Critical thinking is about reflecting on what you have done Mathematics Lessons for Remote Learning Strand: Geometry and Measurement Target: Y7, 8, 9, 10 –NZC Level 3/4 Topic: GM Conversions of SI Length Units Starter – Odd One Out m s g k g mm 1 m g V k m The idea here is to select the odd one . I choose __________ because _____________________ Learning THE DEEP UNDERSTANDING OF GEOMETRY - Being enabled to describe shapes and their properties in the world around us, to reason, to generalise (prove), to make sense of and connect ideas to solve problems. 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. We use the SI sysem for measure. Here is the website for NZ Measurement . Here is what Wikipedia has to say about measure. The French determined the length we call one metre and here is a story about all that. The unit of length is a metre and we break it up into 1/100ths or centimeters, 1/1000ths or millimeters, or group 1000 of them to make a kilometer. The skill of converting from one unit of measure to another is very important. Common conversions include m to cm and cm to m. Builders use mm so m to mm and cm is also a good skill to know. If you know how to multiply and divide by Collaboration is a much needed 21st Century skill
Transcript
Critical thinking is about reflecting on what you have done
Mathematics Lessons for Remote LearningStrand: Geometry and Measurement Target: Y7, 8, 9, 10 –NZC Level 3/4Topic: GM Conversions of SI Length Units
Starter – Odd One Outm s g
kgmm 1
mg V
km
The idea here is to select the odd one .
I choose __________ because _____________________
LearningTHE DEEP UNDERSTANDING OF GEOMETRY
- Being enabled to describe shapes and their properties in the world around us, to reason, to generalise (prove), to make sense of and connect ideas to solve problems.
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.
We use the SI sysem for measure. Here is the website for NZ Measurement. Here is what Wikipedia has to say about measure. The French determined the length we call one metre and here is a story about all that.
The unit of length is a metre and we break it up into 1/100ths or centimeters, 1/1000ths or millimeters, or group 1000 of them to make a kilometer. The skill of converting from one unit of measure to another is very important.
Common conversions include m to cm and cm to m. Builders use mm so m to mm and cm is also a good skill to know. If you know how to multiply and divide by 10,100,1000 then you also can do these conversions. The tricky bit is deciding whether the answer is a bigger answer or a smaller answer. Estmating a length is very useful and that is where we start.
Exercise 1 – Estmate these lengths and then use a ruler, or otherwise, to see if you were about right. (a) The length and width of a piece of A4 paper.(b) The height of your desk or a table that is nearby.(c) The height of the door(d) The distance to school from home(e) The diameter of a bike wheel(f) The circumference of the bike wheel(g) The thickness of a page in a book(h) The height of a power pole(i) The distance around your house or a nearby building(j) The width of a TV
Critical thinking is about reflecting on what you have done
(k) Your girth or measure around your middle(l) The length of your middle finger
Exercise 2 needs some conversion facts. There are 100cm in every m, and 10mm in every cm. There are 1000 mm in a m and 1000 m in a km. The abrieviations used here are m = meter, mm = millimeter, cm = centimeter, km = kilometer.
Exercise 2Think about the size of the answer and if it will be bigger or smaller. The 2km will give a number bigger than 2 because the unit called m is much smaller than a km so more of them are needed.
Length Convert to Bigger or smaller number?12m cm
300cm m2km m bigger
400mm cm400mm m
1.5m cm4.25m mm600m km1km mm
You sometimes multiplied and sometimes divided. The last conversion might have needed two jumps. 1km = 1000m, 1000m = 1,000,000 mm. This is a good strategy when solving a more complicated problem.
Mathematicians
1. Look for a pattern2. Make a rule3. Test the rule
Look for a PatternIn your answers above see of you can find a pattern.
The pattern I notice is ...
Make a rule
I think the rule is ...
Test the Rule
420 km = m = cm = mm20mm = cm = m = km
If your rule worked then continue, otherwise go back and keep looking for a pattern.
Rule of practice #1Measure twice, cut once. If you want evidience that thisis really good advice just ask any carpenter or engineer.
Exercise 3How many dimensions of this world can you name? A dimension is like height and weight. No more help!
Collaboration is a much needed 21st Century skill
Critical thinking is about reflecting on what you have done
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.
Collaboration is a much needed 21st Century skill
Critical thinking is about reflecting on what you have done
Collaboration is a much needed 21st Century skill
Critical thinking is about reflecting on what you have done
AnswersOdd Man Out
I choose _____1_____ because _it is a number___But there is a 1 in all these units!
I changed my mind to choose _____V_____ because _is a measure used in electricity, the Volt___
Exercise 1 – Estmate these lengths and then use a ruler, or otherwise, to see if you were about right. (a) The length and width of a piece of A4 paper - A4 measures 210 × 297 millimeters(b) The height of your desk or a table that is nearby. – usually about 75cm(c) The height of the door – usually about 2m(d) The distance to school from home – This will vary but if you cycle it could 3km. (e) The diameter of a bike wheel – A road bike is about 1m(f) The circumference of the bike wheel – For the same wheel aabout 3m (3x!)(g) The thickness of a page in a book – Tricky! A ream of 500 pages is 55mm so a page is about 1/10 of a mm(h) The height of a power pole – 6m or so(i) The distance around your house or a nearby building – A 100 square m house will be about 40m (j) The width of a TV – 800mm but will vary(k) Your girth or measure around your middle – Mine is about 5cm(l) The length of your middle finger – 95mm
Notice part of measure is using an appropriate unit. Did you use km for your answer to (l)?
Exercise 2Think about the size of the answer and if it will be bigger or smaller. The 2km will give a nnumber bigger than 2 because the unit called m is much smaller than a km so more of them are needed.
Length Convert to Bigger or smaller number?12m 120cm Bigger x10
300cm 3m Smaller ÷1002km 2000m Bigger x 1000
400mm 40cm Smaller ÷10400mm 0.4m Much smaller! ÷1000
1.5m 150cm Bigger multiply by 1004.25m 4250mm Much bigger x 1000600m 0.6km Smaller ÷1000 1km mm Much bigger x1,000,000
Look for a PatternIn your answers above see of you can find a pattern.
The pattern I notice is ... converting to a bigger unit use division, to a smaller unit use multiplication and get more
Make a ruleI think the rule is ....mm to cm ÷10, cm to m ÷ 100, m to km ÷ 1000, km to m x 1000, m to cm x 100, cm to mm x 10, m to mm x1000.
Test the Rule420 km = 420,000 m = 42,000,000 cm = 42,000,000,000mm20mm = 2 cm = 0.02m. = 0.00002km
It might be a good idea to figure out a better way of writing small and big numbers. Example of reflection!
Exercise 3How many dimensions of this world can you name? A dimension is like height and weight. No more help!
How many dimensions are there in the world? - 3What is a dimension, and how many are there? As you've probably noticed, we live in a world defined by three spatial dimensions and one dimension of time. In other words, it only takes three numbers to pinpoint your physical location at any given moment. But then there is mass. So maybe there is more.
Search the web for how many dimensions there are. Here is a list of humopurous units of measure. https://en.wikipedia.org/wiki/List_of_humorous_units_of_measurement
Critical thinking is about reflecting on what you have done
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 .
