I don’t know about everyone else, but by the time November rolls around, I’m ready to cuddle up in my house and focus internally for a while. That doesn’t mean that I forget about my friends or never set foot in my front yard. But I do tend to be drawn to little crafts and DIY projects.
So all month, I’m going to share some ways that I feather my nest before launching into full holiday mode in December. Of course all of these ideas and projects will have some kind of math angle to them — because if you haven’t figured it out yet, math is everywhere!
I thought I’d start out today showing you how I combine geometry and my crochet needle.
This time of year, I love to crochet. Not only is it a great way to pass the time indoors, but as I crochet a blanket, it warms up my lap! There’s lots and lots of counting involved, but I’m a sloppy and lazy crocheter. So instead of counting rows, I depend on geometry to help me figure out how close I am to being finished.
This little trick is pretty much how carpenters can tell if their walls are square. But with fibers–yarn or fabric–it’s even easier, because all you have to do is fold. (Folding a deck is darned near impossible.)
Usually the little dishtowels I make are squares. I don’t use a pattern, so to check my progress I fold the top edge to meet one of the side edges. If I get a perfect triangle, I have a square.
This dishtowel is a square. (Okay, cut me a little slack — it’s been used and washed a few times!)
Ta-da! When I folded the bottom edge to meet the right edge, I get a (somewhat) perfect triangle.
But if I fold along the diagonal and I don’t get a triangle, I know the dishtowel is rectangular.
This dishtowel is a rectangle. (Sort of.)
See! When you try to make a triangle, the edges don’t match up.
Why does this work this way? Basically, it comes down to the Pythagorean Theorem, but in all honesty, you don’t need to know that. Just remember that if you fold a square along its diagonal, you’ll get a right triangle with two equal sides.
How has your basic understanding of geometry helped you with a project? Share your story in the comments section.
And come back tomorrow for a special edition of Math at Work and on Friday for a great nesting project that will put you in the giving mood!
There. I said it. And I think some of you feel the same way. I don’t blame you.
While I think we’ve gotten off to a good start here at Math for Grownups, I also think it’s time to shake things up. There are so many more opportunities to show you how you use math in everyday life — and perhaps teach you some new tricks.
So starting on November 2, there are going to be some changes around here. Good changes.
I’m keeping what’s working (Math at Work Monday) and chucking what isn’t (Film Friday). I’m also shifting my posting schedule a little. Instead of posting on Mondays, Thursdays and Fridays, I’ll post on Mondays, Wednesdays and Fridays.
Plus, I’m introducing monthly themes. Not only will this help me come up with great, timely ideas, but it’ll also tap into things that you are probably already wondering about. Here’s a taste:
November is for Nesting: As the seasons change (for some of us), we turn our thoughts to cozying up our home and spending time with family.
December is for Holidays: Whether you celebrate religious or secular holidays, there’s a festive buzz in the air.
January is for Resolutions: Even if you don’t make New Year’s resolutions, starting something fresh is probably on your mind.
You can still visit on Mondays to see how ordinary folks use ordinary math in their ordinary jobs. But now my interviews will follow that month’s theme. So in November, you can expect to meet folks who help you transition into winter or focus more on home: a radiator technician, a landscaper, a fabric designer and a chef.
On Wednesdays, I’ll post about the math used in these fields. For example, I may teach you how to figure out if your heating bill is accurate or show you the math of winterizing your windows. Or I may investigate how ratios are used by chefs.
And on Fridays, I’ll be scouring the internet and my brain for projects. I might show you how to build radiator covers or sew new curtains or how to be sure the turkey comes out of the oven perfectly cooked. Of course these projects will involve a little math.
Oh, and in November or December, I’ll roll out a new design for the blog. Yay!
This is your chance to make requests. (Okay, it’s not your only chance. You can always tell me what you think.) If you’ve been waiting to see a job profiled or learn about something that’s always bugged you, post in the comments section. These can be monthly theme ideas, projects or general math concepts that you’d like me to illuminate for you. I promise I’ll take everyone’s thoughts into consideration.
And I’m always looking for folks to interview for Math at Work Mondays. Right now, I’m on the prowl for a chef, a landscaper and a candle maker. (Not a butcher, a baker, a candlestick maker — but pretty darned close!) Feel free to email me with your ideas or post in the comments section.
