All posts by mathconfidence

King Henry or Kings Have Diamonds


This is a new Common Core item from PARCC (grade level and link to be revealed at the bottom of this post).

How do your students remember metric conversions?  My favorite was found in the South Bronx on a middle school teacher’s desk while I was observing a student teacher:  Kings Have Diamonds Man Diamonds Cost Money.  A more popular one is shown below.  The metric system is so brilliant because it uses base 10 and why do we use Base 10 anyway? Click here for info on the history of bases.

King   Kilo
Henry  Hecto
Died    Deka
By  Base (meter gram liter)
Drinking  deci
Chocolate  centi
Milk  milli

The table below shows the metric prefix and the matching mnemonic word.

kilo — Kangaroos
hecto — Hop
deca — Down
meter — My
(Change meter to any unit)
deci — Driveway
centi — Carrying
millimeter — M&Ms

Here is the link to this item: (5th grade)

B and C are the correct answers:

B) 7cm is like 7 cents which is .07

C) 1000m = 1km so 7000m = 7km

January 2015 Brain Teaser Solution

Q: I was 29 the day before yesterday and next year I will be 32. This is true only one day in a year. What day is my birthday?

A: December 31st is the birthday so on December 30: age = 29

Dec 31: turns 30

Jan 1 : the day it is ‘now’ in the question

will turn 31 at the end of the current year (it is far away as it is Jan 1 and the birthday is Dec 31)

therefore the person will be 32 at the end of the next calendar year

Test Taking is a Skill: learning from ‘fuzzy errors”

At least 5 times a week, someone will share that their son or daughter is a poor test taker.  We all know people who ace the test with no effort but much can be gained by focused studying and commitment and I do not just mean test scores!

Tests may not always show knowledge and skills — that 7 in Physics was tough freshman year (yes out of 100!) but I learned so much about attention to detail and focus.  How many times do we see 2^3 (2 to the 3rd) = 6 rather than 8?  I call these “fuzzy errors”.  People can improve their test scores and their attention to detail by answering the exact question and noticing the finer points of what they are being asked.

How did I learn to do this?  The hard way — btw, my next score in Physics was exciting because it was double digit — 11!  (because class avg was so low, I still managed a C in the class).

You Make the Call!! 4th Grade Division


It used to be that Math was lots of number crunching but Elementary Math has changed –my theory is the advent of the calculator and Google.  Homework can no longer be a page of straight division problems as they can be Googled for the answer and even for all the steps involved!!!
I came across this working on homework with a 4th grader. Is it 9 divided by 2?  or 9 divided by 4?  Both have a remainder of 1.

See the diagram below for these two ways of interpreting division (albeit division without remainder).Partition division vs Quotition division diagram

Here is another example:

13 can also be grouped by quotition division see above with 3 groups of 4 with remainder 1.  This method will yield the same Math results EXCEPT  for problems like 12 divided by 5 which is 2 remainder 2.  But divide 12 by 2 and we get 6 not  5 remainder 2 b/c the remainder goes in one more time (same goes for divide 21 by 6  is 3 R3 but 21 divided by 3 is exactly 7 not 6 R3.).  So be aware that division these days is about interpretation and not computation.

December 2014 Brain Teaser Solution

Q: Tree A and tree B both have some birds.   The tree A birds tell the tree B birds “if one of you comes to our tree, our population will be the double of yours.”   The tree B birds tell the tree A birds “if one of you comes here, then our population will be equal to that of yours.” How many birds in each tree?

A:  Tree A has 7 birds and tree B has 5 birds

This can be done with guess and check or algebra

This is for statement 1)  A + 1 = 2(B – 1)

This is for statement 2)  A – 1 = B + 1

This is A in terms of B from 2) A = B + 2

Then sub into statement 1 and solve for B

B + 2 + 1 = 2B – 2

B + 3 = 2B – 2

B = 5

then can solve for A using either equation A – 1 = 5 + 1    therefore A = 7