Pre-Algebra curriculum

A bridge from arithmetic into algebra covering number sense, fractions, decimals, ratios, percents, integers, equations, geometry, and data.

Find tutors Get tutor support

Middle school math / Algebra readiness

Pre-Algebra curriculum

A bridge from arithmetic into algebra covering number sense, fractions, decimals, ratios, percents, integers, equations, geometry, and data.

Pacing

8 units, 20-30 weeks self-paced

Units

8 unit sequence

Practice

32 checked answers

Support

Self-paced or tutor-guided

Outcomes

Use arithmetic fluency to solve unfamiliar multi-step problems.
Translate word problems into equations, diagrams, tables, and graphs.
Enter Algebra 1 with fractions, ratios, integers, and variables under control.

Khan Academy companion path

Use these linked courses for video instruction and mastery practice, then return here for PeerTutor original checks and tutor help on the exact unit that got stuck.

Algebra

External video content is linked, not copied. PeerTutor practice is original and cites each source path separately.

Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

01
Whole numbers and place value
- Use operations, exponents, factors, multiples, and order of operations.
- Estimate and check answers for reasonableness.
Practice: Solve a multi-step arithmetic problem and write the estimate that proves the answer is plausible.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Use operations, exponents, factors, multiples, and order of operations.
2. 2
  Worked attempt
  Produce the assignment artifact: Solve a multi-step arithmetic problem and write the estimate that proves the answer is plausible.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Estimate and check answers for reasonableness.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Whole numbers and place value practice set has 12 questions. If 5 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Whole numbers and place value"?
Compare, simplify, add, subtract, multiply, and divide fractions.Estimate and check answers for reasonableness.Use operations, exponents, factors, multiples, and order of operations.Use common denominators and reciprocal reasoning.
Practice artifact
Which practice artifact should you produce for "Whole numbers and place value" before asking a tutor for help?
Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Solve a multi-step arithmetic problem and write the estimate that proves the answer is plausible.
02
Fractions and mixed numbers
- Compare, simplify, add, subtract, multiply, and divide fractions.
- Use common denominators and reciprocal reasoning.
Practice: Explain one fraction operation with a model and one with an algorithm.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Compare, simplify, add, subtract, multiply, and divide fractions.
2. 2
  Worked attempt
  Produce the assignment artifact: Explain one fraction operation with a model and one with an algorithm.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Use common denominators and reciprocal reasoning.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Fractions and mixed numbers practice set has 13 questions. If 6 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Fractions and mixed numbers"?
Compare, simplify, add, subtract, multiply, and divide fractions.Use common denominators and reciprocal reasoning.Use operations, exponents, factors, multiples, and order of operations.Estimate and check answers for reasonableness.
Practice artifact
Which practice artifact should you produce for "Fractions and mixed numbers" before asking a tutor for help?
Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Skip the unit and start a new subject.Explain one fraction operation with a model and one with an algorithm.
03
Decimals, percents, and measurement
- Convert among fractions, decimals, and percents.
- Use units, rounding, and measurement conversions.
Practice: Build a price, tax, discount, or measurement problem and solve it two ways.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Convert among fractions, decimals, and percents.
2. 2
  Worked attempt
  Produce the assignment artifact: Build a price, tax, discount, or measurement problem and solve it two ways.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Use units, rounding, and measurement conversions.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Decimals, percents, and measurement practice set has 14 questions. If 7 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Decimals, percents, and measurement"?
Convert among fractions, decimals, and percents.Use operations, exponents, factors, multiples, and order of operations.Estimate and check answers for reasonableness.Compare, simplify, add, subtract, multiply, and divide fractions.
Practice artifact
Which practice artifact should you produce for "Decimals, percents, and measurement" before asking a tutor for help?
Build a price, tax, discount, or measurement problem and solve it two ways.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Skip the unit and start a new subject.
04
Ratios, rates, and proportions
- Use equivalent ratios, unit rates, and scale factors.
- Solve proportional relationships from tables, graphs, and equations.
Practice: Model a recipe, map, or speed problem with a ratio table and equation.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Use equivalent ratios, unit rates, and scale factors.
2. 2
  Worked attempt
  Produce the assignment artifact: Model a recipe, map, or speed problem with a ratio table and equation.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Solve proportional relationships from tables, graphs, and equations.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Ratios, rates, and proportions practice set has 15 questions. If 8 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Ratios, rates, and proportions"?
