# MPM1D Order of Operations examples 2017-09-18

We spent most of the class working on evaluating expressions. We saw a few new things:

• an exponent that was an expression instead of just a number
• brackets inside brackets (nested brackets, we often say)
• lotsa negative signs

I handed out two more lengthy pages from math-drills.com. The first page only included integers, and the second page included fractions. You should be spending at least 15 minutes outside of class time practising with these questions.

If you’re finding this challenging, you should be spending more than 15 minutes. These are fundamental skills that will serve you well throughout high school – it’s worth taking the time now, I promise!

# MDM4U Combinatorics problems – 2017-09-18

More practice today! We also had a small quiz:

Combinatorics Quiz 1

Solutions will be available in class; the answers are:

#1. 360
#2. 22
#3. (a) 840 (b) 1134 (c) 715

Homework is page 287 #11, 16. Don’t spend forever on them (30 minutes maximum!).

# MDM4U More Combinations 2017-09-15

We took up the homework questions and then practised solving more counting problems. We especially looked at how cases might be necessary to solve some problems.

For homework please complete Page 286 #2, 6, 8, 10.

# MPM1D Starting Order of Operations 2017-09-18

We took up yesterday’s stuff then worked on evaluating expressions using “order of operations” (which most of you call “BEDMAS”).

The big-picture idea is that there are rules about how we evaluate and simplify math expressions so that an expression isn’t ambiguous. For example, $1+2\times3$ is equal to $7$ because we agree that multiplication is resolved (evaluated) before addition.

We practised a bunch of different kinds. Your tiny slice of home is to evaluate this expression:

$(3+4)^2\div7\times2^2-4^3+(2\div7)$

# MDM4U Combinations 2017-09-14

We continued learning about Combinations today:

The number of combinations of $r$ items from a set of $n$ unique items is

$P(n,r)\div r! = _nC_r=C(n,r)=\binom{n}{r}=\frac{n!}{r!(n-r)!}$

We spent some time on Pascal’s Triangle as well, which is a neat structure full of combinations.

Homework today is page 279 #12, 13, 18. See you tomorrow!

# MPM1D Negative Fractions 2017-09-14

We spent most of today working with negative fractions. You have limited experience with them, so we practised adding, subtracting, multiplying, and dividing. I gave 8 small questions for homework:

$\frac{2}{3}\times\left(\frac{-1}{2}\right)$

$\frac{4}{-7}\div\frac{2}{7}$

$\frac{-8}{3}\times\left(\frac{-1}{7}\right)$

$\frac{-2}{3} + \left(-\frac{3}{6}\right)$

$\frac{-8}{5}\times\left(\frac{-1}{2}\right)$

$\frac{3}{7}\times\left(\frac{-7}{3}\right)$

$\frac{5}{-4}\div\left(\frac{-3}{-4}\right)$

$\left(\frac{-1}{2}\right)\left(\frac{-1}{2}\right)\left(\frac{-1}{2}\right)\left(\frac{-1}{2}\right)$

# MDM4U Permutations with some identical items 2017-09-13

We took up our homework questions (and had a fire drill). Then we had a quiz (Permutations Quiz 1 – some identical items) which we looked at right away (remember, quizzes aren’t included in your grade).

We’re just starting to look at Combinations – choosing stuff instead of arranging stuff. Our example in class was something like this:

5 people volunteer to run the Tuck Shop. Only 2 people are needed. How many different pairs are possible?

There are 10 different pairs. If there were “first” and “second” people, then the order in which two people were chosen would matter (for example, Alfred-Bonnie would be a different pair than Bonnie-Alfred). This would give 20 pairs, but that doesn’t make sense for this situation. Since every pair has two “orders”, we divide 20 by 2 to get 10 unique pairs. This is a pretty small number, so you can just list the pairs to see this value.

Tomorrow we’ll generalize this and get a useful formula as well. Stay tuned!