Yes those are really valuable! I mix in a lot of those as I teach a bunch of equation solving, but on a more piecemeal basis. Would be interesting to make another set of practice handouts for those types of variations.
Yes they definitely can. Something I'm perpetually conflicted about is that most teachers I know dislike anything that feels like a worksheet. Stuff like this is easy to misuse: you print it, put it in front of kids, and call it a day. That's not going to do much work on the conceptual side. So I get the issues with worksheets. But the reality is, in whole-class instruction, with kids at a range of levels, we need a significant amount of practice. If you're allergic to worksheets that practice becomes easy to overlook, but worksheets are easy to misuse. No easy solution.
Thank you for sharing! I started following you after reading your first post about incremental fact fluency. I was intrigued by it, but so far, have had trouble finding time for it. After doing a small amount of work around multiplication facts at the end of the year, I have committed to start next year more intentionally. I appreciate your thoughts on the timing debate. I share your concerns that timing may actually limit practice for those who need it most. I think it can also lead to students to employ strategies that improve their speed without improving their fact knowledge (writing more quickly, doing the easy problems first, etc.) I did a research study on the effectiveness of timed math fact tests over 20 years ago. Perhaps one day I will share more about it in detail, but one of the most interesting findings was that the timed math fact tests often painted an inaccurate or incomplete picture of students' actual fact knowledge. For both the pre and post tests, I gave students a timed fact assessment. However, I also assessed students individually using flash cards (Scores were based on number correct in less than 3 seconds per fact). There was a surprising lack of correlation between students' scores on these two assessments.
That's interesting! While I don't have that experience, I have definitely seen proficiency levels vary from one context to another. Finding time is a real challenge and means accepting some tradeoffs, but I just think there's no way around it. Either fact fluency is important or it's not, and if it's important there are no shortcuts. This is where some thoughtful coordination between grades can be really helpful though, prioritizing fluency with different operations in different grades and dividing up the work so it's more manageable. That's not the case where I work now but I can imagine it would be really helpful.
Thanks for sharing all the resources! I would love to have our 6th and 7th grade teachers use these.
Excellent resource thank you. Would you also consider ____= 6 + 1? To develop flexibility around the concept of =? and 6 + ___ = 7 variations?
Yes those are really valuable! I mix in a lot of those as I teach a bunch of equation solving, but on a more piecemeal basis. Would be interesting to make another set of practice handouts for those types of variations.
What I like about this is the thought put into structure and sequencing. Worksheets can have a hidden conceptual agenda, so to speak.
Yes they definitely can. Something I'm perpetually conflicted about is that most teachers I know dislike anything that feels like a worksheet. Stuff like this is easy to misuse: you print it, put it in front of kids, and call it a day. That's not going to do much work on the conceptual side. So I get the issues with worksheets. But the reality is, in whole-class instruction, with kids at a range of levels, we need a significant amount of practice. If you're allergic to worksheets that practice becomes easy to overlook, but worksheets are easy to misuse. No easy solution.
Thank you for sharing! I started following you after reading your first post about incremental fact fluency. I was intrigued by it, but so far, have had trouble finding time for it. After doing a small amount of work around multiplication facts at the end of the year, I have committed to start next year more intentionally. I appreciate your thoughts on the timing debate. I share your concerns that timing may actually limit practice for those who need it most. I think it can also lead to students to employ strategies that improve their speed without improving their fact knowledge (writing more quickly, doing the easy problems first, etc.) I did a research study on the effectiveness of timed math fact tests over 20 years ago. Perhaps one day I will share more about it in detail, but one of the most interesting findings was that the timed math fact tests often painted an inaccurate or incomplete picture of students' actual fact knowledge. For both the pre and post tests, I gave students a timed fact assessment. However, I also assessed students individually using flash cards (Scores were based on number correct in less than 3 seconds per fact). There was a surprising lack of correlation between students' scores on these two assessments.
That's interesting! While I don't have that experience, I have definitely seen proficiency levels vary from one context to another. Finding time is a real challenge and means accepting some tradeoffs, but I just think there's no way around it. Either fact fluency is important or it's not, and if it's important there are no shortcuts. This is where some thoughtful coordination between grades can be really helpful though, prioritizing fluency with different operations in different grades and dividing up the work so it's more manageable. That's not the case where I work now but I can imagine it would be really helpful.