Focus on Math

Helping children become mathematicians!

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

 

Calgary City Teachers’ Conf 2014 February 17, 2014

Screen shot 2014-02-17 at 9.04.21 AMIt was wonderful to share the Friday morning session at the Calgary City Teachers’ Conference with so many new friends! I hope you walked away with some ideas for helping your students understand mathematics is a deeper way. Congratulations to Shannon Muir who won the math coaching session in the draw!

If you remember one idea from the morning, I hope it is one about building understanding in math. Students need to make sense of the concepts using first concrete materials, then with pictorial representations, and then with symbolic (or numeric) representation. Rules for manipulating numbers are not remembered well if they are not based in meaning. Caine and Caine report from their brain research, “The brain resists meaninglessness.”

As promised, I am posting here the tools we used and referred to for your easy access.

100 dot arrays (1 large)

100 dot arrays (6 per page)

100 dot arrays (12 per page)

ten frames (teacher size)

ten frames (mini blank ones, 40 per page)

base 10 grid paper (enlarge as needed)

fraction & percent circles

fraction pocket chart    (link here for more discussion about these)

I think that is everything. If I have missed something let me know. And I would love to hear how this all makes a difference for your students!

Mathematically yours,

Carollee

Screen shot 2014-02-17 at 11.27.57 AM

 

Building Numbers: A Kindergarten or Primary Activity January 23, 2014

building numbers chips 2

I visited Mrs. Merrill’s kindergarten class today. The focus of the math lesson was on building numbers to 10, we did this with a large organizing sheet (11” x 17”), some small dot cards (each student had a set of cards 1 to 10 — download below), and small bingo chips. Students were asked to place a dot card over each square on the paper, and then use the bingo chips to make another set the same size in each box.

Some students chose to lay their cards out in rank order, while others were happy to just lay the cards in any order they pulled the card out the small bag. We also noticed some students organizing and building left to right in the boxes, while others built randomly on the page.

building numbers chips 1

The organizing sheet is very “generic” on purpose allowing it to be used in a variety of ways. The number for building can be generated by a dot card, by rolling a die (or dice), by placing a number word card (e.g., “two”) over the square, by dropping a bean onto a 100 chart, etc. Students can build the number with counters, with little ten frames (I find children love to work with tiny things!), with base-10 blocks, etc.

building numbers 10 frames

I have not figured out how to put a large 11 x 17 paper into Dropbox, but if you will print out the template you want onto legal-sized paper, you can then enlarge at a copier 121% and it will fit the 11 x 17 page rather nicely.

I have created templates for building 8 different numbers as  well as for building 10 different numbers. The latter could be used for 100 Day activities by building 10 in each space for a total of 100.

Dot cards can be downloaded here as well.

I hope you are able to use the activity in one of its “versions” in your classroom!

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;

 

Salt Spring Island Day 2 April 6, 2013

salt spring pic Day 2 was another busy day for me in the town of Ganges on the lovely Salt Spring Island. First off there was a three-hour workshop for Primary teachers. Our focus was on the big ideas about numbers that we should be working to establish in young children, and how those big ideas could be “layered” or built upon for older students. Those number relationships are a huge part of overall “number sense” which we hope students will build as they explore numbers in many different ways.

After lunch was another three-hour workshop, this time for Intermediate teachers. Delightfully, some of the participants from the first workshop were back for more math! We had a grand time, even if I must say so myself! Our focus was on strategies for doing the major operations (addition, subtraction, multiplication, and division) and tools that would support those operations.

Intersperced in both sessions were lots of examples, stories, and of course, the occasional “math woo” when we just could not contain our excitement. (Ok, I was the one doing the most woo-ing, but how can you not get excited over math!)

I mentioned to the participants that I would post some things for them, so here they are

large 100 dot array

small 100 dot arrays (in two sizes)

• mini blank 10 frames for students to use in problem solving: 27 per page40 per page

10 frames for students (with dots)

teacher 10 frames (with dots)

mini 100 blocks of ten frames

problem solving rubric

If I have missed something that I promised, please let me know and I will add it to the download list.

I had a wonderful time talking math with all those who came to the sessions both days. I hope I am privileged to come back for another round one day!

Mathematically yours,
Carollee

 

How Many More to Make 30? February 12, 2013

how many more to make 30 This is an activity I created to use with two grade 2 classes that I work with at Charlie Lake Elementary. In BC, grade two students work extensively with numbers to 100. The activity, like “How many more to make 20?” (see post from Feb. 5, 2013),  is based on one of the foundational number relationships which is, for numbers 1 to 10, anchoring each number to 10.

30 was chosen as the focal point for this activity since multiples of 10 are also important anchoring numbers.

Once again I was delighted to put some special dice to use, in this case 30-sided dice.** Each child rolled the dice and then, using a set of 10 frames, created the number rolled at the top of the sheet, right over the blank ten frames there. Thus, if 14 were rolled, the child placed a full ten frame and a one showing four on the paper, and then recorded the number 14 in the roll column of the T-chart. Then he looked to see how many would be needed to make 30, in this case 6 to fill the partial ten frame and one more full ten. 16 was  recorded beside 14 on the T-chart (see picture).

