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Delving into Number Line


  • 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.


-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


  • 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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