Focus on Math

Helping children become mathematicians!

Jayden’s Rescue (Revisited) January 22, 2014

Screen shot 2011-05-31 at 3.46.07 PMI had the wonderful opportunity to be a guest reader in Mrs. DeGroot’s grade 5-6 classroom this morning. She was ready to start reading the novel Jayden’s Rescue by Vladimir Tumanov aloud to the class, and I had the privilege of starting it off. (See my previous post on the novel for more about the story and the math involved in it.) The students each had a copy of the Four Quadrants processing strategy (created by Susan Close and Carole Stickley) on which to jot ideas, important words, sensory information, and pictures that came to mind as the story was read.

We were also prepared to do the mathematical questions that would arise in the story as part of the rescue task.  The first problem that comes in the book is this:

I am the father of nine sons, all one-eyed monster boys.

I keep an eye on all my lads as they play with their toys.

A three-eyed monster once dropped in and brought his sons along.

Three bulging eyes were on each guest.

Oh! What a blinking throng!

Together all the monsters had exactly forty eyes.

How many three-eyed kids were there?

The numbers tell no lies.                              Jayden’s Rescue, p. 24

It took a bit longer than I had anticipated getting to that question on p. 24 (not to mention that that the lunch period began 15 earlier than I had expected it to!) so the students ended up not having a chance in the morning to share their solutions/strategies to the question. I left that in Mrs. DeGroot’s capable hands to finish up.

I believe the book is presently out of print, but copies are available from used-book sellers. It is definitely a book worth tracking down and reading to a class in the grade 4 to 6 range.

Mathematically yours,

Carollee

 

Math Club for Elementary or Middle School Students November 5, 2013

math club picYou may have heard of math clubs in high schools, but math clubs are a wonderful idea for elementary or middle school students as well. For a number of years I ran a successful weekly math club at the inner city elementary school where I was then teaching. The club was mainly targeted at students in grades 4 to 7 (my school was a K-7 school) although if a grade 3 student were interested in coming, I never turned the child away.

“Euclid Club”, named of course for the Alexandrian Greek mathematician/geometer, met for 30 minutes one day each week after school. It came about simply because I felt there were so many interesting math ideas that just did not fit into my classroom time (or curriculum!) and I wanted the opportunity to share those ideas with kids. Thus Euclid Club was born! I can get pretty excited about mathematics (as anyone who knows me can testify to!) and did not have too much difficulty getting kids to come give the club a try. Our numbers certainly varied over the months depending on what other after-school activities were happening or what other out-of-school activities students were involved in, but we consistently had a pretty good group out at our meetings. I always provided some kind of small snack as well! Certainly not enough to be the main draw, but it was always welcomed by the kids.

There are many benefits to engaging children in math club. For me, first and foremost was that it gave students a chance to build a different perspective about mathematics. Many of them thought of themselves as not being “good” in math and tended to disengage in math in the classroom. The atmosphere in Euclid Club was welcoming, engaging, and lively, and many not only became comfortable with exploring math ideas, but additionally they built a sense of belonging within the club.

So, what kinds of ideas and activities can be explored in that context? Here are some of the things we explored in Euclid Club:
• We learned and played math/thinking games such as Nim, chess, cribbage, etc.
• We examined other number bases, such as base 4, base 2, and base 12. We wrote the value of base 10 numbers in the different bases. We figured out the base 10 value of numbers written in other bases. We added and subtracted in other bases.
• We worked with pentomines, trying to fits sets of pieces into given frames: 6 x 10, 5 x 12, or 8 x 8 (with either the four corners “removed” or the four center squares “removed”).
• We created designs with tangrams.
• We made pattern placemats using cut-out pattern block pieces to make interesting borders on construction paper.
• We used pattern blocks to create designs with one or more lines of symmetry.
• We measured our bodies and compared ratios (e.g., height to arm span; circumference of thumb to circumference of wrist; circumference of wrist to circumference of neck; circumference of neck to circumference of waist, etc.)
• We solved logic puzzles (using ones commercially produced).
• We created tessellations: we found shapes that would tessellate as well as creating our own unusual shapes that would tessellate.
• We made paper quilt squares in a variety of patterns and calculated the fractional part of each colour we used.
• We examined the Fibonacci sequence and looked at real-life examples of where it appears in nature (such as on a pinecone, on flowers, leaves, pineapples, seeds in fruit, etc.
• We created Moebius strips, and marked and cut them to discover interesting properties about them.
• We assigned each letter of the alphabet an amount (a = 1 cent, b = 2 cents, c = 3 cents, etc.) and looked for words whose letters would total $1.00.
• We solved magic squares and then created our own.
• We examined Pascal’s Triangle and looked for patterns on it.
• We created designs with exactly one metre of string glued on to paper (easier to do the basic designing first with dry string, then dip the string in white glue to create the final project).
• We created our own codes using numbers and wrote secret messages to each other.
• We made designs on 100-grid paper using a specific amount of coloured squares (e.g., what designs can be made colouring exactly 50% of the grid? 60%? etc.)
• We created “Guess My Number” puzzles for each other to solve. Each puzzles was to have 3 to 5 clues, first starting with a broad clue and getting more specific each time. (E.g., 1 My number is a prime number less than 30. 2 My number is not part of a pair of twin primes. 3 My number is even.)

