Studying Fractions

It is so crucial to really understand fractions before going on into the more abstract areas of mathematics.  Here students work together to model mixed numbers, using fraction pieces:

Hands On Equations

As we move into solving more complex algebraic equations, one of the tools students will use is a product called "Hands on Equations."  If you are curious about how this might work, here's a quick Youtube video of a young student (age 8) solving an equation using the method 

Factor Rainbows

Today we began working with factors in math class. We talked about making factor rainbows as a way of developing a list of all the factors for a particular number. This work is foundational to further study of factorization, factor trees, and prime factorization -- just ahead. Definitionally, a factor rainbow is a way of showing factor pairs in a list of all the factors of a number. This can be helpful in checking whether a list of factors is correct. Your student will be working on constructing some factor rainbows for homework this evening.

Measurement Mania -- Flying Saucers

One of the activities of our Measurement Mania event was building flying saucers. Students made flying saucers from circles cut out of poster board. We didn't have time to test fly them on that day, but now that our springtime weather has improved, we have gone out and measured how far our saucers fly. Students also had the opportunity to modify their saucers and examine what changing their saucer designs would make. Lots of measuring and lots of discussing what the data that they collected might mean...

Measurement Mania

The very first day after spring break, we staged a daylong event that we called "Measurement Mania." Students, working in small groups, worked their way through a series of six different hands on activites -- all related to measurement. They investigated a crime scene, made flying saucers, built sand clocks, created scale models of traditional Chinese courtyard houses, plotted the change in the mass of chewing gum as it is chewed, and calculated the volume of boxes as their dimensions changed. We had the help of a great, very game group of parent volunteers, and the students had a great time. Here are some pictures taken that day --

Measure Mania

Monday, March 22 will be the first annual 6th Grade Measure Mania here at Nativity. Students will take part in a variety of hands-on labs to help them learn and explore concepts in measurement. Come and help us! Parent volunteers are needed. Actually, we'll take adult help of all sorts, so grandparents, aunts, older brothers and sisters -- all are welcome. You do NOT have to be a math genius to be a part of our day. Just email me if you can be here for part or all of our time together.

Thanks!

Models of Circle Graphs

We're graphing. Lots and lots of different activities that help to review and expand the understandings that kids have of bar graphs, line graphs, and circle graphs... We'll tackle stem and leaf plots and box and whiskers plots in the next week. We'll figure out measures of central tendency. Then, we'll get busy analyzing the statistics of some of the best baseball players ever.

Here, the kids are working together to make circle graphs using adding machine tape and string.

Archimedes and Thales

Archimedes and Thales were Greek mathematicians. Math students are asked to learn about their respective mathematician by visiting these websites: Thales Archimedes

March Madness

For the basketball fans among us, this is THE month -- March Madness has begun in the college basketball world, and the race is on. We're filling out our brackets in math class and talking about the changing probabilities of one team or another making it through the tournament to the championship. If you are interested in ways to use the basketball extravaganza to fuel some at home math practice, this website has lots of ideas for you to use.

Friday the 13th

Wikipedia tells us that Friday the 13th occurs when the thirteenth day of a month falls on Friday, which superstition holds to be a day of good or bad luck. In the Gregorian calendar, this day occurs at least once, but at most 3 times a year.

This year, we had a Friday the 13th in February, and today is our second one. There will be a third occurence of a Friday the 13th in 2009. Can you figure out which month that will be?

Adding Decimals

Some help with how to add decimals--

Some Really Big Numbers -- Math

I found this interesting website as I was surfing around today, and I thought it was a pretty neat way to get a sense of the really BIG numbers in math. Everything here is illustrated in terms of pennies (except when it is illustrated in terms of cows...). Have fun exploring!

Great Math Resource

Today, I shared information with students about a great set of books written for middle school math students. The author is Danica McKellar, perhaps best known for the role fo Winnie in the series "The Wonder Years." If you are interested, you can find more information at her Web Site . To quote from the site: Straight from Hollywood, this one-of-a-kind guide is guaranteed to make middle school math a breeze! In MATH DOESN'T SUCK, internationally known actress and bonafide math genius Danica McKellar — called a "math superstar" by The New York Times — rips the lid off the myth that math "sucks," helping to show that math can be easy, relevant, and even glamorous—while providing the tools needed to ace the next big math test! With Danica as a personal tutor and coach, even the most frustrated student will finally "get" fractions, decimals, rates, ratios, proportions, "solving for x," and more — the very concepts that, if not fully understood in middle school, have been proven to cause continued problems throughout high school and beyond. I'll be using this resource in the math classes this year. There is no requirement to purchase the book, but students may find it to be both helpful and entertaining.

