Connect, connect, connect ideas and concepts! Mathematics Lessons for Remote Learning Strand: Geometry and Measurement Target: Y7, 8, 9, 10 –NZC Level 3/4 Topic: GM Conversions of SI Units Length, Mass and Time Starter – Odd One Out 60 24 365 7 The idea here is to select the odd one . I choose __________ because _____________________ Learning THE DEEP UNDERSTANDING OF MEASUREMENT - Being enabled to quantify size of shape, reason, make sense of and connect ideas to solve problems. Two Fundamental Mathematical Axioms Axiom #0 :One can be anything I choose one to be. Axiom #1: When we combine or compare anything in mathematics we do so using the same size units. The first axiom helps us make a ruler. The second axiom says we can compare or combine measures. Here is a website with all the prefixes such as “kilo” used with measures. https://en.wikipedia.org/wiki/Metric_prefix Take a look and explore the page. I copied the table because it has some important patterns in number and names most of which we do not use at school! Thank goodness. Communication in maths includes words, graphs, diagrams, symbols.
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Connect, connect, connect ideas and concepts!
Mathematics Lessons for Remote LearningStrand: Geometry and Measurement Target: Y7, 8, 9, 10 –NZC Level 3/4Topic: GM Conversions of SI Units Length, Mass and Time
Starter – Odd One Out60 24365 7
The idea here is to select the odd one .
I choose __________ because _____________________
Learning THE DEEP UNDERSTANDING OF MEASUREMENT
- Being enabled to quantify size of shape, reason, make sense of and connect ideas to solve problems.
Two Fundamental Mathematical AxiomsAxiom #0 :One can be anything I choose one to be. Axiom #1: When we combine or compare anything in mathematics we do so using the same size units. The first axiom helps us make a ruler. The second axiom says we can compare or combine measures.
Here is a website with all the prefixes such as “kilo” used with measures. https://en.wikipedia.org/wiki/Metric_prefix Take a look and explore the page. I copied the table because it has some important patterns in number and names most of which we do not use at school! Thank goodness.
Exercise 1Which pattern do you like? Which is your favorite word? See if you can name a measure or word for 10 of these measures. For example a millionaire is a person who has $1,000,000 in cash or assets.
Communication in maths includes words, graphs, diagrams, symbols.
Connect, connect, connect ideas and concepts!
There are seven base units in the SI system: the kilogram (kg), for mass. the second (s), for time. the kelvin (K), for temperature. the ampere (A), for electric current. the mole (mol), for the amount of a substance. the candela (cd), for luminous intensity. the meter (m), for distance.
With each of these we can use the prefixes above and get bigger and smaller units.
Exercise 2 - Convert(a) 65kg to grams(b) 370 seconds to minutes(c) 23.6km to m(d) 3.5hrs to minutes(e) 1 day to seconds(f) 3000mA to A(g) 2V to mV(h) 1Mb to bytes(i) 290K to C
There are few curved balls (unusual or odd problems) in there but you will get the idea.
We can connect these dimensions or measures and get other measures. For example speed is distance travelled divided by the time taken. If we travel 30 km in 3 hours we are travelling at the rate or average speed of 30/3 = 10km/hr. This is a casual bike speed. Top cyclists in the Around Lake Taupo Event travel at more like 35km/hr or even faster.
A derived unit of measure combines 2 or more units or measures listed above. For example the density of matter is Mass/Volume. Lead has a density of a little over 11 tonnes per cu m or 11 grams per cubic centimeter. Here is a website with a few more elements listed. https://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html
Rule of practice #1 - Reminder!Measure twice, cut once. If you want evidience that thisis really good advice just ask any carpenter or engineer.
Exercise 3Combine these measures to make the rate.
(a) I travel 120m in 15 seconds. What is my avearge speed?(b) My mass is 95kg and I have a volume of 0.1 of a cubic meter. What is my density?(c) I use 12litres of fuel to travel 134km. What is my km/L and my L/km rate?You might have noticed in (c) that there are two rates (km/L and my L/km) depending on how the division is done. Both have meaning! Be wary of this because it can be useful!
Activity(a) Get some reasonably strong cardboard and make a 10cm x 10cm x 10cm cube with an open top. Be as exact as
you can. (b) Line the box with thin gladwrap. Zero the weighing machine by placing the empty box on the scale and adjust
so it reads zero. Now fill the box with water. What does it weigh in kg and in g?(c) Calculate the volume of the box in cubic centimeters and using (b) work out the density of water g/cc(d) How many of the 10cm x 10cm x 10cm cubes will fit inside a cubic meter? Nice problem. (e) Now use your answer (b) to work out what 1 cubic meter of water weighs.
