Focus on Math

Helping children become mathematicians!

“Why am I doing this?” August 25, 2016

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Screen Shot 2016-08-25 at 6.36.45 PMIt is nearly the beginning of the school year here in BC, Canada. New beginnings are always special with untold opportunities and challenges before us. As a teacher, educational assistant, or parent who is home schooling a child, it is important to keep one question at the forefront and ask it of yourself daily: “Why am I doing this?”

I am particularly interested in this question in reference to math lessons because I think the intent behind a lesson matters greatly. For most of us, in our past experiences in school, the main point of doing anything in math was to get the answer, and usually with the added hope of getting it quickly and efficiently. Full stop. The answer was what was important. Indeed, it was the only thing that was important.

But is producing an answer quickly really enough? Consider some other intentions you might have for a lesson:

  • I want my students to be able to explain how they arrived at the answer.
  • I want my students to be able to explain why the answer they got makes sense.
  • I want my students to see how this particular aspect of mathematics fits into the bigger mathematical picture.
  • I want my students to understand this math concept and be able to explain the concept with concrete materials and/or visual representations.
  • I want my students to understand how this mathematical concept relates to the real world.
  • I want to make sure that all of my students have an opportunity to link this new knowledge with previous math knowledge.

I hope your answer to the question is not, “This is the next lesson in the book,” or “The curriculum mandates that I teach this.” Both of those things may be true, but I urge you to rethink your lesson and focus on an intention that will make a difference for the learning of your students.

Mathematically yours,

Carollee

 

BCTF New Teachers’ Conf: Seeing Dots February 27, 2016

100 dot array picI am delighted to be here in Richmond, BC, today presenting at the BCTF’s New Teachers’ Conference. I am doing a similar workshop to what I did at the Calgary City Teachers’ Convention two weeks ago, but it is well worth the repeat in this city!

I cannot say enough how important it is for students to be able to visualize and represent numbers in many forms. This tool, the 100-dot array, offers one tool for students to be able to use regularly and thus internalize the number relationships that can be seen when using it.

As before, I am making the handouts available here for downloading:

I will upload the extra large dot sheet (a quarter portion of the regular sized one) which can be made into a poster-sized array once I am home with access to my scanner. Watch for that in the next few days!

Let me know how things go with your students!

Mathematically yours,

Carollee

 

Calgary City Teachers’ Convention: Seeing Dots February 10, 2016

100 dot array picThe 100 Dot Array remains one of my favourite tools for helping students visualize numbers. This session at the CCTC focuses mainly on its use with students in grades 2 and 3, although it can be used at many other grade levels. We will be talking about the best way to introduce the tool to students, showing an early activity to help with general number sense, and using the number in problem solving situations. A variety of problem are included to show its diverse use.

Here are the downloads available from the session:

Please let me know how it goes with using the 100 dot arrays with your students! I love to hear about kids using tools and strategies in math.

Mathematically yours,

Carollee

 

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

 

“Number of the Day” Sheets: Choosing the Number January 5, 2015

Num of Day III eqn picI recently received an email from Stephanie, a grade 2 teacher in Newfoundland, inquiring about choosing the number for the Number of the Day sheets:

“I really love the Number of the Day sheets you have produced and the opportunities for differentiating the instruction. Just wondering how you set this up? Do children do this everyday or on designated days? How do you decide on the number for the day?”

I thought others might be asking this same question, so have decided to post an edited version of my response to Stephanie’s question:

As for setting up the Number of the Day sheets, things are really flexible. There is no one right way — you want what works best for your students and your time constraints. That being said, I have found that if you are able to have the kids do them really regularly (daily if possible) over a good number of weeks, the students are able to really get into the meat of them. By sharing about them after they have worked them, students get to hear what others have tried and will often stretch themselves to try to match what others are doing. They have a chance to really play and explore the number relationships that are brought out in the sheets’ activities.

The number can be picked in a variety of ways — everything from you choosing, a student choosing, drawing a number from a jar or dropping a bean on a 100 chart! Sometime I have chosen specific “repeats” (e.g., every number that week has a 9 in one’s place) sot the kids to see and compare what happens in such cases. What is the same as before? What is different? Or I might pick several numbers within a “decade” (e.g., 33, 37, 31, 35, 38) and again have students compare/contrast over those days.

No matter what number is chosen, one question that is really great to ask is “What do/did you notice?” When that is asked often in the math classroom, students get in the habit of paying attention to details, looking for patterns, making comparisons, and such.

I am happy with random numbers, too, but sometimes choosing numbers with a particular relationship is good so you can really draw out the depth of the relationship.

I hope you will try the Number of the Day sheet(s) with your students. More information about the sheets as well as the downloadable versions, can be found in the links below.

Mathematically yours,

Carollee

Number of the Day Sheets to Download:

Level 1 (English and French)

Level 2  (English and French)

Level 3 (English and French)  (pictured above)

 

 

 

 

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