9G (2.6) Operations with Units

(2.6)
Operations with Units

You know what units are.
10 is a number
cookies are units

10 cookies

Multiple Choice

$$10\ cookies\ +\ 12\ cookies\ =\ ?$$

• 22 cookies

• 20 cookies

• 18 cookies

• 24 cookies

• 21 cookies

What you might not know is that we take them pretty seriously sometimes. They are really part of the calculations

Multiple Choice

$$13\ cookies\ -\ 9\ cookies\ =\ ?$$

• 4 cookies

• 5 cookies

• 3 cookies

• -3 cookies

• -4 cookies

Multiple Choice

$$9\ cookies\ -\ 13\ cookies\ =\ ?$$

• 4 cookies

• 5 cookies

• 3 cookies

• -3 cookies

• -4 cookies

Open Ended

What could -4 cookies mean?

Multiple Choice

$$\ 3\ cookies\left(\ 3\ cookies\right)\ =\ ?$$

• 9 cookies(cookies)

• 9 cookies

• 6 cookies

• 6 cookies(cookies)

• 10 cookies

Multiple Choice

$$\ 3\ cookies\left(\ 3\ cookies\right)\ =\ ?$$

• $$9\ cookies^2$$

• 9 cookies

• 6 cookies

• $$6\ cookies^2$$

• 10 cookies

Open Ended

What could $$9\ cookies^2$$ mean?

Multiple Choice

$$\ 3\left(\ 3\ cookies\right)\ =\ ?$$

• $$9\ cookies^2$$

• 9 cookies

• 6 cookies

• $$6\ cookies^2$$

• 10 cookies

Multiple Choice

Let's give a more realistic example:

$$4\ feet\ +\ 8\ feet\ =\ ?$$

• 12 feet

• 10 feet

• 11 feet

• 13 feet

• 9 feet

Multiple Choice

$$9\ feet\ -7\ feet\ =\ ?$$

• 12 feet

• 4 feet

• 2 feet

• 3 feet

• 16 feet

Multiple Choice

$$4\ feet\ \left(5\ feet\ \right)=\ ?$$

• 20 feet(feet)

• 25 feet(feet)

• 9 feet(feet)

• 20 feet

• 21 feet

Multiple Choice

$$4\ feet\ \left(5\ feet\ \right)=\ ?$$

• $$20\ feet^2$$

• $$25feet^2$$

• $$9\ feet\ ^2$$

• 20 feet

• 21 feet

Open Ended

What does $$20\ feet^2$$ mean?

It means 20 of these green squares. We measure the size of a house using square feet

Multiple Choice

$$10\ feet\ \left(7\ feet\ \right)=\ ?$$

• $$70\ feet^2$$

• $$70feet^{ }$$

• $$17\ feet\ ^2$$

• 17 feet

• 71 feet

Multiple Choice

$$9\ inches\ \left(5\ inches\ \right)=\ ?$$

• $$45\ inches^2$$

• $$45\ inches^{ }$$

• $$40\ inches^2$$

• $$14\ inches^2$$

• $$14\ inches$$

Multiple Choice

$$-12\ inches\ \left(4\ inches\ \right)=\ ?$$

• $$-48\ inches^2$$

• $$48\ inches^{ }$$

• $$-60\ inches^2$$

• $$-60\ inches^{ }$$

• $$-8\ inches$$

Multiple Choice

$$9\ feet\ \left(9\ feet\ \right)=\ ?$$

• $$81\ feet^2$$

• $$81\ feet^{ }$$

• $$18\ feet\ ^2$$

• 18 feet

• 99 feet

Multiple Choice

$$9\left(9\ feet\ \right)=\ ?$$

• $$81\ feet^2$$

• $$81\ feet^{ }$$

• $$18\ feet\ ^2$$

• 18 feet

• 99 feet

Multiple Select

What's the difference between $$81\ feet^2\ and\ 81\ feet$$ ?

• $$81\ feet^2$$ is 81 small squares, each of which is 1 foot tall and 1 foot wide

• There's no difference.

• 81 feet is a line that is 81 feet long

• One is talking about a persons foot and one is talking about the unit of measurement

Multiple Choice

$$2\ feet\left(9\right)=\ ?$$

• $$81\ feet^2$$

• $$81\ feet^{ }$$

• $$18\ feet\ ^2$$

• 18 feet

• 99 feet

Multiple Choice

$$17\left(2\ cookies\right)=\ ?$$

• $$34\ cookies^2$$

• $$19\ cookies$$

• $$19\ cookies^2$$

• $$34\ cookies$$

• $$36\ cookie$$

Multiple Choice

$$8\ pounds\ \left(6\ pounds\ \right)=\ ?$$

• $$48\ pounds^2$$

• $$48\ pounds^{ }$$

• $$14\ pounds^{ }$$

• $$14\ pounds^2$$

• $$42\ pounds^2$$

Multiple Choice

$$17\ brownies\left(2\ cookies\right)=\ ?$$

• $$34\ cookies^2$$

• 19 brownies(cookies)

• $$19\ cookies^2$$

• 34 brownies(cookies)

• $$36\ cookie$$

Multiple Choice

$$12\ feet\left(6\ inches\right)=\ ?$$

• $$72feet\left(inches\right)$$

• $$72\ feet^2$$

• $$72inches^2$$

• $$18feet\left(inches\right)$$

• $$36\ feet\left(inches\right)$$

Multiple Choice

$$10ft\left(\ 7\ lbs\right)5s\$$

Where ft means feet, lbs means pounds and s means seconds

• 350 ft(lbs)s

• 350ft(lbs)

• 350ft(s)

• 350lbs(s)

Multiple Choice

$$3ft\left(\ -8\ lbs\right)2s\$$

Where ft means feet, lbs means pounds and s means seconds

• -48 ft(lbs)s

• -48ft(lbs)

