Algebra 1

What this covers

• Solving multi-step linear equations with variables on both sides, fractions, and distributed brackets, including identifying identities and equations with no solution
• Solving and graphing linear inequalities on a number line, including compound inequalities and the sign flip when multiplying or dividing by a negative
• Laws of exponents (product, quotient, power of a power, zero and negative exponents) and simplifying expressions with scientific notation
• Rearranging literal equations and formulas to isolate a chosen variable, such as solving A = P(1 + rt) for r
• Translating word problems into equations: rate, mixture, percent change, consecutive integers, and age or distance setups
• Function notation, evaluating f(x), reading domain and range from a table or simple graph, and telling functions from non-functions

Where learners get stuck

Flipping the inequality sign at the wrong time

Students memorise 'flip the sign' as a rule attached to negatives in general, so they flip when subtracting a negative or when the variable happens to be negative. The rule only applies when both sides are multiplied or divided by a negative number, and the reason for it (order reverses on the number line) is rarely made explicit.

Treating -3^2 and (-3)^2 as the same thing, or writing x^-2 as a negative number

Exponent notation is compressed and students read it left to right like text. Negative exponents get mapped onto 'negative answer' because the word 'negative' already means 'below zero' everywhere else in their maths experience.

Cancelling terms instead of factors when simplifying fractions like (x + 4)/4

In arithmetic, students cancelled matching digits successfully for years. Nothing in that experience distinguishes a term joined by addition from a factor joined by multiplication, so the habit transfers to algebra and produces confident wrong answers.

What a session looks like

A typical session starts with two or three problems spoken aloud so Evelyn can hear where the reasoning breaks down rather than only seeing a final answer. The tutor asks the learner to say each step and justify it, stops at the first slip instead of at the end, and then gives a near-identical problem to check the fix held. Word problems are worked by naming the unknown out loud before any symbols are written. Sessions usually end with the learner talking through one problem from start to finish unaided.

Helpful to know first

• Fluency with integer arithmetic, including operations with negative numbers
• Adding, subtracting, multiplying, and dividing fractions without a calculator
• Order of operations and the distributive property
• Plotting points on the coordinate plane and reading values from a graph

Questions

My child got through pre-algebra fine but is stuck in Algebra 1. What changed?

Pre-algebra problems usually have a single unknown at the end of a computation. Algebra 1 asks students to hold a symbol as an object and operate on it, and it penalises shaky fraction and negative-number skills that were previously survivable. Sessions usually spend the first few meetings finding which of those foundations is actually leaking.

Does this cover graphing lines and slope?

Only lightly, as it comes up. Slope, intercepts, and graphing are the focus of the Linear Functions topic; this topic covers the equation-solving, exponent, and function-notation skills those lessons assume.

Can Evelyn help with homework problems my child is stuck on tonight?

Yes. The learner can read or describe the problem and work through it with the tutor step by step. Evelyn asks for the learner's reasoning first rather than reading out a solution.

How long does it take to fix a gap like negative exponents or sign errors?

Sign and exponent errors are procedural habits, so they usually need repeated short exposures rather than one long explanation. Expect the misconception to reappear across several sessions before it stops.