Mathematics, grade 7, mapped

95 claims across 9 strands · 131 of 155 skills in grades 5-7 appear here

41 more claims reach back to a grade below this window. They are named in the lists below and not drawn — the picture holds grades 5-7 and nothing else.

Pick a skill to light what it rests on.

Algebraic reasoning

  1. 5.4.F rests on 5.4.E simplifying inside the brackets first takes the brackets as already meaning something
  2. 5.4.H rests on 5.4.G solving for a volume takes the formula as already read off a stack of cubes
  3. 5.4.D leans on 5.4.C having generated both kinds makes the difference visible, though a given table can be read cold
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 6.7.A leans on 5.4.A from another strand the prime factorization half leans on prime and composite numbers already identified
  10. 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
  11. 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
  12. 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
  13. 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
  14. 7.8.A rests on 5.4.G from another strand the prism-pyramid volume relationship takes the prism volume formula already developed from objects and pictures
  15. 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
  16. 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
  17. 5.4.B rests on 4.5.A from grade 4, below this window four operations in one problem extends the multi-step work a letter already stood in for
  18. 5.4.B leans on 4.4.H from grade 4, below this window a multi-step problem leans on the one- and two-step versions coming out right
  19. 5.4.E leans on 4.5.B from grade 4, below this window brackets are a mark on a numerical expression, which leans on expressions already being written down
  20. 5.4.G leans on 4.5.C from grade 4, below this window a formula pulled out of a model leans on that having been done once already with perimeter and area
  21. 5.4.H leans on 4.5.D from grade 4, below this window the rectangle problems are these with one dimension fewer in them
  22. 5.4.C rests on 4.5.B from grade 4, below this window a rule written y = ax generates the same table the input-output work fills in
  23. 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. 5.9.B leans on 5.9.A paired data leans on data already being something collected and put on a display
  2. 5.9.C rests on 5.9.B answering from a scatterplot takes the scatterplot as already drawn
  3. 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
  4. 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
  5. 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
  6. 5.9.A rests on 4.9.A from grade 4, below this window adding bar graphs and decimal measurements extends the frequency table, dot plot and stem-and-leaf already drawn
  7. 5.9.C rests on 4.9.B from grade 4, below this window the one- and two-step data questions are the same ones, with the scatterplot added to the list of displays

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. 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
  26. 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
  27. 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
  28. 6.7.A leans on 5.4.A from another strand the prime factorization half leans on prime and composite numbers already identified
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 7.8.A rests on 5.4.G from another strand the prism-pyramid volume relationship takes the prism volume formula already developed from objects and pictures
  37. 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

Geometry and measurement

  1. 5.6.B rests on 5.6.A counting layers takes a unit cube as already the thing being counted
  2. 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
  3. 5.8.C leans on 5.8.B a described process makes plotting repeatable, though children often plot first and describe after
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 5.8.A rests on 4.6.A from grade 4, below this window two perpendicular number lines takes perpendicular as a word already attached to a picture
  13. 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
  14. 5.8.C leans on 4.5.B from grade 4, below this window the pairs to plot often arrive in an input-output table, which leans on the table already generating them

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. 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
  8. 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
  9. 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

