Focus on Math

Helping children become mathematicians!

Calgary City Teachers’ Convention: PS February 10, 2016

It is my pleasure to present this session “Power Up Your Problem Solving” to the participants of this session.

Regular problem solving is a powerful way to help students develop conceptual understanding in the various strands of mathematics. Since there is a tradition in North America of “teaching by telling” (the “here’s-how-to-do-it-go-practice-50-of-these” method), it may take many weeks to develop a culture of deeper thinking in a classroom. Students need a variety of thinking tools and strategies to work with, as well as skills and practice in talking about math problems, but the time it takes to help students gain these needed things is time well spent. The payoff is huge!

I hope many of you will be encouraged to begin building a regular problem solving program with your students. It works at every grade level!

All the here are the downloads for the problem solving session:

I would love to hear from you how it goes in your classrooms!

Mathematically yours,

Carollee

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GAD Workshop, Surrey, BC October 23, 2015

learning to speak math picThanks to the teaching staff of GAD Elementary in Surrey, BC, for their warm welcome and heartfelt participation as we delved into problem solving, math tools and strategies, and math processes (especially communication). Changing our teaching practice is not an easy feat, but if we commit to some small changes, practice them regularly, add more changes, practice those regularly, and keep on going in that manner, we can end up making a significant and lasting change that will benefit students greatly.

Remember, “math talk” does not just happen. We have to plan ways to incorporate it into each math lesson. It is a good idea to create math partners so students are responsible to talk to someone about their math thinking. Modeling (letting students hear YOU talk through a demonstration problem) is always a good idea. Responding to students with proper math language/vocabulary (when they have not used such) is helpful. Posting “sentence stems” is a great way to give them an easier start in speaking math. Additionally, try creating a “math words” chart with the students that they can use as an on-going reference in both their speaking and writing (click here to see an example of a “math words” chart.)

As promised, I am adding links from this post to the handouts from today’s session (see bottom of the post) and some that we just talked about.

I would LOVE to hear from any of the GAD staff of how things go in your math lessons in the next weeks. You all listed something that you could begin to do right away in your classrooms, and I hope you will share what you are doing and the effect it is having on the students.

Remember, understanding “lives” in the processes! Reflect on your teaching regularly to see if you are embedding those processes into math classes. It will make a big difference in students’ understanding if they are immersed in the processes!

Mathematically yours,

Carollee

 

Download materials here:

100 dot array (teacher size)

100 dot arrays 4 per page

100 dot arrays 6 per page

100 dot arrays 12 per page

break apart number sheet – 2’s

break apart number sheet – 3’s

problem solving assessment rubric

10 frames (teacher size)

10 frames (student size)

10 frames blank mini’s

 

10 New Year’s Resolutions for the Math Classroom December 31, 2014

Screen Shot 2014-12-31 at 2.59.05 PM

1. praise effort, not correct answers
2. make sure my students know their intelligence is not fixed: hard work pays off
3. make my classroom a safe place for students to take risks
4. encourage students to take risks
5. give my students rich problems that require they engage in problem solving
6. build a class repertoire of strategies
7. have “thinking tools” handy
8. give regular attention to basic facts (for students who do not know them)
9. give students lots of opportunity to talk to each other when solving problems
10. support math vocabulary learning with a word wall chart

Mathematically yours,

Carollee

 

What’s Important to Have in a Grade 1 Classroom? October 2, 2014

Screen Shot 2014-10-02 at 10.02.55 AMI was recently contacted by a former colleague, Dawn, regarding what manipulatives a grade one classroom might need to have on hand to support effective learning math. It seems a friend of Dawn’s is in a classroom which really has nothing for the children to use for hands-on math learning and they were wondering what was needed.

First off the classroom needs counters — counters in different shapes, sizes, etc. They can be purchased ones (such as mini plastic teddy bears) or ones gathered from home (such as bread tags, but†ons, etc.). But the need to be abundant and available.

Students need a way to count efficiently, especially in tens and ones. Egg cartons cut down to 10 holes, blank 10-frames printed on paper or card stock, or commercially produced 10-frames can all be used. I even like using cookie sheets (non-aluminum) and marking them with coloured tape as a giant 10-frame for use with magnets.

