Ratio Mixer

What are ratios?

A ratio compares two amounts. Say you have a bag with 3 red marbles and 2 blue marbles. The ratio of red to blue is 3 to 2.

You write a ratio as 3:2, or 3/2, or "3 to 2." They all mean the same thing: for every 3 red, there are 2 blue.

It has been years since most parents have seen one of these. You are not behind. It is just a way to compare two things.

What is this module?

The Ratio Mixer is a paint-mixing toy. There are two sliders, one for red paint and one for blue paint. Move them and the color on the screen changes.

The number shown like 3:2 is the ratio of red to blue. In this module the first number is always red and the second is always blue.

What they're learning

The idea is that a ratio compares two amounts. You can make both amounts bigger or smaller and keep the same mix. If your kid gets that, they're most of the way there.

• How to read a ratio. 3:2 means 3 parts red to 2 parts blue.
• Bigger numbers don't always mean more red. 4:2 is the same mix as 2:1.
• How to turn a ratio into a fraction. With 3 red and 2 blue, red is 3 out of 5 parts, so red is 3/5 = 0.6 of the whole.
• Doubling both numbers keeps the same color. 3:2 and 6:4 are the same mix.

Aliases

• Ratios
• Proportions
• "For every"
• Equivalent ratios
• Ratio tables

Refresher

A ratio compares two amounts. 3:2 means 3 of the first thing for every 2 of the second. Multiply or divide both numbers by the same amount and the mix stays the same, only the total gets bigger or smaller.

Try this together

You don't have to sit down and teach a whole lesson. Two or three minutes at the table is enough.

1. Set red to 3 and blue to 2. Ask your kid to read the ratio out loud.
2. Switch to Mixed. Ask what will happen if you add more blue, then do it.
3. Set red to 6 and blue to 4. Ask if the color looks any different. It should look the same.
4. Press "Find Equivalent Ratio." It gives a target ratio. Move the sliders until the mix matches the target.

If they pick it up quickly, try Ordered mode. It lines the parts up so you can count them.

If you're stuck too, that's normal. Change one slider at a time and watch the color. You don't have to know the answer before you start.

Words you might hear

These come up in the module and in the worksheet. You don't need to memorize them. Just know what they mean.

• Ratio: a comparison of two amounts, like 3:2. Also written 3/2 or "3 to 2."
• Part: one share. "3 parts red" means 3 shares of red.
• Equivalent ratios: different numbers, same mix. 3:2, 6:4, and 30:20 all make the same color.
• Red fraction: how much of the whole mix is red. With 3 parts red and 2 blue, the red fraction is 3/5 = 0.60. The module shows it as a decimal.

If the order of the numbers feels backwards, remember that red comes first here.

Deeper dive

Three red and two blue is the ratio 3:2. Double both and you get 6 red and 4 blue, which is the same color, because it is still three red for every two blue. Multiply both by ten and 30:20 is the same mix again.

To turn a ratio into a fraction, count the parts. With 3 red and 2 blue there are 5 parts, so red is 3 out of 5, or 3/5 = 0.6. The first number is always red in this module.