Introduction
For many second graders, the beginning of the year is a time for revisiting knowledge and skills learned in first grade. The summer months away from mathematics instruction along with little opportunity for practice and guidance sometimes means a loss of strong understanding of concepts. Addition and subtraction of numbers to 100 is a Common Core Standard for first-grade students, although many struggle with this fundamental concept even throughout second grade. This curriculum unit is designed to increase my students' understanding of the number line as a tool to help them master two-digit addition and subtraction, improve their base-ten number sense and increase their fluency in mathematical operations.
Edgewood Magnet School in New Haven, Connecticut is an arts magnet school, integrating the arts across the curriculum. Students in this school are encouraged to use the strategies of observation, interpretation, and analysis to increase their thinking skills in every subject. With this mission, the teachers and students use unique and exciting approaches to “the basics” and work together to ensure that all students are learning successfully. This unit is designed with the school's mission and vision in mind.
Our district mathematics curriculum for Kindergarten through Grade 5, Math in Focus Singapore Math, is one based on the highly successful mathematics instruction model which introduces students to concepts through the CPA approach – using concrete, then pictorial, and finally abstract activities to introduce, practice and master mathematical concepts. Although the early activities in this program include an introduction to the relationship between counting and addition and subtraction, the first weeks of the second grade school year are an important time to remind and reintroduce this fundamental understanding.
In this curriculum unit, students will begin their work with the number line as they learn to connect measurement with counting. By using rods and cube train manipulations and transferring the bars to the number line, students will see the relationship between length and counting. The start of the school year will include a review of addition and subtraction using small numbers, sums equal to or less than ten, to help students become familiar with this connection and begin to actually use the number line as a tool just as they use counters, cubes, and base-ten blocks as tools. Making numbers and combining numbers using ten frames shows values concretely and helps students write equations, using the abstract mode of conceptual understanding.
The students will then move on to higher addition facts that include regrouping, recognizing the connection to the base ten structure and specifically understanding that the teen numbers are ten and some more. Once they are proficient with teen numbers, the students will then be ready to focus on the multiples of ten - twenty, thirty, forty, fifty and so on - applying the same strategies for regrouping they've already mastered.
Math in Focus for Grade Two does not include the number line as a tool for addition and subtraction but instead uses a hundred board (tens stacked on tens) to help students with the notion of our base ten system. Students can easily see that counting up by tens starting at 23 means the pattern will continue on the same vertical path to 33, then 43, to 53 and so on. What they do not see visually is the linear jumps up the number line and the length connection to the counting by tens. This focus of this unit will help students recognize the relationship between bar models, number sentences, and number patterns.
Through the Every Day Counts Calendar Math program, an enrichment component to the Math in Focus curriculum, the students build a number line. The Counting Tape, as it is called, is a linear timeline for recording each passing day of school in second grade. As students watch one new square being added to the counting tape each day and see the number for that day of school recorded, they become familiar with increasing quantities and the numbers that represent them. Counting the groups of ten and the extra ones reinforces students' understanding of place value. Every ten days, the color of the square alternates (orange to yellow) to help students see patterns between decades. From the 101st day on, the students see the pattern from the first 100 days repeated. This process helps students develop a connection between counting and length; a good start to the concrete step of learning.
For the duration of this unit and in addition to the Counting Tape, we make use of the open hallway outside of the classroom to create an interactive number line, taking advantage of the longer distance than our room offers, writing number sentences to solve and creating challenging problems to share with classmates. Maybe we will even be able to answer the question "How long is a thousand line?"
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