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Prime Climb Number Activity

Highlights:

  • Dan Finkel's Video for Teachers

  • Enhancing Number Sense Through the Connection of Dan's Number Activity and My Daily Math Routine

At our October staff meeting we watched the video by Dan Finkel Ted X titled “Five Principles of Extraordinary Math” and after watching the video we engaged in the game called Prime Climb.

 

Without a doubt, Dan Finkel makes many valid and crucial points regarding the teaching of mathematics.  I differ in my opinion with regards to one of the principals, and that was not to tell students they are wrong.

I've been teaching for 25 years and despite my experience, I'm aware I don't have all the answers. I believe, however,  that it is important for our young students to make mistakes and even fail at interesting problems. We are not and cannot always be right and failure can bring about great success. I tell my students they are incorrect, but it is not done rudely or in a demeaning way. We work at figuring out why the error was made and through that we often come to the right answer. And the right answer sometimes doesn’t come at that moment or during that math class. It can come a day later, a week later or a month later. It happens when children make a meaningful connection through scaffolding and practice. I know for a fact that when they do make that connection they are so proud of themselves.

Perhaps you have a difference of opinion in dealing with children's mistakes. We may have different beliefs/ideas and ways in which we teach, but I believe the most crucial factor in our classroom is to create an intellectual community that is willing to take risks and share their ideas, right or wrong, with one another.  Creating this environment is not always an easy task, but the time and effort are well worth it because the outcome is incredible. Not only are the children successful in their learning, they are also loving math class. My first and foremost goal in my classroom is to get my young students to enjoy learning math. If I can do this then I can present to them many challenging and interesting problems without having to deal with the negative attitude that many students tend to have and it’s not because they are not capable, it is because they have not felt the confidence in their mathematical ability. With this said, Prime Climb, is undoubtedly one of these challenging and interesting problems to give to students.

 

I am going to backtrack to my staff meeting where our administration engaged us in Prime Climb.  Up on the SmartBoard screen were circles with numbers 1 to 20 and each circle was color coded.  We were asked to pair ourselves up and communicate our thoughts. I believe it is beneficial for teachers to engage in mathematical activities to unpack their own mathematical knowledge. However, if I would have led this activity I would have provided teachers with manipulatives, just as I would with my own students.

 

So, I decided to try this game with my class . On Nov. 1st, Day 39 of school. I paired my students to play Prime Climb. I provided each pair with a number line 1 to 20 and a hundreds chart. I told the students to start off by talking about their thoughts. Then I told them they can pull out their crayons and choose to use the number line and/or hundreds chart to see what they can come up with. Listening to their conversations was fascinating as these young students are only in Grade 3.

It is important to know that my daily routine, right from the first day of school, includes the learning and understanding of what the school day number is divisible by or what factors there are . For example on Day 2, you can count by 1’s two times and by 2 one time, Day 8 we determined we can count by 1 eight times, by 8 one time, by 2 four times and by 4 two times. We have determined factors of numbers from school day 1 to school day 38 using a hundreds chart. And yes, my students use the vocabulary divisibility, factors and multiples, and I also have taught them about prime and composite numbers.

 

 

So what did I hear about the circles? I heard that all the numbers you can count by two’s had orange, all the numbers you can count by 3 had green, all the numbers you can count by 5’s had blue, etc. I also heard that two was orange and 4 had 2 orange because 2 x 2 is 4 and 8 had 3 oranges because 2x4 is 8 and 15 had blue and green because 3 x5 is 15. I also heard 11, 13, 17 and 19 were red because they were prime numbers.

I then asked the students if all the numbers divisible by 5 had blue, what is the next number after 20 to be colored blue? They were able to tell me 25, 30, 35, etc. I asked them to look at the 7 and it was colored purple, where was the next purple? 14  So then where would the next purple come after 20? They used their hundreds chart and I got 21. Then I asked would 21 be solid purple or would it come with another color. Many were uncertain, but I had one little girl (who is average in ability) say it would also be green because seven 3’s is 21. Within my program we discuss groupings of 7 within our calendar routine because there are 7 days in a week.

 

I will definitely come back to this activity a few times so we can further solidify our understanding to 20 and then extend beyond. I would be interested in challenging them with the questions, which are the next numbers after 20 to have 1 color? 2 colors? 3 colors? 4 colors?

