Mathematics, grade 8, mapped

99 claims across 7 strands · 135 of 161 skills in grades 6-8 appear here

29 more claims reach back to a grade below this window. They are named in the lists below and not drawn — the picture holds grades 6-8 and nothing else.

Pick a skill to light what it rests on.

Expressions, equations, and relationships

  1. 6.6.B rests on 6.6.A writing the equation for the relationship takes knowing which quantity depends on which
  2. 6.6.C rests on 6.6.B representing a situation four ways including the equation takes that equation already written from a table
  3. 6.7.C rests on 6.7.D deciding whether two expressions match takes equivalent expressions already generated with the properties
  4. 6.9.B leans on 6.9.A showing solutions on a number line leans on the equations and inequalities already written
  5. 6.9.C rests on 6.9.A writing problems from given equations takes equations already written from problems, run the other way
  6. 6.10.A rests on 6.9.A modeling and solving one-step equations takes those equations already written from problems
  7. 6.10.A leans on 6.8.C the geometric half leans on area and volume problems already carrying their own equations
  8. 6.8.C rests on 6.8.B writing equations for area and volume problems takes those area formulas already modeled by rearranging parts
  9. 6.8.D rests on 6.8.C finding solutions for those area and volume problems takes the equations already written for them
  10. 7.8.B leans on 7.8.A the triangular prism-pyramid relationship leans on the rectangular one already modeled
  11. 7.8.C leans on 6.8.B circle circumference and area from models lean on area formulas already modeled by decomposing shapes
  12. 7.9.A rests on 7.8.B volume problems across the four solids take the prism-pyramid relationships already connected to their formulas
  13. 7.9.B rests on 7.8.C finding circumference and area takes the approximate formulas already connected to the actual ones
  14. 7.9.C rests on 7.9.B composite figures with semicircles and quarter circles take circle area already determined
  15. 7.9.C rests on 6.8.D the rectilinear pieces of those composites take the area solutions already determined for them
  16. 7.9.D rests on 6.8.D surface area read off a shapes net takes the area solutions already determined for its pieces
  17. 7.10.A rests on 6.9.A writing two-step equations and inequalities takes the one-step versions already written from problems
  18. 7.10.B rests on 7.10.A showing two-step solutions on a number line takes those two-step equations already written
  19. 7.10.B leans on 6.9.B those two-step solutions lean on one-step solutions already shown on a line
  20. 7.10.C rests on 7.10.A writing problems from two-step equations takes two-step equations already written from problems, run the other way
  21. 7.11.A rests on 7.10.A modeling and solving two-step equations takes those equations already written
  22. 7.11.B leans on 7.11.A testing values against two-step equations leans on the solving moves they would be checked against
  23. 7.11.C rests on 6.8.A equations from triangle sums and angle relationships take triangle properties already extended
  24. 7.11.C rests on 7.11.A solving those geometry equations takes two-step equations already modeled and solved
  25. 8.6.B rests on 8.6.A the cylinder-cone relationship takes the cylinder volume already described through its base and height
  26. 8.6.B rests on 7.8.A that same relationship takes the prism-pyramid one already modeled with congruent bases and heights
  27. 8.6.C leans on 6.8.A explaining Pythagoras with models and diagrams leans on triangle properties already extended
  28. 8.7.A leans on 8.6.B volume of cylinders and cones leans on the cylinder-cone relationship already connected to its formulas, with the sphere volume standing beside it
  29. 8.7.B leans on 7.9.D surface area for prisms leans on lateral and total surface area already solved from nets, with the cylinder surface standing beside it
  30. 8.7.C rests on 8.6.C solving with Pythagoras and its converse takes the theorem already explained with models and diagrams
  31. 8.7.D rests on 8.7.C distance between two points on a plane takes Pythagoras already used to solve problems
  32. 8.8.A rests on 7.10.A equations with variables on both sides take two-step equations already written from problems
  33. 8.8.B rests on 8.8.A problems written from those equations take those equations already written from problems, run the other way
  34. 8.8.C rests on 8.8.A modeling and solving those equations takes those equations already written
  35. 8.8.C rests on 7.11.A the solving half takes two-step equations already modeled and solved
  36. 8.8.D rests on 6.8.A angle sums, transversals, and angle-angle similarity take triangle properties already extended
  37. 6.6.C rests on 6.4.A from another strand the y equals kx and y equals x plus b forms are the two rules already told apart
  38. 6.9.B rests on 6.2.C from another strand those number-line solutions take integers and rationals already located, compared, and ordered on a line
  39. 7.7 rests on 6.6.C from another strand linear relationships in words, tables, graphs, and equations take situations already represented those four ways
  40. 8.2.C leans on 6.7.A from another strand scientific notation leans on whole-number exponents already generated with order of operations
  41. 8.7.D rests on 6.11 from another strand those two points take locations on a plane already identified in all four quadrants
  42. 6.6.A leans on 5.8.C from grade 5, below this window spotting independent and dependent quantities in tables leans on graphing ordered pairs from input-output tables
  43. 6.7.A rests on 5.4.F from grade 5, below this window equivalent expressions with exponents and prime factorization take expressions with two levels of grouping already simplified
  44. 6.7.A leans on 5.4.A from grade 5, below this window the prime factorization half leans on prime and composite numbers already identified
  45. 6.7.B leans on 5.4.B from grade 5, below this window telling expressions from equations leans on multi-step problems where a letter already stood for the unknown
  46. 6.7.D leans on 5.4.F from grade 5, below this window generating equivalent expressions with the properties leans on grouped expressions already simplified with them
  47. 6.9.A rests on 5.4.B from grade 5, below this window writing one-step equations for problems takes multi-step problems already represented with a letter for the unknown
  48. 6.10.B leans on 5.3.K from grade 5, below this window testing a value in an equation is substituting and computing, which takes rational add-and-subtract already fluent
  49. 6.8.A rests on 5.5 from grade 5, below this window triangle angle sums and side rules take two-dimensional figures already classified in a hierarchy
  50. 6.8.B rests on 5.4.H from grade 5, below this window modeling area formulas by decomposing shapes takes perimeter and area problems already represented and solved
  51. 7.8.A rests on 5.4.G from grade 5, below this window the prism-pyramid volume relationship takes the prism volume formula already developed from objects and pictures
  52. 8.6.A rests on 5.4.G from grade 5, below this window a cylinder as base area times height takes the prism volume formula already developed from objects and pictures

