Asking students to solve problems mentally, without paper and pencil, is always revealing and often surprising. I thought that asking students to solve 100 ÷ 3 would be sort of a slam dunk. My, was I wrong!
I just learned about Factors and Multiples, a shelter-at-home game that’s engaging as solitaire and can be played as a two-person game either cooperatively or competitively. (I’ve played it both ways.) It’s intriguing for both adults and kids (as long as players know about factors and multiples of numbers up to 100). It’s a keeper.
Good Questions for Math Teaching is a Math Solutions book that has long been one of my favorites. It’s a resource that I dip into when I feel the need for something fresh. And it speaks directly to our current shelter-in-place coronavirus crisis as many of us look for ways to mathematically engage students online, children at home, or both. Here are samples to get you started. I’ll continue to post more ideas on Twitter (@mburnsmath).
I’m a huge fan of math games, especially when they involve both strategic thinking and luck. And I’m always on the search for games that work with a span of grade levels. The Two-Dice Sums Game fits both. Learn about the game and read the letters of advice that 7th graders wrote to 2nd graders.
Last year, I agreed to meet with a friend’s sixth-grade son. Oscar’s math teacher had raised an alarm for my friend and her husband about Oscar’s math progress. They were shocked. Oscar did his homework and was proficient with paper-and-pencil math. What was the problem?
Have you ever asked students to solve 12.6 x 10, and they respond that the answer is 12.60? I have, many times. Students who do this apply a pattern that works when they multiply whole numbers by 10—they tack on a zero to the end of the number they’re multiplying. But then they apply the same pattern when working with decimals. What can we do?
When teaching students to add decimals, I wind up reminding students to “line up the decimal points.” This makes sense to some students while others follow the rule without understanding. How can we teach adding decimals to develop understanding and skill? Here’s a possible suggestion: Give the correct answer up front.
I believe strongly that mistakes are learning opportunities. At least that’s what I regularly tell students. But it sometimes feels different when the mistakes are mine . . . and especially when they are pedagogical mistakes that I make while teaching. That happened to me recently when teaching a lesson to fourth graders.
I love Twitter. On November 3, 2017, I saw this image in a Tweet posted by @MarkChubb3. The image stuck with me for several days. After talking about it over dinner with a teacher friend, and then again over lunch with another, I became curious to find out what students might think. I made arrangements to “borrow” three fifth-grade classes and made plans to teach the same lesson in each class.
A friend and I were talking recently about how much work we put into planning lessons. Even after all these years of teaching, I have to think through lessons as carefully as possible, both about the logistics and about the mathematical thinking I want to keep in mind and support. Here’s an example.
The card game Oh No! 99! is a keeper! It gives practice with mentally adding one- and two-digit numbers and with adding and subtracting 10 from two-digit numbers. The game encourages strategic thinking as students decide which cards to play and which to keep, and it’s also useful as an informal assessment. Read about how the game was used with second and fifth graders.
The children's book 17 Kings and 42 Elephants by Margaret Mahy is one of my long-time favorites. In this post I describe a division lesson that I’ve taught to third graders but recently revisited with fourth- and fifth-grade classes. With the older students, we tried extensions that differentiated the experience and put students in charge of deciding on problems for themselves. It was exciting to me to expand a lesson I've taught many times into a multi-day investigation.
Will Multiplication Bingo guarantee that students learn the multiplication facts? No. But it will help familiarize them with factors and multiples, engage them in a game that involves both luck and strategy, encourage them to make conjectures, and have them use data to guide decisions. Plus, the game provides a way to send home information to families about how their children are being asked to think and reason in math class.
Lessons using beans and scoops have long been part of my teaching repertoire. I’ve used beans, scoops, and jars to engage students in all grade levels with a variety of mathematical ideas. In this post, I write about how I recently taught a lesson to give students experience with estimation, averages, multiplication, and more. Read about how I planned the lesson, how it unfolded, and suggestions for extensions and other lessons.
When should a teacher resolve a question for students and when is it OK, or even a better instructional decision, to let confusion ride? I recently was confronted with this situation with fourth graders. Read about what happened and what I did.
Teachers have always told me that paper-and-pencil subtraction when problems call for regrouping is hard to teach and hard for students to learn. Much harder than addition. So why subtract when you can always add? That’s what my friend Nicholas thought, and he taught me how.
I was recently planning to teach my friend Ruth Cossey’s elementary math methods class at Mills College in Oakland, California. Digging through my collection of student work, I found a paper from a third grader I had interviewed. When doing interviews, I typically ask students to figure out answers in their heads, but I agreed when Nomar asked for paper and pencil for some of the problems.
I like the multiplication game of Pathways. It engages students’ interest, helps develop their familiarity with the times table, and encourages them to think strategically. It's been a part of my teaching for a long time. Recently I came up with a way to introduce the game that made it easier for students to learn to play. It was a huge success. Read about what I did and how the students reacted.
Place value is one of the most important foundational concepts about our number system. Watch my assessment interviews of second graders and learn how you can find out what your students understand about place value.
Students begin learning about the equal sign in the early grades, and Quack and Count by Keith Baker is a terrific children’s book for helping with this in kindergarten and grade 1. It’s one of my favorite children’s books for teaching math. (Yes, yes, I know I have lots of favorites.) Here I describe the lesson I taught and what occurred.