You tried flashcards, timed tests, songs, even games and nothing is working. There are still some students in your class who are not mastering their multiplication facts. What do you do? What if we embrace the idea that students don’t need to be able to do 100 multiplication facts in under ten minutes to be …
What to do if they STILL don’t know their multiplication facts Read More »
If you want to avoid drilling students on multiplication facts, games are a great way to encourage fluency. In one study, researchers used multiplication games instead of worksheets or timed tests with third graders in a Title I school. At the end of the school year, students were tested on 100 multiplication facts. All the …
3 games to help students master multiplication facts Read More »
I hear a variation on the following question almost every time I talk with middle school teachers: How am I supposed to teach ratios (or algebra or operations with signed numbers or …) when my students don’t even know their multiplication facts? Yes. There are middle school students who don’t know their multiplication facts. I …
Recently, I’ve been investigating Realistic Math Education (RME). I like the idea of building on what is real to the student. Because I spend a lot of time thinking about fractions, I wanted to know how RME approaches them. Luckily, Streefland wrote about his three-year teaching experiment in the Netherlands. In the experiment, students were introduced to the “Fractured …
Dan Meyer recently posted about how students aren’t easily fooled by attempts to make make tasks “real world” by placing a photo next to them. I found myself nodding along at what he described. I once naively asked a fourth grade class to write real world problems about fractions and received the following response: The …
Realistic Math Education: Defining the “real” in real world Read More »
One of the most important things students need to understand to reason proportionally is the difference between comparing two quantities in relative (multiplicative) versus absolute (additive) terms. Students often struggle with making the move to thinking multiplicatively. How can we begin to help them make this transition? The research suggests one way: Make the two …
Another way to introduce ratios: develop relative thinking Read More »
As I’ve mentioned before, proportional reasoning is complicated. Researchers refer to it as a “watershed” concept because of its role as both the capstone of K-8 mathematics and the cornerstone of high school mathematics. How do we begin to tackle such a complex concept? One of the most important things students need to understand in order …
Proportional Reasoning: Absolute vs. Relative Thinking Read More »
We know that students struggle with understanding ratios and reasoning proportionally. The cross-multiply algorithm doesn’t make sense to them. What can we do to help ratios make sense to students? Whenever I’m thinking of how to introduce a new concept, I like to start by thinking about what students already know that can be built …
One way to introduce ratios so they make sense to students Read More »
At a workshop last week, the following task caused a bit of confusion: If a small gear has 8 teeth and the big gear has 12 teeth and the small gear turns 96 times, how many times will the big gear turn? Several participants were convinced it was 144. As we discussed the problem, it …
Teaching proportions: Hold off on the cross-multiply algorithm Read More »
Student mistakes are important. It’s important to know what mistakes students make and why they make those mistakes. For example, last time, we looked at why simplifying expressions isn’t so simple for students and why they tend to make mistakes like 2a +5b=7ab. When we can anticipate what mistakes students commonly make and why they make them, …
5 ways to make simplifying expressions make sense Read More »