I am sure there are other things we did, but those are the ones that I remember at the moment! I am sure you can find other ideas and topics to explore as well.

I hope you will consider giving Math Club a try (but give it a cool name! Kids love that!)

Mathematically yours,
Carollee

 

Math Bowling October 1, 2013

math bowling pic This “Math Bowling” activity is one that students tend to love! It is great for practicing math facts as well as for stretching students’ thinking.

The activity is done as follows (students alone or in pairs):
Roll three dice (your choice whether to use regular six-sided dice or include one or more different dice, such as a ten-sided die). Write the numbers in the boxes marked “strike”. Using all three numbers each time exactly once, students work to write equations to equal each of the numbers 1 to 10 of the “pins” marked on the sheet and thus “knock them down”. Students may use whatever operations they understand: addition, subtraction, multiplication, and division are standard, but students may also use exponents, roots, and factorials if those are in their realm of mathematical knowledge.

For instance, if the numbers rolled are 2, 3, and 6, students might “knock down”
1 = 6 – 2 – 3 OR 1= 6/(2 x 3)
3 = [( 3!)/6] + 2
4 = (2 x 6) ÷ 3
5 = 6 + 2 – 3
6 = (6 ÷ 2) + 3
7 = 3 + 6 – 2
9 = (6 ÷ 2) x 3

If the students did equations for those 7 numbers/pins, that would constitute the first throw of the ball. Since all the pins are not knocked down, the player may roll the dice a second time, record the numbers in the boxes marked “spare” and try to knock down the three remaining pins using that second set of numbers to score a spare. If that is not accomplished, the student scores the number of pins knocked down in the two “throws”.

If you wish, as players take multiple turns, you can calculate scores in the manner that 10-pin bowling is actually scored. As someone who was on a youth bowling league in my younger days, I know the scoring system well. There is some good math in the score keeping, too! If you are not familiar with that scoring system, here is a website which will walk you through the scoring process.

http://www.bowling2u.com/trivia/game/scoring.asp

Download the “Math Bowling” sheet here.
Download the score sheet here.

I hope you will give math bowling a try with your class.
Mathematically yours,
Carollee

math bowling score picScreen shot 2013-11-07 at 6.56.30 PM

 

Ten Uses for Sticky Notes in Math Class September 9, 2013

Sticky notes title pic Sticky notes (that wonderful — though accidental — invention that 3M first marketed as Post-It Notes©) are a wonderful tool to use in mathematics. I have always found that students enjoy using those little sticky pieces of paper! So here are ten ideas for incorporating them into math lessons:

1) Ordering numbers: Write 4 or 5 different numbers on sticky notes and have students work in pairs to put them in order from least to greatest. This is great practice for multi-digit numbers, for decimals, for fractions, etc.
2) Creating numbers: Write 4 or 5 different digits on sticky notes and have students work to create specific numbers: greatest possible; number closest to a particular given number (whole number or fraction); a number between two given numbers, etc.
3) Using operations: write several digits on sticky notes. Then use them and operations that the students know how to use to make number equations with as many different answers as possible or to get as close as possible to a particular answer.
4) Writing word problems: Give students numbers, operation signs, and possibly other math symbols (such at a percent sign) on sticky notes and have them create a word problem that uses all of the notes.
5) Graphing: Create the axis of a graph on chart paper or the chalkboard. Add your categories (4-6 work well). Give each student a sticky note and have them create a bar graph with then .(I usually have kids make their choice at their seats and write it on their notes so they don’t just add to a single category to make it “win”.) graph pic
6) Scavenger hunt: each student has a sticky note with math geometry word on it. Students must find an example in the room to represent the term and place the sticky note there (e.g., perpendicular lines, acute angle, sphere, etc.).
7) Measuring area: Cover a book or other object with sticky notes and calculate the area using the notes as the unit of measure. A particular book or surface may be covered by notes of one size, then by notes of another size and the area calculations compared.
8) Estimating on a number line: draw a number line on the board with only the endpoints marked (endpoints may vary according to grade: 0-10, 1-100, 0-1, 20-80, 1-1000, etc.). Give each student a number that appears on between the endpoints and have them come and place their number where they think it would go and explain their reasoning for placing it there.
9) Commenting on each other’s work: teach students to peer-evaluate problem solving work. Students can exchange their papers after working on an open-ended problem. The evaluator can make comments and ask questions regarding the strategies, visual representations, etc. by writing their comments on sticky notes.
10) Transformational geometry: Use sticky notes to show transformations, often called “flips”, “slides”, and “turns”. Light coloured sticky notes tend to be translucent. Using a sticky note, student can trace a shape from its original location on a grid and then use the sticky note to show the desired transformation (e.g., down two, left three; 90 degree clockwise rotation; reflection over a particular line).

