3:1 / 3:2 / 1:3 / 10:3
Three to one / Three to two / One to three / Ten to three
3
1 / 3
2 / 1
3 / 10
3
6:2 / 6:4 / 2:6 / 20:6
The gasoline cost $3.00 per gallon. / The cook put 3 cups of flour for every 2 cups of sugar. / Dustin got one hit every three times at bat. / Every ten minutes, there were three commercials.
The unit ratio is three to one. / The unit ratio is
1.5 to one. / The unit ratio is
one third to one. / The unit ratio is
3 and 1/3 to one.

Last summer I was watching TV and got bored because I viewed 10 commercials for every 30 minutes of TV show. This worked out to be a ratio of 1 commercial every 3 minutes! (1:3) So, I decided to leave my house and see if I could get tickets to a Red Sox game. My car only drives 20 miles for every gallon of gas (20m : 1g) and since gas cost $4.00 for every gallon I bought ($4 : 1g.), I decided to take the train. The train was really crowded; it seemed like there 12 people standing for every 2 people sitting (12:2 = 6 to 1)

I got to the game, paid, and went inside. Josh Beckett was pitching and program said he is only allowing 2.6 runs per every 9 innings. That’s a great ratio! And Big Papi had ratio of 336 hits for every 1000 at bats (.336 :1)! All this made me hungry so I hurried to the concession stand. They had a HUNGRY MAN special:

I didn’t know which was a better deal! So I had a Snickers bar instead. On the back of the Snickers wrapper, I noticed the ratio of Protein to Fat was like 1:100, (not too good) but there were 6 nuts for every 1 bite (6 to 1), so it was worth it. I went back to the game, but someone told me that since there were 30 teams the odds the Red Sox would win the World Series were 29 to 1: out of 30 things there were 29 chances they wouldn’t win, and only 1 chance to win.

This depressed me so I went home. Maybe I was just hungry…

Ratio Lesson Plan:

Prepare: Get the sorting activity ready. Copy story for overhead.

Explain: Read story above, say, “Type One Writing: What did you notice about my day last summer? Write 4 lines or more.” 2:00 minutes.

Turn to your neighbor and add something below the line.

Develop/Draw out of students:

  1. Ratios/fractions/proportions: mathematical way to compare and show relationships between things. They are everywhere!
  2. Three ways to express: 3:1 three to one 3/1 (order is important)
  3. Unit rates/ratio when you compare something to one unit $3.00 per gallon
  4. Ratios can be equivalent, and they can be simplified.

Re-teach your partner what you know so far!

Explore: Give pairs the ratio sort.

Day 2: Do the lesson on body ratios.

Assess: Which is the better deal?

End with a Type Two

Length of your foot
Length of your elbow to wrist
Your height
Length around your wrist
Length from your thumb to index finger
Length around your neck
Length of distance around head

Estimates:

Ratio of foot length to elbow to wrist ______

Ratio of foot length to height ______

Ratio of wrist to thumb/index finger ______

Ratio of wrist to neck length ______

Ratio of neck to head ______

Ratio of head to height ______

There are many classroom activities that can be implemented with primary students that introduce and immerse them in ratio investigations. Some enjoyable tasks include finding the ratio of tongue rollers to non-tongue rollers in the classroom; left-hand dominant to right-hand dominant; right-thumb over left-thumb when clasping the hands to left-thumb over right-thumb, and so on. Children also enjoy looking at body ratios and finding that their foot is the same length as the distance from their wrist to their elbow; that their wrist circumference is half their neck circumference, which is half their head circumference (or near enough), or that their height is almost the same as 7 of their feet.

a. one thumb-to-middle finger length = 1 wrist

b. two thumb-to-middle finger lengths =1 neck

c. three thumb-to-middle finger length = 1 head

d. 7 foot lengths (footsteps) = 1 height

e. 7 foot lengths (footsteps) = 1 arm span

f. 1 arm span = 1 height

head to height, 1:3

neck to wrist: 2:1

BUG DENSITY

Estimated ratio of insects to humans is 200 million to 1, 40 million insects per acre of land, estimated 400 lbs. of insects per acre in the USA, compared to 14 lbs. of humans.

Pedigo, Larry P. 1999. Entomology and Pest Management, Third Edition.Prentice Hall. P. 1.