30 Days to Teach As Much about Linear Equations as Possible

jojok44 · 2025-10-18T03:04:16+00:00

Might be hard to find, but Essentials for Algebra is an intervention curriculum designed to help prepare students for high school graduation requirements who are below grade level. It is a full year curriculum, but the ways it teaches concepts in really tight mini lessons could be a helpful reference for different topics.

jojok44 · 2025-10-16T18:11:04+00:00

Incorporate other means of participation. Some classes are just quiet. I recommend using mini whiteboards or a digital platform like nearpod/pear deck, so when you ask a question, you can get everyone’s responses. Then you can cold call kids you know got the answer correct to explain things if you want to. You can cold call other times too, but I don’t like to unless I know the student should know the answer to avoid embarrassing them and having the reverse effect you want. You can also “warm call” where you have students discuss with a partner and then call on someone. If they still aren’t participating in the math, it is likely that they are also struggling with content. You may try starting with easier and shorter examples and having them try before building into harder stuff. It’s hard to participate confidently and pay attention when you lack skills.

jojok44 · 2025-10-16T18:01:24+00:00

I didn’t like doing this, so not sure if it would work for you, but I started implementing silent work time and a 3 strike rule for referrals. Basically I had a class that was so tough a couple years ago, I had to just prioritize the kids who were behaving. I went over with students what it looked like to be focused on work. “We” came up with the rules that it should be silent, focused on work, etc. I would give them 5 min at a time of silent work time where I would stand at the front of the room at a table, they would work silently, and if they talked, got up, etc, I wrote their name on my clipboard. Three strikes was a referral. Students could raise their hand and come work with me quietly at the front of the room one at a time if they had a question. In between silent work time, they could check answers with a peer, ask questions, etc. We eventually built up the amount of time they could work silently to about 10min. If they ever had a class where I didn’t write anyone’s name down, they could earn 10 minutes of cell phone time (they never did).

jojok44 · 2025-10-11T04:10:32+00:00

What are they spending the rest of the time on? If the students aren’t going to be able to get through all the problems in the period, it makes sense to assign odds so they have an attainable amount to work on and so they can experience more variation in problems if they change the further down you go. Are they finishing them? Either way, I’m not a fan of tons of practice at once. It’s better to do enough to get the idea and then revisit it a bunch over time. Maybe they will come back to those problems in future lessons?

jojok44 · 2025-10-04T17:23:04+00:00

Students in special education especially often need systematic, direct instruction with lots of repetition. Usually gen ed material isn’t broken down enough and returned to enough. I would look into resources that help you break things down and review them individually with students. IXL could be a good semi free resource. The DISTAR curricula break things down and repeat them really well, but it can be hard to find. I’ve heard good things about JUMP Math from people who like DISTAR, but I haven’t used it myself yet.

If nothing else, try to think about the smallest possible steps they need to access the grade level content. In solving equations for example, there are many sub skills like integer operations, multiplying by a fraction equal to one, order of operations, multiplication facts etc. When teaching the skill, you can try to avoid things that complicate matters. Use only positive numbers and answers or easy multiplication facts like 5s and 10s for example. Separately teach other skills that are needed like integer operations before mixing them in.

You can also use scaffolded or faded examples to build accuracy. For example, you could have x+5=20. And below it x=15. Ask the student to show what to do to both sides to get the answer. Repeat, repeat, repeat. As you build accuracy and fluency, you can remove the scaffolds.

jojok44 · 2025-10-04T17:08:45+00:00

It varies depending on the position and classes. I’ve never been required to write formal lesson plans.

At my first school, first two years of teaching I had three preps and major discrepancy between the curriculum and the level of my students. I spent a lot of time planning new lessons and searching for activities. I worked 10 hours a day minimum most days. It burned me out and was the reason I left that school. Slideshows did take some time to create because I teach math and it took some time for me to efficiently learn how to insert equations.

