Tuesday, June 25, 2013

Round and Round the Garden - Area and Perimeter

Gardening is of course just one of several ways a sound understanding of area and perimeter can be put to good use. And of course, what's mathematics without some horticulture thrown in for good measure? Below you will find several different projects for teaching area and perimeter, including additional slides to help teachers and students create more excersizes for their own classrooms. We have more in mind to come, but here are the first four. There's just so many ways to teach area!

Unit by unit area measurement - https://app.box.com/s/381op67m5zanmgsdbs4a
Students use single square units to fill in the area of images on different slides, counting them individually. The first slide focuses on simple rectangles while the second introduces some shapes with twists and turns.

Filling a Garden - https://app.box.com/s/i50i3y6xi1rthm73dm4k
Two types of problems are presented here. The first is another unit by unit fill in excersize. Afterwards, students are challenged to create gardens using images of tomato, eggplant, caggabe and broccoli plants. And don't worry - all four plants require roughly 1 square foot of space to grow so students can stack them along side each other as equal units.

Non-standard Triangle unit measurement - https://app.box.com/s/rnudthm3tti8h9axfek7
Instead of squares, this excersize challenges students to measure a variety of shapes using equilateral triangles. This excersize can also help facilitate a discussion about the relationships between triangles and parellelograms or hexagons

Grid block measuring - https://app.box.com/s/9fi0vgchzcsicmwotuee
Instead of measuring unit by unit, students are encouraged to measure irregular shaped objects by using colour coded grids of single unit blocks to isolate sections. The extra slides at the end of the project enable students and teachers to make additional problems.

Area Pond - https://app.box.com/s/a1hirv57u5c6057x7j4e
Here students can look at the relationship between area and volume by filling a pond with fish, lily pads and ducks! By locking the scale of  each item, they can compare how many fish, lily pads or ducks are needed to fill the pond. Possible questions include:
Which unit of measure do you think makes the best indication of pond size? Why?
If you knew the depth of the pond, how would you calculate the ponds volume?

Monday, June 24, 2013

Calculator Games for all! - Order of Operations

Calculator games! Creating these problems is easy, but its incredible what a headscratcher a well placed multiplication sign can result in.

These games force students to make choices about where in a multi-step problem they will place a limited number of digits. Once the free moving calculator buttons run out, so too do their options. However, some problems can still be solved multiple ways, resulting in discussions about the relationships various numbers share.

Teachers can choose to either make digits for incorrect answers available or use the handy trash can icon on the side, allowing students to obtain needed clues. The games come in various levels, with each increase in level adding an additional step to the problem. Finally, Level 5 flips the whole excersize on its side (literally) and asks students to balance equations. Each level comes with a blank slide at the end that will help teachers - or students - to make additional challenges.

Level 1 - https://app.box.com/s/abk4nk4meixwx9y8jj9x

Level 2 - https://app.box.com/s/nobhj24pbwxfroc0ennk

Level 3 - https://app.box.com/s/b6wsvvjr1yhv14qbfoo9

Level 4 - https://app.box.com/s/3budui8du8xpaycjmkdf

Level 5 - https://app.box.com/s/7gqe1q7pmlsdmr3blsga

Cake or Book? - Fractions

There are truly endless ways to represent a fraction and knowing that, isn't it far more fun to have a cheerful way of thinking of fractions? Below are several projects designed to help teach students about equivalent fractions as well as a few ideas for how problems can be constructed using these colourful manipulatives.

The first is a rather simple piece that provides a few pie chart manipulatives for helping students measure equivalent fractions. The pies are divided into fourths, fifths, eigths and tenths.

Next is the bookcase. Using the transparent books, students can compare the lengths of different sizes of various fractions as they fill the shelves. A single dictionary fills 1/2 the shelf, but what about the entire case? Then it only fills 1/6. How many copies of "Treasure Island" would be needed to fill the case? The books can also be compared on a number line ranging from 0 through 1. On the final slide, students can practice adding fractions by combining the first two shelves into a single string of books at the bottom.

Finally, everything is better with cakes, and of course that includes fractions! Students stack layers of cake to create giant, teetering monstrosities of birthday merriment. A few "finish the cake" problems are included and the vertical alignment gives another concrete way of thinking about how fractions can be presented in day to day life.

Pie Chart Fractions - https://app.box.com/s/80jpejfc4eg8x0cktzm4

Book Fractions - https://app.box.com/s/fhk7ee0mkbodxoexjakf

Cake Fractions - https://app.box.com/s/48k8sab9eiwmoi1wcaue

When snakes go to war - Cartesian grids

Over the past several weeks, we've been working hard to put together some more fun projects that will help bring mathematics to life in your classrooms. Now we have some ready to share and are very excited to be doing so!

First off, we have Battlesnake - a search and destroy style game for teaching kids about graphing lines on a Cartesian plane. Students can use one of the two boards to position their own snakes (either green or blue) and then use the other grid to keep track of their opponent as they hunt down the opposing colour. Simply name a coordinate point and - if your friend is hiding a snake there - SPLAT! Move one of the hit markers over that spot on the page. Keep track of how many snakes you've hit and the first to kill all of the opposing team's snakes wins!

The first few boards simply use positive integer coordinates and horizontal or vertical snakes. Later boards allow students to try to hunt down snakes in all four quadrants and along sloping lines. They may discover relationships between the points the snakes cover. Board 6 has even more varied shapes, including a parabola snake and a Fibonacci spiral.

Happy hunting to all!

Board 1 - horizontal snakes https://app.box.com/s/7vx0ck7o5586gchhhuir

Board 2 - vertical snakes https://app.box.com/s/3fmmc8cihbs1kruc2vwf

Board 3 - horizontal and vertical snakes, single quadrant https://app.box.com/s/179xrd2xhqxvnj3k14c0

Board 4 - horizontal and vertical snakes, four quadrants https://app.box.com/s/0ie1yqlw03231g10fydq

Board 5 - sloping snakes https://app.box.com/s/lruxzzke80dp5kovsmdl

Board 6 - elaborate snakes https://app.box.com/s/58ehorowf10agkitwo0j