Raise your hand if you’ve heard of M.C. Escher. Now raise your hand if you know what tessellations are.
Surprise! If you know of M.S. Escher’s work, you are also familiar with tessellations — even if you don’t recognize the term. In fact, if you have or have seen a tiled floor, tessellations are familiar to you.
A tessellation is a pattern of identical, interlocking shapes. There can be no space between the shapes and none of the shapes can overlap. Escher created complex tessellations of birds, lizards and fish. But even simple, square tiles are tessellations.
This video shows how they are made. Don’t watch it expecting a tutorial. Just look at how the shapes are formed and then replicated and rotated to form the tessellation. A design like this one is pretty complex, but it’s interesting to see it in motion.
(There is no sound with this video, so there’s no need to crank up your speakers.)
Bonus! I found this really great video that shows how to make a tessellation. Check it out.
Where have you seen tessellations? When do you think they’re useful or interesting to see? Leave your comment!
Two things you should know: First off, I once worked in the marketing and public relations department at Virginia Stage Company, an Equity theatre. Second, I love to sew (and don’t have enough time these days to delve into my stash of fabric). So, I am absolutely thrilled to welcome Katie Curry to Math for Grownups today. As a costume designer and technician, she’s worked forthe Berry College Theatre Company and the Atlanta Shakespeare Festival. She recently started her own venture called Nancy Raygun Costuming that caters to folks who are into cosplayand conventions or just want a fun costume.
What do you do for a living?
I design and build costumes for theatre productions as well as make custom clothing for individuals. I sketch my ideas and then make them into real pieces for people to wear.
When do you use basic math in your job?
I use basic math every time I sit down to work. Sewing is full of fractions — the standard seam allowance is 5/8 of an inch — and drafting costume pieces is all about angles where different pieces meet. It would slow me down a whole lot if I couldn’t add and subtract fractions as I go.
Do you use any technology to help with this math?
Most of the time I just end up using the calculator on my phone or just old school pencil and paper when I’m figuring out how much I need to take in a garment or that kind of thing. There are a number of computer-assisted drafting programs that can come in handy when it comes to design, but since I’m just getting started I don’t have all the fun toys that a lot of designers do. So for now, just a calculator and some brain power.
How do you think math helps you do your job better?
From Eurydice, a play by Sarah Ruhl, at the Berry College Theatre Company in 2010.
With just the actor’s measurements, you can draft costume pieces just using a little math. That means, you don’t have to go through the tons of fittings to drape a pair of pants. Just put the measurements into a series of equations, and you get the exact lengths and angles that you need to draw in order to start construction.
How comfortable with math do you feel?
I am in no way comfortable with math. I have never been the type who could make sense out of a lot of numbers, so I was pretty bummed when I walked into my first costuming classes and was immediately handed a ruler. It took me a while to warm up to the idea that I would be doing math regularly, when all I wanted to do was make costume pieces. But once you see the end results of a long drafting session, everything starts to make a lot more sense. I don’t feel incredibly comfortable with a lot of other math outside of my profession, though. I can do basic things like balance my checkbook, but don’t ask me complicated things about statistics unless you just want a blank stare.
What kind of math did you take in high school?
In high school I took the simplest math I could get away with. I’ve taken algebra I and II, geometry and statistics and I’ve disliked every one of them. If I brought home a B in an English class it was a travesty, but if I brought home a C+ in a math class the sentiment was, “All you have to do is try your best and somehow manage to pass.” I am in no way a math-minded individual, so I’ve always tried to avoid doing it as much as I can.
From The Beaux’ Stratagem, by George Farquhar, at the Berry College Theatre Company in 2010.
Did you have to learn new skills in order to do this math for your job?
I definitely had to learn new skills for building costumes. Costume drafting isn’t exactly something that gets covered in high school math classes, so there were a lot of equations and fractions that I was unfamiliar with that I needed to get very comfortable around. Despite the fact that I’d taken classes that were fraction heavy, I’d never actually had to use them on a daily basis until I started sewing every day.