My students really enjoyed this activity… one of my struggling students said this is fun. Now please keep in mind that 26 out of 26 students did not figure out what was going on at this time, but about 18-20 did. We won’t have 100% success with every activity we put forth, but what every activity should do is connect and/or be a scaffolding activity to that which they are learning and also provide a challenge for them. If they can’t figure it out during one math class it is perfectly ok. My plan is to do this activity again on Day 57. I shall post again after the 2nd round.

As you can see I was granted permission by Daniel Finkel himself to post the image of the circles 1 to 20 for the purpose of this blog post. I am grateful for his permission and I believe his work is valuable.

 

Math-4-Love

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Delving into Number Line

Highlights:

  • Understanding relationship of number

  • Young children's understanding of negative & positive numbers

  • Building other number-related skills

Delving deep into number enhances number sense and this of course, is the goal through activities connected to the Big Ideas. One of the Big Ideas for the elementary classroom is number line. Through number line young children can learn number pattern, relationship of number, addition, subtraction, multiplication, division, fraction, decimals… and much more.

In my grade 3 classroom we begin with the very basics to understand relationship of number. Where are numbers located in relationship to other numbers and what the relationship between two numbers are by looking at their location (eg. to the right or to the left of each other tells us if they are greater or less and by how many). We often think elementary children are not ready developmentally to learn specific concepts/outcomes (Eg. negative numbers).

I have learned through my own teaching experiences to never underestimate what young children can learn. One day at the beginning of October during numberline instruction, we were having a conversation about zero and it has meaning just as all the other numbers have. I had one boy raise his hand and ask, Miss Kusick, if zero is represented as nothing then how do we represent negative numbers? At that time we connected it to temperature (which I do daily in my math routine because a thermometer is a vertical number line) and I also discussed being in the black in a bank account. However, I am unsure if my students are making these connections at this time in the year.

Within the next couple of days I was reading an article in one of the  Teaching Childrens Mathematics magazines published by NCTM. I subscribe to this magazine yearly because they are full of rich articles and activities that are written by teachers. At the back of the magazine is always an activity that can be modified at every level Kindergarten to Grade 6. This was unbelievable timing because the activity was showing ideas to help young children understand negative and positive number along a linear number line through personal experiences.

  img_20161031_152024_01

-10   -9   -8   -7   -6   -5   -4   -3    -2    -1    0   1   2   3    4     5    6     7    8    9     10

Students will label 0 as their time/year of birth. Then if his/her brother was born 2 years before they will label that at -2. If their parents married 5 years before, he or she will label that at -5. If they had ear surgery at age 2 they will label that at 2. If they started kindergarten at 5 they will label that at 5.

I thought what a great way for kids to make meaning of number, both negative and positive, through their own personal experiences. I sent a note home to parents asking them to sit with their child and identify significant times in their lives 10 years before their birth and up to their current age… births of siblings, marriage or meeting of their parents, moving, surgeries, broken bones, special awards or activities they have been involved with. This information came in and the first thing I did was model this for them by choosing significant times in my life. Children love to know about their teacher. Then their work began. Before students could label information along their number line they had to identify 0 by folding the paper in half. Then they had to use finger iterations to identify 1 to 10 and -1 to -10. Finger iterations has been a part of our number line work since September. Learning iterations came from an article I read last year  titled, “Iteration: Unit Fraction Knowledge and the French Fry Tasks". The initial learning is to help children understand the repeat strategy, but lends itself to nurture children's’ understanding of fractions.

The students seemed to really enjoy the activity and I observed many of my 25 students have ‘aha’ moments. For example, one young boy said “this is so cool cause my brother is 4 years old and it is at the number 4 on my number line because he was born 4 years after me. And I am eight now so that is 4 years younger than me.”  

This activity was successful in  helping my students gain further understanding of the negative numbers, but there was also some confusion. Some students couldn’t connect the years of events taking place in relationship to their birth (0). For example, one young girl was born in 2008 and she had a brother born in 2006 which meant he was born 2 years before her, but she labelled this at -6 (taking the last digit in the year rather than making the connection that 0 (her birth) is 2008 so 2006 is 2 spaces to the left of 0. Out of my 25 students I would say approximately 10 weren’t making this connection. |Keep in mind we have been engaging in number line work from the first day of school and some students had numberline instruction in Grade 1 and 2 and there were others that did not.  

This activity was done middle of October. It still shows me further work is needed to master understanding of negative numbers using various strategies and activities. Students need continue practice and repetition to make connection and meaning. Remember teachers, we are working towards conceptual understanding, not memorization.

