Math Mammoth in particular has really excellent supplemental texts:
www.mathmammoth.com/blue-series
and I've successfully used RightStart's fraction work for several years (excellent manipulatives):
rightstartmath.com/shop/rightst...
enjoyed this post from @dylanpkane.bsky.social about the problem of insufficient practice. h/t to @michaelt1979.bsky.social 's server for alerting me to it.
This is one reason why I like using tech, for that unlimited practice. Another option is to buy supplemental curriculum, which I do.
If you repeat this process out to four decimal digits, you can get all the way to the thousandths place, which is good enough for most purposes.
After we learned this, I taught them how to use interpolation to find the roots of decimal numbers and larger numbers. Because why not?
Let's take that average again, (5.2 + 5.19)/2 = 5.195
27 ÷ 5.195 = 5.197
This is good! We have the same digits to the hundredths place. Let's square 5.19, to test. We get 26.936, which rounds nicely to 27.
We can say that the approximate square root of 27 to the hundredths place is 5.19.
27 ÷ 5.3 is 5.09 and change. We can round that to 5.1
Our answer was pretty bad! But it gives us a place to start. Let's average our prior estimate, 5.3, with our current quotient, 5.1. That gives us 5.2
Again, let's test this. 27 ÷ 5.2 is 5.19 Not exactly the same, but close. We can do better.
Therefore, the first digit of our answer will be 5. What about the rest?
We need an estimate of how far 27 is from 25 (2) and how far it is from 36 (9). 25 to 36 is 11.
So, 2 steps out of 11 steps is about 1/4 of the way there. We can use .3 as a decimal equivalent.
Let's test it!
First, learn your perfect squares. 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9
Second, choose a square root. Let's say, for the sake of this, we choose the square root of 27.
Now, we know that the perfect square 25 is the closest on the smaller side and the perfect square 36 is the closest on the larger side.
I'm having fun teaching my pre-algebra students how to calculate square roots by hand.
Why are we doing this? It's good number sense!
In case you don't know how, here are the steps:
Well-Trained Mind Academy Pre-Algebra (traditional Dolciani style) Integers, equations, graphing, roots, and more There were forty-five seats available and there are now 18 seats available. It runs from August 10, 2026 to May 14, 2027. Monday/Wednesday 11am and 1pm, Tuesday/Thursday 10am. New York City timezone. Suitable for students working at the 7th grade level/lower Key Stage 3. Mrs. Courtney Ostaff, Instructor. Registration Open Now. www.wtmacademy.com
Come learn with me!
In Morgantown, Courtney Ostaff pays about $100 a month for cable-based internet service. But, she still worries about outages, impacting her remote job.
mountainstatespotlight.org/2026/01/25/b...
I asked my oldest students to do a project of their choice to explore a concept from the semester as their final assessment. I got some thoughtful, amazing art and research in response! I have the best students!
One of the neat things about teaching is that I get to explain lots of things. For example, today I am explaining the CNO process in nuclear fusion in the heart of stars, how to create the three basic shapes through geometric construction, and the concept of scientific notation.
I have so much fun with my classes. This morning, my astro lab students calculated the mass of the supermassive black hole at the center of the galaxy. So cool!
Did the Unit 2 test (integers, exponents (pos, neg, etc)) and got 80% of students passing with an 80% or better, and that is DEEPLY satisfying.
I get to talk about the theory of special relativity this week and class and honestly it's my favorite topic all week!
One of the parts of teaching I most enjoy is a weekly selection of an example of the excellent work that my students are doing and asking parental permission to share it. Reminds me that my work matters, and that I can share that joy with my students and their parents.
Screencaps of a series of videos I'm recording for my math classes I'm teaching. Video 1: All About Al - Math in Society - 8:23 Video 2: All About Al - Math in Society - What are Neural Networks? - 14:14 Video 3: All About Al - Math in Society - Training Neural Networks - 14:08
Pleased with this series I'm working on:
Collins termed "the Stockdale Paradox." As Collins described, drawing upon Stockdale's experiences as a prisoner-of-war: You must maintain unwavering faith that you can and will prevail in the end, regardless of the difficulties, and at the same time, have the discipline to confront the most brutal facts of your current reality, whatever they might be.
Enjoyed this from Michele Caracappa during my morning coffee:
michelecaracappa.substack.com/p/a-new-scho...
Thank you! And yes, I’d take that in a heartbeat 😂
First day of class! No matter how many times I’ve done this, I always get a few jitters!
INTEGERS, EQUATIONS, GRAPHING, ROOTS AND MORE PRE-ALGEBRA REGISTRATION OPEN NOW traditional Dolciani style 7 seats available August 12, 2025-May 16, 2026 - Monday/Wednesday 12pm Eastern (New York City) time - Monday/Wednesday 1pm Eastern (New York City) time - Tuesday/Thursday 10am Eastern (New York City) time www.wtmacademy.com
Four More Weeks
DECIMALS TO THE PYTHAGOREAN THEOREM MATH FUNDAMENTALS formerly prep for pre-algebra 4 seats available August 12, 2025 to May 16, 2026 Tuesday/Thursday 12 pm Eastern suitable for students working at the 4th-6th grade level / Upper Key Stage 2 Mrs Courtney Ostaff instructor registration open now www.wtmacademy.com homeschool afterschool private school public school students all welcome WTMA is a an approved course vendor with many states
I've got some space left. Take care of next school year's math now and enjoy your summer break without having to think about it. I say this every year, but it's true—I have the kindest, hardest working students. Have your student join them and get ready for Algebra!
If we leave the acquisition of morphological knowledge to children's reading, what information is there in books to be acquired? @kathyrastle.bsky.social has answers (open). www.nature.com/articles/s41...
Wrote about my problems with that World Bank "ai tutoring" study. pershmail.substack.com/p/ai-is-mayb...
Running my end of year stats for my largest math class, and I'm feeling pretty good:
- 80%+ made an 80% or above
- 89% completion ratio
- for the first time ever, every single student who stuck with it passed the class
Well-Trained Mind Academy Registration Open Math Fundamentals (former Prep for Pre-Algebra) 5 seats available August 12, 2025 - May 16, 2026 Tuesday/Thursday 12pm Eastern suitable for students working at the 4th-6th grade level / Upper Key Stage 2 Mrs. Courtney Ostaff, Instructor www.wtmacademy.com
WTMA is a WV HOPE Scholarship vendor! Have your student come learn with me: we go from decimals, fractions, and percents all the way to the Pythagorean theorem. Only five seats left for the August start.
a picture of a 1950s era passenger train with West Virginia Central written on the side
Took my youngest to the Ramp and Rails festival (the indigenous allium and a tourist train ride in Elkins, WV), and snagged the last couple of seats on the train.