Amazing Math Patterns

Sometimes, things happen with really simple mathematics that just fascinate me. Take a look at the patterns and symmetry that these number sentences create -- 1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 987654321 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111=12345678987654321

Some Fraction Math...

A typical adult heart pumps about 1/3 of a pint with every heartbeat, and pumps about 70 beats per minute (while resting)… so about how much blood would an adult heart pump in a typical day?

Can you solve this one using "mental math?" How many times does 3/4 fit into 15 6/8?

There are two small holes in a tub filled with water. If opened, one hole will empty the tub in 3 hours; the other will empty it in 6 hours. If both holes are opened at the same time, how long will it take to empty the tub?

Here's a mystery picture, fraction practice: Mystery Picture

The weather forecaster says that it is 200 C in London but
only 7/10 as hot in New York. How hot is it in New York?

Last year, Mr Murrin weighed 60 kg. This year he weighs 2/5
more. How much does Mr Murrin weigh this year?

Zoo Math Days -- Thursday

Thursday is our trip to the zoo for Zoo Math Days. We'll be tackling all kinds of real life math problems from comparing sizes of birds in the Zoo to determining the microclimates in Manatee Springs. These real world problems will serve as our transitional activity as we move from the study of geometry to work on number sense and algebra for the last part of our year together.

We are working to prepare the needed measuring tools, and will be gathering information that will be helpful when we arrive at the zoo.

Check the permission slip for a list of helpful things to bring with you to the zoo. Let's pack those lunches, put on our comfy clothes and head off. I'm looking forward to a great day.

Geometric Solids -- Nets

In geometry, the "pattern" or "template" that will create a solid figure is called a "net." We've been studying geometric solids, and specifically, rectangular prisms, using product boxes to create "nets." Here, students are measuring their boxes to determine the dimensions -- height, length, and width. They then cut the boxes apart to create the flat net, and then used their measurements to create scaled drawings of their nets.

As part of this unit of study, students calculate the volume and surface area of their boxes, and consider how these two values are related.

They also make nets of cubes, and explore ways that a net can be drawn to create the solid figure, and ways that will not make the solid. Working in this very concrete way, builds understanding of the relationships between all the geometric formulas that are connected to the area and volume of solids.

Geometry Project -- Boxes

We'll soon be starting an exploration in geometry that will be built around work with a box. Each student will need to bring in a box to work with. The best kind of box is usually some sort of food packaging because these are light weight enough to be cut easily, and are of a reasonable size. So keep an eye out for a box that might be emptied in your kitchen or pantry. Cereal boxes, rice or pasta boxes, tea boxes, and the like are perfect. Sometimes the kind of packages that are used for over the counter medicines or soap products are good too. The 64 Math group needs their boxes by Tuesday, Feb. 19, and the 63 Math group will need to bring in boxes by Monday, Feb. 25.

Capture / Recapture Modelling -- Math Class

Wildlife biologists use a method called capture / recapture to estimate populations of animals in the wild. For example, if a biologist wants to know how many deer are in a particular forest, or how many trout occupy a certain pond, it is impossible to capture and count all of them. Capture / recapture is a method which involves capturing a certain number of animals, tagging (or marking) them in some fashion, releasing them back into the larger population -- and then taking repeated periodic samples from the population to count how many of the tagged animals are recaptured in the sample groups. Mathematical proportions can then be used to calculate the estimated number of animals in the larger population.

That's exactly what we did in class -- we introduced a "tagged" sample of multi-colored goldfish crackers into a "pond" of the more common goldfish crackers. Then we recaptured samples from the ponds and counted how many tagged fish there were in each sample. We used those samples to calculate estimated numbers of fish in our ponds... It worked pretty well (except in a few cases where some of our samplers ATE the fish!!!). EEEEEKKKKK!

Probability and Area

As we continue to study probability, we've moved into looking at how probability relates to area... how can we make predictions about where an object might fall, land, hit, etc., based on the area of the target? Students began this particular exploration by dropping barley onto a target grid... We will transfer what we are discovering about all of this to questions of how likely it is that we might be in the section where those prize T-shirts land at Great American Ball Park, or what are the probabilities of scoring on your opponent when playing a game like "Battleship."