As I write this I am sitting on my porch basking in the spring sunshine. It is finals week at Aim Academy and all thoughts are turning to summer. I’ve posted before about avoiding the “summer slide effect” by keeping your brain mathematically active in the upcoming months. But with vacations, beach trips, and summer sports I decided to make it as easy as possible for you to incorporate some math into your summer routine…thus a new blog series on summer math 🙂
Today’s post is about a wonderful math game you can play any time of year but I have fond memories of whipping this out with my math club friends when the school year was over. It is a very simple premise. Using all of the numbers on the card and the operations addition, subtraction, multiplication and division you must find a way to get 24. Here is a level 1 card from the 24 website.
4+2 is 6. 3+1 is 4. 6*4=24 and voila! Pretty straightforward.
That is the easiest level, it can get far more challenging.
You can order the game or find out about the online app here.
Are you looking for some great math word problems to round out the school year? Or if you’re like me you view May as the time for engaging math projects that you can work on while basking in the sunshine. When I taught public school I always liked to end the year with real-world scenarios that helped us synthesize our knowledge. And home schooling is no different.
At Mathalicious you will find dozens of wonderful math lessons that are based on real-life situations. It is a subscription service but many of their lessons are free. I particularly loved the Fall of Javert which aligns perfectly with the quadratic functions my algebra 1 students were just studying.
Tutors are the go to option when a student is stuck, but it can be a wonderful or painful (and expensive!) experience. Having tutored for over a decade I want to share a few suggestions for creating a more effective experience.
1. Find someone who is a good fit. Admitting that you need help from a math tutor is often embarrassing for students and spending an hour working on math is challenging enough. It is even worse if they feel uncomfortable talking with their tutor, especially if they are intimidated and don’t want to open up about what confuses them. Involve your student in the process of picking a tutor, they might even suggest someone you didn’t expect.
2. Supply as much information as possible beforehand. Each session should be worth its weight in gold, wasted time means wasted money. Before the first session give the tutor copies of tests or an extra textbook if you have one. Be as clear as possible about your goals. Describe how the school year has gone, how your child has succeeded or struggled with math in the past, and why you decided to hire a tutor in the first place.
3. Create a plan and follow up. Work with the tutor to create a schedule and a tentative list of topics. There should be an agenda for each session and clear assignments for the student to complete afterwards. The best use of time is to have the student working on some of the math outside of the tutoring session. This also allows you to monitor their mastery of the material. After the tutoring session is over follow up and ask the tutor to keep you updated on progress.
Tutoring can be the turning point for many math students and if you follow these tips there is an even greater chance that it will be successful.
My first teaching experience in Philadelphia was summer school geometry, an intensive 5-week program for students who had failed the class previously. Two hours of geometry every day throughout July in a building with questionable air conditioning. My biggest challenge was keeping my students awake!
Although I don’t think that was a very positive experience for my students it does raise a good question about math in the summer. Our library is already promoting its reading programs and home school parents are assigning their kids summer reading lists so their brains don’t turn to mush. But what about math? If you take four months off from numbers completely it takes the whole month of September just to get back in the groove. Yet even as I write this post I can hear the voices of the unenthusiastic math students. Math in the summer? Noooooo!!!! What could be worse?
But it doesn’t have to be an agonizing 12-week calculus course with weekly quizzes and 50 practice problems a day. Here a three ways you could incorporate some math this summer:
Hire a tutor. The school year is winding down which naturally leads us to reflect on the year and evaluate the strengths and weaknesses of the year. If you’re looking back and math is the subject that fell to the bottom of the pile now is the time to address that. It is very tempting to sweep the problem under the rug especially since a student who struggled with math probably won’t be excited to continue it over the summer. But if you address the problem head on you will receive double the benefits. First, a tutor can go back over the material from the past year and fill in the gaps. Second, when your child starts school in the fall they won’t have experienced the “summer slide” effect. It will be fresh in their mind and that added boost can give them the confidence they need to start the upcoming year successfully. For more on finding an effective tutor see this post.
