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Algebra For Beginners: Concepts, Tricks & Applications

Understand the steps. Explain the shortcuts. Solve real problems.

16 Units84 MissionsAbout 20 hoursCourse map

Complete the Course to Earn a Certificate and Join the Hall of Fame

An algebra workshop: an unknown tile and small counters sit beside a bright curved graph. This cover invites exploration; it is not a scale diagram or an exercise.
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A number x passes through multiply by two and add three, then reaches a check mark.

A CLOSER LOOK

Read and rewrite algebra

Make unknown quantities clear. Choose a useful method, explain each step and check the result.

See it. Try it. Make it yours.

  1. Read and rewrite algebra

  2. Solve equations

  3. Describe allowed answers

Beginners, including learners with limited English. · What to know before you start

Bring with you: Add, subtract, multiply and divide small positive whole numbers. Read =, +, −, × and ÷. Read whole numbers, simple decimals and common fractions such as 1/2. No algebra knowledge is assumed.

Make unknown quantities clear. Choose a useful method, explain each step and check the result.

A connected first course through equations, functions, systems, powers, polynomials and quadratics. Arithmetic bridges prepare the tools before use.

By the end, you can…

  • Read letters and expressions. Calculate with signed numbers and fractions. Rewrite without changing value.
  • Find unknown values and check each solution in its original equation.
  • Solve and graph inequalities, including combined conditions.
  • Read slope and intercepts. Solve two conditions together.
  • Connect inputs, outputs, graphs, distance and changing rules.
  • Use sequences, exponent rules, roots and repeated growth with their conditions.
  • Multiply, factor, graph and solve quadratic expressions and equations.
  • Choose a suitable model, solve it and explain its limits.

For another Course

  • Complex numbers
  • Logarithms
  • Trigonometry
  • Matrices
  • Polynomial division
  • General rational-function algebra
  • Calculus

YOUR LEARNING PATH

One idea leads to the next.

0 of 84 Missions completed or proven
Unit 1

Letters stand for numbers

Read, build and check simple algebra.

  1. Both sides have the same valueMission 1 of 84Locked. Use equality to find and check a missing amount.
  2. A letter holds a numberMission 2 of 84Locked. Interpret a variable and its repeated uses.
  3. Read the parts of an expressionMission 3 of 84Locked. Read multiplication, terms, coefficients and constants.
  4. Put a value in place of a letterMission 4 of 84Locked. Evaluate expressions and test a proposed solution.
Unit 2

Numbers you will use

Calculate with negative numbers, fractions and powers.

  1. Numbers on both sides of zeroMission 5 of 84Locked. Order signed numbers and find opposites.
  2. Add and subtract signed numbersMission 6 of 84Locked. Explain signed addition and subtraction.
  3. Multiply and divide signed numbersMission 7 of 84Locked. Use sign rules with reasons and zero restrictions.
  4. Keep fraction sizes clearMission 8 of 84Locked. Rename, compare, add and subtract fractions.
  5. Multiply and divide fractionsMission 9 of 84Locked. Multiply and divide fractions and decimals.
  6. Powers and calculation orderMission 10 of 84Locked. Evaluate powers and grouped calculations correctly.
Unit 3

Rewrite without changing value

Simplify and build expressions with reasons.

  1. Collect the same kind of termMission 11 of 84Locked. Combine like terms with signed and fractional coefficients.
  2. Multiply every part of a groupMission 12 of 84Locked. Expand brackets, including negative multipliers.
  3. Different forms, the same valueMission 13 of 84Locked. Check and explain equivalent expressions.
  4. Turn a situation into algebraMission 14 of 84Locked. Build expressions that preserve order and grouping.
Unit 4

Solve and check equations

Find unknown values and explain each legal step.

