Grade 2 · printable course

Number, Shape, and Measure: Grade 2 Mathematics

Grade 2 · 293 pages · 78 lessons · PDF, print at home

A concrete-first grade 2 math course for one child and one parent, delivered through an adaptive app. Students build place value to 1000, fluent addition and subtraction within 100 (with regrouping into the hundreds), equal groups and arrays as a foundation for multiplication, measurement in standard units, time to five minutes, money, shape attributes, and halves/thirds/fourths as fair shares. Every new idea is introduced with real or pictured objects before any written number sentence appears. Aligns to CCSS Mathematics grade 2 domains OA, NBT, MD, and G.

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What is inside

Every unit and lesson in this book, in order. The same lessons are taught online at lettersanddevotion.com, so a family can move between paper and screen.

Number, Shape, and Measure: Grade 2 Mathematics

78 lessons · try a lesson online free

Unit 1: Place Value to 1000: Bundles of Ten8 lessons
  1. 1.A bundle of ten ones as one ten
  2. 2.A bundle of ten tens as one hundred
  3. 3.Reading and writing 3-digit numbers as hundreds, tens, ones
  4. 4.Flexible grouping of the same quantity across hundreds, tens, and ones
  5. 5.Comparing three-digit numbers using <, =, >
  6. 6.Skip-counting sequences by 5s, 10s, and 100s
  7. 7.Place value of hundreds, tens, and ones digits in an unfamiliar 3-digit number
  8. 8.Place value of hundreds, tens, and ones applied to a real, non-block quantity context
Unit 2: Adding and Subtracting Within 100 (and Thinking in Hundreds)10 lessons
  1. 9.Regrouping ten ones as one ten
  2. 10.Two-digit addition with regrouping
  3. 11.Two-digit subtraction with regrouping
  4. 12.Addition as a check for subtraction
  5. 13.Adding multiple two-digit addends
  6. 14.One-step word problems within 100
  7. 15.Two-step word problems within 100
  8. 16.Addition and subtraction facts within 20
  9. 17.Regrouping applied to an unfamiliar bundling context
  10. 18.Two-step word problem in an untaught real-world context
Unit 3: Equal Groups and Arrays: The Road to Multiplication9 lessons
  1. 19.Arrays as rows and columns of equal-sized groups
  2. 20.Finding an array's total by repeated addition of equal rows
  3. 21.Repeated-addition sentence as a record of an array's structure
  4. 22.Invariance of an array's total under rotation (rows vs. columns)
  5. 23.Even and odd numbers as splitting a count into two equal groups
  6. 24.Which whole numbers of objects can form a rectangular array without leftovers
  7. 25.Reasoning about rectangular arrays for an unfamiliar, unpracticed count
  8. 26.Repeated-addition sentences as records of pictured arrays
  9. 27.Transfer of the rectangle-array test to an unfamiliar real-world object context
Unit 4: Measuring Length and Time in Standard Units11 lessons
  1. 28.Measuring length in whole inches using a ruler aligned at zero
  2. 29.The inverse relationship between unit size and the count produced when measuring the same length
  3. 30.Estimating length in whole-unit increments prior to measuring
  4. 31.Comparing two measured lengths and determining their difference
  5. 32.Using a number line model to add and subtract whole-number lengths
  6. 33.One-step addition/subtraction word problems set in a length context
  7. 34.Telling time to the nearest five minutes with a.m./p.m. distinction
  8. 35.Reading whole-hour times on an analog clock (short hand on the number, long hand on 12)
  9. 36.Elapsed time reasoning with an unfamiliar story context
  10. 37.Ordering times using a.m./p.m. labels within a daily routine
  11. 38.The general principle that smaller measuring units always produce larger counts for the same length, applied to unfamiliar units
Unit 5: Money: Counting and Comparing Coin and Bill Values11 lessons
  1. 39.The value of penny, nickel, dime, and quarter
  2. 40.Skip-counting a single coin type to a total
  3. 41.The ordering step in counting mixed coins
  4. 42.The total value of a mixed coin group
  5. 43.The mismatch between coin size and coin value
  6. 44.Comparison of total value between two unequal-looking coin groups
  7. 45.Dollars-and-cents notation ($ and ¢ symbols)
  8. 46.One-step money word problems (buying with exact amount)
  9. 47.Making change with simple coin amounts
  10. 48.Comparing a coin total to an unstated two-item combined price
  11. 49.The equivalence between one dollar bill and 100 cents in coins
Unit 6: Shapes and Their Attributes9 lessons
  1. 50.Side count as the naming rule for triangles, quadrilaterals, pentagons, and hexagons
  2. 51.Side of a polygon as a countable, touchable part
  3. 52.Vertex as the meeting point of two sides
  4. 53.Equal versus unequal side length within one shape
  5. 54.Grouping shapes by side count rather than appearance
  6. 55.The idea that appearance (size, color, orientation) does not determine a shape's name, but side/angle count does
  7. 56.Constructing a shape from a stated rule about side count and equal length
  8. 57.The pattern that a polygon's name follows its side count, extended beyond the four names taught
  9. 58.Applying side-counting and equal-length comparison to a real-world object outside the shape-card context used throughout instruction
Unit 7: Fractions as Equal Shares: Halves, Thirds, and Fourths10 lessons
  1. 59.The number words for equal shares (half, third, fourth)
  2. 60.Circles and rectangles partitioned into two equal shares
  3. 61.The fold-and-check procedure for making two equal shares from one whole
  4. 62.Equal versus unequal partitions of the same whole
  5. 63.The justification that equal shares requires equal size, not equal count of pieces
  6. 64.Differently-shaped but equal-area halves of one whole
  7. 65.Physical partitioning of paper shapes into a requested number of equal shares
  8. 66.The relationship between number of equal shares and the size of each share
  9. 67.Fraction naming as relative to its own whole rather than an absolute size
  10. 68.Equal-size sharing among people applied to an untaught, non-geometric real-world context
Unit 8: Year-End Integration: Mixed Problem Solving10 lessons
  1. 69.Addition and subtraction within 100 in word-problem context
  2. 70.Place value representation of two-digit numbers
  3. 71.Arrays as repeated addition
  4. 72.Identifying problem type from problem context across all prior units
  5. 73.Estimation as an approximate check on an exact measurement
  6. 74.Equality of partitioned shares in fractions
  7. 75.The difference between count of parts and equality of parts
  8. 76.Multi-step problem combining money, measurement, and fractions
  9. 77.Selecting an appropriate strategy in an unfamiliar combined context
  10. 78.Selecting the correct operation and problem type in a real-world context with no visual cue from this unit's material families