Expressions & Equations

6th grade math is where arithmetic quietly becomes algebra, and for a lot of kids that transition is genuinely jarring. One day they’re computing with numbers they can see, and suddenly there’s a letter sitting in the middle of an equation asking them to do something they’ve never done before. This 9-week program works through that shift in a way that actually sticks — starting with numerical expressions and exponents, moving into writing and evaluating algebraic expressions, then solving equations and inequalities, and finishing with two-variable relationships. Each week builds on the last so nothing feels like it came out of nowhere.

Week 1 is all about exponents and order of operations — the mechanical foundation everything else depends on. Students work through reading exponent notation, writing repeated multiplication in compact form, and evaluating expressions step by step using PEMDAS. There’s also a worksheet focused on error analysis, where students find the mistakes in someone else’s work. That one is particularly useful because a lot of 6th graders have shaky PEMDAS intuition and finding another person’s error forces them to slow down and actually think through the order rather than just racing to a number. By the end of the week they can handle multi-step expressions like (6 - 2)³ ÷ 8 + 1 without guessing.

Week 2 introduces variables. Students learn to identify the parts of an algebraic expression — terms, coefficients, constants — and practice translating verbal phrases like “5 less than twice a number” into 2n - 5. Weeks 3 and 4 extend that into evaluating expressions by substituting values, combining like terms, and applying the distributive property. These four weeks together cover the full A cluster of 6.EE standards, and by the end students aren’t just manipulating symbols — they understand what equivalent expressions actually mean and why 3(x + 4) and 3x + 12 are the same thing.

From Expressions to Equations

The shift from expressions to equations is where most kids hit a wall. An expression is something you evaluate. An equation is a statement that something is true — and solving it means finding the value that makes it true. Week 5 starts there, with the balance model. Students don’t just memorize “do the inverse operation.” They think through why you have to do the same thing to both sides, which is a conceptual move that pays off all the way through high school. From there they practice solving addition, subtraction, multiplication, and division equations, then move into week 6 where they write and solve equations from real-world word problems. The word problem work is probably the hardest stretch in the whole program — translating a situation into an equation is a skill unto itself — but by this point students have enough vocabulary and confidence to handle it.

Week 7 covers inequalities, which most 6th graders find either confusing or strangely fun. They learn to write constraints like “you must be at least 48 inches tall” as h ≥ 48, graph solution sets on a number line, and understand why there are infinitely many solutions instead of one. Week 8 moves into two-variable relationships: identifying independent and dependent variables, writing equations like d = 55t, completing tables of values, and plotting ordered pairs. It’s a clean bridge toward 7th grade ratio work and eventually functions.

Week 9 is cumulative review and a unit assessment. Students work through all nine standards across five worksheets, including a final assessment where every problem maps back to a specific 6.EE standard. The review worksheets are mixed rather than organized by topic, which is intentional — interleaved practice is significantly better for retention than blocked practice, and by week 9 the goal is for students to recognize problem types quickly rather than being prompted by section headings.

What’s in the Pack

Each week includes 5 worksheets and a complete answer key. The worksheets are designed to be done one per day, roughly 20-30 minutes each. They follow a progression within the week — understand, apply, apply, analyze, evaluate/create — so there’s a built-in gradient from straightforward practice toward problems that require more reasoning. The word problems use realistic contexts: earning money, measuring recipes, splitting players into teams. Nothing absurd or artificially cheerful, just situations that make the math feel like it has a reason to exist.

This pack covers all nine standards in the Common Core 6.EE domain: 6.EE.A.1 through 6.EE.A.4 (expressions and exponents), 6.EE.B.5 through 6.EE.B.8 (equations and inequalities), and 6.EE.C.9 (two-variable relationships). If your kid’s class is working through these standards over the course of a semester, the weekly structure lines up cleanly with that pacing. If you’re using this for summer work or extra practice, the cumulative week-9 review gives you a solid way to check where they are before 7th grade starts.