Measurement and data

  1. 6.12.B rests on 6.12.A describing center, spread, and shape from the graphs takes those graphs already drawn
  2. 6.12.C leans on 6.12.B summarizing with mean, median, range, and interquartile range leans on center, spread, and shape already described
  3. 6.13.A rests on 6.12.A interpreting data summarized in those plots takes those plots already drawn
  4. 6.13.B leans on 6.12.B telling data with variability from data without it leans on center, spread, and shape already described
  5. 7.12.A rests on 6.12.B comparing two groups by shape, center, and spread takes center, spread, and shape already described
  6. 7.12.C rests on 7.12.B comparing two populations from their samples takes the single-sample inference already made
  7. 8.11.B leans on 6.12.C mean absolute deviation as average distance from the mean leans on center and spread already summarized numerically
  8. 7.6.G leans on 6.12.D from another strand part-to-whole comparisons across bar, dot, and circle graphs lean on categorical summaries with mode and percent bars already made
  9. 8.5.C leans on 8.11.A from another strand contrasting data that suggest a linear relationship with data that do not leans on scatterplots already addressing association
  10. 8.11.C rests on 7.6.F from another strand simulating random samples as representative takes inferences from random samples already made
  11. 6.12.A rests on 5.9.A from grade 5, below this window histograms and box plots beside the older displays take the bar graphs, dot plots, and stem-and-leaf plots already drawn
  12. 6.12.D rests on 5.9.A from grade 5, below this window summarizing categories with mode and percent bar graphs takes the bar graphs and frequency tables already drawn
  13. 8.11.A rests on 5.9.B from grade 5, below this window scatterplots addressing association take discrete paired data already represented on a scatterplot