Similarly, if 7 were rolled, the child placed a ten frame showing seven on the paper, and then recorded the number 7 in the roll column of the T-chart. He could see that to make 30 he would need 3 more to fill the partial ten frame and two more full 10 frames, and thus 23 was recorded on the T-chart (see picture).

As in the “How many more to make 20?” activity, some of the children stopped making the numbers with their ten frames soon into the activity. Clearly they could imagine the anchoring relationship in their minds and did not need to manipulate the cards to “see” the numbers. Other children needed the support for every roll, but they were still able to be successful because of the scaffolding the ten frames provided.

 

I hope you will try the activity with your students!

Mathematically yours,

Carollee

Download the recording page here.

**If you do not have 30-sided dice, having students draw numbers from a bag or spinning numbers on a spinner will do nicely. You could even give students the page with the first column already filled in with numbers of your choice.

 

How many more to make 20? February 5, 2013

make 20 This is an activity I created to use in a grade one classroom here my school district. (In BC grade one students work extensively with numbers to 20.) It is based on one of the foundational number relationships for numbers 1 to 10: anchoring each number to 10. A set of ten frames is a fabulous tool to help build this relational understanding with young children. The ten frames provide a visual representation of each number and clearly show how far away each number is from 10.

Along with 10 being an anchoring number, multiples of 10 are also important
anchors. With this in mind, I felt it was important to give grade one children the opportunity to practice anchoring numbers to 20.

I had some 20-sided dice that were perfect for the activity**. Each child rolled a die and then, using a set of 10 frames, created the number rolled at the top of the sheet, right over the blank ten frames there. Thus, if 14 were rolled, the child placed a full ten frame and a one showing four on the paper, and then recorded the number 14 in the roll column of the T-chart. Then he looked to see how many would be needed to make 20, in this case 6, and recorded it beside 14 on the T-chart.

Similarly, if 7 were rolled, the child placed a partially filled ten frame showing seven on the paper, and then recorded the number 7 in the roll column of the T-chart. He could see that to make 20 he would need 3 more to fill the partial ten frame as well as a full ten more, and thus recorded 13 on the T-chart.

Some of the children stopped making the numbers with their ten frames soon into the activity. Clearly they could imagine the anchoring relationship in their minds and did not need to manipulate the cards to “see” the numbers. Other children needed the support for every roll, but they were still able to be successful because of the scaffolding the ten frames provided.

I hope you will try the activity with your students!
Download the recording page here.

Download ten frames here.

Mathematically yours,
Carollee

**If you do not have 20-sided dice, having students draw numbers from a bag or spinning numbers on a spinner will do nicely. You could even give students the page with the first column already filled in with numbers of your choice.

 

Dot Plate Workshop: Early Numeracy Concepts October 9, 2012

dot plate workshop 2012This week some of the teachers in the district attended a workshop held here at the SD#60 board office. Our focus for the session was early numeracy, in particular, number relationships that are important for young learners. We focused on these “big four” relationships:
• One more/one less (extending to two more/two less)
• Visual/spatial relationships
• The benchmarks or anchors of 5 and 10
• Whole-part-part

I particularly refer to the whole-part-part relationship in that manner (as opposed to part-part-whole often used by others). I like stating “whole” first because the emphasis of that relationship is that a number can be pulled apart into two smaller parts, not the joining together of two parts to make a larger whole. This distinction is not just a matter of semantics, but rather a spotlighting of the pulling apart. “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, 2005).

Understand that there is a lot of counting that must take place as children work to build these relationships. They must repeatedly work with counters as well as dice, dominoes, ten frames, dot cards, dot plates, and other things that show patterned arrangements of numbers to build a deep understanding about the numbers, first 1-10, then extending to 20, to 100 and beyond.

The workshop participants went home with a set of dot plates they made from small paper plates and bingo daubers (see photo). They also took home 4 sets of small dot cards printed on colourful cardstock. Lastly they took away larger paper plates with dot patterns on them (the patterns from either mini dot cards or mini ten frames) that could become spinners for games or made into activities for math centres.

One other tool that we talked about was a grid of tools that both the teacher and students could use for representing numbers. When one looks at the grid and possible combinations of materials, it is easy to see that having a few good tools on hand allows for many different ways for young children to be involved in representing number.

Download the Representing Number Grid here.

dot card spinner picDownload the dot card spinner here.

Download the ten frame spinner here. ten frame spinner cn pic

I hope you will think deeply about the ways you are having your young learners interact with numbers! You are laying the foundation for later mathematical learning.

Mathematically yours,
Carollee

PS My apologies to the participants — I had intended to post this blog by the end of last week and did not get to it, and over the weekend I did not have access to the visuals I wanted to post with it. So, hopefully, this is a case of better late than never!

Reference
Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.

 

 
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