I hope you try one or more of these in the next weeks. Let me know how it goes!
Mathematically yours,
Carollee

 

Math Camp 2013 Reflections… August 28, 2013

Screen shot 2013-08-27 at 7.13.49 PMWow! Math Camp 2013 was a resounding success! The focus each day was on how we can structure routine activities for our students that will allow them to build number sense. We also talked about Carol Dweck’s research about mindsets and looked at how we could help our students build a ‘growth mindse’t in mathematics and not be stuck in a ‘fixed mindset’. (If you have not read Dweck’s book Mindset, I encourage you to get a copy asap!)

We looked at visual routines, counting routines, and routines involving number quantity, and discussed how each of these can be utilized for learning.

Our visual routines involved using 10 frames, dot cards, dot plates, 100 dot arrays, fraction pocket charts, percent circles, base-10 grid paper, and number lines (I always have students draw these rather than use ones that are pre-drawn and pre-marked). See end of post to download the various tools.

Our counting routines involved choral counting, counting around the circle, and stop and start counting, and counting up and back.

Our routines for number quantity involved mental math, number strings, “hanging balances”, and decomposing numbers.

It would take too long to write here in one post about how best to use/do each of these ideas, but over time I will get to them. Are you interested in something in particular? Email me and let me know and I’ll get to that one right away!

All of the “math campers” went away with lots of ideas that can be implemented in the classroom right away. I’ll be excited to hear from them how it goes it their classrooms.

I’ll leave you with my favourite definition of number sense: “Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Hilde Howden, Arithmetic Teacher, Feb., 1989, p.11).

There is much food for thought in that quote alone!

Mathematically yours,

Carollee

Click to download: student 10 frames , teacher 10 frames; student dot cardslarge 100 dot array, 12 small 100 dot arrays, 6 small 100 dot arrays, 4 small 100 dot arrays, teacher dot cards set 1, set 2, set 3; template for making dot platesbase-10 grid paper, percent circles; directions for making fraction pocket charts;

 

Summer Math Fun for Families or Play Groups! June 21, 2013

Screen shot 2013-06-21 at 11.11.21 AM Parents, if you are interested in some math fun that encourages some great learning, you will want to check out this site– Moebius Noodles: Math Adventures. It is all about problem solving for the young, the very young, and the young at heart! There will be 10 lessons that the Moebius group will present during July for parents to try with their kids of any age (and adapt as needed), with a chance to connect with the Moebius group via computer. The Math Adventures would even be a great project for a play group or math club!

The main course activities will happen July 7th through July 28th. The organizers say you should expect to spend about two hours a week on course-related fun. The results of all the participants will be combined to produce an open-licence book about mathematics education.

Information about the project as well as copies of the previous book (in either pdf format or paperback) can be found on the main page for Moebius Noodles.

If you want to formally participate in the group, you need to sign up soon (they request that you sign up and complete prep tasks by July 7, 2013).

It sounds like a great opportunity to me! What’s not to love about more math!!!
Mathematically yours,
Carollee

 

Math Bulletin Board: Square Number Towers May 23, 2013

square number tower bb pic Recently I had two of my classes represent visually the idea of “squaring” a number: namely, that a number times itself is literally the area of a square with side length of that beginning number. The students cut squares from centimetre grid paper representing 10 x 10, 9 x 9, … 1 x 1 and them glued them onto construction paper. To each square they added the multiplication fact represented, as well as showing the exponential form of the number. Square numbers show up quite a bit in secondary mathematics, and helping students understand these numbers (as well as memorizing the sequence of them!) is beneficial for them as they move on.

I am always looking for math ideas to display on a bulletin board, and I think this is a good one!
Mathematically yours,
Carollee
square numbers towers 3 pic