5th grade math lessons

Every 5th grade lesson Lux teaches, unit by unit, in the order a school year reaches them.

Unit 1: Decimal place value

Usually taught in August

Unit 2: Adding and subtracting decimals, and money

Usually taught in September

  • Adding decimals to thousandths8.72 + 3.032: estimate 9 + 3, write 8.720, then add place by place.
  • Subtracting decimals with regrouping5.2 − 3.8 with place value disks: trade 1 one for 10 tenths.
  • Check against the estimateFixes a mistake6.32 + 2.8 is near 6 + 3, so 6.60 cannot be right. The 8 is tenths.
  • Money problems in steps$37.81, two $10 checks, and 30 half dollars: enough for a $72.29 toy? Estimate, then each step.
  • Finish every stepFixes a mistakeThe total spent is not the answer when the story asks for the change.
  • Taxes, gross and netA $500 paycheck before taxes is gross income. After $60 of payroll tax, $440 is net income. Then sales tax on a purchase, and property tax on a home.
  • Balancing a budgetIncome $200, expenses $230: the budget is $30 short. Cut or change spending until expenses are no more than income, and keep a record.
  • Estimate to check4.87 + 3.12 is about 5 + 3, or 8, so 7.99 is reasonable and 79.9 is not. 9.21 − 3.9 is about 9 − 4, or 5, so 5.31 makes sense. 18.6 ÷ 3 is about 18 ÷ 3, or 6, so 6.2 makes sense and 62 or 0.62 does not.

Unit 3: Multiplying whole numbers

Usually taught in September and October

  • Multiplying bigger numbers1,834 × 23 with the standard algorithm, each row said in place value, checked against 1,800 × 20.
  • Estimate each rowFixes a mistakeA second row with a carry never added: 26,680 is far from its estimate, 36,000. Estimate each row before adding.

Unit 4: Dividing whole numbers

Usually taught in October and November

Unit 5: Multiplying and dividing decimals

Usually taught in November and December

Unit 6: The coordinate plane and patterns

Usually taught in December

  • Points on the coordinate planeTwo number lines meet at (0, 0). (3, 5) is 3 right, then 5 up.
  • Right first, then upFixes a mistake(2, 4) is not (4, 2). Go across first, then up.
  • A zero puts it on an axisFixes a mistake(0, 6) sits on the y-axis: 0 steps right, 6 up.
  • Points that tell a story4 bracelets an hour for 5 hours: a table, then points from (1, 4) to (5, 20), read as hours and bracelets.
  • A rule as an expression9, 13, 17, 21 adds 4 each time: 4n + 5, so the 16th term is 69.
  • The rule fits every termFixes a mistake3, 6, 9, 12: "double it" fits 3 to 6 only. Adding 3 fits every pair, so the rule is 3n.
  • Input and output tablesThe rule 10 + 2n for inputs 1, 2, and 3, then 10, 11, and 12, one row at a time.
  • Which column is which?Fixes a mistakeA kid's table for 10 + 2n puts 14 in the input column, and gets 36 for input 3 by adding first. Inputs left; multiply first.
  • Tables from a ruleA party costs $100 for the room and $4.50 for each student. A table: 10 students cost $145, 20 cost $190, 30 cost $235. Each 10 more students adds $45. A spreadsheet works out the same table from one formula.

Unit 7: Adding, subtracting, and multiplying fractions

Usually taught in January and February

Unit 8: Fractions as division

Usually taught in February and March

Unit 9: Shapes and volume

Usually taught in March

  • Triangles two waysBy sides: equilateral, isosceles, scalene. By angles: acute, right, obtuse. Each triangle gets one of each.
  • Every name that fitsA square is a rectangle, a rhombus, and a parallelogram, on a family chart of quadrilaterals.
  • Not only the last nameFixes a mistakeA square is still a parallelogram. The most exact name is not the only one.
  • Solid figuresPrisms, pyramids, cylinders, cones, and spheres by their faces, bases, and apex.
  • Turning does not change itFixes a mistakeA pyramid on its side is still a pyramid.
  • Volume by packing cubesA box packed layer by layer: 6 rows of 4, 6 layers, 144 cubic units.
  • No gaps, no overlapsFixes a mistakeSame-size cubes, packed tight, or the count is wrong.
  • Volume by formulaV = l × w × h and V = B × h for a 15 by 32 by 10 foot room: base area times layers.
  • The base is an areaFixes a mistakeB in V = B × h is the area of the base, not one side.
  • Find the missing edge120 cubic inches on a 3 by 10 inch base: 120 = 30 × h, so h = 4.
  • Two boxes put togetherAn L-shaped figure split into two boxes, their volumes added.
  • Nets of solidsA box unfolds into 6 rectangles, a cube into 6 squares, and a square pyramid into a square and 4 triangles. Match each net to the solid it folds into.
  • Area of parallelograms and trianglesCut a triangle off a parallelogram and slide it over: a rectangle, so the area is base × height. A triangle is half of that.
  • The angles of a triangleTear off a triangle's three corners and line them up: a straight line, 180 degrees. With 50° and 70° known, the third angle is 60°.
  • Area of a trapezoidA trapezoid with parallel sides 6 and 12, height 4, and slanted sides 5. Cut it into a 6 by 4 rectangle and two triangles with base 3 and height 4. 24 plus 6 plus 6 is 36 square units, the same as half of 6 plus 12, times 4. Its perimeter, 6 + 12 + 5 + 5, is 28 units.
  • Estimating around a curveA pond on grid paper with a curvy edge. Follow the edge with short straight pieces and add them: about 18 units. A square inside it has perimeter 12 and a square around it 24, so 18 is reasonable.
  • Radius and diameterA compass opened to 3 centimeters draws a circle. From the center to the edge is the radius, 3 cm. Edge to edge through the center is the diameter, 6 cm, twice the radius.
  • Perimeter, area, or volume?A fence around a garden needs perimeter, the length around. Grass seed to cover the garden needs area. Sand to fill a sandbox needs volume.
  • Surface area with a netA box 4 by 3 by 2 unfolds into 6 rectangles: two 4 by 3, two 4 by 2, and two 3 by 2. 12 + 12 + 8 + 8 + 6 + 6 is 52 square units.