Number and operations

  1. 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
  2. 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
  3. 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
  4. 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
  5. 5.3.E leans on 5.3.B dropping the points and multiplying whole numbers leans on that algorithm being reliable
  6. 5.3.F leans on 5.3.D the product model and the quotient model are one rectangle with a different side missing
  7. 5.3.G rests on 5.3.F computing the quotient takes the model that says where the point lands
  8. 5.3.G leans on 5.3.C dividing 4.68 by 12 leans on the whole-number version of the same algorithm
  9. 5.3.J leans on 5.3.I equal groups with a factor missing is one reading of the sharing picture
  10. 5.3.K rests on 5.3.H fluency with unlike denominators takes the models and properties that made the sum come out
  11. 5.3.L rests on 5.3.J computing the quotient takes the object or area model that showed what it means
  12. 6.2.C rests on 6.2.A ordering integers and rationals on a line takes the classification of which numbers are which
  13. 6.2.B rests on 6.2.C an opposite and an absolute value are positions and distances read off that line
  14. 6.2.D rests on 6.2.C ordering a set drawn from context is the number-line ordering applied to new numbers
  15. 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
  16. 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
  17. 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
  18. 6.3.B leans on 5.3.A judging whether a fraction grows or shrinks its partner without computing takes estimating solutions already practiced
  19. 6.3.C leans on 6.2.C integer models drawn on a line lean on locating and ordering integers on that same line
  20. 6.3.D rests on 6.3.C fluent integer computation takes the concrete models already connected to the algorithms
  21. 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
  22. 7.3.A rests on 6.3.D fluent computing with rational numbers takes fluent computing with integers
  23. 7.3.A rests on 6.3.E that same fluency takes the multiplying and dividing of positive rationals already fluent
  24. 7.3.B rests on 7.3.A solving problems with rational operations takes those operations already fluent
  25. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 5.2.A rests on 4.2.B from grade 4, below this window the thousandths column is one more step right along the expanded notation the hundredths already opened
  32. 5.2.B rests on 4.2.F from grade 4, below this window ordering to thousandths is the hundredths comparison with a third place after the point to sort on
  33. 5.2.C rests on 4.2.D from grade 4, below this window rounding a decimal to the nearest hundredth is the named-place rounding carried right of the point
  34. 5.3.A rests on 4.4.G from grade 4, below this window estimating across all four operations extends the rounding and compatible numbers already used on sums
  35. 5.3.B rests on 4.4.D from grade 4, below this window three digits by two is the two-by-two algorithm with each of its two partial products a digit longer
  36. 5.3.C rests on 4.4.F from grade 4, below this window a two-digit divisor is the same long division with a harder guess at each step
  37. 5.3.D rests on 4.4.C from grade 4, below this window a hundredths area model is the two-digit rectangle with each side cut into tenths
  38. 5.3.D leans on 4.2.E from grade 4, below this window shading three tenths of four tenths leans on tenths and hundredths already having a picture
  39. 5.3.F rests on 4.4.E from grade 4, below this window a decimal quotient drawn as a rectangle is the whole-number quotient picture with a smaller side on it
  40. 5.3.H rests on 4.3.E from grade 4, below this window thirds plus fourths is the equal-denominator addition once both are rewritten to one denominator
  41. 5.3.H rests on 4.3.C from grade 4, below this window 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 from grade 4, below this window three times two fifths is six unit parts, which is what a sum of 1/b already counts
  43. 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
  44. 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
  45. 5.3.K rests on 4.4.A from grade 4, below this window the decimal half of a rational sum is the standard algorithm with the points lined up

Other

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 5.5 rests on 4.6.D from grade 4, below this window a hierarchy of sets sorts on the same parallel sides and angle sizes the classifying already looks for
  8. 5.5 leans on 4.6.C from grade 4, below this window sorting triangles by angle is one branch of the tree, and the branch leans on that sorting already being done
  9. 5.7 rests on 4.8.B from grade 4, below this window a conversion inside a problem takes the conversion itself as already workable
  10. 5.7 leans on 4.8.C from grade 4, below this window carrying units through an addition or a division leans on those problems already being solvable

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.F leans on 5.10.B a budget leans on take-home pay rather than on the larger number it came out of
  4. 5.10.F leans on 5.10.D balancing leans on there being a record of what actually came in and went out
  5. 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
  6. 6.14.A leans on 5.10.C comparing checking and debit costs leans on the payment methods already weighed for advantages and drawbacks
  7. 6.14.B leans on 5.10.C telling debit cards from credit cards leans on those same payment methods already compared
  8. 6.14.C rests on 5.10.D balancing a register of deposits, withdrawals, and transfers takes the record-keeping system already developed
  9. 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
  10. 6.14.F leans on 6.14.E what reports are worth to borrowers and lenders leans on those same contents and retention
  11. 6.14.H leans on 5.10.B comparing salaries and their lifetime effects leans on gross and net income already told apart
  12. 7.13.A rests on 5.10.A calculating sales and income tax takes income, payroll, sales, and property tax already defined
  13. 7.13.B leans on 5.10.F those budget components lean on a simple budget already balanced
  14. 7.13.C rests on 5.10.D an assets and liabilities record with a net worth statement takes the record-keeping system already developed
  15. 7.13.D leans on 7.13.B a household budget from an estimator leans on budget components already identified with their shares
  16. 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
  17. 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
  18. 7.13.F leans on 7.4.D from another strand weighing sales, rebates, and coupons leans on percent increase and decrease already solved
  19. 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
  20. 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
  21. 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
  22. 5.10.D leans on 4.10.A from grade 4, below this window the columns a record sorts into lean on a fixed expense and a variable one already being told apart
  23. 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. 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. 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
  20. 6.4.D rests on 6.2.E from another strand giving rates as quotients takes a/b already meaning a divided by b
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 7.13.F leans on 7.4.D from another strand weighing sales, rebates, and coupons leans on percent increase and decrease already solved

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