“Look, Patchett! You did math! And it’s correct!” one of my 9th grade students pipes up after I help with a homework question.
I roll my eyes when my students get excited because I did their grade level math. They act like I’m not able to do it! I tell them (often) that math was my second highest test score. I’m able to do it — it just doesn’t make my heart get all fluttery like reading does.
Today I want to focus on what I do to help kids who get butterlies of dread in their stomachs when it comes time to do math. Let’s talk math interventions!
Understanding the Pillars of Math
Let’s take math back to the basics. There are four pillars that mathematical learning stands on. They are Number Sense, Operational Sense, Proportional Reasoning and Alebgraic Thinking. But what exactly are these?
Number Sense
Understanding the amounts or quantity based on the symbol is number sense. This skill builds from being able to identify there are two people in a room, to counting to 100. From there it becomes the foundation to do fractions as the student realizes that eating two of the four squares of chocolate means they have eaten half of the candy bar. This skill is usually formed in the pre and primary grades and developed through all levels of math.
Operational Sense
The understanding of number systems (addiction, subtraction, multiplication, and division) and when to use them to solve a problem is having operational sense. Knowing to increase a number means using addition or multiplication, and decreasing a number means subtracting or dividing is a skill in this area. System fluency is built here. That fluency moves students out of calculation into problem solving. Core curriculum says that students should have these mastered by 5th grade. Middle school uses these systems in more complex manners.
Proportinal Reasoning
Proportinal reasoning is the foundational thinking that allows students to look at numbers in abstract ways. This is the skill of thinking about two quantities and how they are linked together. If something happens to one, how does it affect the other? Although this skill is usually seen as a middle school skill (used in fractions, decimals, measurement, graphing, and ratios), the foundations actaully begin in earlier grades.
Algebraic Thinking
Using patterns to understand complex problems and make predictions is the basis of algebraic thinking. Grades 4-9 focus on the skills of graphing, tables and charts to explain data, and solving algebraic problems.
Structured Intervention
There are three things I focus on during my 30 minute math lessons: fluency, skill practice, and journaling. In case you are wondering how this breaks down
Fluency: 5 minutes
Skill practice: 20 minutes
Journaling: 5 minutes
Sometimes I’m lucky and get to teach a longer block of instruction (like when I teach junior high instead of elementary). In those cases, I do three rotations:
Teacher Table: 20 minutes. Broken into 5 minutes fluency, 15 minutes skill practice.
Computer: 20 minutes. My school is currently curriculm based on the computer. This is a chance for them to work on missing assignments in the general education class or Math180.
Small Group: 20 minutes. This table is an activity that applies the skill we have been working on. If I’m lucky enough to have an aide, this is where they work. Sometimes I have task cards and sometimes it is a math game.
Fluency
When I teach my intervention classes, I like to start off with fluency drills. Automaticity in math facts means more energy spent on solving the problem and less on calculation. Plus, this is an easy thing to track so students see progress quickly.
One program I have found and love is Rocket Math. No, I’m not being paid to endorse them. I genuinely like their product and how affordable it is. I use the worksheets for a quick practice and 1 minute fluency timing. Each week the kids do a level up timing, and I record their score on their rocket. They get to see how their scores improve and I get to see what specific system skills they are missing.
When a kiddo needs more support, I turn to products that I sell. Yes, if you purchase these from me I do make a commission.
I’m sure you probably have seen the Learning Wrap-ups at some point in your education. They are like flash cards, but more interactive. I also have a 10 days to mastery book for the the four systems. The Wrap-ups come in the four systems, fractions, states and capitols, and music theory. You can check out my book store for the complete offering. Just the wrap-up sell for $9.99. A 10 Days to Mastery book sells for $4.99. A set of book and wrap-up is $14.99.
Learning Palette plays like a game and players self-correct once all of the pieces have been put into play. I’ve used it one-on-one as well as two against each other — one was the solids and the other was the holes. Competition is fierce, but when they get one wrong, I make them explain the reason they picked their answer and why the correct one is correct. These sets go from K-5th grade in math and pre-k to 3rd grade in language arts. The base sells for $14.99, a single set of 12 cards sells for $19.99, and a Complete grade set sells for $69.99. You can look over the sets online at my store.
Skill Practice
My groups are separated into ability groups based on a Math Inventory assessment the kids all take the first week of the month. This assessment shows them growth as they improve and tells me what areas of the core curriculm they are missing. Skill lessons are based on these holes in understanding.
I talk data with my students All! The! Time! Here is a copy of the data record sheet I have in the front of their binders. When we finish an assessment, I record their scores in my data binder and on their record sheet. This way they can see their progress and ask specific questions about their data.
In my classroom, I use the Scholastic Reading Inventory, Scholastic Math Inventory, easyCBM.com, and in class fluency and writing prompts for progress data. I like that all of the information is on one sheet and it makes it easier to report home with comparison data.
Journaling
Final step for the day is being able to journal the steps they took today in their learning. I fully subscribe to the school of thought that if you can explain it to someone younger, you have mastered the concept.
CREATE A MATH JOURNAL
Recommended Products
Here are some of my favorite math products from my business. Yes, I get paid commission if you purchase.
Illustrated Math Dictionary — one for elementary and one for upper grades. I love these because they explain the concept and have pictures! $12.99 plus tax and shipping each.
Understanding Mathematics is a fantastic book for those who want to undertand the stroy behind the math. Why did we start looking at mat in the first place, how were different things discovered. I personally love this entire series — written for kids but packed full of information even an adult can learn from! The books are $12.99 each plus tax and shipping.
For those just starting out with one-to-one correlation and symbol recognition, I highly recommend any of our 1001 Things to Spot books. Everything from farm animals, to vacations, to fairyland and pirates! I loved doing this with little man when he was in preschool, and he quickly started to recognize the number symbols. Books are $9.99 each plus tax and shipping.
Wipe-Clean books are another awesome tool to have. They are pretty independent work, but can also be done together. Our books go from beginners who are learning pen control all the way through intermediate skills like division and fractions. Prices range from $6.99 to $29.99 depending on the book, card pack, or set.
