Mathematics, grade 6, mapped

114 claims across 9 strands · 137 of 158 skills in grades 4-6 appear here

56 more claims reach back to a grade below this window. They are named in the lists below and not drawn — the picture holds grades 4-6 and nothing else.

Pick a skill to light what it rests on.

Algebraic reasoning

  1. 5.4.B rests on 4.5.A four operations in one problem extends the multi-step work a letter already stood in for
  2. 5.4.E leans on 4.5.B brackets are a mark on a numerical expression, which leans on expressions already being written down
  3. 5.4.F rests on 5.4.E simplifying inside the brackets first takes the brackets as already meaning something
  4. 4.5.D rests on 4.5.C solving a perimeter or area problem takes the formula as already worked out from a model
  5. 5.4.G leans on 4.5.C a formula pulled out of a model leans on that having been done once already with perimeter and area
  6. 5.4.H rests on 5.4.G solving for a volume takes the formula as already read off a stack of cubes
  7. 5.4.H leans on 4.5.D the rectangle problems are these with one dimension fewer in them
  8. 5.4.C rests on 4.5.B a rule written y = ax generates the same table the input-output work fills in
  9. 5.4.D leans on 5.4.C having generated both kinds makes the difference visible, though a given table can be read cold
  10. 5.4.B leans on 4.4.H from another strand a multi-step problem leans on the one- and two-step versions coming out right
  11. 4.5.D leans on 4.4.D from another strand a rectangle 24 by 16 leans on two-digit multiplication being reliable
  12. 5.4.G rests on 5.6.B from another strand l x w x h names what layers times the area of the base was already doing
  13. 5.8.C leans on 4.5.B from another strand the pairs to plot often arrive in an input-output table, which leans on the table already generating them
  14. 5.4.C leans on 5.8.B from another strand graphing the pattern leans on there being a described way to put a pair on the plane
  15. 6.4.A rests on 5.4.D from another strand telling y equals ax from y equals x plus a takes the additive and multiplicative patterns already told apart
  16. 6.5.A rests on 5.4.C from another strand representing ratio problems with tables, graphs, and proportions takes the numerical patterns already generated and graphed
  17. 6.7.A rests on 5.4.F from another strand equivalent expressions with exponents and prime factorization take expressions with two levels of grouping already simplified
  18. 6.7.A leans on 5.4.A from another strand the prime factorization half leans on prime and composite numbers already identified
  19. 6.7.B leans on 5.4.B from another strand telling expressions from equations leans on multi-step problems where a letter already stood for the unknown
  20. 6.7.D leans on 5.4.F from another strand generating equivalent expressions with the properties leans on grouped expressions already simplified with them
  21. 6.9.A rests on 5.4.B from another strand writing one-step equations for problems takes multi-step problems already represented with a letter for the unknown
  22. 6.8.B rests on 5.4.H from another strand modeling area formulas by decomposing shapes takes perimeter and area problems already represented and solved
  23. 4.5.A rests on 3.5.B from grade 3, below this window a strip diagram for a multi-step problem is the one-and-two-step diagram with more strips in it
  24. 4.5.A rests on 3.5.A from grade 3, below this window a multi-step strip diagram with a letter for the unknown takes one-and-two-step addition and subtraction already representable with equations
  25. 4.5.A leans on 3.5.D from grade 3, below this window a letter standing for the unknown leans on the unknown already being something to solve for
  26. 4.5.B rests on 3.5.E from grade 3, below this window an input-output table is the table of number pairs with the rule written out
  27. 5.4.A leans on 3.4.F from grade 3, below this window asking whether anything besides one and thirteen divides it leans on the fact table being at hand
  28. 5.4.A leans on 3.4.I from grade 3, below this window an even-or-odd rule already sorts numbers by whether something divides them, and prime widens that question
  29. 4.5.C rests on 3.7.B from grade 3, below this window the 2l + 2w shorthand comes out of having added the four sides one at a time
  30. 4.5.C rests on 3.6.C from grade 3, below this window the l x w formula names what counting rows of unit squares was already doing
  31. 5.4.D leans on 3.5.C from grade 3, below this window three times as much and three more than are the two patterns, and reading the first as a comparison helps