  1. Change both sides fairlyMission 15 of 84Locked. Explain operations that keep an equation true.
  2. Undo addition and subtractionMission 16 of 84Locked. Solve one-step additive equations and check.
  3. Undo multiplication and divisionMission 17 of 84Locked. Solve equations that multiply or divide an unknown.
  4. Undo two steps in reverse orderMission 18 of 84Locked. Solve two-step equations without changing their meaning.
  5. Gather letters from both sidesMission 19 of 84Locked. Solve equations with brackets and variables on both sides.
  6. One answer, no answer or every answerMission 20 of 84Locked. Recognise identities and contradictions after simplifying.
  7. Clear fractions without losing a termMission 21 of 84Locked. Solve equations containing fractional or decimal terms.
  8. Make a different letter the subjectMission 22 of 84Locked. Rearrange formulas and state restrictions.
  9. Let the units guide the calculationMission 23 of 84Locked. Use rates and unit conversions in equations.
  10. Build an equation from a situationMission 24 of 84Locked. Model totals, rates and geometry with equations.
Unit 5

Describe a range of answers

Solve inequalities and explain boundary values.

  1. More than, less than and includingMission 25 of 84Locked. Read inequalities and show their solution sets.
  2. Keep the comparison trueMission 26 of 84Locked. Solve inequalities including negative scaling.
  3. Meet one condition or twoMission 27 of 84Locked. Solve and interpret compound inequalities.
  4. Find the allowed choicesMission 28 of 84Locked. Translate limits into inequalities and apply whole-number restrictions.
Unit 6

Draw and understand lines

Connect coordinates, slope, equations and real quantities.

  1. Locate a point with two numbersMission 29 of 84Locked. Read and plot ordered pairs on coordinate axes.
  2. An equation can describe many pointsMission 30 of 84Locked. Connect two-variable equations, tables and graphs.
  3. Measure change with slopeMission 31 of 84Locked. Calculate and interpret a constant rate of change.
  4. Where a line meets an axisMission 32 of 84Locked. Find intercepts and connect slope to y=mx+b.
  5. Draw and read a whole lineMission 33 of 84Locked. Graph lines using slope and intercepts.
  6. Build a line from a pointMission 34 of 84Locked. Write point-slope and slope-intercept forms.
  7. Choose a useful line formMission 35 of 84Locked. Use standard form and compare line directions.
  8. Use a line to model a situationMission 36 of 84Locked. Interpret linear models with units and restrictions.
Unit 7

Solve two conditions together

Use graphs, substitution and elimination to solve systems.

  1. Find a point that fits both rulesMission 37 of 84Locked. Interpret a system and its graph solution.
  2. Replace a letter with an equal expressionMission 38 of 84Locked. Solve systems by substitution.
  3. Cancel one variable fairlyMission 39 of 84Locked. Solve systems by adding or subtracting equations.
  4. When lines never meet or fully overlapMission 40 of 84Locked. Identify the number of solutions to a linear system.
  5. Use two conditions in one problemMission 41 of 84Locked. Build and solve a system from a new situation.
Unit 8

Think with functions

Connect inputs, outputs, rules, graphs and restrictions.

  1. Each input gets one outputMission 42 of 84Locked. Recognise functions and read function notation.
  2. Decide which values make senseMission 43 of 84Locked. Find domain and range with mathematical and contextual limits.
  3. Read what a graph saysMission 44 of 84Locked. Read function features and average rate of change.
  4. Change a rule and follow the outputsMission 45 of 84Locked. Interpret shifts, scales and reflections of functions.
  5. Compare rules shown in different waysMission 46 of 84Locked. Compare functions using equations, graphs, tables and words.
Unit 9

Show regions of answers

Graph inequalities and their shared solutions.

  1. Shade all points that workMission 47 of 84Locked. Graph a linear inequality in two variables.
  2. Find the shared regionMission 48 of 84Locked. Graph systems of inequalities and interpret feasible points.
Unit 10

Distance and changing rules

Use absolute value and piecewise rules.

  1. Absolute value measures distanceMission 49 of 84Locked. Evaluate absolute value and solve simple distance equations.
  2. Distance within or beyond a limitMission 50 of 84Locked. Solve absolute-value inequalities.
  3. Read a V-shaped graphMission 51 of 84Locked. Graph shifted and scaled absolute-value functions.
  4. Use a different rule in each regionMission 52 of 84Locked. Evaluate and graph piecewise functions.
Unit 11

Describe number patterns

Build and compare arithmetic and geometric sequences.