Number and operations

  1. 6.2.C rests on 6.2.A ordering integers and rationals on a line takes the classification of which numbers are which
  2. 6.2.B rests on 6.2.C an opposite and an absolute value are positions and distances read off that line
  3. 6.2.D rests on 6.2.C ordering a set drawn from context is the number-line ordering applied to new numbers
  4. 6.3.A rests on 6.2.E dividing by a rational as multiplying by its reciprocal takes a/b already meaning a divided by b
  5. 6.3.C leans on 6.2.C integer models drawn on a line lean on locating and ordering integers on that same line
  6. 6.3.D rests on 6.3.C fluent integer computation takes the concrete models already connected to the algorithms
  7. 6.3.E rests on 6.3.A the division half of that fluency runs on dividing by a rational as multiplying by its reciprocal
  8. 7.3.A rests on 6.3.D fluent computing with rational numbers takes fluent computing with integers
  9. 7.3.A rests on 6.3.E that same fluency takes the multiplying and dividing of positive rationals already fluent
  10. 7.3.B rests on 7.3.A solving problems with rational operations takes those operations already fluent
  11. 8.2.B rests on 6.2.C locating those approximations on a number line takes integers and rationals already located and ordered on one
  12. 8.2.D rests on 8.2.B ordering reals from context takes the irrational approximations already located on a line
  13. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  14. 6.9.B rests on 6.2.C from another strand those number-line solutions take integers and rationals already located, compared, and ordered on a line
  15. 6.11 leans on 6.2.C from another strand those ordered pairs of rationals lean on rationals already located and ordered on a number line
  16. 7.2 rests on 6.2.A from another strand extending sets and subsets to rationals with a visual representation takes the whole, integer, and rational sets already classified
  17. 8.2.A rests on 7.2 from another strand describing real-number sets and subsets visually takes the rational sets and subsets already described that way
  18. 8.2.C leans on 6.7.A from another strand scientific notation leans on whole-number exponents already generated with order of operations
  19. 6.2.E rests on 5.3.L from grade 5, below this window reading a/b as a divided by b takes the unit-fraction divisions where the notation already meant that
  20. 6.3.B rests on 5.3.I from grade 5, below this window judging whether a fraction grows or shrinks its partner takes the whole-by-fraction product as meaningful
  21. 6.3.B leans on 5.3.A from grade 5, below this window judging whether a fraction grows or shrinks its partner without computing takes estimating solutions already practiced

Other

  1. 6.11 leans on 6.2.C from another strand those ordered pairs of rationals lean on rationals already located and ordered on a number line
  2. 7.2 rests on 6.2.A from another strand extending sets and subsets to rationals with a visual representation takes the whole, integer, and rational sets already classified
  3. 7.7 rests on 6.6.C from another strand linear relationships in words, tables, graphs, and equations take situations already represented those four ways
  4. 8.2.A rests on 7.2 from another strand describing real-number sets and subsets visually takes the rational sets and subsets already described that way
  5. 8.3.B leans on 6.11 from another strand the coordinate half leans on points in all four quadrants already graphed with rational pairs
  6. 8.4.C rests on 7.7 from another strand the intercept half takes linear relationships already represented with tables, graphs, and equations
  7. 8.5.A rests on 7.7 from another strand proportional situations in tables, graphs, and y equals kx take linear relationships already shown those ways
  8. 8.5.B rests on 7.7 from another strand non-proportional situations in y equals mx plus b take the y equals mx plus b relationships already represented
  9. 8.7.D rests on 6.11 from another strand those two points take locations on a plane already identified in all four quadrants
  10. 8.9 rests on 8.5.I from another strand verifying the x and y satisfying two linear equations takes those equations already modeled graphically
  11. 6.11 rests on 5.8.C from grade 5, below this window graphing points in all four quadrants takes ordered pairs from patterns and input-output tables already graphed in the first