Data analysis

  1. 4.9.B rests on 4.9.A answering from a dot plot takes the plot as already readable
  2. 5.9.A rests on 4.9.A adding bar graphs and decimal measurements extends the frequency table, dot plot and stem-and-leaf already drawn
  3. 5.9.B leans on 5.9.A paired data leans on data already being something collected and put on a display
  4. 5.9.C rests on 5.9.B answering from a scatterplot takes the scatterplot as already drawn
  5. 5.9.C rests on 4.9.B the one- and two-step data questions are the same ones, with the scatterplot added to the list of displays
  6. 4.9.A leans on 4.3.G from another strand a dot plot marked in halves leans on fractions already having places on a line
  7. 5.9.B rests on 5.8.C from another strand a scatterplot is a first-quadrant graph of ordered pairs with the data supplying the pairs
  8. 6.12.A rests on 5.9.A from another strand histograms and box plots beside the older displays take the bar graphs, dot plots, and stem-and-leaf plots already drawn
  9. 6.12.D rests on 5.9.A from another strand summarizing categories with mode and percent bar graphs takes the bar graphs and frequency tables already drawn
  10. 4.9.A rests on 3.8.A from grade 3, below this window a stem-and-leaf plot is one more summary of a set the frequency table already organises
  11. 4.9.B leans on 3.8.B from grade 3, below this window the scaled-graph questions are these with whole numbers only

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. 6.6.A leans on 5.8.C from another strand spotting independent and dependent quantities in tables leans on graphing ordered pairs from input-output tables
  11. 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
  12. 6.7.A rests on 5.4.F from another strand equivalent expressions with exponents and prime factorization take expressions with two levels of grouping already simplified
  13. 6.7.A leans on 5.4.A from another strand the prime factorization half leans on prime and composite numbers already identified
  14. 6.7.B leans on 5.4.B from another strand telling expressions from equations leans on multi-step problems where a letter already stood for the unknown
  15. 6.7.D leans on 5.4.F from another strand generating equivalent expressions with the properties leans on grouped expressions already simplified with them
  16. 6.9.A rests on 5.4.B from another strand writing one-step equations for problems takes multi-step problems already represented with a letter for the unknown
  17. 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
  18. 6.10.B leans on 5.3.K from another strand testing a value in an equation is substituting and computing, which takes rational add-and-subtract already fluent
  19. 6.8.A rests on 5.5 from another strand triangle angle sums and side rules take two-dimensional figures already classified in a hierarchy
  20. 6.8.B rests on 5.4.H from another strand modeling area formulas by decomposing shapes takes perimeter and area problems already represented and solved

