And on TW, Susan Russo used difference of two squares, which I hadn't thought of.
Cool!
https://twitter.com/Dsrussosusan/status/1628146466098188289?s=20

#MTBoS #iTeachMath #TryMathLive #MathEd #MathStratChat

I am happy with those 3 versions of mentally computing 83 x 97.

Please share your #ProblemSolving strategies here or on the post https://karendcampe.wordpress.com/2023/02/04/february-calendar-problems/

More #MathStratChat on Wednesdays from @pwharris
& mental math Mondays from @howie_hua

#MTBoS #iTeachMath #TryMathLive

Here's another multiplication using the area model to show double distribution.
Same four partial products as above:
80•90 + 80•7 + 90•3 + 7•3
Total = 8051

#MathStratChat #TryMathLive #MTBoS #iTeachMath #ProblemSolving #MathEd

How about decompose with a target number?

83 • 97
83•(100 – 3)
83•100 – 83•3
8300 – 249 [bc 80•3 + 3•3]
8300 – (250 – 1)
8300 – 250 + 1
8050 + 1 = 8051

#MathStratChat #TryMathLive #MTBoS #iTeachMath #ProblemSolving

83 x 97
My first thought is decompose & distribute:

(80 + 3)•(90 + 7)
80•90 + 3•90 + 80•7 + 3•7
7200 + 270 + 560 + 21

Now combine by place value:
7200 + 200 + 500 = 7900
70 + 60 + 21 = 151

Total = 8051

#MathStratChat #TryMathLive #MTBoS #iTeachMath #MathEd

Here is problem 1.
Reminder that for #TryMathLive I am sharing my thinking process... no need to jump in with suggestions (altho your own #ProblemSolving always welcome at the end of the thread).

#MTBoS #iTeachMath #MathStratChat
Explain how to multiply 83 x 97 using mental arithmetic.

Reminder that I posted a February Calendar of Problems from an old nctm journal. Please share w/your students or try #ProblemSolving yourself!

https://karendcampe.wordpress.com/2023/02/04/february-calendar-problems/

In this thread, I will #TryMathLive with one of the problems!
#MTBoS #iTeachMath #MathStratChat #MathEd

6x + 9 = 51
--> x = 7

Now to find h, use 1st eq:
\( 7^2 + h^2 = 25^2 \)
Yay! That seems to be a pythagorean triple... 7:24:25 (if my Ss don't remember it, just use pyth thm)

h = 24

#Geometry #TryMathLive #ProblemSolving

I'm doing another #TryMathLive #TryMathsLive #ProblemSolving from my January Calendar of problems.

Problem 2:
"In a triangle, the lengths of the sides are 3, 25, & 26. Find the length of the altitude to the shortest side."

Ok, I think I've solved Problem 1 three different ways.

Any other solution pathways you've thought of? Please share!

#TryMathLive #ProblemSolving #Algebra #Arithmetic
#MSmathChat #MTBoS #iTeachMath

Another thought is about averages.

If 5 integers' sum is 155, then average (arithmetic mean) is 155/5 = 31

So I think 31 must be my middle number. Choose 2 integers below and 2 above 31.

29 + 30 + 31 + 32 + 33 = 155

#TryMathLive #ProblemSolving #Arithmetic

Let first of our integers = n
Then next is n+1, then n+2, n+3, n+4

So, sum of 5 consec integers is
n + n+1 + n+2 + n+3 + n+4 --> 5n + 10
This sum = 155, so
5n + 10 = 155
5n = 145
n = 29
--> five integers are 29, 30, 31, 32, 33

#TryMathLive #ProblemSolving

#TryMathLive / #TryMathsLive intended to show my thinking, including false starts, wrong turns, & hopefully a few ways to solve.
(So no need to jump in to tell solution while I'm in progress... however would love others' thinking shared at end.)
#MTBoS #iTeachMath #ProblemSolving

ICYMI, I posted a set of January Calendar Problems from an old nctm journal at beginning of the month.
I'm going to #TryMathLive #TryMathsLive for a couple Qs in this thread.
Happy solving & please SHARE your solutions!
https://karendcampe.wordpress.com/2023/01/01/january-calendar-problems/
#MTBoS #iTeachMath #problemsolving

@samurai Yes indeed!!!
What I was doing in the thread was "Try Math(s) Live" : showing my thinking from the beginning, including wrong turns & dead ends. (I wasn't presenting a polished solution.)
My friend David Butler does this frequently on TW, to show how doing math isn't linear & can be messy.
#TryMathLive #TryMathsLive

I did another #TryMathLive #ProblemSolving from my December Calendar of problems.

Here's the #probability problem #8
Bag contains 50 blue & 50 green marbles.
2 selected randomly.
If GG --> box A
If BB --> box B
If one G one B --> box C
What is P(boxes A & B contain same # of marbles)?
#MTBoS #iTeachMath #MathEd

I decided to do another #TryMathLive #TryMathsLive today on Tw, with another problem from my December Calendar of Problems blog post.

Here's the Tw thread:
https://twitter.com/KarenCampe/status/1602417451479797771?s=20&t=EDQEJd5LlIPAlebHmmbvYw

Note that a goal of TryMathLive : show problem-solving isn't always neat & going in linear --fashion toward solution; it's messy & has some dead ends.

Here's the Tw thread with my thinkings and workings.

https://twitter.com/KarenCampe/status/1600258598872891392?s=20&t=01s05WhNh-CvGWGGeFQGoQ

If you try out some problems from the calendar, please share your working out (spoilers welcome).
Thanks for the inspiration from David K Butler who always models trying math when you don't know the answer in advance.
#MTBoS #iTeachMath #MathEd #TryMathLive #TryMathsLive

ICYMI, I posted a set of Calendar Problems for December (from an old nctm journal).

I decided to #TryMathLive #TryMathsLive for one of the problems today on Twitter.

Here's the blog post:
https://karendcampe.wordpress.com/2022/12/03/december-calendar-problems/

#MTBoS #iTeachMath #MathEd