# Focus on Math

## Helping children become mathematicians!

### BCTF New Teachers’ Conf: Seeing DotsFebruary 27, 2016

I 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.

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 DotsFebruary 10, 2016

The 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.

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

### Calgary City Teachers’ Convention: PS

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!

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

Mathematically yours,

Carollee

### GAD Workshop, Surrey, BCOctober 23, 2015

Thanks 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

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

### Simple Definitions Too Simple?August 10, 2015

Math definitions matter! There are many words we use in mathematics that have one meaning in that discipline and another in ordinary life. Take for instance the word “difference”. In regular conversation, if I ask you to find the difference between two things you are looking for some way in which the items are not the same. However, in mathematics, finding the “difference” specifically refers to finding the answer to a subtraction problem.

But we as teachers might be sending some confusing messages to students, sometimes even when we think we are right on track with our definitions. One example of this is the seemingly easy-to-define term “even”. How would you explain to a young child what an even number is?

There are two popular ways this property of even is explained to primary students: First, many teachers suggest that we can do an “even check by examining whether a particular number of items can be split into two equal groups. Armed with this definition, children should see that six is even since there can be two groups of three, but five is not even because there are two groups of two and one left over.

Alternately, teachers often suggest that students look at the value of the one’s place digit of the number in question. If there is a 2, 4, 6, 8, or 0 in one’s place, then a number is even. Using this method children should conclude that 74 is even since there is a 4 in one’s place, but 73 is not since there is a 3 in one’s place.

The problem is that both of these simple definitions are not fully correct. There are exceptions to them that, in fact, that are incorrect.

Concerning the “two equal groups” definition, young children figure out quickly that when sharing 5 cookies between two friends, each can have 2 ½ cookies. There are two equal groups, but the number 5 is still an odd number. What important detail have we failed to communicate here?

Concerning the “one’s place digit of 2, 4, 6, 8, or 0” definition, a student can declare that 74.3 is even since it fulfills the definition stated. Again, what important detail have we failed to communicate here?

Some might argue that these exceptions above the student; that we need not muddy the waters, so to speak, by giving extraneous information that we think is above our students’ heads. I disagree. I feel that if we just mention the restrictions as we talk about the definition, that it becomes part of the language the students are used to. We often underestimate how much students can understand, and we “dumb down” the language as a result. I would love to challenge your thinking along that line. In the case of primary children in particular, they love to learn what I refer to as “27-syllable” dinosaur names, yet we are afraid of using good math language with them!

I hope you will stop and think about the simple definitions you are using with your students and reflect on whether or not there are some hidden exceptions that need to be teased out and exposed.

Mathematically yours,

Carollee

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

I 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.

Mathematically yours,

Carollee

Level 1 (English and French)

Level 2  (English and French)

Level 3 (English and French)  (pictured above)

### 10 New Year’s Resolutions for the Math ClassroomDecember 31, 2014

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