Geometry and measurement

  1. 4.6.C rests on 4.6.A sorting triangles by their angles takes the right angle as already identifiable
  2. 4.6.D rests on 4.6.A classifying on parallel and perpendicular takes both as named things to look for
  3. 4.7.A rests on 4.6.A an angle cut out of a circle takes the vertex and the two rays as already named
  4. 4.7.B rests on 4.7.A one degree is one of 360 of those cut-out parts, so the part comes first
  5. 4.7.C rests on 4.7.B reading a protractor takes the degree as already meaning something
  6. 4.7.D rests on 4.7.C drawing to a given measure is the protractor reading run the other way
  7. 4.7.E rests on 4.7.B two adjacent angles add because each is a count of degrees out of the same circle
  8. 4.8.B rests on 4.8.A a conversion runs in the direction the relative sizes give it
  9. 5.6.B rests on 5.6.A counting layers takes a unit cube as already the thing being counted
  10. 5.8.A rests on 4.6.A two perpendicular number lines takes perpendicular as a word already attached to a picture
  11. 5.8.B rests on 5.8.A describing how to plot a pair takes the axes, the origin and the two coordinates as already named
  12. 5.8.C leans on 5.8.B a described process makes plotting repeatable, though children often plot first and describe after
  13. 4.8.B leans on 4.4.B from another strand metres into centimetres is a product of 100 with a unit attached
  14. 4.8.C leans on 4.4.H from another strand the multiplication and division measurement problems are these with a unit on every number
  15. 5.5 rests on 4.6.D from another strand a hierarchy of sets sorts on the same parallel sides and angle sizes the classifying already looks for
  16. 5.5 leans on 4.6.C from another strand sorting triangles by angle is one branch of the tree, and the branch leans on that sorting already being done
  17. 5.4.G rests on 5.6.B from another strand l x w x h names what layers times the area of the base was already doing
  18. 5.7 rests on 4.8.B from another strand a conversion inside a problem takes the conversion itself as already workable
  19. 5.7 leans on 4.8.C from another strand carrying units through an addition or a division leans on those problems already being solvable
  20. 5.8.C leans on 4.5.B from another strand the pairs to plot often arrive in an input-output table, which leans on the table already generating them
  21. 5.4.C leans on 5.8.B from another strand graphing the pattern leans on there being a described way to put a pair on the plane
  22. 5.9.B rests on 5.8.C from another strand a scatterplot is a first-quadrant graph of ordered pairs with the data supplying the pairs
  23. 6.6.A leans on 5.8.C from another strand spotting independent and dependent quantities in tables leans on graphing ordered pairs from input-output tables
  24. 6.11 rests on 5.8.C from another strand graphing points in all four quadrants takes ordered pairs from patterns and input-output tables already graphed in the first
  25. 4.6.B leans on 2.8.E from grade 2, below this window a line of symmetry is the halving cut with the two parts landing on each other
  26. 4.6.D leans on 3.6.B from grade 3, below this window the quadrilateral sorting is this with a shorter list of attributes to check
  27. 4.7.A leans on 3.3.C from grade 3, below this window a part of a circle leans on a whole already being something that comes apart into parts you can name
  28. 4.7.B leans on 1.7.B from grade 1, below this window a degree is still a same-size unit counted off, bent around a vertex instead of laid along an edge
  29. 4.7.C leans on 2.9.D from grade 2, below this window a protractor is a scale read to the nearest mark, the way a ruler is
  30. 4.7.E leans on 2.7.C from grade 2, below this window a missing angle is the unknown-term reading with the whole angle standing in for the total
  31. 4.8.A leans on 2.9.B from grade 2, below this window ranking a metre against a centimetre leans on the inverse of unit size and count already being stated
  32. 4.8.C leans on 3.7.C from grade 3, below this window time is the quantity that does not run on base ten, and the minute intervals are where that shows
  33. 4.8.C leans on 3.7.E from grade 3, below this window a problem about liquid volume or mass leans on those quantities already being obtainable with a tool
  34. 5.6.A rests on 2.9.F from grade 2, below this window filling a box with unit cubes and no gaps is the square-unit covering with a third direction added
  35. 5.6.A leans on 3.6.A from grade 3, below this window a cube and a rectangular prism lean on the solids already having been sorted and named
  36. 5.6.B rests on 3.6.C from grade 3, below this window the number of cubes in the bottom layer is the area of the base, found by rows times squares
  37. 5.8.A leans on 2.9.C from grade 2, below this window an axis is a number line with a fixed zero, which leans on distances already being read off one

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. 6.12.A rests on 5.9.A from another strand histograms and box plots beside the older displays take the bar graphs, dot plots, and stem-and-leaf plots already drawn
  6. 6.12.D rests on 5.9.A from another strand summarizing categories with mode and percent bar graphs takes the bar graphs and frequency tables already drawn

