Math

# Grades 9–12 Math Activity Set 1: Precision and Accuracy and More

We're providing five days of lessons designed to engage your high schooler in mathematics. This week’s lessons are about precision and accuracy, significant digits, and errors in measurement, which will help them with the Measuring Objects lab. The last lesson continues with ways to convert measurements.

### Materials Needed:

Each lesson has an answer sheet that provides guidance on the lesson and describes the key concept and questions from the lesson. Use this sheet to check your answers. The student sheet can be printed and completed by the student, or the student can write his or her answers on a blank sheet of paper.

You will also need:

• Scale (can use a food scale set to grams or a bathroom scale)
• Hint: If using a bathroom scale set to kilograms, find the grams by dividing the number by 1,000. If using a bathroom scale set to pounds, find the grams by dividing the number by 454.
• Block of wood, metal, or other solid uniform material in the shape of a rectangular prism

## Activity 1: Precision and Accuracy

The terms precision and accuracy are often used interchangeably in everyday speech, but they have distinct meanings in mathematics.

Use this lesson to compare the precision and accuracy of measurements and learn about tolerance.

## Activity 2: Significant Digits

The number of digits in a measurement is related to the precision of the measurement. Significant digits are those digits of a measurement that contribute to the precision of the measurement.

Use this lesson to learn how to identify significant digits and how to use the correct number of significant digits in reporting the result of a calculation.

## Activity 3: Errors in Measurement

The significance of an error in measurement depends on both the accuracy of the measurement and the magnitude of what is being measured.

Use this lesson to understand both absolute error and relative error, and explore how when measurements are used in calculations, the relative error is influenced by the accuracy of the measurements being used.

## Activity 4: Measuring Objects Lab

The density of a material is its mass per unit volume.

In this lab, you will use what you have learned about precision, accuracy, significant digits, and measurement errors to calculate the density of an object.

## Activity 5: Converting Measurements

An essential idea behind using conversion factors is the concept that when you multiply a measurement by 1, the value of the measurement is unchanged.

Use this lesson to learn how to convert measurements within and between systems, and how to convert derived units (for example, meters per second to miles per hour).

### Extend the Lesson: Math at Work

Explore the Math at Work web series on the HMH YouTube channel. Watch Math Meets Homebuilding.