Solve proportional relationships from tables, graphs, and equations.Use operations, exponents, factors, multiples, and order of operations.Compare, simplify, add, subtract, multiply, and divide fractions.Estimate and check answers for reasonableness.
Practice artifact
Which practice artifact should you produce for "Ratios, rates, and proportions" before asking a tutor for help?
Model a recipe, map, or speed problem with a ratio table and equation.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Skip the unit and start a new subject.
05
Integers and rational numbers
- Add, subtract, multiply, and divide signed numbers.
- Represent signed quantities on number lines and in context.
Practice: Create a temperature, elevation, or account-balance problem and justify every sign.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Add, subtract, multiply, and divide signed numbers.
2. 2
  Worked attempt
  Produce the assignment artifact: Create a temperature, elevation, or account-balance problem and justify every sign.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Represent signed quantities on number lines and in context.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Integers and rational numbers practice set has 16 questions. If 9 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Integers and rational numbers"?
Estimate and check answers for reasonableness.Compare, simplify, add, subtract, multiply, and divide fractions.Add, subtract, multiply, and divide signed numbers.Use operations, exponents, factors, multiples, and order of operations.
Practice artifact
Which practice artifact should you produce for "Integers and rational numbers" before asking a tutor for help?
Memorize vocabulary without checking any examples.Skip the unit and start a new subject.Create a temperature, elevation, or account-balance problem and justify every sign.Watch videos without writing or solving anything.
06
Expressions and equations
- Use variables, substitution, and expression simplification.
- Solve one-step and two-step equations.
Practice: Translate a word problem into an equation, solve it, and check in the original context.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Use variables, substitution, and expression simplification.
2. 2
  Worked attempt
  Produce the assignment artifact: Translate a word problem into an equation, solve it, and check in the original context.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Solve one-step and two-step equations.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Expressions and equations practice set has 17 questions. If 10 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Expressions and equations"?
Estimate and check answers for reasonableness.Use operations, exponents, factors, multiples, and order of operations.Solve one-step and two-step equations.Compare, simplify, add, subtract, multiply, and divide fractions.
Practice artifact
Which practice artifact should you produce for "Expressions and equations" before asking a tutor for help?
Skip the unit and start a new subject.Translate a word problem into an equation, solve it, and check in the original context.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
07
Geometry foundations
- Use angle relationships, perimeter, area, surface area, and volume.
- Apply formulas with units and diagrams.
Practice: Design a simple room, container, or garden plan and compute its measurements.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Use angle relationships, perimeter, area, surface area, and volume.
2. 2
  Worked attempt
  Produce the assignment artifact: Design a simple room, container, or garden plan and compute its measurements.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Apply formulas with units and diagrams.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Geometry foundations practice set has 18 questions. If 11 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Geometry foundations"?
Use angle relationships, perimeter, area, surface area, and volume.Compare, simplify, add, subtract, multiply, and divide fractions.Estimate and check answers for reasonableness.Use operations, exponents, factors, multiples, and order of operations.
Practice artifact
Which practice artifact should you produce for "Geometry foundations" before asking a tutor for help?
Design a simple room, container, or garden plan and compute its measurements.Skip the unit and start a new subject.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
08
Data, graphs, and probability
- Read tables, line plots, bar charts, histograms, and coordinate graphs.
- Use mean, median, range, and simple probability.
Practice: Collect a small dataset, graph it, and write three true statements from the display.
Unit work plan
1. 1
  Source study
  Start with Prealgebra 2e and OpenStax Math. Take notes until you can explain: Read tables, line plots, bar charts, histograms, and coordinate graphs.
2. 2
  Worked attempt
  Produce the assignment artifact: Collect a small dataset, graph it, and write three true statements from the display.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Use mean, median, range, and simple probability.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Data, graphs, and probability practice set has 19 questions. If 12 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Pre-Algebra unit "Data, graphs, and probability"?
Use mean, median, range, and simple probability.Use operations, exponents, factors, multiples, and order of operations.Estimate and check answers for reasonableness.Compare, simplify, add, subtract, multiply, and divide fractions.
Practice artifact
Which practice artifact should you produce for "Data, graphs, and probability" before asking a tutor for help?
Watch videos without writing or solving anything.Skip the unit and start a new subject.Collect a small dataset, graph it, and write three true statements from the display.Memorize vocabulary without checking any examples.