Number and operations

  1. 4.2.B rests on 4.2.A expanded notation out to the hundredths takes each column as ten times the one on its right
  2. 4.2.E leans on 4.2.A a tenths grid leans on the column right of the ones being worth a tenth, and just as often is how that lands
  3. 4.2.F rests on 4.2.E ordering two hundredths grids takes the grids as already drawable
  4. 4.2.F leans on 4.2.C comparing left to right across the places is the whole-number move carried past the decimal point
  5. 4.2.G rests on 4.2.E calling the shaded part three tenths and 0.3 at once takes one model that holds both names
  6. 4.2.H rests on 4.3.G reading a decimal off a marked point takes tenths and hundredths as already having places on the line
  7. 5.2.A rests on 4.2.B the thousandths column is one more step right along the expanded notation the hundredths already opened
  8. 5.2.B rests on 4.2.F ordering to thousandths is the hundredths comparison with a third place after the point to sort on
  9. 5.2.B leans on 5.2.A deciding between 0.406 and 0.46 leans on the third place having a value of its own
  10. 5.2.C rests on 4.2.D rounding a decimal to the nearest hundredth is the named-place rounding carried right of the point
  11. 5.2.C leans on 5.2.A keeping or dropping the thousandths digit leans on it being readable as a digit with a place
  12. 4.4.A leans on 4.2.B lining the decimal points up leans on hundredths already having a column of their own
  13. 4.4.G rests on 4.2.D estimating with rounded numbers takes rounding to a named place as already doable
  14. 4.4.B rests on 4.2.A multiplying by ten shifts every digit one column left, which is the ten-times relationship itself
  15. 4.4.D rests on 4.4.C the standard algorithm is the partial products of the array collected into columns
  16. 4.4.D leans on 4.4.B the second row of a two-digit multiplication is a product of ten, and knowing why it shifts helps
  17. 4.4.E leans on 4.4.C an area model read from the product back to a missing side is the same rectangle either way
  18. 4.4.F rests on 4.4.E long division is the area model recorded step by step
  19. 4.4.F leans on 4.4.D each step of a division algorithm multiplies back, and a reliable product makes that quick
  20. 4.4.H rests on 4.4.F fluency with two-step problems takes the division algorithm as already working
  21. 5.3.A rests on 4.4.G estimating across all four operations extends the rounding and compatible numbers already used on sums
  22. 5.3.B rests on 4.4.D three digits by two is the two-by-two algorithm with each of its two partial products a digit longer
  23. 5.3.C rests on 4.4.F a two-digit divisor is the same long division with a harder guess at each step
  24. 5.3.C leans on 5.3.B each step of a two-digit division multiplies the divisor back, which leans on that product being quick
  25. 5.3.D rests on 4.4.C a hundredths area model is the two-digit rectangle with each side cut into tenths
  26. 5.3.D leans on 4.2.E shading three tenths of four tenths leans on tenths and hundredths already having a picture
  27. 5.3.E rests on 5.3.D working out 0.3 times 0.4 takes the model that shows why the answer lands in hundredths
  28. 5.3.E leans on 5.3.B dropping the points and multiplying whole numbers leans on that algorithm being reliable
  29. 5.3.F rests on 4.4.E a decimal quotient drawn as a rectangle is the whole-number quotient picture with a smaller side on it
  30. 5.3.F leans on 5.3.D the product model and the quotient model are one rectangle with a different side missing
  31. 5.3.G rests on 5.3.F computing the quotient takes the model that says where the point lands
  32. 5.3.G leans on 5.3.C dividing 4.68 by 12 leans on the whole-number version of the same algorithm
  33. 4.3.B rests on 4.3.A finding a second way to split it takes one way as already written down
  34. 4.3.D leans on 4.3.C rewriting one fraction to match the other leans on equivalence being testable first
  35. 4.3.E rests on 4.3.A adding fifths is counting unit parts, which is what a sum of 1/b already says
  36. 4.3.E leans on 4.3.G the number line the statute builds toward is easier once fractions sit on one as distances
  37. 4.3.F leans on 4.3.E having a worked sum to check against helps, though a benchmark estimate is made without one
  38. 4.3.F leans on 4.3.D putting a fraction against one half leans on comparing two unlike fractions being familiar
  39. 4.3.G leans on 4.2.E the decimal half of this leans on tenths and hundredths already having models behind them
  40. 5.3.H rests on 4.3.E thirds plus fourths is the equal-denominator addition once both are rewritten to one denominator
  41. 5.3.H rests on 4.3.C rewriting one fraction to match the other takes a test for whether two are the same value
  42. 5.3.I rests on 4.3.A three times two fifths is six unit parts, which is what a sum of 1/b already counts
  43. 5.3.J leans on 5.3.I equal groups with a factor missing is one reading of the sharing picture
  44. 5.3.K rests on 5.3.H fluency with unlike denominators takes the models and properties that made the sum come out
  45. 5.3.K rests on 4.4.A the decimal half of a rational sum is the standard algorithm with the points lined up