Tidy up your mess!
Problems (a) How old are you in seconds? You can make this problem a bit more complicted by finding out your exact birth
time, and use the exact time now, and include Leap Years! The answer is about half a billion. This is about the number of heart beats your blood pump has made so far.
(b) How many times around this planet could light travel in 1 second?(c) How long does light take to get to Earth from our nearest star, the Sun?(d) How long is a light year?.It is the distance light will travel in one year. Our Milky Way Galaxy is about
100,000 light years across. See Power of Ten Video or exoplanets.nasa.govt(e) What is an Angstrom?(f) What country still uses miles, foot and inch?
Communication in maths includes words, graphs, diagrams, symbols.
Connect, connect, connect ideas and concepts!
JournallingToday I learned ________________________________________________________________And I would like to know about ___________________________________________________
CommentsMake any comment you feel like making here.
Math Language: List all the math words you can find in this document and write what you think it means beside the word. Eg subtraction means to take away or to find the difference. Keeping a list of these words is a very good idea.
Communication in maths includes words, graphs, diagrams, symbols.
Connect, connect, connect ideas and concepts!
AnswersOdd Man Out
60 24365 7
The idea here is to select the odd one . Notice these numbers are all time numbers.
I choose ____60______ because __ it is the count of two measures____Exercise 1Which pattern do you like? I see the way the zeros form a slanting triangular shape. Which is your favorite word? “nano”. Not sure why, just like the sound. Perhaps its “Nano Girl” Google the name. See if you can name a measure or word for 10 of these measures.
- a millionaire is a person who has $1,000,000 in cash or assets. Millimeter, Centimeter, Megabyte, microsecond, millisecond, hectogram, nanometer, nanosecond, decimeter, hectometer.
Exercise 2 - Convert(a) 65hg is 65,000 grams, x1000(b) 370 seconds is 6.1666 minutes or 6 min and 10 seconds. (c) 23.6km is 23,600 m, x 1000(d) 3.5hrs is 210 minutes, x60(e) 1 day is 86,400seconds, x60x60x24(f) 3000mA is 3 A, divide by 1000(g) 2V is 2000 mV, x1000(h) 1Mb is 1,000,000bytes, x by 1 million(i) 290K is 17C, add Absolute Zero which is -273C
Exercise 3Combine these measures to make the rate.
(a) I travel 120m in 15 seconds. What is my avearge speed? Ans is 8m/s(b) My mass is 95kg and I have a volume of 0.1 of a cubic meter. What is my density?Ans is 950kg per cu m(c) I use 12litres of fuel to travel 134km. Ans. My km/L rate is 11.2 and my L/km rate?
Is 0.09. We usually use L/100km so that would be 9L/100km.
Activity(a) Give yourself a prize if you made a box of the correct size!(b) What does it weigh in kg and in g? Ans is 1kg = 1000g(c) The volume of the box is 1000cc and (b) work out the density of water g/cc is 1g/cc or 1T/cu m(d) You will get 1000 10cm x 10cm x 10cm cubes to fit inside a cubic meter?(e) Now use your answer (b) to work out what 1 cubic meter of water weighs. 1Tonne/cu m
Extra activity, get some 1m long sticks and make a cubic m shape to hang up and look at.
Problems (a) How old are you in seconds? For a 13 year old the answer is 13x365x24x60x60 = 409,968,000s(b) How many times around this planet could light travel in 1 second? Nearly 7 times. (c) How long does light take to get to Earth from our nearest star, the Sun? About 8m and 20seconds. (d) A light year is actually a distance measure. It is the distance light will travel in one year. Our Milky Way
Galaxy is about 100,000 light years across. See Power of Ten Video or exoplanets.nasa.govt(e) What is an Angstrom? One angstrom is equal to 10−10 m or 1/10th of a nanometer. Very tiny. (f) What country still uses miles, foot and inch? USA is one of these countries.
FeedbackStudents and teachers are welcome to email [email protected] with comments. This was a lesson that could be given to a NZC Level 2, 3, 4, 5 student for some placevalue learning and revision. Students should select a set time each day and perhaps using the timer on a cell phone set 45 minutes or so to learn and practice mathematics. Keep trying on problems and expect to struggle. Persevering and struggling are great competencies to develop. You can learn more about these from https://www.youcubed.org/resource/growth-mindset/. We have a great math website in Nzwith a special resource called e-AKO https://nzmaths.co.nz/information-about-e-ako-pld-360 .
Communication in maths includes words, graphs, diagrams, symbols.
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