Base 10 blocks are also great for young students. These a generally in the form of small 1 cm cubes for “ones”, sticks for the “tens”, and flats for the “100’s”. I do want to make a critical point here: students may be engaged in a game of trading 10 cubes for a stick, or 10 sticks for a flat with every appearance of understanding the “ten-ness” of our base-10 number system. But be careful here. Student can be following your rule of trading 10 for 1 without that understanding. They might be just as happy to trade 8 for 1 or 12 for 1. The manipulatives give a opportunity for students to develop that important base-10 understanding, but moving blocks around correctly does not necessarily indicate that the understanding has been built in the student’s mind.

I think a grade one classroom needs “pop cubes” (multi-link cubes) — those blocks about 1inch in each dimension that can be attached together. I like to store them sticks of 5. If students need a particular amount for an activity, say 18, we discuss how many sticks each student will need, and then go get them. I also use these in many quick number-sense building activities. If I have students hold up a certain number of blocks, I want them to do so to model a ten frame. If I ask for 9 blocks and a student were to hold up a single stick of 9, I, as the teacher, cannot tell from a distance if the student is holding 8, 9, 10, or 11 blocks. But if he holds up a five stick beside a four stick, I can tell at a glance that he has the correct number. Pop cubes can be used in a multitude of math activities and should be on-hand for regular use.

Another must-have in my book are pattern blocks. They are particularly great for patterning activities for exploring symmetry, not to mention the creativity factor! I love them!

There are a number of things that I think should be in the classroom that are “make-able” such as dot cards, dot plates, printed ten-frames, even printed dominoes (click for more info on these)— all useful in exploring numbers, in building number sense, and  in helping students develop the skill of subtilizing. Students need to SEE the numbers in math, and these materials can help develop that “seeing” in the children.

Of course there are many other things that are fun to have in the math classroom, such as dice, dominoes, blocks, playing cards, geoboards, plastic coins, bingo chips, square tiles, Cuisenaire rods, and two-colour counters, to name a few. But lots of math learning can take place with some thoughtfully crafted lessons and activities and just the basics.

I hope you will focus on the math understanding with whatever materials you have at your disposal!

Mathematically yours,
Carollee

 

Seeing Dots: NCTM 2014 New Orleans Presentation April 11, 2014

Screen shot 100 dot arrayI am excited to be here in New Orleans at the 2014 NCTM conference. Yesterday was a great day of sessions for me, and I am delighted to be presenting a session in just a couple of hours! “Seeing Dots: Using Arrays to Add, Subtract, Multiply and Divide” will focus on all the different ways the 100 dot array can be used to help students visualize and represent numbers — something which leads to a deeper understanding of numbers.

I am posting the handout from the workshop as well as links to 100 dot arrays is the different sizes.

I hope you try using the 100 dot array in your elementary classroom!

Download the conference handout here.

Download a 100 dot large array here.

Download 4 arrays on a page here.

Download 6 arrays on a page here.

Download 12 arrays on a page here.

Mathematically yours,

Carollee

 

Dot Plate Make-and-Take: A Great Success! November 23, 2013

Screen shot 2013-11-23 at 1.46.43 PMThe Dot Plate Make-and-Take workshop was a rousing success! In spite of the nearly -30 C temperatures and the slippery road conditions, the registrants all showed up, some driving an hour or more to come.

We talked about number concepts for students in kindergarten to grade 2, mainly focusing on the “big four” relationships that we want students to understand regarding numbers 1 to 10:

  • One more/one less (and two more/two less above K)
  • Anchors of 5 and 10
  • Whole-part-part
  • Visual/spatial relationships

With those firmly established, we are able, over time and grades, to take those same relationships and help students make those same connections with other larger and more complex numbers.

Participants made a set of Dot Plates using desert-sized paper plates (we used sturdy ones), bingo daubers and a pattern guide. They also received copies of small dot cards (4 sets printed onto coloured card stock), a set of large card stock dominoes. All of these are visual tools that can be used to build the above “big four” relationships. We also discussed the use of ten frames (large, teacher-sized ones, small student-sized printed ones, and blank five- and ten-frames) which are particularly good for anchoring numbers to 5 and 10.

 

Download here:

 

 

Go to the bottom of the Math Camp 2013 blog post to download the following:

  • Dot plate pattern sheet
  • Small dot card pattern pages
  • Large dot card pattern pages set 1, set 2, set 3
  • Student ten frames
  • Teacher ten frames

 

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;