  46. 5.3.L rests on 5.3.J computing the quotient takes the object or area model that showed what it means
  47. 6.2.C rests on 6.2.A ordering integers and rationals on a line takes the classification of which numbers are which
  48. 6.2.B rests on 6.2.C an opposite and an absolute value are positions and distances read off that line
  49. 6.2.D rests on 6.2.C ordering a set drawn from context is the number-line ordering applied to new numbers
  50. 6.2.E rests on 5.3.L reading a/b as a divided by b takes the unit-fraction divisions where the notation already meant that
  51. 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
  52. 6.3.B rests on 5.3.I judging whether a fraction grows or shrinks its partner takes the whole-by-fraction product as meaningful
  53. 6.3.B leans on 5.3.A judging whether a fraction grows or shrinks its partner without computing takes estimating solutions already practiced
  54. 6.3.C leans on 6.2.C integer models drawn on a line lean on locating and ordering integers on that same line
  55. 6.3.D rests on 6.3.C fluent integer computation takes the concrete models already connected to the algorithms
  56. 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
  57. 5.4.B leans on 4.4.H from another strand a multi-step problem leans on the one- and two-step versions coming out right
  58. 4.5.D leans on 4.4.D from another strand a rectangle 24 by 16 leans on two-digit multiplication being reliable
  59. 4.8.B leans on 4.4.B from another strand metres into centimetres is a product of 100 with a unit attached
  60. 4.8.C leans on 4.4.H from another strand the multiplication and division measurement problems are these with a unit on every number
  61. 4.9.A leans on 4.3.G from another strand a dot plot marked in halves leans on fractions already having places on a line
  62. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  63. 6.4.E leans on 5.2.A from another strand representing ratios and percents with decimals leans on decimal values through thousandths already represented
  64. 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
  65. 6.10.B leans on 5.3.K from another strand testing a value in an equation is substituting and computing, which takes rational add-and-subtract already fluent
  66. 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
  67. 4.2.A rests on 3.2.B from grade 3, below this window the one-tenth direction is the base-ten description read to the right of the ones column
  68. 4.2.C rests on 3.2.D from grade 3, below this window comparing to a billion is the to-100,000 comparison with four more places to sort on
  69. 4.2.D rests on 3.2.C from grade 3, below this window rounding to a named place works from the two consecutive multiples a number sits between
  70. 4.2.E leans on 2.5.B from grade 2, below this window a dollar sign and two digits after the point is the first decimal most children read, though a grid works too
  71. 4.2.G leans on 3.3.C from grade 3, below this window tenths are the unit fraction with b at ten, and grade 3 writes that definition for any whole number b
  72. 4.2.H leans on 3.3.B from grade 3, below this window naming the point rather than placing it is the fraction-line reading with a decimal on the answer
  73. 4.4.A rests on 3.4.A from grade 3, below this window the standard algorithm is the within-1,000 fluency written down in columns
  74. 4.4.G leans on 3.4.B from grade 3, below this window compatible numbers turned up the year before on sums, and the thousands are the only new part
  75. 4.4.C leans on 3.4.G from grade 3, below this window two two-digit factors is partial products with the second number broken apart as well
  76. 4.4.C leans on 3.6.C from grade 3, below this window the area model is the rows-times-squares picture with the squares left uncounted
  77. 4.4.E rests on 3.4.J from grade 3, below this window drawing a four-digit quotient takes division and multiplication as two views of one fact
  78. 4.4.E leans on 3.3.E from grade 3, below this window a quotient is a share handed out, and sharing pictorially is where quotients start
  79. 4.4.H leans on 3.4.K from grade 3, below this window the two-step problems within 100 are these with smaller numbers and no remainder to read
  80. 4.3.A rests on 3.3.D from grade 3, below this window five thirds is the same sum of unit parts with the count allowed past the denominator
  81. 4.3.C rests on 3.3.G from grade 3, below this window deciding whether two are equivalent applies the same-point test rather than building the pair
  82. 4.3.D rests on 3.3.H from grade 3, below this window unlike numerators and unlike denominators is the same-one-or-the-other comparison with both changed at once
  83. 4.3.E leans on 3.6.E from grade 3, below this window combining pictured parts takes the whole already decomposed into named equal-area parts
  84. 4.3.G rests on 3.7.A from grade 3, below this window tenths as a distance from zero extends the halves, fourths and eighths already placed that way
  85. 5.3.I leans on 3.4.E from grade 3, below this window a whole number times a fraction leans on multiplication already picturing equal groups
  86. 5.3.J leans on 3.4.H from grade 3, below this window one third shared among seven leans on division already meaning the size of each equal share

