reap maths... · web viewlogical thinking is developed by studying mathematics. logic turns up in...

Logic is a system of reasoning in all of mathematics

Mathematics Lessons for COVID19 Home LearningStrand: Number and Algebra Target: Y7, 8, 9 –NZC Level 2/3/4Topic: LOGIC

Starter – Odd One Out

ifbecause

then

hence

The idea here is to select a word that you think is the odd one out.

Odd one is ______________ Reason ______________________________________

LearningTHE DEEP UNDERSTANDING OF LOGIC

- being able to infer and deduce in order make sense of and solve problems.

Logical thinking is developed by studying mathematics. Logic turns up in Number, Algebra, Measurement, Geometry, Probability and Statistics. The “if-then” statement is at the core of logical thought. An example is “If a quadrilateral has all sides and angles equal then it is a square”. Logical thinking is in most areas of learning.

Here are a series of contexts and problems that need logical thought to solve. Persevere! One of the best hints for solving these and most other problems is to understand very clearly what the problem actually is. Read carefully! There are no tricks involved but reading carefully is needed.

Problem #1I have a huge box of white sicks and black socks all mixed up. Without looking in the box I randomly select a sock and take it out. How many times do I need to do this to get a pair of socks!

Problem #2There are three boxes and they all contain socks but the labels are all wrong. Your task is to describe how to select one sock from one box and be able to relabel the boxes correctly.

Problem #3This is a visual algebraic problem and your task is to work out the value of each different shape and hence, or otherwise, figure out the “?”. The numbers is the sums of the rows or columns.

Problem #4This is a visual and a word logic problem. Four pets are kept in separate cages in the back yard. There is a rabbit , a hen, a guinea pig and a rooster. The pet names are Chip, Tommy, Mickey and Dale. Use the clues and the boxes layout to match all the names to the pets.

• The guinea pig is next to the hen and the rooster.• Dale is opposite the guinea pig• The hen is called Chip• Mickey is opposite the hen.

Drawing or visualising ideas and concepts is a powerful way to understand

Large box of black socks and white socks

White socks only

White socks and

Black socks

Black socks only


Problem #5I have two coins and 15c in my hand. One of the coins is not a 5c piece. What are the denominations of the coins?

Drawing a Logic Diagram Problem #6

Jesse has four playing cards in her hand. There is a heart, a diamond, a club and a spade. One of the cards is a King, one is a Queen, one is a 10 and the other is a 5. • The heart is the highest card.• The 10 is not black.• The spade is lower than the club. The diagram lists the items to match up in a grid.

Clue #1 “The heart is the highest” means the match K and “ ” is a “

” and in the empty boxes in the rest of the row and column there must be a “ ”. The rest is up to you. Your task is to list the four cards. This is an effective and visual way to work out logic problems where each is matched to another in one and only one way.

Problem #7Amy, Bianca and Carla went on a picnic together. One took sandwiches in a chilly bin, the one who went in her mother’s van took chippies and the one who biked to the picnic took the fizzy.

• Amy’s mother drives a new car• Carla doesn’t have a bike becuase it is too jhilly where she lives. • Bianca’s mother borrowed a chilly bin for her for the day.

Draw a table and using this deduce who took what to the picnic? [The three names head the table in the first row and the three foods are in the first column.]

Problem #8Here is the famous Zebra problem first published in 1962.

1. There are five houses.2. The Englishman lives in the red house.3. The Spaniard owns the dog.4. Coffee is drunk in the green house.5. The Ukrainian drinks tea.6. The green house is immediately to the right of the ivory house.7. The Old Gold smoker owns snails.8. Kools are smoked in the yellow house.9. Milk is drunk in the middle house.10. The Norwegian lives in the first house.11. The man who smokes Chesterfields lives in the house next to the man with the fox.12. Kools are smoked in the house next to the house where the horse is kept.13. The Lucky Strike smoker drinks orange juice.14. The Japanese smokes Parliaments.15. The Norwegian lives next to the blue house.

Who drinks water? Who owns the zebra?

The grid will help but use names. I put clue 9 in as an example. Good luck!


KQ105

House 1 2 3 4 5Colour

NationalityDrink Milk

SmokePet


SolutionsStarter – Odd One Out

ifbecause

then

hence

The idea here is to select a number that you think is the odd one out.