Do you have questions for Katie? (Do you need a costume?) Ask them in the comments section, and she’ll come by sometime to respond.
Earlier this week, I provided a guest post about math anxiety and kids for Imp3rfect Mom. I wasn’t surprised to get a comment from a reader asking about how to deal with her math anxiety.
My son is an adult so my question concerns me. I’m almost 60 and I’ve been mathphobic (big time) since I was in 6th grade. At that point math just crashed and burned for me and I struggled for the rest of school. Now I am self studying for a designation related to my job (the job itself doesn’t require math ability) but I have to learn some equations for the Time Value of Money for the last exam. I look at that chapter and just freeze. I actually am telling myself “well, if I just skip that part and study real hard, I’ll still pass the test.” This is ridiculous! How do I conquer 50 years of Fear of Math?
I’m sure you can hear the frustration in her writing. (Do you ever feel the same way?) I anxious about certain things–making difficult phone calls, traveling to places where English is not the predominant language, or asking someone for help when I’m lost. (That last one is so silly, isn’t it?)
I’ve talked about the roots of math anxiety–the insistance that the goal is the right answer, timed calculations and an expectation of perfection–but now it’s time to share some ways to cope.
Allow yourself to fail. This is not so easy when you’re dealing with your finances or preparing to take a test. But when you’re learning (or relearning) something, you will make mistakes. Heck, even when you have something down cold, you can screw up. If you’re feeling anxious about math, set up low-stakes scenarios when failure isn’t a big deal. Try things on your own, for example, and allow someone you trust to check your work.
Ask yourself, “How hard can it be?” I’ve said this before, if I can do this stuff, so can you. I don’t have the typical “math brain.” I can’t do mental calculations, and sometimes I forget really basic facts like 6 x 7. And believe me, if a fourth grader can do these tasks, so can you.
Make it fun. I swear, I’m not violating math secret #3 (You Can Skip the Love). You don’t have to have fun or love math to be good at it. Still, if you’ve read my book, you know what I mean. Too often, math is cut-and-dry, boring numbers. When it’s presented or explored using real-world stories with funny characters, it’s a lot more tolerable. So, whether you’re studying for a test or trying to explain a concept to your kid, try making up problems using Sesame Street characters or your crazy Aunt Miriam who has 76 cats and wears a fedora. The sillier the better.
Find resources that work for you. I’m a big DIYer. And everything I know about sewing, painting, renovations and carpentry, I learned from Google. I promise. Besides my book, there are amazing resources out there for folks who need a little refresher. You can even find videos on YouTube or Flickr tutorials. But be careful: sometimes mathematicians think they’re being really helpful, when they’re not. Don’t let yourself be overwhelmed by minute details or unrelated tangents. Click through these resources quickly until you find what you need.
Trust your gut. Just because a textbook or a friend has the information you need, doesn’t mean you need to follow that advice or process. This is the beauty of being a grownup–we don’t have to follow the rules that a teacher sets out for us. Think about when you feel comfortable with math. Is it in the kitchen? When you’re gardening? When you’re doing your budget? What is it about that process that is less threatening? Use what you know about yourself–and your learning style–to step into these other, scary places.
So I’d love to hear from you now. What tricks have you used to conquer your anxiety or fear–about anything? If you have dealt with math anxiety in the past, what has helped? Share your ideas in the comments section.
You probably find it pretty darned easy to encourage literacy. In fact, there are countless magazine articles and books and workshops out there on this very subject. And so all good parents read to their kids every night, play word games with them, give them magnetic letters for the fridge.
But what about math? If you’re like most parents, the idea of working math into the day probably seems down right daunting. Scary even.
It’s not as hard as you think, especially if you’re willing to give into your children’s demands for a regular allowance. Money is an instant math lesson—and can motivate even the most reluctant student (adult or child).
Would you like me to guest post at your blog? Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest. I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow. Get the details here.
So you think you don’t use math on a daily basis? Think again.
You may not be solving for x, and the distance formula may not roll off the tip of your frontal lobe—mainly because you haven’t used it in years and years. But if you can put “parent” among your titles, you do math. I promise.
Just look at a typical day:
Read the rest of my guest post at Math is Not a Four Letter Word. You might be surprised by how much math the average parent does in a day!