Other

  1. 5.5 rests on 4.6.D from another strand a hierarchy of sets sorts on the same parallel sides and angle sizes the classifying already looks for
  2. 5.5 leans on 4.6.C from another strand sorting triangles by angle is one branch of the tree, and the branch leans on that sorting already being done
  3. 5.7 rests on 4.8.B from another strand a conversion inside a problem takes the conversion itself as already workable
  4. 5.7 leans on 4.8.C from another strand carrying units through an addition or a division leans on those problems already being solvable
  5. 6.4.H rests on 5.7 from another strand converting with proportions and unit rates takes the within-system conversions solved in an earlier year
  6. 6.8.A rests on 5.5 from another strand triangle angle sums and side rules take two-dimensional figures already classified in a hierarchy
  7. 6.11 rests on 5.8.C from another strand graphing points in all four quadrants takes ordered pairs from patterns and input-output tables already graphed in the first
  8. 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

Personal financial literacy

  1. 5.10.B leans on 5.10.A net income leans on the payroll and income taxes already having names
  2. 5.10.D leans on 5.10.C a record of what was paid leans on the ways of paying being tellable apart
  3. 5.10.D leans on 4.10.A the columns a record sorts into lean on a fixed expense and a variable one already being told apart
  4. 5.10.F leans on 5.10.B a budget leans on take-home pay rather than on the larger number it came out of
  5. 5.10.F leans on 5.10.D balancing leans on there being a record of what actually came in and went out
  6. 5.10.E leans on 5.10.F closing a gap leans on having laid the two columns out and seen them fail to match
  7. 6.14.A leans on 5.10.C comparing checking and debit costs leans on the payment methods already weighed for advantages and drawbacks
  8. 6.14.B leans on 5.10.C telling debit cards from credit cards leans on those same payment methods already compared
  9. 6.14.C rests on 5.10.D balancing a register of deposits, withdrawals, and transfers takes the record-keeping system already developed
  10. 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
  11. 6.14.F leans on 6.14.E what reports are worth to borrowers and lenders leans on those same contents and retention
  12. 6.14.H leans on 5.10.B comparing salaries and their lifetime effects leans on gross and net income already told apart
  13. 4.10.A leans on 1.9.C from grade 1, below this window a fixed expense and a variable one are both spending, which leans on spending being its own idea
  14. 4.10.B leans on 2.11.F from grade 2, below this window profit leans on the cost to produce the thing already being something to work out
  15. 4.10.B leans on 3.4.C from grade 3, below this window profit subtracts cost from money taken in, which takes a collection of coins and bills already valuable
  16. 4.10.C leans on 3.9.E from grade 3, below this window weighing one savings option against another leans on there being reasons to save at all
  17. 4.10.D leans on 3.9.F from grade 3, below this window splitting an allowance three ways leans on spending, saving and giving already being named decisions
  18. 4.10.D leans on 1.9.D from grade 1, below this window setting a share aside leans on giving already being one of the things money does
  19. 4.10.E leans on 2.11.C from grade 2, below this window keeping money safe leans on a deposit and a withdrawal already being different things
  20. 4.10.E leans on 2.11.E from grade 2, below this window a bank lending leans on lending already being a thing with benefits and costs on both sides
  21. 5.10.A leans on 1.9.A from grade 1, below this window a tax on income leans on income already being the word for money earned
  22. 5.10.C leans on 3.9.D from grade 3, below this window a credit card leans on credit already being borrowing with a payment owed back
  23. 5.10.C leans on 2.11.C from grade 2, below this window a debit card leans on a withdrawal already being a different thing from a deposit
  24. 5.10.E leans on 3.9.C from grade 3, below this window cutting an unplanned expense leans on planned and unplanned spending already being weighed against each other

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. 6.4.A rests on 5.4.D from another strand telling y equals ax from y equals x plus a takes the additive and multiplicative patterns already told apart
  9. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  10. 6.4.E leans on 5.2.A from another strand representing ratios and percents with decimals leans on decimal values through thousandths already represented
  11. 6.4.H rests on 5.7 from another strand converting with proportions and unit rates takes the within-system conversions solved in an earlier year
  12. 6.5.A rests on 5.4.C from another strand representing ratio problems with tables, graphs, and proportions takes the numerical patterns already generated and graphed
  13. 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

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

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