Personal financial literacy

  1. 6.14.D leans on 6.14.E why a positive history matters leans on what the report holds and how long it keeps it
  2. 6.14.F leans on 6.14.E what reports are worth to borrowers and lenders leans on those same contents and retention
  3. 7.13.D leans on 7.13.B a household budget from an estimator leans on budget components already identified with their shares
  4. 8.12.A leans on 7.13.E how rate and loan length affect credit cost leans on simple and compound earnings already calculated and compared
  5. 8.12.B rests on 8.12.A total repayment cost under rates and periods takes rate and length effects on credit cost already compared
  6. 8.12.C leans on 7.13.E small regular investments growing over time lean on interest earnings already calculated and compared
  7. 8.12.E leans on 6.14.B advantages and drawbacks of payment methods lean on debit and credit cards already told apart
  8. 8.12.F leans on 6.14.D judging financially responsible decisions leans on why a positive credit history matters already explained
  9. 8.12.G rests on 6.14.G estimating college cost with a savings plan takes the college payment methods already explained
  10. 7.13.B rests on 6.5.B from another strand figuring each budget category as a percent of the total takes the whole, part, and percent already found
  11. 7.13.E leans on 6.5.B from another strand simple and compound interest earnings lean on parts and percents of a whole already found
  12. 7.13.F leans on 7.4.D from another strand weighing sales, rebates, and coupons leans on percent increase and decrease already solved
  13. 6.14.A leans on 5.10.C from grade 5, below this window comparing checking and debit costs leans on the payment methods already weighed for advantages and drawbacks
  14. 6.14.B leans on 5.10.C from grade 5, below this window telling debit cards from credit cards leans on those same payment methods already compared
  15. 6.14.C rests on 5.10.D from grade 5, below this window balancing a register of deposits, withdrawals, and transfers takes the record-keeping system already developed
  16. 6.14.H leans on 5.10.B from grade 5, below this window comparing salaries and their lifetime effects leans on gross and net income already told apart
  17. 7.13.A rests on 5.10.A from grade 5, below this window calculating sales and income tax takes income, payroll, sales, and property tax already defined
  18. 7.13.B leans on 5.10.F from grade 5, below this window those budget components lean on a simple budget already balanced
  19. 7.13.C rests on 5.10.D from grade 5, below this window an assets and liabilities record with a net worth statement takes the record-keeping system already developed

