Mathematics Essentials 12 Module 1 - Measurement
Specific Curriculum Outcomes
- 1.1 Demonstrate an understanding of the meaning and uses of accuracy and precision
- 1.2 Use a measuring tape to measure tactile items in both imperial and SI units
- 1.3 Identify the difference between length, area, and volume
- 1.4 Demonstrate an understanding of the meaning and uses of significant figures
- 1.5 Demonstrate an understanding of, and be able to solve problems using dimensional analysis
- 1.6 Identify, use, and convert among and between SI units and Imperial units to measure and solve measurement problems
- 1.7 Estimate distances by using a personal benchmark such as walking pace
- 1.8 Demonstrate an understanding of, and be able to solve problems using the Pythagorean Theorem
1.1 Activities - accuracy and Precision
This outcome is very similar to Math at Work 12 M01.
- What's the difference between accuracy and precision? a TEDEd video from Matt Anticole - This video explains the difference between accuracy and precision using the story of William Tell.
- Accuracy Versus Precision Beanbag Toss - Student create a target of concentric circles, put it on the floor, and then throw three bean bags (you can make cheap bean bags out of old kids socks or use an alternative item to throw). Students measure distance of each back to the center (accuracy) and also measure the distance from the two bean bags that are farthest apart (precision). They record their data in a table.
- Precision and Accuracy Dart Game - A virtual dart game. Try throwing three darts and the computer will calculate your accuracy (how close your worst throw is from the bulls-eye) and precision (the radius of the circle enclosing all your shots). You could use actual suction cup darts on a white board, and then have students take the actual measurements to make this more hands on.
1.2 and 1.3 Activities - Measuring Length, Area and Volume
This outcome should focus on using actual measuring tape with both metric and imperial measurements to measure the length area and volume of physical objects. This outcome is similar to Math at Work 10 M01, M02 and M03.
- Tape Measure Pro Tips video - Learn some tricks about your tape measure!
- The Ruler Game - Use this game to improve how you read a ruler. After you click on the button that says, "Start New Game," the name of a measurement will appear in the text box labeled, "Click on:." As soon as you see the measurement appear, click on the corresponding measurement on the ruler at the top of the screen.
- Long Jump Measurement Activity - Use painter’s tape to create a line on the floor. Students stand at the line and jump forward as far as they can. Mark where they landed with the painters tape. Now use the measuring tape to measure how far your student jumped.
1.4 Activities - Significant Figures
- Intro to Significant Figures from Khan Academy - A short video to introduce the topic.
- Significant Figures Stations from Sarah Carter - A series of five stations that students can rotate through in groups. Any of these activities could also be done as a whole class activity.
- Colouring Significant Figures - This activity asks students to colour zeros different colours depending on their placement in the number. Students will use these colours to determine the rule for significant figures.
- Triangle Area Measurement - Make a large triangle on the floor with painters tape. Ask students to measure the base and height of the triangle to calculate the area. To find the height, measure the line that is perpendicular (90˚ angle) to the base and intersects the corner opposite the base Do this three times (once using each side as the base) keeping track of significant digits. If all of your measurements for the triangle had been perfect, what should have been true about all the area values you calculated? Why do we use significant figures when
reporting a calculated values such as area?
1.5 and 1.6 Activities - Converting Units and Dimensional Analysis
- Unit Conversions - A site with some nice examples of dimensional analysis.
- Would You Rather Have a Pound of Quarters or a Pound of Dimes? from Would You Rather - You could change this up to be a pound of quarters or a kilogram of dimes (or nickels) in order to add in the conversion between SI and metric units. You could also change this to linear measurement.
1.7 ACTIVITIES - Estimate with Personal Benchmarks
This outcome is similar to Mathematics Essentials 10 D3 (estimate distances in metric units and in imperial units by applying personal referents).
- Estimate the Length of a Garden Hose from Estimation 180 - How long (ft. or m) is the garden hose?
- Estimate the Height of a Lamppost from Estimation180 - What is the height of the lamppost?
- Estimate How Many Licorice Ropes I can Hold from Estimation180 - How many pieces of red licorice are in my hand?
1.8 activities - Pythagorean Theorem
This outcome should focus on practical applications of the Pythagorean Theorem. This outcome is similar to Mathematics 8 M01, Math at Work 10 G02 and Mathematics Essentials 11 E2 (understand and apply the Pythagorean Theorem).
- 3-4-5 Method - This video demonstrates how to get a perfect right angle when laying out the foundation for a structure. Students can practice this application using painters tape on the floor to lay out a perfect 3' x 4' rectangle or could use string and tent stakes to layout a larger rectangle outside on a grassy area.
- TV Space Task from Timon Piccini - Will Mr. Piccini's new 40" LCD HD TV fit in the space he has available on the wall? You'll need to know about Pythagorean Theorem and the height to width ratio of an HD TV to find out.
- Watson Save from Yummy Math - In the 2005 AFC divisional football championship game between the New England Patriots and the Denver Broncos, Benjamin Watson stopped a touchdown in the last instant. He did this by running diagonally across the entire football field. Watch the video to see the play and listen to the commentary.
- Pythagorean Theorem Game - Split the class into small groups. Each player takes turns rolling two dice. Using the numbers on the two dice as the legs of a right triangle, find the length of the hypotenuse using the Pythagorean Theorem (always round to the nearest whole number). The player earns this number of points. (e.g. If I roll a 2 and a 3, then the length of the hypotenuse is sqrt(2^2+3^2) = sqrt(13) = 3.606 giving me 4 points). The first player to 25 points wins.