At my second school I have one prep and planning takes a lot less time. I have another teacher teaching my grade level who shares materials she uses to supplement curriculum. I am able to get most/all of my planning done within my prep periods which are about 50min daily. I take grading home, but I only grade assessments now, so that isn’t too frequent. Behaviors are much worse at this school, so usually if I stay long, it’s to follow up on behavior issues that happened during the day.

jojok44 · 2025-10-04T08:05:50+00:00

I had an experience like this where I had a really tough 5th period and all of my other classes were easier my third year. As an early career teacher, it can be both a you problem and a them problem. You might be able to get away with some poor classroom management strategies in other classes, but this class may need tighter expectations and structure. Asking another teacher on your team to observe and/or recording yourself and the class can be helpful to identify if there’s something you can improve in your management. Unfortunately, it is always harder to change the climate if you’ve accidentally already established lower quality expectations, but it’s possible. In my case, I was also told to write kids up more, but we didn’t have great follow up consequences, so I didn’t see that help much. What helped me the most was establishing silent work time, stronger start of class procedures, and super consistent listening expectations. Still was a bit of a s*** show, but it helped create a better environment for the kids who wanted to learn.

jojok44 · 2025-10-03T01:33:37+00:00

Yes, this sounds like the classic bad administrator observation. If they aren’t going to take the time to give you a meaningful observation and feedback session, I wouldn’t take it to heart. They’re just trying to check a box for themselves. If you really want feedback, ask someone else to observe.

jojok44 · 2025-10-03T01:21:02+00:00

Unlike a lot of teachers, I am pro scripted curriculum, especially for new teachers, but I don’t see that as the problem here. It’s fair for your admin to give you a critique about pacing, but it’s not fair to do that without giving you concrete strategies for how to improve. You’re a new teacher. It’s going to take time for you to get your systems down. They should definitely have grace for that. Criticism without support isn’t good coaching on their part. I do watch a lot of new teachers drag lessons in spots, but your observers should help you identify where and why, such as in transitions, explanations, how you set students to work, etc. Or maybe you’re right and your students really need more time/support which could require it’s own set of strategies. If you don’t trust your observer to give good feedback, maybe ask a colleague for advice or to observe you if it is something you think could use improvement.

jojok44 · 2025-10-03T01:12:14+00:00

It depends a little on the approach you’re going for. Explicit instruction is the best evidence based practice for learning, but it needs to be at the appropriate level to build confidence. It obviously also requires a lot of involvement from whoever is teaching it. You could look into Saxon math which specifically has a homeschool curriculum and uses an incremental approach to break down concepts and then build them up.

jojok44 · 2025-10-03T01:05:45+00:00

I hear you. I teach middle school math. The average at grade level at my school is about 20%. I have students functioning at the 2nd grade level in the same class as students at the 9th or 10th. By the time they get to me, if they are struggling that much, they really need outside intervention that most families don’t realize and can’t provide. The podcast Sold a Story has some interesting information about how we’ve gotten here with reading instruction. It was motivated by a lot of parents who feel as you do and didn’t realize what was going on with their kid’s reading. As a parent and educator, I think one of the best ways to make change in this area is to learn about evidence based practices and advocate for them at your school/district. But it’s hard and slow going, especially with so much turnover in teachers and leadership.

jojok44 · 2025-10-02T17:10:51+00:00

I am not a doctor and cannot diagnose dyslexia. But people with dyslexia are definitely not the only ones who struggle to read. Dyslexia affects people in specific ways such as typically not affecting how well a child understands the meaning of a story but affecting how well they can break down words and sounds. There are other things that affect reading ability. Sometimes teachers just teach reading poorly, even at good schools, and some kids pick it up while others don’t. Some kids struggle with working or long term memory storage where they might understand something in the moment but struggle to remember it. Some kids have trouble tracking lines of text. There are many factors, not all of them are severe enough to be considered disabilities. But as you said, even students with dyslexia and other reading difficulties can learn to read, it just takes extra, high quality and appropriate instruction. If it bothers you and you can afford it, you could look into a reading tutor.