By the way, would you like me to guest post at your blog? Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest. I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow. Get the details here.
Boy, do I remember those early days of parenting my daughter. I was working full time, coddling a strong-willed toddler, trying to serve balanced meals, selecting great books to read to her and trying to keep my house and yard clean enough that my neighbors wouldn’t call Child Protective Services on me.
Adding one more thing to the list would have made my head blow off of my shoulders.
And yet, today, we are being asked to do that one more thing: introduce numeracy to our little Janes and Johns. In other words, math.
Want some tips on how parents can develop numeracy in their little kids–and keep their own heads on their shoulders, right where they belong? Read the rest of this post at Words To Eat By, where I guest posted today.
By the way, would you like me to guest post at your blog? Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest. I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow. Get the details here.
A pattern snippet from one of Marie Grace’s original designs.
If you don’t knit, a knitwear pattern probably looks like a random selection of letters and numbers. But that special code actually reveals beautiful creations–sweaters, hats, booties and blankets. Marie Grace Smith is the founder ofMarie Grace Designs, and she lives these patterns. You might be surprised to learn how much math is involved in developing these patterns. Marie Grace was!
“If I had known how much math I would need to do to make a living playing with yarn I would have become a painter or something. Just kidding. Sort of.”
What does a children’s knitwear designer do? I design and write patterns for hand-knitting. I have my own pattern line and have had patterns published in various knitting magazines.
When do you use basic math in your job? I use math for almost every aspect of what I do. It takes a lot of math to get from an idea and a ball of yarn to a written pattern somebody else can follow to make a finished sweater (or hat, or blanket, etc…)
The first thing I have to do to work up a new design is figure out the stitch and row gauges–or the number of stitches and rows in an inch of knitting with the yarn I’ve chosen for the design. To do this, I knit a square and then measure it, dividing the width measurement by the number of stitches across and the length by the number of knit rows. This gives me the number of stitches per inch (stitch gauge) and the number of rows per inch (row gauge). Every measurement after this–chest width, sweater length, sleeve circumference–all must be converted from standard inch measurements to stitch and row gauge. That means lots of math. Additional things like fancy stitch patterns, button and buttonhole placement, and shaping for armholes and necklines mean even more math.
Maggie Knit Blouse, one of Marie Grace’s designs
Once I’ve worked out all the counts and directions for my sample sweater I also need to figure all those same counts and measurements for various other sizes of the same design… sometimes as many as 8 sizes total. That way when you buy one of my knitting patterns you can knit sizes 2, 6 or 10 and have all the accurate directions and counts needed for the final product to turn out just like my original design sample. I also include how much yarn you’ll need for any given size which means–you guessed it–even more math.
Along with all the design stuff, I also have all the same responsibilities as any other business owner as far as figuring my incoming and outgoing funds, expenses, and taxes. More math!
Do you use any technology to help with this math? Spreadsheets! Lots and lots of spreadsheets. I’m sort of a spreadsheet junkie. Most of the math I use is basic math, but its very repetitive so spreadsheets save lots of time and cut down on mistakes. It would take a ridiculous amount of time and effort to work up a new design from beginning to end if I didn’t have tools like spreadsheets.
How do you think math helps you do your job better? I couldn’t do my job with any sort of accuracy without math.
How comfortable with math do you feel? I’m relatively comfortable with day-to-day math but I wouldn’t say I’m good at it. I have to stop and think things through one step at a time and I often scribble things down on paper even for simple calculations, just to be sure I’m on the right track. I’m much more comfortable with the math I do for work, simply because its so repetitive. Its sort of like doing multiplication drills on a regular basis.
Marie Grace Smith
What kind of math did you take in high school? I went through Algebra, Geometry, Trigonometry, and Calculus by the time I was out of high school. I didn’t like math, and I don’t think I was naturally good at it. But I can figure things out given time and scrap paper. I think that’s how I managed through all the math in school.
Did you have to learn new skills in order to do this math? The math I do for designing is all pretty much basic math (addition, subtraction, multiplication, and division), along with some algebra and percentages. It’s all stuff we all learn in school.
Do you have questions for Marie Grace? Ask them in the comments section, and I’ll be sure that she sees them.
