Dear all,

No school this Sunday:P

I have created a “test” in Google Classroom. Each student will view it in their “classwork”.

Watch the video: https://www.youtube.com/watch?v=1PoljZjZjBM&feature=youtu.be

And fill in the Google Form below.
https://forms.gle/ENQNXs2i5CBJJfp2A

6 problems, 100 points 🙂
Enjoy!

Best,
Lijia

Lesson review

• A numeral is a representation of a number.
• Base number systems
• Base (radix, or scale)

Homework

• p.142 Ex.8.2.1(a) (d)
• p.145 Ex.8.3.1(b), 8.3.2(c), 8.3.3, 8.3.6(a)(d)(g)
• p.148 Ex.8.4.2
• p.152 Ex.8.5.2(a)(c), 8.5.3(a), 8.5.4
• P158 Ex.8.6.2 (a,c,d,e), 8.6.4
• p160 Ex.8.23

• Ex. 8.6.2, please use a “smart” way to convert. For example, from 3^2 to 3, from 2^4 to 2, from n to n-1, try to think about the methods we explained in the class.
  
• Extra Resources

• https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/number-systems-introduction
• https://www.youtube.com/watch?v=nEBKpX8JZ04
• https://www.youtube.com/watch?v=jxC7_0dqHT4
• https://www.mathsisfun.com/numbers/bases.html
• https://betterexplained.com/articles/numbers-and-bases/

*Another way to determine Perfect/Abundant/Deficient Number

Thanks to Jason’s Daddy’s sharing!

for example, 300 = 2^2  × 3 × 5^2.  

The sum of all positive divisors of 300

=(4+2+1)x(3+1)x(25+5+1) 

=7x4x31=868 > 2 x 300. 

Therefore 300 is abundant.

See you next next Sunday!

According to NCLS calendar, there is no school next week (4/12). 

Please take care and stay healthy!

We are going to learn Ch.9 Base Number Arithmetic on 4/19.

 Lesson Review

• A generalized form of a group of numbers is an algebraic expression common to all of the numbers in the group.
• Parameters: the variables that dictate the values of generalized expressions
• Algebraic factorization

Homework

p.136-137

• Ex. 7.10 to 7.13
• Ex. 7.16, 7.17
• Ex. 7.20 to 7.23
• Ex. 7.27

Sorry that the connection from my laptop to my “Tiny Blackboard” failed to work today☹ However, we had great fun playing Kahoot! I will redesign more Kahoot! Game in our future class.

Please remember to turn in the weekly homework by each Saturday night at 10:00 pm in Google Classroom. Next week we will learn Ch.8 Base Number Systems.  Take care and see you then!

Lesson Review

• A Mersenne prime: 2^p-1 (p: prime number)
• A Fermat prime: 2^2n +1 (n: nonnegative integer)
• Twin primes: a pair of primes that differ by 2
• n factorial: n!=n(n-1)(n-2)…2*1
• a palindrome: an integer that reads the same forward as it does backward.

Homework

• p.109 Ex. 6.2.1, 6.2.2
• p.113 Ex. 6.3.2 to 6.3.5, 6.3.7
• p.115 Ex. 6.4.4  (6.4.1 classwork)
• p.118 Ex. 6.5.1 to 6.5.3
• p.120 Ex. 6.26*

Other Resources

• https://mathworld.wolfram.com/TwinPrimes.html
• https://byjus.com/maths/perfect-numbers/
• https://www.mathsisfun.com/definitions/palindromic-numbers.html
• https://nrich.maths.org/2574

Something Else

Please join our Google Classroom (Code: mtl4kzb). Students should turn in the weekly homework by each Saturday night at 10:00 pm.

Take care and look forward to seeing you all next Sunday. We will learn Ch.7 Algebra with Integers.

Lesson Review

• formula to find the t (n) number of positive divisors of a positive number n
• A proper divisor of a positive integer is any divisor of other than. itself
• Any positive perfect square has an odd number of positive divisors;
• If m and n are any two positive integers such that gcd(m,n)=1, then t(mn)=t(m)*t(n)
• product of the positive divisors of a positive integer n: Pn=N^(t(n)/2)

Homework

• P.92 Ex 5.2.1(e)(f)(i)(l); 5.2.3
• P.98 Ex 5.3.1, 5.3.4, 5.3.7, 5.3.9
• P.101 Ex 5.4.3, 5.4.4, 5.4.6
• P.104 Ex 5.17
• P.105 Ex 5.21, *5.26, *5.27

Other Resources

• https://www.math.upenn.edu/~deturck/m170/wk2/numdivisors.html
• http://mathonline.wikidot.com/the-number-of-positive-divisors-of-an-integer
• https://www.youtube.com/watch?v=Be5fd7h4aQo
• https://www.youtube.com/watch?v=IeyVdRHOPzc

Ch.5 is not easy. If you have any questions, please feel free to reach out and Ms. Li will be happy to help. Remember to turn in your homework by next Sat night, so that I can grade and give it back to you before our class. Next week, we will spend some time discussing the leftover problems in Ch.5.