• -48ft(s)

• -48 lbs(s)

• 48 ft(lbs)s

Multiple Choice

$$-48ft\left(lbs\right)s\left(10\ wheels\right)$$

Where ft means feet, lbs means pounds and s means seconds

• -480 ft(lbs)s(wheels)

• -480 ft(lbs)(wheels)

• -480 ft(s)(wheels)

• -480 lbs(s)(wheels)

• 480 ft(lbs)s(wheels)

Multiple Choice

$$-\frac{480ft\left(lbs\right)s\left(w\right)}{4\ cars}$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$-120\frac{ft\cdot lbs\cdot s\cdot w}{cars}$$

• $$-120\frac{ft\cdot lbs\cdot w}{cars}$$

• $$-120\frac{ft\cdot s\cdot w}{cars}$$

• $$-120\frac{lbs\cdot s\cdot w}{cars}$$

• $$-120ft\cdot lbs\cdot s\cdot w$$

Multiple Choice

$$\frac{10}{10\ }=\ ?$$

• 1

• 10

• 5

• 2

Multiple Choice

$$\frac{10023\cdot76}{10023}=\ ?$$

• 761748

• 76

• 10023

Multiple Choice

$$\frac{15\cdot16}{15}=\ ?$$

• 16

• 67362

• 15

Multiple Choice

$$\frac{15}{15\cdot16}=\ ?$$

• $$\frac{1}{16}$$

• $$\frac{1}{263}$$

• $$\frac{1}{15}$$

Multiple Choice

$$\frac{10\ feet}{2\ feet}=\ ?$$

• 5 feet

• 5

• $$5\ feet^2$$

Multiple Choice

$$\frac{25\ feet}{5feet}=\ ?$$

• 5 feet

• 5

• $$5\ feet^2$$

Multiple Choice

$$\frac{25\ feet}{5}=\ ?$$

• 5 feet

• 5

• $$5\ feet^2$$

Multiple Choice

$$\frac{25}{5feet}=\ ?$$

• 5 feet

• $$\frac{5}{1\ feet}$$

• $$5\ feet^2$$

Multiple Choice

$$25\left(\frac{1}{5feet}\right)=\ ?$$

• 5 feet

• $$5\left(\frac{1}{1feet}\right)$$

• $$5\ feet^2$$

Multiple Choice

$$12feet\left(6\ inches\right)=\ ?$$

• $$72feet\left(inches\right)$$

• $$72\ feet^2$$

• $$72inches^2$$

• $$18feet\left(inches\right)$$

• $$36\ feet\left(inches\right)$$

Multiple Choice

$$\frac{72feet\left(inches\right)}{9\ inches}$$

• $$72feet\left(inches\right)$$

• $$72\ feet^2$$

• $$72inches^2$$

• $$8feet$$

• $$8feet\left(inches\right)$$

Multiple Choice

$$\frac{40brownies\left(cookies\right)}{8\ brownies}$$

• $$5brownies\left(cookies\right)$$

• $$5$$

• $$4brownies\left(cookies\right)$$

• $$5\ cookies$$

• $$8feet\left(inches\right)$$

Multiple Choice

$$\frac{30ft\cdot lbs\cdot w}{6w\cdot s}$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$5\frac{ft\cdot lbs}{s}$$

• $$5ft\cdot lbs$$

• $$5\frac{ft\cdot lbs\cdot w}{s}$$

• $$5ft\cdot lbs\cdot s$$

Multiple Choice

$$\frac{45w\cdot s}{9lbs\cdot s\cdot ft}$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$5\frac{w}{lbs\cdot ft}$$

• $$5\frac{w\cdot s}{lbs}$$

• $$5\frac{w}{ft}$$

• $$5\ \frac{w\cdot lbs}{ft}$$

• $$5\frac{w\cdot s\cdot ft}{lbs}$$

Multiple Choice

$$20\ \frac{ft}{s}\left(4w\right)$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$80\frac{ft\cdot w}{s}$$

• $$80\ ft\cdot w$$

• $$80\ \frac{w}{s}$$

• $$80\ \frac{ft4w}{s}$$

• $$80\ \frac{ft}{s\cdot w}$$

Multiple Choice

$$15\frac{ft}{s}\left(10\ \frac{ft}{s}\right)$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$150\frac{ft^2}{s^2}$$

• $$150\frac{ft^{ }}{s^2}$$

• $$150\frac{ft^2}{s^{ }}$$

• $$150\frac{ft^{ }}{s^{ }}$$

Multiple Choice

$$\frac{12}{60}\ =\ ?$$

• $$\frac{1}{5}$$

• 5

• $$\frac{1}{4}$$

• 4

• 6

Multiple Choice

$$\frac{1}{5}\left(19\right)\ =\ ?$$

• $$\frac{19}{5}$$

• 19

• $$\frac{10}{4}$$

• $$\frac{19}{95}$$

• $$\frac{9}{2}$$

Multiple Choice

$$150\frac{ft^2}{s^2}\left(\frac{1\ s^2}{3\ ft}\right)$$

Where ft means feet, lbs means pounds, s means seconds and w means wheels

• $$50ft$$

• $$50\frac{ft^{ }}{s^{ }}$$

• $$50\frac{ft^2}{s^{ }}$$

• $$50\frac{ft^{ }}{s^{ }}$$

Multiple Choice

How many inches are in a mile?

$$1\ mile\ \left(\frac{5280ft}{1\ mile}\right)\left(\frac{12inches}{1ft}\right)=?$$

• $$63360\ miles\cdot ft\cdot inches$$

• $$63360\ ft\cdot inches$$

• $$63360\ ft$$

• $$63360\ inches$$

That was called a unit conversion. We will do more of that next time