Study for the SATs. Suppose you had a great year in math, but you just don’t want to lose the momentum. Also, the upcoming school year might be packed with AP classes, a fall sport, or a lead role in the home school musical. Taking an SAT prep course in the summer addresses both of these issues. During the summer you can set aside one hour a day to work on problems (first thing in the morning I hope) and you’ll be able to thoroughly review everything before the test. No cramming needed. When September rolls around with research papers, lab reports, and week night activities you’ll be so thankful the SATs are already out of the way.
Start a math club. This can be an organized weekly meeting with other families or something you just do at home with siblings. I participated in one when I was in school (nerd alert!) and it was really fun. For me it wasn’t about the math, I was just excited to see my friends. We played math games (set, 24, petals around the rose). Keep the material lighter, work on logic puzzles and solve riddles. I’ve posted lots of fun word problems on my blog that generate discussions and fun to solve. Anything to help keep numbers in your mind.
There are many other ways you can incorporate a little math into your summer, but those suggestions should get you started. Grab your shades and some sunblock and challenge someone to a game of 24 🙂
When I was in college I learned that proving the Pythagorean theorem is a favorite hobby of mathematicians. There are dozens of proofs for the Pythagorean theorem, both geometric and algebraic. Even President Garfield discovered his own method.
My favorite proofs are visual because they really help students understand where the Pythagorean Theorem came from. And if they understand that they will be less likely to apply it to triangles that do not contain a right angle (a very common mistake!).
We’re talking about the Pythagorean Theorem today in my algebra class and I’m showing this video…a proof in 60 seconds. Pretty cool.
In my algebra class we are rapidly closing in on our final chapter of content and that means the cumulative final is just around the corner. Finals can be exceedingly stressful for students, suddenly they must recall all the information they learned throughout the whole year. But in my 8 years as a high school teacher I’ve become more and more convinced that a cumulative final is essential.
First, because it forces you to sit down and synthesize all the material you learned. Whether you noticed it or not all the different skills you learned are connected. And if you can recognize these connections you have a much better chance of remembering them long term. As you worked through your textbook chapter by chapter you were focused on the trees, now it is time to step back and see the forest.
Second, studying for a final isn’t just an opportunity to improve your math skills it is an wonderful time to improve your studying skills. In high school most finals are worth about 10% of your final grade, in college they can be worth up to 50%! Take advantage of a less stressful opportunity now to learn how to effectively study.
To help you with this I have attached a handout I use in my online classes. It is a worksheet they the students complete for each chapter we covered.
Print one out for each chapter and fill it out as you review the book, old homeworks, and most importantly your graded quizzes and tests. There aren’t right or wrong answers, the idea is that filling out the worksheet forces you to summarize the material. And then it serves a double purpose as a condensed study sheet for you. Pull them out to look over right before your final and even keep them in a safe place to look over when you are getting ready for your math class next year.
Ideally you could even complete these throughout the year each time your class finishes a chapter.
I also attached a sample of what the worksheet looks like filled out.
I found this site this morning on twitter and originally thought it was a very simple concept. Decide which number (or shape) doesn’t belong in the set. As simple as Sesame Street, right? Wrong! 30 minutes later I’m still staring at my computer screen telling myself I really need to get going on today’s to-do list…but…I…just…can’t…pull…myself…away. That’s when you know it is a great math problem, you want to procrastinate so you can work on it.
So here’s what makes it cool. There is no answer key and that is intentional. The idea isn’t to find the right answer, but to decide which number you think doesn’t belong and then be able to justify your answer. And to step up the cognitive thinking skills see if you can find a reason why each of the numbers doesn’t belong. For instance,…
43… it doesn’t belong because it is not a square number
16…doesn’t fit in because it is the only number that is even.
9…it is the only number whose digits do not add up to 7.
25…it is the only number that is divisible by 5. (and this one is bugging me, I feel like there should be a strong reason. Any ideas?)
That required some serious thinking and it is one of the simpler puzzles. It is so much harder to justify your answer than to just find the right one. You have to use good math vocabulary and answer the challenges of other students who disagree. This is why I love a good math argument when I am teaching.
Here is another puzzle to really get you thinking.