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Ratios and Data 6-8 / Week 01 / Friday
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Week 01 · Ratios

Friday

Ratios all around
// Two quantities, one comparison
⏱ about 20 min

Friday: Ratios All Around

Rocket sprawls on the kitchen floor with a tape measure. "Ratios are only for paint and lemonade, right?"

Raven points at the bike by the door. "Two wheels for every one bike. That is a ratio."

"Four legs for every chair," Rocket says, sitting up. "Eight legs for two chairs!"

Nova circles the room, her light flicking from object to object. "Keep going. What do you notice about the windows and doors?"

"Three windows, one door. 3:1," Rocket says. "Same as the lemonade."

Raven writes it all in the log. "Ratios were here the whole time. We just started counting."

Ratios in everyday life

A ratio shows up any time two quantities go together: wheels and bikes, legs and chairs, steps and breaths.

A recipe is a set of ratios. A map scale is a ratio. The beat of a song compares counts to seconds.

When you spot two things that come in a fixed pattern, you have found a ratio.

  • Wheels to bikes: 2:1. Four bikes have 8 wheels.
  • Legs to chairs: 4:1. Three chairs have 12 legs.
  • Water to lemon juice in Raven's recipe: 3:1.
  • Blue to yellow in the Field Day green: 2:3.
REVIEW: RATIO LANGUAGE
  • Read the question.
  • Tap your answer.
The bike rack has 2 wheels for every 1 bike. What is the ratio of wheels to bike?
The kitchen has 4 legs for every 1 chair. What is the ratio of chair to legs?
The green mix has 2 spoons of blue for every 3 spoons of yellow. What is the ratio of spoons of blue to all of it?
REVIEW: SCALE IT
  • Read the question.
  • Tap your answer.
2 wheels for every 1 bikes. With 6 bikes, how many wheels?
4 legs for every 1 chairs. With 5 chairs, how many legs?
3 spoons of yellow for every 2 spoons of blue. With 8 spoons of blue, how many spoons of yellow?
1 cups of lemon juice for every 3 cups of water. With 18 cups of water, how many cups of lemon juice?
StatementTrue or false?
2:1 is the same ratio as 8:4.?
4:1 is the same ratio as 12:3.?
2:3 is the same ratio as 6:9.?
2:3 is the same ratio as 4:5.?
The ratio 3:1 and the ratio 1:3 mean the same thing.?
WHY THIS EXERCISEThe week's two big ideas: order matters, and equivalent ratios come from multiplying both parts.
COMPARE AND MATCH
  • Read the question.
  • Tap your answer.
Two mixes of green. Mix P is 3 blue for every 4 yellow. Mix Q is 1 blue for every 2 yellow. Which is bluer?
Which ratio is equivalent to 2:1?
Which ratio is equivalent to 3:4?
Three pitchers: Pitcher X is 6 water to 2 juice, Pitcher Y is 8 to 2, Pitcher Z is 12 to 4. Which does not match?

Look ahead: rates

Next week the crew times runs for Field Day. A run compares meters to seconds, two quantities with different units.

A ratio with different units is called a rate. Speed is a rate, and you already know how to scale it.

Try it
Count two things in one room that come in a fixed pattern, like legs and chairs.
Write the ratio, then predict how many legs 6 chairs would have. Check by counting if you can.
Draw one everyday ratio from today as a picture, with the two quantities labeled and the ratio written under it.

A full week of ratios. Next week the crew times runs and turns ratios into rates and speed.

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