When I wrote the note home to parents I did specify to identify how many years before or after birth these events happened verses identifying the year in which they took place. For younger students (K to Gr. 3) keep it at the number of years before and after and for older students (Gr. 4 to Gr. 6) ask for the years of events to make it more challenging. But remember you will have students at a Grade 3 level who can connect the years as I had so this is where differentiation  of learning can happen. Even if the parents didn’t right down the years of events you can ask students the year they were born and they can connect the years to the numbers -10 to 10 along the number line.

This was undoubtedly a valuable activity for my students to engage in to enhance their number sense, but there is still much more learning to do to master understanding.  I will continue to work with number line throughout the entire year using other strategies and activities. I am thinking I  will do this activity again but have the students bring in personal information about a family member (mom, dad, grandma, grandpa).  This could be a great way to tie in some Social Studies and learn some history.

Supporting Book Recommendations

Less Than Zero

A Place for Zero

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My Math Journey

Highlights:

  • About Me

  • What Brought Me Here

Hello, my name is Darlene Kusick. I am a teacher with 25 years of teaching experience. I have achieved my Master of Education in elementary math and science and have achieved an Excellence Teaching Award in 2012. From 2001 to the present year I have written and published teacher guide books from Kindergarten to Gr. 6. My work is known as Math For Success. Presently, my Grade 7 book is in pilot mode in the Northern Lights School Division. The teacher in lead of this is Marjorie Charles, a very talented young teacher, who is a math lead teacher in her school. This Grade 7 book will be published when I feel it is at its best for teachers and students.

I would like to take this time to backtrack to my own school years as a high school student. Math gave me challenges throughout my elementary and junior high years, but believe it or not, I almost failed high school math. I had the intelligence and achieved well in other subject areas but just couldn’t wrap my head around the math concepts. When I attended University to achieve my Bachelor of Education degree, my thought was just make it through the math curriculum and instruction course, and that is what I did.

When I started to teach I felt I was letting my students down. I was teaching students like I was taught and I knew that wasn’t helpful to my own success. At that time, the curriculum was being taught in units or what one principal referred to as snapshot mathematics. Children were not mastering their learning nor were they seeing the connections or integration between strand/outcomes/ concepts, which is so important to number sense. After 3 temporary/part-time positions in a Grade 1, Grade 5 and Grade 4 classroom, I was hired as a full-time Grade 2 teacher in Sundre, Alberta. I was bound and determined to teach math in a way that would help my young students feel and be successful. I believe the biggest obstacle to overcome is the negative attitude students demonstrate towards the learning of mathematics. I recently had a close friend tell me her young grandson refers to math class as torture time.

In order to help my Grade 2 students I, myself needed to unpack my own mathematical understanding of the curriculum outcomes. The curriculum became my bible and I explored and played, teaching the outcomes in an integrated approach rather than a unit by unit approach. The students were learning AND they were having fun! Math class for my students wasn’t a traditional setting in which I taught and then they completed worksheets or a workbooklet. We were communicating our thoughts and answers orally, in writing and with manipulatives. It was a busy and sometimes noisy classroom, but students were talking and engaged in the mathematics. How could math class be so fun? Other teachers in the school began popping their heads in to see what the students were so excited about.

One of the Grade 3 teachers began encouraging me to get these ideas on paper so more teachers and students could benefit. In 2001, I took a 5 month sabbatical to write and publish my first teacher guide book for Grade 2, titled Math For Success and I have been on a journey ever since. I am passionate about mathematics and want more than anything to help teachers gain understanding,  knowledge and confidence in mathematics to benefit their own students. It is not just about the academic learning, but also about the love of mathematics...playing with and manipulating number with ease, creativity and flexibility, which is what numeracy entails. Math literacy is just as important as reading/writing literacy and yet it always seems to take a back seat.

I am a life-long learner and will continue my journey with my own learning so I can help teachers and students. To deliver the math curriculum effectively to our students we have to have the confidence in ourselves and this comes from unpacking our own mathematical knowledge. By empowering yourself, you will empower your students.

I ask you to think what are the challenges you face when teaching mathematics to your students? Is it not knowing the what problems to pose? What guiding questions to ask?  What strategies to teach? What activities/games to incorporate? If we can begin by sharing what our challenges are it will lead to many valuable conversations, as well as guide me where to begin with on-line courses and resources and/or mentorship opportunity with you and your students.

I have, through my journey, ignited a passion within myself for mathematics which I never would have imagined. Let me ignite your passion and help you gain insight, skill, knowledge and confidence to ignite the passion within your students.

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