I’m still on my virtual book tour, visiting a variety of interesting spots all over the blogosphere! Due to a technical glitch, my scheduled podcast at Out of the Storm News is postponed to next week, but you can catch up on last week’s travels at these links:
Today, I’m visiting Frisco Kids, a blog written by my friend and fellow freelancer, Debbie Abrams Kaplan. She has posted a Q&A with me about Math for Grownups, and as well as my thoughts about kids and math. I hope you’ll visit and even post a comment!
By the way, would you like me to guest post at your blog? Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest. I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow. Get the details here.
Math for Grownups blog readers tend to fall into two camps: grownups who are not parents and really hate math (or think they’re not good at it), and parents who are worried that they’re going to pass along their math anxiety to their kids. And so I thought I’d spend a little bit of time addressing some of the concerns of these parents.
Earlier this week, my friend and fellow freelancer, Debbie Abrams Kaplan forwarded the summary of a new bit of research on kids and math. Debbie is the author of two great blogs: Jersey Kids and Frisco Kids, and she figured that I might find some blog fodder from this study.
Boy did I! A couple of things jumped out at me:
No one has ever studied how the basic math skills of first graders affect their later understanding of math throughout elementary school. (Compare that with the many studies of early reading skills, and this fact will blow your mind, too.)
There are three basic skills that will help first graders become good fifth-grade math students.
I’m going to tell you those skills a little later, but first I want to introduce the concept of numeracy. Quite simply, numeracy is the ability to work with and understand numbers. When children are young, numeracy includes the ability to count, recognize the symbols that we use for numbers (which is akin to learning the alphabet), and even do some very simple operations (like 1 + 1 = 2). For high school students, numeracy includes more complex problem solving skills and properties of real numbers.Among math educators, there are big debates about how we can better teach numeracy. I guess this is like the debates about phonics vs. context support methods in reading education. But now that this study is out, it’s clear parents can help lay a firm foundation for our kids’ later success in math. According to this study, published by a team of University of Missouri psychologists, rising first graders should understand:
Numbers — I’m going to take this to mean whole numbers, since most first graders aren’t very familiar with fractions or decimals.
The quantities that these numbers represent — In other words, kids should be able to match a number with that same number of objects (five fingers, two cats, etc.)
Low-level arithmetic — And I’m guessing researchers mean things like adding and subtracting numbers that are smaller than 10 (excepting problems with negative answers).
If you’re like most parents, this is probably a duh moment. What’s so hard about recognizing whole numbers or understanding what five objects are? But I don’t think many parents spend much time emphasizing these ideas — at least not in the way that we commit to reading to our children every night.So here are a few ways that you can help instill numeracy in your pre- or elementary-school aged children.
Count things. Count everything — like the stairs that your climbing or the cars that pass your house or blocks as you take them out of the box or those adorable little toes!
Have your child count things. You can do this in really simple ways. Ask him to get you five spoons so you can set the table. When she wants some goldfish, tell her she can have 10 (and watch her count them). When you’re planning his birthday party, have him tell you which 10 friends he wants to invite. (Write them down for him, so he has something visual to count.)
Notice numbers. When she’s really tiny, ask her to say the numbers that are on your mailbox or on a license plate. Older kids can name multi-digit numbers, like 157 or 81. (And if you want to really be precise and prep your kid for school, don’t say things like “one hundred and fifty-seven. In math, “and” represents a decimal point, which is something most elementary school teachers will really drive home.)
Teach your child to count backwards. This can be a great way for kids to start understanding subtraction. If you know you have 10 steps in your staircase, count backwards as you go down the stairs. Then count frontwards as you go up!
Start adding and subtracting. Give your child 5 raisins and show her how to “count up” to 7 by adding 2 raisins to the pile. Then as your child eats the raisins one by one, “count down” to find out how many are left.
You don’t need to make a big deal about math. And for goodness sakes, skip the worksheets, flashcards and even video games — unless your kid really loves them. Integrate these basic skills into your daily life, and you’ll see your child’s understanding grow. (And you probably won’t feel so stressed out about it all!)What kinds of things do you do with your young elementary-age kids? Any teachers out there want to share their thoughts with the class? Post in the comments section.
