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

Monday

What a ratio is
// Two quantities, one comparison
⏱ about 20 min

Monday: What a Ratio Is

Rocket drops a stack of paper onto the kitchen table. "Field Day needs signs. Green signs. Lots of them."

Raven sets out two jars of water-based paint, one blue and one yellow. "We mix the green ourselves."

Rocket grabs a spoon and adds blue, then yellow, then more blue. The puddle turns a muddy teal.

"What do you notice?" Raven asks. "Too much blue," Rocket admits.

Nova hovers over the tray, her light steady. "A good mix is a recipe. How many spoons of each color made the green you liked?"

Raven checks her notebook. "Two spoons blue, three spoons yellow. Every time."

Rocket grins. "Then this table is the Numbers Desk now. We are going to need a lot of green."

Rocket, Raven and Nova at the Numbers Desk, the kitchen table. Paper strips, two colors of counters and paint jars sit between them.

Two quantities, one comparison

A ratio compares two quantities. Raven's green uses 2 spoons of blue for every 3 spoons of yellow.

We write that ratio as 2:3, or 2 to 3. The order matters: blue first, then yellow.

The ratio of yellow to blue is 3:2. Same paint, opposite order.

A ratio can also compare a part to the whole. Each batch has 5 spoons in all, so blue to all the paint is 2:5.

A tape diagram: Blue is 2 equal boxes and Yellow is 3 equal boxes

Worked example: a bigger batch

Rocket wants a batch twice as big. He doubles both parts: 4 spoons of blue and 6 spoons of yellow.

The ratio 4:6 is equivalent to 2:3. Both parts were multiplied by 2, so the green stays exactly the same.

If he doubled only the blue, the ratio would change. So would the color.

RATIO LANGUAGE
  • Read the question.
  • Tap your answer.
Raven's mix has 2 spoons of blue for every 3 spoons of yellow. What is the ratio of spoons of blue to spoons of yellow?
Raven's mix has 2 spoons of blue for every 3 spoons of yellow. What is the ratio of spoons of yellow to spoons of blue?
Raven's mix has 2 spoons of blue for every 3 spoons of yellow. What is the ratio of spoons of blue to all of it?
Raven's lemonade has 3 cups of water for every 1 cup of lemon juice. What is the ratio of cups of water to cup of lemon juice?
MAKE THE BATCH BIGGER
  • Read the question.
  • Tap your answer.
2 spoons of blue for every 3 spoons of yellow. With 6 spoons of yellow, how many spoons of blue?
2 spoons of blue for every 3 spoons of yellow. With 9 spoons of yellow, how many spoons of blue?
2 spoons of blue for every 3 spoons of yellow. With 15 spoons of yellow, how many spoons of blue?
PART OR WHOLE?
  • Read the question.
  • Tap your answer.
Raven's lemonade has 3 cups of water for every 1 cup of lemon juice. What is the ratio of cups of water to all of it?
Raven's lemonade has 3 cups of water for every 1 cup of lemon juice. What is the ratio of cup of lemon juice to cups of water?
Which ratio is equivalent to 2:3?
One batch of green uses 2 spoons of blue and 3 spoons of yellow. How many spoons of paint is that in all? Type the number.
WHY THIS EXERCISEKnowing the whole lets you write a part-to-whole ratio like 2:5.
Try it
Lay out counters in two colors, like dried beans and paper squares, to show 2:3.
Make a second group that shows 4:6. Line the groups up and compare them.
Say each ratio aloud three ways: 2 to 3, 2:3, and 2 for every 3.
Safety first
Small counters stay away from children under three and from pets.
Nothing from the Numbers Desk goes in anyone's mouth.
Draw a tape diagram for 2 spoons of blue to 3 spoons of yellow. Label each row.

Strong start. Tomorrow Raven builds a ratio table so the crew can mix any size batch.