Focus on Math

Helping children become mathematicians!

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

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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

 

Making a Difference November 25, 2015

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Screen Shot 2015-11-25 at 11.25.37 AMIt is always wonderful to hear when what you do makes a difference, and I wanted to share with my readers the wonderful email I recently received from a student who took a university course (Designs for Learning Mathematics: Elementary — a “how to teach math to kids” course) with me a few years back. I love the “ripple effect” that happens when I can help teachers and student teachers change their approach to teaching mathematics, which in turn can make a great change for how students understand mathematics!

Thank you, Laura, for taking time to share this! Here is Laura’s letter with only a couple of edits for clarification. Woohoo!

Hey Carollee,

Don’t know if you remember me, but I took your Simon Fraser University course a couple of years ago. My husband and I relocated to Ontario and I just started my first teaching contract 3 weeks ago in a grade 2/3 French immersion class. My students are very weak in math… but since I have  started teaching the way you taught me to, I can already see the ideas flowing in their heads! They are really starting to get it!!!

Two days ago we did our first word problem… they were blown away when I put the answer on the board and told them I didn’t care about the answer, but instead how they got to it! The first day they were a bit shy to try and fail, but by the 3rd day boy were they trying everything! number  lines, dot array, hundreds chart, blocks, pictures!!! I felt such joy!!!!

So… I guess  I just wanted to say thank you… and to let you know that  you are changing children’s understanding of math… EVERYDAY!

THANK YOU, THANK YOU… THANK YOU!!

Laura Fusco

 

Number of the Day – Level III March 10, 2014

Num of day tally picToday I am posting the third Number of the Day sheet. I cannot overstate that I believe that elementary school students should be involved with numbers everyday they are in school!

Level III is one to primarily use with numbers to 100. The section “100 chart tic-tac-toe” will not be familiar to most. I had devised that math game based on the positioning of a number on the 100 chart. For instance, if 26 is written in the centre of the chart, then the middle line is to show one more and one less than 26. (25, 26, 27 across). Above the middle number is 10 less, in this case 16. Below 26 is 10 more, 36 in this case. The corners can then be filled in using the horizontal or vertical relationships already established. (For more on the use of 100 chart tic-tac-toe, see my previous blog post.)

When using 100 dot arrays, I have students use highlighters to colour the numbers. I also stress marking efficiently – we do NOT colour each individual dot; rather a line or partial line is coloured with a swipe of the marker.

At every level breaking apart the number of the day is an important component of the sheet. Quoting John Van de Walle once again, “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.” [Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.]

I did have one teacher ask a question about the breaking apart section. She was used to having students only break apart numbers according to tens and ones. Thus 26 could be broken apart as 20 and 6 or 10 and 16. But sometimes it is easier to work with numbers when we break them in ways other than ten and ones. Consider the thinking that might happen when adding 26 + 27. If a student knows that 26 comes apart as 25 an 1 and that 27 comes apart as 25 and 2, it is easy to put the 25′s together to get 50, then add the 1 and the 2 —total 53. Students who use the 100 dot array often get especially comfortable with 25′s. Also consider adding 97 and 36. If a student notices that 97 is just 3 away from 100, it makes sense to split 36 as 3 and 33. Breakng apart in tens and ones are definitely useful, but so are other “break-aparts”. If students do not practice this kind of thinking they are not likely to ever do it!

I had one teacher here in my district that was using this sheet and her students were getting tired of making tallies for large numbers. So I am including a second English version of the sheet asking for equations for the number instead.

Again, a French version is offered as well with thanks to my friend and colleague Lynn St. Louis for her translation.numero du jour III pic

 Download the English version (tallies) here.

Download the English version (equations) here.

Download the French version here.

Mathematically yours,

Carollee

Num of Day III eqn pic

 

Number of the Day – Level II March 6, 2014

Numero du jour II picIn keeping with my belief that elementary school that students should be involved with numbers everyday in math time, I am posting my Number of the Day Level II sheet in English and French.

Today’s sheet is one to use primarily with numbers to 30. As in the Level I sheet, most of the components are self explanatory, and again the colouring on the 100 chart can be done either by colouring the individual number or by colouring all numbers up to and including the number of the day.

As mentioned before, breaking the number apart in different ways is an import thing for students to practice. As John Van de Walle wrote, “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.” [Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.]

I am delighted to offer this sheet in a French version, as well. Merci to my friend and colleague Lynn St. Louis for her translation. number of the day II pic

Download the English version here.

Download the French version here.

I’d LOVE to hear from you if you try either version!

Mathematically yours,

Carollee

 

Number of the Day – Level I March 5, 2014

Screen shot 2014-03-05 at 7.55.19 PMI have long believed that in elementary school that students should be involved with numbers everyday in math time. This may not always be the case — the teacher might be teaching a unit on pattering or geometry, for instance. While those are worthwhile concepts, I still remain convinced that students need some time each day to think about and work with numbers.

One way this can be accomplished is through the use of Number of the Day sheets. The idea of using such a sheet is not new – indeed, there are many versions available on the Internet.

I have added my own version of the Number of the Day sheet into the mix. In fact, I will be adding several versions over the next few days that are targeted at different levels of learners

The Number of the Day sheet I am posting today is one that can be used in Kindergarten classes, but it may be useful in Grade one classes early in the school year. The components are self-explanatory, although I did have one teacher who started using the sheet call me and ask about colouring on the 25 chart. She asked, “If the number of the day is 12, am I supposed to have students just find and colour the numeral 12, or are they supposed to colour all the boxes up to and including 12?” My response was, “Yes!” Either way is good, with each method focusing on something slightly different about the number 12.

Breaking the number apart in different ways is an import thing for students to practice. As John Van de Walle wrote, “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.” [Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.]Screen shot 2014-03-05 at 7.55.36 PM

I am delighted to offer the sheet in a French version as well. Merci to my friend and colleague Lynn St. Louis for her translation.

Download the English version here.

Download the French version here.

Mathematically yours,

Carollee

 

Wanted Posters Revisited February 4, 2014

wanted poster picDoing wanted posters for numbers is a great way to have kids think about specific properties of particular numbers. The posters make a great display, too —  and I am always looking for ideas for math bulletin boards!

The idea is useful at lots of grade levels. You could have older students choose a proper fraction (e.g., 5/8), a mixed number (e.g., 4 1/3), or a square or cube root (e.g. the square root of 50).I wrote about these posters before — click here for the link to the previous write-up where you can download the template.

Give them a try and send me a picture of your display!

Mathematically yours,

Carollee