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.