they must show clear, complete work. I do not accept work with just an answer. My reasoning for this is because it becomes more difficult to give feedback for students to fix mistakes when its not clear they've done incorrectly.

Check- Finally students should wrap up their problem solving by checking their work. They should start by checking their work against their estimate; if their answer is close then they most likely solved correctly. To check their work more thoroughly students have the option of checking using the inverse operation, re-working the problem, or using models if they chose to solve with the standard algorithm. Any checking strategy is acceptable as long as students are showing strategic thinking for checking to see if they solved correctly.

I usually start teaching this process for solving word problems in the very beginning of the year with lots of guided practice, questioning around reasoning and feedback. I have found that students make faster progress when they have exemplars to refer back to when they are working independently. Posters and interactive math notebooks come in handy for my students when developing their independence with problem solving.

If you are looking for resources to start helping your students with problem solving check out my UPESC Problem Solving Pack and my Interactive Math Notebooks for Bar Models. These products along with consistent practice and feedback, are sure to help develop the reasoning skills that students need to tackle word problems.

        
    

What do you do to help your students with their problem solving? Share your strategies by leaving a comment down below!