Number and Operations in Base Ten
Overview
Another major area of primary mathematics is building an understanding of number and operations in base ten. Students need a solid understanding of this because much of the mathematics in higher grades builds from this understanding. The standards outline a clear progression of learning beginning with the teen numbers in kindergarten to the tens in first grade and the hundreds in second grade. Many textbooks speed through this progression. This results in students memorizing algorithms, mnemonics, and other tricks. These build a shaky foundation which often results in difficulties later on.
When thinking about base ten topics, I try to think about going deeper with my students rather than going faster. In kindergarten, this means focusing on counting up to 20 objects and building an understanding of teen numbers by making a group of 10 objects and identifying the extras. The numbers 11, 12, and even 13 can be very tricky because they do not follow the pattern of the other teen numbers, e.g., four-teen. Do not rush this learning!
In first grade, students need a lot of practice working with groups of ten. They need to build the understanding and trust that a group of ten really has ten in it. They do this by working with multiples of ten at first and counting and grouping ten objects for each ten. Then they can count by tens if they are ready to, and they can count each of the objects again to check if their counting by tens is correct. From there, they move on to counting groups of tens and some extra ones. Addition and subtract grows in a similar manner. Students begin by adding two multiples of ten. Next, they add a multiple of ten and a two-digit number (20 + 34), and then they add two two-digit numbers without regrouping (25 + 34). After working with and building an understanding of these situations, students finally move to adding two two-digit numbers with regrouping.
In second grade, students expand their understanding of the base ten system to include hundreds. They build this understanding similarly to the progression in first grade, but now they also add expanded notation and word forms of the numbers. Students need time and space to build this understanding and practice these new skills.
When thinking about base ten topics, I try to think about going deeper with my students rather than going faster. In kindergarten, this means focusing on counting up to 20 objects and building an understanding of teen numbers by making a group of 10 objects and identifying the extras. The numbers 11, 12, and even 13 can be very tricky because they do not follow the pattern of the other teen numbers, e.g., four-teen. Do not rush this learning!
In first grade, students need a lot of practice working with groups of ten. They need to build the understanding and trust that a group of ten really has ten in it. They do this by working with multiples of ten at first and counting and grouping ten objects for each ten. Then they can count by tens if they are ready to, and they can count each of the objects again to check if their counting by tens is correct. From there, they move on to counting groups of tens and some extra ones. Addition and subtract grows in a similar manner. Students begin by adding two multiples of ten. Next, they add a multiple of ten and a two-digit number (20 + 34), and then they add two two-digit numbers without regrouping (25 + 34). After working with and building an understanding of these situations, students finally move to adding two two-digit numbers with regrouping.
In second grade, students expand their understanding of the base ten system to include hundreds. They build this understanding similarly to the progression in first grade, but now they also add expanded notation and word forms of the numbers. Students need time and space to build this understanding and practice these new skills.
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