Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Students will be able to:
1. perform mathematical functions using significant figures in order to properly express values such as data and measurements in the biotechnology laboratory.
2. correctly apply the concept of significant figures to measurement and mathematics operations.
NATIONAL BIOTECHNOLOGY STANDARD:
BT.12.4 Express appropriate numbers of significant figures for calculated data, using scientific notation where appropriate.
Engage (Activate Student Thinking)
Introduce the topic of significant figures to students and set the purpose for the lesson.
“Using significant figures helps prevent the reporting of measured values that the measuring equipment is not capable of determining. A significant figure is comprised of the fewest digits capable of expressing a measured value without losing accuracy. Normally, as the sensitivity or PRECISION of the measurement equipment increases, so does the number of significant figures. Today we will review the rules for working with significant figures.”
How will the proper use of significant figures ensure the precision & accuracy of your measurements and data?
Explore (Guided/Student-Centered Activity)
Significant figures are a way of showing the precision of a number or group of numbers. Significant figures are important because they tell us about the quality of our data. Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. In this animated tutorial, students learn how to identify and work with significant figures as well as determine the relationship between the measurements scientists make in the lab and the precision of those measurements.
1. What are significant figures or digits?
2. How do you spot significant figures or digits?
3. How many significant figures should be reported?
4. How will the use of various measurement tools affect the measured value of the same item?
Significant Figures Lab Training Course
Students will access the following URL - http://lsteam.org/iet/significantfigures/index.html and complete the digital course lesson guide which will enable them to record their observations.
Explain (Formulate Ideas)
Rules Governing Significant Figures
1. All non-zero digits are significant. (i.e. 1-9)
2. Zeros between non-zero digits are always significant. (i.e. 3,606 has 4 sig. figs.)
3. Leading zeros or zeros appearing before a non-zero digit are not significant. (i.e. 0.009 has 1 sig. fig.) Trailing zeros are not significant. (i.e. 360,600 has 4 sig. figs.)
4. In a number with a decimal point, all zeros to the right of the first non-zero digits are significant. (i.e. 3.60 has 3 sig. figs. and 3.6 has 2 sig. figs.)
Addition and Subtraction Rule
The number of significant figures in a sum or difference is equal to that of the least accurate measurement in the equation. The answer must contain the same number of decimal places as the least accurate measurement.
Example: Without using significant figures: 606.02 – 65.3 = 540.72 however using significant figures: 540.7
Multiplication and Division Rule
The number of significant figures in a product or quotient is equal to that of the least accurate measurement in the equation. The answer must contain the same number of decimal places as the least accurate measurement.
Example: Without using significant figures: 606.02 x 63 = 38,179.26 however using significant figures the answer would be 38,000 (has only 2 sig. figs. based on “63”).
Elaborate (Apply and Extend Understanding)
This kinesthetic activity helps students grasp the difficult concept of significant figures. Student groups compete with each other to generate answers to questions about significant figures (also called significant digits) in the Sig Figs/Sci Notation Card Game. Each student holds a card with a single digit (0 to 9), decimal, or negative sign.
1. Review the significant figure rules presented in the Explain section. Display examples of measuring equipment with variations in the level of precision.
2. Distribute one set of Sig Figs/Sci Notation Game Cards to each individual student.
3. Ask basic significant figure questions and monitor students as they race to hold up cards that form the correct answers.
4. Continue asking questions which are progressively more difficult. For example, after the basic questions ask addition and subtraction questions. Then ask multiplication or division questions. Finally provide clues in similar fashion as the game “Who Am I?” by giving the parameters for a number and the students must use the clues to build a number with the correct number of significant digits.
a. Example: The teacher will ask, “How many significant figures are in 1,500?” Students should hold up the number 2.
b. Example: On your desk, build a number between –1 and 1 that has 5 significant figures. Teacher should circulate around the room checking the values that the students have built.
NOTE: Now that your students are becoming masters of Sig Figs this may also be a great time to review or reintroduce the rules that govern Scientific Notation and how they correlate with the use of significant figures!
Evaluate (Monitor Understanding)
To conclude this lesson students can complete the following significant figures problems as further independent practice, group work, or as a homework assignment – Significant Figures Practice Problems, Scenarios and Answer Key.