Summer is on the horizon! *No more pencils, no more books! No more teachers dirty looks!* Even I am looking forward to not having to ask my oldest about homework, studying for tests, projects, etc. Time for relaxing by the pool, reading books, and just taking a break.

That being said, summer is a great time to build in some meaningful mathematics with your children. For the next few posts, we will explore ways you can integrate mathematics into your summer plans without making it feel like “school math”.

Jo Boaler, author of What’s Math Got To Do With It? Helping Children Learn To Love Their Least Favorite Subject, states that *one of the most parts of being mathematical is an action called reasoning. This involves explaining why something makes sense* (or doesn’t make sense)… This is one of the most important pieces of mathematics, and yet is one of the first teachers say is missing or lost in math programs. And it goes beyond simply asking, “Does your answer make sense?” A student who can reason mathematically realizes that

*mathematics is a subject that*(she)

*can have her own ideas about, a subject that can invoke different perspectives and methods, and a subject that is connected through organizing concepts and themes*. It is not a page of math problems a day or a lesson a day where it feels you are learning something new and different every day of the week.

How can we as parents help our children with reasoning? Make math meaningful in the home. Talk about how you use math in your day. Have your older children help make decisions, such as how much paint you need to buy for a room or how much weed killer you need to buy for your yard. Bake. Use real money (cash!) to purchase items so they get a feel for what money is (Great for addition/subtraction!). These are all ideas we will explore later…

My favorite way to get students engaged in reasoning is called, **“What’s Wrong With This?!!!”** All junior high kids like to express you are wrong. Why not use it to discuss math? Find advertisements, comments in media, or just conversations you hear that are mathematically unreasonable and have a conversation about why it is wrong. Then get them looking for mistakes as well. It is easy, it makes math interesting, and you are building reasoning skills in your children.

Here is a pic I took from down the road (of my school) when I was getting gas. So what’s wrong?

The amount advertised (I believe) is meant to represent 99 cents. Does it? You can show 99 cents as 99¢, showing that you could use 99 pennies, or as $0.99, representing that you have one less cent than the value of a dollar. **What does 0.99¢ mean? **It means you are paying less than one cent; less than a penny. You are paying 99/100 of a penny. Meaning, if I give the cashier a penny, he owes me some change!

Most students won’t see it. In fact, when I really started looking at their decimal work (applying to money) I realized at least 2-3 students per class EACH YEAR were making this same mistake. They weren’t connecting the relationship (and difference) between writing the value in dollars verses cents. They simply knew something about each, and jumbled it together, **WITHOUT MAKING SENSE**.

Why is this so important? Is it really worth knowing that 0.99¢ is wrong? Well, this idea that money can go “beyond cents” creeps up on us in different places. Take the marquis at a gas station.

Letting the fact that this marquis also indicates that I am paying $395 per gallon (Decimal, where are thou???)… $3.95 9/10? What does this mean? Can I pay the 9/10 of a penny? This is actually a great advertising tactic. It is found (See link below for a great article!) that more people will buy if you leave an amount at $0.99 rather than bumping up to the nearest dollar. Significantly more people will buy the $4.99 than the $5.00, because they relate the $4.99 as being closer to $4 than $5. Doesn’t make sense, but that is how we perceive it. So when looking for the cheapest gas, we would gladly take$ 2.19 9/10 versus $2.20, even though the $2.20 location is closer! Don’t believe me? Be mindful of how you choose prices for the next few weeks (And let your kids in on this great experience!) and if you are like me, you will be shocked at how true this is.

0.99% financing. Is that a lot? What if I am buying a car? Would I rather pay 1% financing or 0.99% financing? Why?

Well, this week the cents mistake came up again!

One of my students from last year emailed me this picture with the following message. *Hi Mrs. M! I have to tell you that I am ALWAYZ looking for math mistakes now. My mom doesn’t like when I call her out tho. I found this one and thought you would like to have it. I made my mom look at it and said they would have to give me change for my penny. She thought I was crazy! Ha ha. Thanks for making math fun. *

So whether you are out at the store, on vacation, or driving hundreds of miles, look for how math shapes our world. Is the math you are seeing making sense or are there mistakes in the reasoning? You will be surprised; **the more you make math meaningful, the more your kids will appreciate it.**

Want your child to read more about the money symbols (and why there isn’t a cent sign on the keyboard? Hmmm…), go here! http://www.charlieanderson.com/centsign.htm

For more information regarding the psychology of advertising dollars versus cents, go here! http://www.fastcompany.com/1826172/psychology-behind-sweet-spots-pricing

Love the idea of framing in a way of ‘spotting the math mistakes.’ Makes for a fun activity if you find a lot and just post it up and ask students if they see any mistakes. Awesome 🙂

Took the following picture the other day: https://goo.gl/t7DZWO

At first, just thought ‘oh you can only get 20% off the $100 so you only save $20’ but then realized it said you can ‘save $100’ and I thought ‘how much would you have to spend to get $100 of savings.’ Just finished up our percents unit but we’ll try it next year 🙂

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Please let me know how it goes in your class next year. Always wanting to learn more!

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