Odd one is ____if_____ Reason _____implies a question is asked______

Problem #1Taking out just three socks ensures a pair of either white or black socks.

Problem #2Taking a sock out of the middle box to decide if this box is White or Black and hence the first correct label. The other label is wrong so just swap it over and put the B&W label on the last box. A very cool problem.

Problem #3Adding the first two Columns gives 2 circles, 2 squares and 2 stars and totals 28.Halving this will give 1 circle 1 square and 1 star and a total of 14. This is the same as the first Row and makes ? = 14.Subtracting Row Two from Row One gives triangle – star = 5 hence triangle = 5 + star. Substituting for triangle in Row 3 gives 3 stars plus 5 = 14 hence star = 3 and triangle 8.In Column One 2 circles = 12, hence circle = 6In Column Two 2 squares = 10, hence square = 5. Check with any Row or Column to see this all works. Nice problem.

Problem #4The rabbit is Dale, the hen is Chip, the guinea pig is Tommy and the Rooster is Mickey.

Problem #5The other coin is the 5c. Sorry about that!

Problem #6The four cards are the King of Hearts, the 10 of Diamonds, the 5 of Spades and the Queen of Clubs.

Problem #7Bianca took the sandwiches, Carla took the chippies and Amy took the fizzy.

Problem #8The Norwegian drinks water and the Japanese person owns the zebra. Complete solution below.


Must be Black or White!


But check out https://en.wikipedia.org/wiki/Zebra_Puzzle for more information.

JournallingToday I learned ________________________________________________________________

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.


https://en.wikipedia.org/wiki/Zebra_Puzzle


Answers 82 could be odd because it is not a multiple of 11, 9 only uses one placevalue, many answers here, the grid was made on Xcel using the =RANDBETWEEN (1,99) calculation in each cell. Exercise 1.

(a) 623 = 600 + 20 + 3(b) 82 = 80 + 2(c) 5,555 = 5,000 + 500+ 50 + 5(d) 12,345 = 10,000 + 2,000 + 300 + 40 + 5(e) Which number in (d) has the most value? Answer is the 1, value is 10,000.

Exercise 2.(a) Add 123 to 345 = 100 + 20 + 3 + 300 + 40 + 5 = 400 + 60 + 8 = 468(b) Subtract 123 from 345 = 222(c) Add 1,234 and 5,678 = 6,912(d) Subtract 1,234 from 5,678 = 4444(e) Add 23, 34, 45, 56, 67 and 78 = 303(f) Subtract 23 and 134 from 900 = 743

Zero is a special number for the operations of addition and subtraction. Write an explanation of why this might be. Zero is a place holder and does not have value. It is also the number that can be added or subtracted without changing the original number. (Identity element for addition). Any number of zeros can be written in front of a number without changing its value. There is a book called ZERO. Zero was invented when people started to trade using money. Every placevalue system uses a zero! Exercise 3. Write out these numbers in full or as you would say them.

(a) 234 = two hundred and thirty four(b) 89 = eighty nine(c) 463 = four hundred and sixty three(d) 7,120 =seven thousand one hundred and twenty(e) 6,007 = six thousand and seven(f) 34,567 = thirty four thousand five hundred and sixty seven(g) 1,234,567 = one million two hundred and thirty four thousand five hundred and sixty seven

Exercise 4.Write these written numbers using numerals.

(a) Forty seven = 47(b) Five hundred and six = 506(c) Two thousand three hundred and ninety nine = 2395(d) Five hundred and six thousand two hundred and twelve = 506, 212(e) Twelve million and one = 12,000,001

Puzzle A.Write this number in numerals

“Eleven thousand, eleven hundred and eleven”

11,000 + 1,100 + 11 = 11,000 + 1,000 + 100 + 10 +1 = 12,111 – a bit sneeky!Puzzle B.I think of a number, say 2,846, and make another using the same digits, say 6,842. I then subtract the smaller one from the larger one. My answer is 3,996. I add these digits 3 + 9 + 9 + 6 = 27. I add these digits 2+7 = 9.

You think up a number and repeat the steps. What do you notice? They always add to 9! Try and figure out why but we return to this later and answer that.

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 .


https://nzmaths.co.nz/information-about-e-ako-pld-360

mailto:https://www.youcubed.org/resource/growth-mindset/

mailto:[email protected]

reap maths... · web viewlogical thinking is developed by studying mathematics. logic turns up in...

Documents