  1. Add the same amount each timeMission 53 of 84Locked. Describe arithmetic sequences recursively and explicitly.
  2. Multiply by the same factor each timeMission 54 of 84Locked. Describe geometric sequences recursively and explicitly.
  3. Build and compare sequence modelsMission 55 of 84Locked. Choose a sequence model and state its limits.
Unit 12

Powers, roots and real numbers

Explain exponent rules, roots and exact values.

  1. Count factors to explain exponent rulesMission 56 of 84Locked. Use product and quotient rules with their conditions.
  2. A power can act on a productMission 57 of 84Locked. Use powers of powers, products and quotients.
  3. Explain zero and negative exponentsMission 58 of 84Locked. Use reciprocal powers and scientific notation.
  4. Undo a square or a cubeMission 59 of 84Locked. Interpret square and cube roots and their real domains.
  5. Find exact forms for rootsMission 60 of 84Locked. Simplify radicals using square factors.
  6. A fractional exponent means a rootMission 61 of 84Locked. Connect rational exponents to roots.
  7. Exact numbers need not be fractionsMission 62 of 84Locked. Distinguish rational and irrational numbers.
  8. Check after undoing a rootMission 63 of 84Locked. Solve simple radical equations and reject extra answers.
Unit 13

Model repeated growth and decay

Build, read and compare exponential models.

  1. Turn a percentage into a multiplierMission 64 of 84Locked. Build repeated percentage growth and decay models.
  2. Read an exponential modelMission 65 of 84Locked. Interpret exponential tables, graphs and parameters.
  3. Choose adding or multiplyingMission 66 of 84Locked. Compare linear and exponential models.
Unit 14

Multiply and factor expressions

Use products, areas and common factors to rewrite polynomials.

  1. Work with polynomial termsMission 67 of 84Locked. Classify, add and subtract polynomials.
  2. Multiply each term by each termMission 68 of 84Locked. Expand polynomial products using distribution and area.
  3. Take out a shared factorMission 69 of 84Locked. Factor expressions and verify by expansion.
  4. Find two numbers that build a quadraticMission 70 of 84Locked. Factor x²+bx+c with integer factors.
  5. Factor when x² has a coefficientMission 71 of 84Locked. Factor nonmonic quadratics using grouping.
  6. Use special products with reasonsMission 72 of 84Locked. Recognise and factor difference-of-squares and square trinomials.
Unit 15

Understand and solve quadratics

Connect quadratic graphs, forms, roots and applications.

  1. Meet the parabolaMission 73 of 84Locked. Connect a quadratic rule to its graph.
  2. Read a quadratic in vertex formMission 74 of 84Locked. Graph y=a(x−h)²+k and interpret its features.
  3. A zero product reveals solutionsMission 75 of 84Locked. Solve factored quadratic equations.
  4. Solve by taking square rootsMission 76 of 84Locked. Solve quadratics built around a square.
  5. Build a complete squareMission 77 of 84Locked. Rewrite a quadratic by completing the square.
  6. Use a square to solve or find a vertexMission 78 of 84Locked. Complete the square for general quadratic equations.
  7. Use one formula for any quadraticMission 79 of 84Locked. Explain and use the quadratic formula.
  8. Know how many real roots to expectMission 80 of 84Locked. Interpret the discriminant and choose a solving method.
  9. Use a quadratic in a real problemMission 81 of 84Locked. Build quadratic models and interpret their solutions.
Unit 16

Choose, explain and apply

Choose a model, diagnose errors and solve mixed problems.

  1. Choose a model and check its limitsMission 82 of 84Locked. Choose and test a suitable algebraic model.
  2. Find the first broken stepMission 83 of 84Locked. Diagnose and repair algebraic arguments.
  3. Use algebra from start to finishMission 84 of 84Locked. Model, solve, compare and justify unfamiliar problems.Mastery Challenge

A Debsie Course · Beginners, including learners with limited English.