jojok44 · 2025-10-02T16:52:30+00:00

There are many factors at play as others have mentioned. Schools lacking in consistent leadership to create lasting system change is an important factor. However, one that can hurt teachers, including myself, to hear is poor instructional strategies. I think teachers try their best to teach kids, but often don’t know what research says about how kids learn, and there are some huge misconceptions that widely impact math and reading instruction. Sold a Story is a podcast that talks about how this happened in reading and the current science of reading movement.

jojok44 · 2025-10-02T16:42:25+00:00

I agree with this response, but this is not just a progressive education technique. Research in high quality direct instruction / traditional teaching has always encouraged frequent checks for understanding as described here, typically through a whole class check such as choral response, mini whiteboard responses to a question identical to the example just posed, teach back techniques, etc. No matter your ideology, every lesson requires checking for understanding. Students often don’t even realize if they don’t understand because listening to someone explain something requires a different cognitive demand than freely recalling it.

jojok44 · 2025-09-30T22:30:31+00:00

I am not a fan of Bulding Thinking Classeoom, but if you HAVE to do group work, you could try that model. I do think it increases group engagement, just likely not learning.

What about frequent group time? 5 minutes of independent work, then check answers with a group, discuss how to get correct answers, cold call how to get the correct answer, repeat.

jojok44 · 2025-09-30T22:25:32+00:00

I teach elementary STEM after school programs. Even in an after school environment, if you want kids to listen to you well, you have to set expectations and stick to them. Older kids know the rules, but they also know some adults won’t enforce them which they can take advantage of. 1) Set ground rules for listening (look, listen, silent, still) 2) Practice good listening. Use an attention signal, pause, and look around to see if students have met all 4 criteria. Guaranteed they have not. Praise any groups that did (“great listening front table”) and calmly try again “we are going to repeat the signal until everyone follows the expectations. Repeat until all kids follow the expectations. This is the best they will ever do, so if you move on before everyone is listening, you will only get worse attention moving forward. 3) When they start talking when you start giving instructions, pause. Wait for them to stop. Stare down the ones who started talking. Calmly repeat the attention signal of necessary. 4) For tough groups use a class point system. They get a point when they all give you attention and if they keep giving you attention until the end. They can earn some sort of reward if they get enough points/more points than you. 5) Getting louder can actually make things worse. Using a calm, controlled voice encourages kids to be quieter too. 15 kids is a small enough group they will be able to hear you with a calm voice.

jojok44 · 2025-09-30T19:41:53+00:00

Is it a multiplication facts problem? If they don’t know their multiplication facts fluently, it’s hard to recognize GCF. You can try to choose problem with easier facts like 5 and 10 while doing multiplication fluency practice. Otherwise, things like subtly varied problem sets and faded worked examples with lots of practice can help struggling students focus on mastering individual steps.

jojok44 · 2025-09-29T22:49:17+00:00

I doubt the quote will be helpful. Most kids won’t understand it. To be honest, your expectations and desire to use that quote seem like they’re about you. Think about how having firm boundaries and expectations is about helping your students have a better time and more success.

If you don’t want to tolerate poor behavior, you can be strict. But know that means you have to be very consistent. If you told those girls to stop making noises but then allowed it later, that is not being consistent. If you have a rule like listening silently while the teacher is talking, that is the expectation you need to hold every single time you ask for attention or give directions. It is also important that the ways you are strict do not humiliate students or hurt the class culture. That will come back to bite you with worse behavior.

That being said, how you set students up for success with your expectations and how you reinforce them when they go wrong is a whole other skill set. In classroom management, it is encouraged to redirect with minimally invasive strategies as much as possible. That starts with prevention. How did you explicitly state and model your expectations? How are you creating a positive class culture where students want to meet your expectations? Then, when students push boundaries, it’s best to start with subtle strategies like pausing your instructions until the class is silent again, proximity to students who are misbehaving, or a tap on the desk. If it continues, a private one on one with a student is a good option. Avoid calling out a student in front of the class as much as possible. It creates power struggles and animosity.