Graham Laing is my brother, and I don’t think he’d be offended by my telling you that some of us in the family were a little worried that he might not amount to anything. But that’s another story for another day. Today, he’s a fish hatchery technician, which basically means he raises trout — “from eggs to eating size,” he says. That means he moves truckloads of live fish from pond to pond (and raceway and stream) according to their size, and he treats them for parasites and other oogie things. He also does a lot of weed whacking and mushroom hunting.
You might not think that a guy who works outside all day long would use math, but Graham does. And I think his approach is pretty unique. As you read through this, see if you can figure out what he’s not doing. I’ll share my thoughts at the end.
Graham wrestles a snapping turtle. Yes, this is part of his job (but I don’t think the turtle does math).
When do you use basic math in your job?
I use basic math every day. When we load the trucks in the morning, we’re told to load a certain amount of pounds of fish per tank on the truck. Since we can’t load all of the fish at one time, we’re handed a net of fish that usually weighs between 40 and 50 pounds. We have to keep track, in our heads, of how many pounds we have in each tank until it is loaded.
I also use basic math when we treat fish for parasites, using either salt or formalin. Salt baths depend on volume, so I find the volume of the tank in cubic feet and then multiply that by the number of gallons in a cubic foot–to get the total number of gallons to be treated. Then I have to multiply that by the number of pounds in a gallon of water to find the total number of pounds of water to be treated. Since we usually do a 5% salt bath, we find the number of pounds in 5% of the volume and weigh the salt. Finally, we can mix the salt in the water.
When treating with formalin, we have to calculate a gallons-per-minute flow rate. We find this by counting the number of seconds it takes to fill a gallon and then divide that number into 60. (There are 60 seconds in a minute.) So if it takes 10 seconds to fill a gallon, the flow rate is 6 gallons per minute. Since the treatment runs for an hour, I multiply by 60 and then multiply that number by 0.0036, which is the number of grams of formalin needed per gallon. Finally, I multiply by the parts-per-million needed for the treatment, which depends on the water temperature.
Do you use any technology to help with this math?
I use calculators for sampling and for calculating the treatments. If we’re doing a lot of samples at one time, we plug the numbers into an excel spreadsheet that has the formulas we need. Calculators reduce error. One blown sample due to error could cause us to underestimate the number of fish in a raceway. Or it could cause us to underfeed a raceway, resulting in a large size-variation of the fish.
How do you think math helps you do your job better?
Graham is also a master at finding little critters like this toad. Click on the picture to see it up close. (Photo courtesy of Mary Bruce Clemons)
My whole job revolves around math. Without math, the fish would die or become infected with parisites. We would not know how many fish we have on the farm, and we wouldn’t know if we were reaching our stocking goal set forth by the state.
How comfortable with math do you feel? Does this math feel different to you?
I feel very comfortable with math and have since I was a very small child. When I got this job, I had all the skills I needed — it just took a little remembering to become adept at using them.
What kind of math did you take in high school? Did you like it or feel like you were good at it?
I took algebra, geometry, and trig. I was forced to take trig, so I didn’t do so well in it. I slept through trig everyday and was still able to make 40s and 50s on the tests just by intuition.
Trust me. If you met Graham you wouldn’t know he’s a math geek. He doesn’t give a whit about calculus or abstract algebra or fractals. He’s just really good at mental math.
Here’s the interesting thing about Graham’s process: All of the math he describes above can be represented by formulas. And when Graham uses a spreadsheet for the math, he has to use the formulas. BUT when he uses math in the field, he unpacks each formula into a set of steps. (First multiply, then divide, then multiply, etc.) He doesn’t have to memorize a formula to do the work. Instead, he thinks about the process, and he’s attached meaning to each step (“divide by 60 because there are 60 seconds in a minute”), so he doesn’t forget to do something. This is the foundation of mental math — breaking up complicated problems into doable steps.
I’m betting many of you do the same thing. Want to share that process in the comment section? I sure hope you will!
And if you have questions for Graham — whether they’re about huge snapping turtles, tiny toads or wildlife management in general — post them, and I’ll be sure to get Graham to answer them. (I am his big sister, so I can boss him around — a little bit.)
