Search Results for: rectangles

Fraction Division via Rectangles

I appreciate Christopher Danielson’s post on common numerator fraction division because it’s important to examine how various algorithms work and how we can help our students become more flexible with their thinking. It’s not surprising that I teach fraction division using rectangles, and I really believe the kids seem to grasp it better because it’s visual. I’ll start with this problem: 3/4 […]

Posted in Course 1 (6th Grade Math) | Tagged , , , | 47 Responses

More Rectangles and One Good Read

I just started reading this book on Ramanujan, and I highly recommend it. Curmudgeon just posted this Painter’s Puzzle yesterday on Christmas Day — what a nice gift for us! A painting contractor knows that 12 painters could paint all of the school classrooms in 18 days. They begin painting. After 6 days of work, though, 4 people were added […]

Posted in Algebra, Problem Solving | Tagged , , , , , , , , | Leave a comment

Drawing Rectangles Instead of Writing Equations

I don’t see dead people but I see rectangles all the time. The first time I saw a multiplication fact, like 3 x 5, as a rectangular array was after I’d graduated from college. And because I was so very late to this game, I thought drawing rectangles must be how everyone else — at least math […]

Posted in General, Problem Solving | Tagged , , , , , , | 7 Responses

Common Denominator

I already wrote about dividing fractions here and here. I use the explanation of “dividing by one” to explain why 5/6 divided by 2/3 is the same as 5/6 times 3/2. But when I was asked recently about how the “common denominator” strategy worked, my muted response was, “Because it does.” I didn’t mean to […]

Posted in Course 1 (6th Grade Math) | Tagged , | 1 Response

Six Ways to See Visual Pattern #324

I know you weren’t asking, but I see n overlapping squares. — Hunter Patton (@professorpatton) November 12, 2019   What about you? How do you see the pattern in the tweet above growing? Please take a look before I completely ruin it for you. (So much for my rule of “never tell an answer.”)   […]

Posted in Course 1 (6th Grade Math), Course 2 (7th Grade Math), Math 8, Problem Solving | Tagged , , , , | 2 Responses

Green Olives

My 7th graders are working on “percentages of” problems currently, and late last night, I saw this problem on one of Don Steward’s handouts. There are 75 olives, 40% of which are green. I eat some of the green olives until 10% of the olives that remain are green. How many green olives did I […]

Posted in Algebra, Course 2 (7th Grade Math) | Tagged , , , | 11 Responses

Dividing Fractions

My 6th graders have been working with dividing fractions for the last two weeks. We explore these four ways, in this order: Number line Rectangles — I wrote about this here. Dividing by one Common denominator It’s completely intentional that we work with the number line and rectangles first. I want my kids to see the answer and that it should […]

Posted in Course 1 (6th Grade Math) | Tagged , , , | 10 Responses

A Book: Thinking Mathematically

I’m re-reading Thinking Mathematically, an assigned book from a math course I took years ago in Portland. I was teaching science at the time but signed up anyway because I’ve always loved math. Thinking is still so good and resonates much more now that I’ve been teaching mathematics. In the Introduction, under “How to use this […]

Posted in Problem Solving, Teaching | Tagged , , , , | 8 Responses

Four Square and Other Questions

One afternoon during recess I noticed that the Four Square grid at our school had been enlarged. Naturally I yelled out to the kids, “Hey kids, when did they make this larger? I wonder what percent increase this is. What do you think?” Taking a nanosecond pause from their game, they yelled out their estimates, anywhere from 50% to […]

Posted in Course 1 (6th Grade Math), Geometry | Tagged , , , , , , | 3 Responses

A Simpler Solution

I’m guessing this was about 5 years ago. I was at an all-day workshop when a high school math teacher, sitting next to me, asked about the PoW (from mathforum.org) that I had assigned to my students. I happened to have an extra copy in my backpack and gave it to her. Dad’s Cookies [Problem #2959] Dad bakes some […]

Posted in Problem Solving | Tagged , , , , , | 8 Responses