Ratios & Rates

Ratios and rates are one of those 6th grade topics that shows up everywhere — and I mean everywhere. The store, the kitchen, a map, sports statistics, a recipe that needs to feed more people than planned. The math itself isn’t hard once it clicks, but a lot of kids hit 6th grade and realize nobody’s ever actually explained what a ratio is. They’ve seen fractions. They can divide. But this idea of comparing two quantities in a relationship? That needs its own introduction, and it needs to be built slowly.

This 9-week program covers the full 6.RP domain — from reading and writing ratios for the first time all the way through using rate reasoning to solve multi-step real-world problems. Each week is five worksheets with a full answer key, and the progression is deliberate: you’re not jumping to unit rates until ratio notation is solid, and you’re not doing complex rate problems until equivalent ratios make sense. That structure matters more than people think.

What Your Kid Will Actually Practice

Week 1 starts at the beginning. What is a ratio? How do you write one — as 3:4, as 3/4, as “3 to 4”? What’s the difference between comparing part-to-part (boys to girls) and part-to-whole (boys to total students)? These aren’t tricks. They’re the conceptual groundwork that every later problem depends on. The first worksheet has kids writing ratios from plain English descriptions — a bowl with 6 apples and 9 oranges, a parking lot with 20 cars and 4 trucks — until the notation becomes automatic.

From there, simplifying ratios. Then equivalent ratios: if 2:5 = ?:15, what fills in the blank? That scaling logic is the bridge to almost everything. Unit rates come next — $3.60 for 4 cans means $0.90 per can, which means you can now compare prices, speeds, distances, and a hundred other things. The program works through tables, graphs, and eventually the full 6.RP.A.3 standard, which asks students to use ratio and rate reasoning to solve real-world problems across all those contexts.

The later weeks get harder in a good way. Week 4 introduces error analysis — here’s a student’s work, find the mistake. That format is underrated. It forces kids to reason about why something is wrong, not just compute the right answer. Week 5’s challenge problems include things like scaling a recipe and then calculating total cost with different ingredient prices, or figuring out how a student council’s composition changes as membership grows. These aren’t contrived — they’re the kind of thinking that shows up on state assessments and in real life.

All 9 weeks spiral back. Later worksheets include review problems from earlier skills, so a kid doesn’t just learn equivalent ratios and then forget them by the time unit rates arrive. The interleaving is built in.

How This Fits the Standards

The three standards this program covers — 6.RP.A.1, 6.RP.A.2, and 6.RP.A.3 — are the entire Ratios and Proportional Relationships domain for 6th grade Common Core. That’s not coincidence. This program is designed to cover the domain completely, not cherry-pick the easy parts.

6.RP.A.1 is the foundation: understanding what a ratio is and using ratio language precisely. 6.RP.A.2 adds unit rates — that a/b form, what it means, how to calculate it and talk about it in context. 6.RP.A.3 is the application standard, and it has a lot of sub-parts: equivalent ratios, unit pricing, measurement conversion, percent problems, and coordinate plane representations of ratio relationships. Each of those shows up across the nine weeks.

If your 6th grader is heading into a state assessment, struggling with how ratios connect to fractions, or just got back a test where the ratio problems were clearly guesswork — this is the systematic practice that fixes that. Print it out, work through one sheet a day, and check the answer key together. The explanations in the key are clear enough that you don’t need a math background to help.