Learning path · Preparing for algebra
Pre-algebra
Connect arithmetic to algebra through signed numbers, fractions, proportions, equations, and graphs. Review the specific foundation that blocks the next step.
5 units · 10 skills
Starting point: Preparing for algebra
For learners ready to extend whole-number calculation into rational numbers and unknown quantities. The material often appears in middle-school study, but readiness rather than age determines the starting point.
What this path connects
- Use signed and fractional quantities in a relationship.
- Explain proportional reasoning and percentage calculations.
- Move from a verbal relationship to an equation or graph.
The learning sequence
See what each unit covers and open the skill you want to understand. The order gives you a route through the material.
Unit 1
Extend the number system
Review negative values, equivalent fractions, and decimals before using them in expressions and equations.
- Signed numbersUse a number line to make sense of positive and negative numbers. Distinguish a value’s position from its distance from zero and explain changes in either direction.
- Equivalent fractionsExplain why different fractions can name the same number. Scale the numerator and denominator together and connect the calculation to equal parts of one whole.
- DecimalsRead tenths and hundredths as fractional units. Compare decimal values and align place values when adding or subtracting them.
Unit 2
Compare and scale quantities
Identify a unit rate, preserve a proportion, and name the base of a percentage. Check whether the real situation supports the chosen relationship.
- ProportionsIdentify a proportional relationship and scale it consistently. Use a unit rate or equivalent ratios while keeping the meaning and units of both quantities clear.
- PercentagesInterpret a percentage as a fraction of a stated base. Calculate a percentage amount and a percentage change without confusing the original and final values.
Unit 3
Find an unknown while keeping equality
Use inverse operations and a substitution check to solve a linear equation. Explain why the chosen transformation is valid.
Unit 4
Represent a changing relationship
Connect coordinates and graphs to equations, then use function notation to identify inputs and outputs.
- Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.
- Function notationRead f(x) as the output of a function at an input. Evaluate a rule carefully, check its domain, and connect notation to a table or graph.
Unit 5
Read quantities and chance in context
Interpret data summaries and simple probabilities without losing their labels, units, or assumptions.
- Reading dataRead a table or chart in context and summarize a small data set. Distinguish mean, median, and range instead of expecting one number to tell the whole story.
- ProbabilityDefine an event and the possible outcomes before calculating its probability. Use fractions to describe chance and check whether successive events are independent.
Make the path useful to you
Locate the first uncertain step
A difficult equation may hide an earlier fraction or sign error. Keep the original attempt and review that smaller skill before trying the whole question again.
Explain the choice of operation
A correct calculation is only part of the task. State what the unknown represents and why the equation or proportion describes the situation.
Use the path as preparation
Pre-algebra is a course arrangement across several mathematical areas, not a separate kind of number. These canonical skills also appear in school courses and adult refreshers.
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