Take care and look forward to learning Ch. 6 with all of you next Sunday.

Lesson review:

• factor tree
• prime factorization
• rational numbers
• lowest form (reduced form) vs. unreduced form
• gcd (a,b)
• lcm [a,b]
• ab = gcd (a,b)*lcm [a,b]
• gcd(ac,bc) = cgcd (a,b)
• lcm [ac,bc] = clcm [a,b]

Homework:

• P.68 Ex.4.2.1 (b) (k) (p)
• P.71 Ex.4.3.2, 4.3.4
• P.74 Ex.4.4.1 (b) (f), 4.4.2 (b) (d)
• P.77 Ex.4.5.1 (d) (e) (g) (h)
• P.79 Ex.4.6.1, 4.6.5
• p.83 Ex.4.7.1 to 4.7.4
• * bonus: p.86 Ex. 4.36, 4.37, 4.38, 4.39

Other Resources:

• https://www.mathsisfun.com/prime-factorization.html
• https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-prime-factorization-prealg/v/prime-factorization

Lesson Review:

• Common divisor
• GCD (Greatest Common Divisor) or GCF (Greatest Common Factor)
• Relatively prime or coprime
• Common multiple
• LCM (Least Common Multiple)
• gcd(m,n)
• lcm[m,n]
• The Division Theorem: a = bq + r (0≤r<b) a:dividend, b:divisor, q: quotient, r: remainder
• Euclidean algorithm: gcd(m,n) = gcd (m-n,n)
• The extended Euclidean algorithm: gcd(m,n) = gcd (m-n,n) = gcd (m-kn,n) = gcd (r,n)

Homework:

• Page 40: Ex 3.2.5
• Page 43: Ex 3.3.2
• Page 45: Ex 3.4.1 (d) (g)
• Page 50: Ex 3.5.3
• Page 53: 3.6.1, 3.6.6
• Page 59: 3.7.1 (b)
• Page 61: 3.24 (d), 3.32, 3.33, 3.34

Other Resources:

• https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm
• https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-greatest-common-divisor/v/greatest-common-divisor

Take care, and wish everyone to stay safe and healthy!

Sums of Consecutive Counting Numbers

by Mr. John Bookston

Definition:  A sum of consecutive counting numbers can start with any counting number add at least the next bigger counting number and stop adding after any number of consecutive integers.

Examples:  3+4 = 7                   7 is a consecutive sum of counting numbers

   1+2+3+4+5 = 15    4+5+6 = 15 and 7+8 = 15     15 is a consecutive sum in 3 distinct ways.

Investigation: 

For numbers that are consecutive sums, investigate patterns to predict the number of distinct ways larger numbers can be written as consecutive sums.  

Starters:       1 and 2 are not consecutive sums

Every odd integer starting with 3 can be written as a consecutive sum of two counting numbers:

                                      (n-1)/2  +  (n+1)/2  =  n       for every odd number, n.

Make a conjecture about which numbers are expressible as “the sum of 3 consecutive counting numbers”. 

Extension: Do the same for numbers that can be expressed as sums of 4,5 and 6 consecutive counting numbers.

Extension:  Consider the prime factorization of the counting numbers that cannot be expressed as a consecutive sum.  Make a conjecture as to which counting numbers less than 1000 fall into that category.

Enjoy.             

Good luck. 

Dear all,

Enclosed please find the excel file with the answer to the bank question in our brain stretcher last week. Many thanks to Mr. Zhang (Jason’s dad) for sharing!

Q4: Bank of America has money in the forms of $1, $5, $10, $20 and $100. How many different combinations can Tony withdraw $100 dollars at the counter?

https://docs.google.com/spreadsheets/d/1_GSWdR27K8XLUscFJAIIvpCTKWQFYNtYVfrSxpwv00s/edit?usp=sharing

There is no school for the following two weeks, but please feel free to contact me if you have any questions regarding our previous chapters/exercises. I will be very glad to help.

Enjoy the spring break, and I look forward to meeting you all when we are back!

Best,

Lijia