I’ve been enjoying my year teaching Introduction to Algebra. This portion of Unit 3 isn’t any different as we are working with scientific notation. Last year, I wrote a post about how teachers have traditionally discussed this concept in this post and this post. Therefore, I wanted to do my very best at presenting this concept through the lens of place value understanding.
Our first activity was connecting base ten blocks, powers of 10 and decimal notation or standard form through the context of a number line. Hindsight, this would have been a great bridge to implementing clothesline number lines. What we actually did was create a human number line. As we transitioned from concrete to representational, we constantly referred back to our physical number line and the equivalent values.
Looking at the numerical representation, students were able to identify patterns among the powers of 10 and exponents. Beginning with base ten blocks made the transition to converting between decimal notation and scientific notation very simple. We looked at 3 cubes and determined not only did they represent 3,000 but also 10^3 three times or 3 x 10^3. We tried a few examples using the blocks we actually had before extending it out to the millions.
By now you may be thinking, how did we discuss exacting how to convert a number in standard form to scientific notation. Of course the topic of the decimal point moving can up, mainly because students heard this terminology within their science class. I used a draw place value chart to demonstrate how the digits shift and the decimal stays put. Later, I was introduced with this site which helps to illustrate my point. During our discussions, I would explicitly state when the digits shifted and how many spaces and connect it to a pattern previously identified by a student.
Another benefit of the base ten blocks:
3 flats is 3 x 10^2
6 flats is 6 x 10^2
9 flats is 9 x 10^2
10 flats is 10 x 10^2 which students were able to determine was equivalent to 1 x 10^3. We were able to conclude is scientific notation is written with a whole number coefficient less than 10. Students had a conceptual understanding of why it is a whole number less than 10.