Proportionality

  1. 6.4.C rests on 6.4.A giving ratios as multiplicative comparisons takes the multiplicative relationship already told from the additive one
  2. 6.4.B leans on 6.4.E those predictions also lean on ratios and percents already represented with models, fractions, and decimals
  3. 6.4.F rests on 6.4.E benchmark percents on grids and number lines take ratios and percents already represented with models and decimals
  4. 6.4.G rests on 6.4.E generating equivalent fraction, decimal, and percent forms takes ratios and percents already shown in each form
  5. 6.5.B rests on 6.4.G finding the whole, the part, or the percent takes the equivalent forms already generated
  6. 6.5.B leans on 6.5.A those percent problems lean on ratio problems already represented with tables, graphs, and proportions
  7. 6.5.C rests on 6.4.G showing equal parts with equivalent forms takes those forms already generated from real-world problems
  8. 7.4.A rests on 6.5.A constant rates of change in six representations take ratio and rate problems already shown with tables, graphs, and proportions
  9. 7.4.B rests on 7.4.A calculating unit rates takes constant rates of change already represented
  10. 7.4.C rests on 7.4.B finding the constant of proportionality takes the unit rate already calculated
  11. 7.4.D rests on 6.5.B multi-step percent increase and decrease take the whole, part, and percent problems already solved
  12. 7.4.E rests on 6.4.H converting between measurement systems takes converting within one system with proportions and unit rates already done
  13. 7.5.A leans on 6.5.A generalizing similarity through ratios within and between shapes leans on ratio problems already worked with scale factors
  14. 7.5.B leans on 6.4.C describing pi as circumference over diameter leans on ratios as multiplicative comparisons of the same attribute already given
  15. 7.5.C rests on 7.5.A similar-shape and scale-drawing problems take the critical attributes of similarity already generalized
  16. 7.6.B rests on 7.6.A simulations of simple and compound events take the sample spaces already listed and diagrammed
  17. 7.6.D rests on 7.6.A predicting from theoretical probability takes the sample spaces directly, with no data in between
  18. 7.6.E rests on 7.6.A an event and its complement take the sample space listing everything that could happen
  19. 8.3.A rests on 7.5.A proportional sides through dilation take the critical attributes of similarity already generalized
  20. 8.3.B rests on 8.3.A comparing a shape with its dilation on a plane takes corresponding sides already generalized as proportional
  21. 8.3.C rests on 8.3.B explaining a scale factor algebraically takes the shape and its dilation already compared attribute by attribute
  22. 8.4.A rests on 7.5.A slope from similar right triangles takes similar shapes with their within and between ratios already generalized
  23. 8.4.B rests on 7.4.B graphing proportional relationships with unit rate as slope takes unit rates already calculated from rates
  24. 8.4.B rests on 8.4.A calling that unit rate the slope takes slope already built from similar right triangles
  25. 8.4.C rests on 8.4.A reading slope off a table or graph takes the rate comparing change in y to change in x already built
  26. 8.5.A leans on 8.4.B those proportional situations also lean on proportional relationships already graphed with unit rate as slope
  27. 8.5.D rests on 8.5.C predicting from a trend line takes linear and non-linear bivariate data already contrasted graphically
  28. 8.5.E rests on 8.5.A direct variation problems take proportional situations already represented in tables, graphs, and equations
  29. 8.5.F rests on 8.5.A telling proportional from non-proportional situations takes the proportional form already represented three ways
  30. 8.5.F rests on 8.5.B that same telling takes the non-proportional form already represented beside it
  31. 8.5.H rests on 8.5.F spotting proportional and non-proportional functions takes those two situations already told apart
  32. 8.5.I rests on 8.5.B modeling with y equals mx plus b takes non-proportional situations already represented in that form
  33. 8.5.I rests on 8.4.C that modeling takes rate of change and intercept already read off tables and graphs
  34. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  35. 6.6.C rests on 6.4.A from another strand the y equals kx and y equals x plus b forms are the two rules already told apart
  36. 7.6.G leans on 6.12.D from another strand part-to-whole comparisons across bar, dot, and circle graphs lean on categorical summaries with mode and percent bars already made
  37. 7.13.B rests on 6.5.B from another strand figuring each budget category as a percent of the total takes the whole, part, and percent already found
  38. 7.13.E leans on 6.5.B from another strand simple and compound interest earnings lean on parts and percents of a whole already found
  39. 7.13.F leans on 7.4.D from another strand weighing sales, rebates, and coupons leans on percent increase and decrease already solved
  40. 8.3.B leans on 6.11 from another strand the coordinate half leans on points in all four quadrants already graphed with rational pairs
  41. 8.4.C rests on 7.7 from another strand the intercept half takes linear relationships already represented with tables, graphs, and equations
  42. 8.5.A rests on 7.7 from another strand proportional situations in tables, graphs, and y equals kx take linear relationships already shown those ways
  43. 8.5.B rests on 7.7 from another strand non-proportional situations in y equals mx plus b take the y equals mx plus b relationships already represented
  44. 8.5.C leans on 8.11.A from another strand contrasting data that suggest a linear relationship with data that do not leans on scatterplots already addressing association
  45. 8.9 rests on 8.5.I from another strand verifying the x and y satisfying two linear equations takes those equations already modeled graphically
  46. 8.10.A leans on 8.3.B from another strand orientation and congruence across rotations, reflections, translations, and dilations lean on shapes and dilations already compared
  47. 8.10.D rests on 8.3.C from another strand linear and area effects of dilation take a rational scale factor already explained on the plane
  48. 8.11.C rests on 7.6.F from another strand simulating random samples as representative takes inferences from random samples already made
  49. 6.4.A rests on 5.4.D from grade 5, below this window telling y equals ax from y equals x plus a takes the additive and multiplicative patterns already told apart
  50. 6.4.E leans on 5.2.A from grade 5, below this window representing ratios and percents with decimals leans on decimal values through thousandths already represented
  51. 6.4.H rests on 5.7 from grade 5, below this window converting with proportions and unit rates takes the within-system conversions solved in an earlier year
  52. 6.5.A rests on 5.4.C from grade 5, below this window representing ratio problems with tables, graphs, and proportions takes the numerical patterns already generated and graphed

Two-dimensional shapes

  1. 8.10.B rests on 8.10.A telling transformations that preserve congruence from those that do not takes those properties already generalized
  2. 8.10.C rests on 8.10.A algebraic effects of translations, reflections, and rotations take those transformations already generalized with their properties
  3. 8.10.A leans on 8.3.B from another strand orientation and congruence across rotations, reflections, translations, and dilations lean on shapes and dilations already compared
  4. 8.10.D rests on 8.3.C from another strand linear and area effects of dilation take a rational scale factor already explained on the plane

Back to mathematics, grade 8

Texas Essential Knowledge and Skills · CC BY 3.0 US · D2L Corporation · verified 2026-09-05

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