Unit 10: Data

Usually taught in April

  • Line plots in halves, thirds, and fourthsCups of water in ten glasses, an X over each amount.
  • Line graphsA kitten's mass each day, points joined, and the change between days.
  • Count in fractionsFixes a mistakeThe mark after 1 1/4 is 1 2/4, not 2. Name each tick as a fraction.
  • Mean as a fair shareTowers of 3, 5, 7, and 9 cubes leveled out to 6 each. Then add and divide.
  • Four measures from a line plotPies eaten by 10 contestants: the mean, median, mode, and range.
  • Mean or median?Fixes a mistakeOne big value pulls the mean to 7 while the median stays at 4.
  • Double bar graphsTwo bars for each month, one for each class. Read each pair against the scale, compare them, and say what the graph shows.
  • Sample spacesToss a coin and roll a number cube: list every pair, or multiply 2 × 6 = 12 outcomes. Heads and a 3 is 1 of 12, so its probability is 1/12.
  • ScatterplotsHours practiced and free throws made for 6 players: each pair is one dot. Then read the plot: who made the most, and how many more than the player who practiced 2 hours?
  • The shape of the dataA line plot of books in each backpack: most dots stack at 2, 3, and 4, and one sits far out at 11. The data clusters from 2 to 4, and 11 is an outlier. A new student most likely carries 2 to 4 books.
  • Pick the right graphTemperatures over a week fit a line graph, which shows change. Votes for pets fit a bar graph, which compares groups. A bar graph whose bars are not drawn to scale misleads the reader.
  • Clean the data firstA table of jump-rope counts: one says twenty, one is blank, one says 4000. Write twenty as 20, leave the blank out, and check the 4000, likely a typo for 40.

Unit 11: Expressions and equations

Usually taught in April and May

  • Words to expressions"Divide the difference of 20 and 5 by the sum of 4 and 1" is (20 − 5) ÷ (4 + 1).
  • Times the sum, or plus it?Fixes a mistake5(9 + 3) is 5 times the sum, not 5 + (9 + 3).
  • Order of operations62 − 8 × 4 + 3 − (18 ÷ 9): parentheses, then × and ÷ left to right, then + and − left to right.
  • Left to right, not M before DFixes a mistake24 ÷ 4 × 2 is 12, not 3. Multiply and divide share one step.
  • True or false, with parentheses13.8 − 6 + 3 = 4 × 1.2 is false: 10.8 against 4.8. Work each side to one number.
  • An equal sign is not a run-onFixes a mistake3 × 4 = 12 + 5 = 17 is false: 12 is not 17. Both sides must be the same.
  • An equation for the unknown96 cookies, 21 students, 12 kept: 21 × n + 12 = 96, so n = 4.
  • Undo to solve(8 × n) + 155 = 315: take away 155, then divide by 8. n = 20.
  • Read before you computeFixes a mistakeThe story with its numbers hidden first. Plan the operations, then write the equation.
  • Expressions with a letter5 more than a number is n + 5, 4 less than a number is n − 4, and 3 times a number is 3 × n. When n is 7, n + 5 is 12. The area formula A = l × w with l = 5 and w = 6 gives 30; an area of 24 with w = 4 gives l = 6.
  • Is it true for this number?1.5 + n < 10. Try n = 2.8: 4.3 is less than 10, so it is true. Try n = 9.2: 10.7 is not less than 10, so it is false. A story: Sam spends less than his $10. 3 × n = 24 tells of 3 bags of n apples, true for n = 8. 5 + 6 = 4 + □ makes the box 7; 3 × 8 < 3 × □ needs a box more than 8.

Unit 12: Converting measurements

Usually taught in May

Watch the lessons with Lux.

With Lux, each lesson is a narrated video and a printed page. Then Lux helps with the same math on your kid's own worksheet.

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