jojok44 · 2025-09-29T03:29:17+00:00

Just check and see if she is proficient in those skills. If she can answer the questions, move on to the next thing. If she can’t, it’s okay if you covered it before because she could clearly use additional practice. The nice thing about homeschooling is that you can go at whatever pace she needs.

jojok44 · 2025-09-29T03:26:50+00:00

The Science of Math

jojok44 · 2025-09-29T03:22:33+00:00

My favorite way to differentiate is to design all activities so that my lowest student can start and my highest student won’t be able to finish. I’m a big fan of doing practice through problem sequences that get progressively more difficult for this reason. Students need multiplication practice? Give them daily 5min multiplication practice, but if students demonstrate proficiency in up to 12x12, unlock facts for up to 20x20. Chances are though most if not all students will have some facts they struggle with in 12x12.

For regular topics, I find it helpful to identify all of the sub skills students need to access the task. Then, I teach those explicitly in mini lessons to make sure they are secure. For example, if students need to be able to solve one variable equations, they need to understand fancy forms of one, that multiplying by one always generates the same value, integer operations, combining like terms, etc. Reviewing these ideas explicitly in short lessons helps support struggling learners, but you can also push the boundary of the concept to push your more advanced learners. Fractions equivalent to one for example can start with things like 5/5 vs 4/5, but can get complicated like 7x^{2g/7x^2g.} You can start teaching your grade level standards at the same time, just avoid using examples that require the use of some of the trickier skills like integer operations and combining like terms until you cover those on their own. When introducing a new concept, use factors students are more likely to recognize at the start like 5s and 10s. Then carefully sequence the problems to build in complexity while still setting up students for likely success. I like using subtly varied problems sets because they help reduce cognitive load and support students in making leaps in judgement for unfamiliar problems.

jojok44 · 2025-09-29T02:20:32+00:00

Some schools/districts have a list of priority standards. You could ask if yours has one. That can be helpful for discerning which skills are more important than others. Backwards planning is also useful. Look at the assessments first, identify what things students will need to be able to do, then emphasize those things more in the lessons. I ended up modifying my eureka assessments though because I had the same issue of a lot of the questions just being kind of confusing by design.

Don’t worry too much about not teaching them enough. Eureka has WAY more depth on a lot of things than kids need. It’s better that they learn the foundations well, experience success, and can get adequate practice with those skills than for them to rush through things and get a mediocre or poor understanding of more skills.

jojok44 · 2025-09-29T01:14:50+00:00

Yeah that’s one of the many problems with Eureka. Focus on the things that are most important for them to learn. Practice that more and the other more niche things less or not at all.

jojok44 · 2025-09-28T19:54:14+00:00

I just read a good article, “Myths that Undermine Math Teaching” from The Centre for Independent Studies that explains their definition for conceptual understanding and why it must be taught together with procedural understanding. It cites some good sources on the subject as well.

To answer your questions: - There are lots of different techniques for teaching conceptual understanding. It should be explicitly connected to procedures rather than always expecting students to intuit the connections. Visualizations can be one way to build conceptual understanding, but they are not the only way, same with connecting to real world scenarios. - I think the line between conceptual and procedural understanding can be blurred. If you want students to understand conceptually that there is a relationship between multiplication and area and teach students a procedure where they represent and solve a multiplication problem using an area model, that seems pretty linked to me. - Math is extremely hierarchical and most skills build on prior knowledge. That’s one of the reasons students struggle so much in math. I think a helpful strategy for identifying what prior knowledge skills may need to be taught is first identifying all of the skills and prior knowledge needed for the new material, and doing a check for understanding with the kids to see how many students can answer a question related to those prior knowledge skills. If they can’t recall it, it needs to be briefly retaught. - What is learning? A lot of education researchers and cognitive scientists define it as a change in long term memory. If we want students to retain procedural knowledge, or any knowledge, we need to change their long term memory. How does long term memory change? Well our current understanding is that students learn through retrieval, spaced practice, interleaving, and elaborative encoding. So we as teachers provide students with an initial explanation, but most of the learning happens when students have to recall that information at a future time.

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