Grade 3 · printable course

Number, Shape, and Pattern: Grade 3 Mathematics

Grade 3 · 314 pages · 69 lessons · PDF, print at home

A full-year grade 3 math course built from pictures to symbols. Students move from equal-group and array drawings into multiplication and division facts, then use those facts to measure area and read scaled graphs. Place value extends to 10,000 with rounding. Fractions are built as shaded parts of a bar and located as points on a number line before any fraction arithmetic. Perimeter, time to the minute, and data round out measurement. Every unit reuses the vocabulary and models of the units before it.

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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 Pattern: Grade 3 Mathematics

69 lessons · try a lesson online free

Unit 1: Equal Groups, Arrays, and the Meaning of Multiplication8 lessons
  1. 1.Equal-groups pictures as a model of multiplication
  2. 2.Arrays: rows, columns, and total
  3. 3.Factor and product vocabulary
  4. 4.Commutative property shown by rotating an array
  5. 5.Equal-groups and array pictures as two representations of one fact
  6. 6.Equal-groups word problems within 100
  7. 7.Limits of the repeated-addition analogy for multiplication
  8. 8.Commutative property as evidenced by array rotation
Unit 2: Division, Fact Families, and Fluency Within 1009 lessons
  1. 9.The four related facts (fact family) shown by one array
  2. 10.The vocabulary labels divisor, dividend, quotient mapped onto an already-drawn array
  3. 11.Division as splitting an array into equal rows or columns
  4. 12.Division facts within 100 (10x10 table)
  5. 13.Unknown-factor multiplication equations
  6. 14.Whole-number answers versus leftover amounts in equal-sharing situations
  7. 15.Unknown-factor problems embedded in multi-step word problems
  8. 16.Regularity in repeated reasoning within the multiplication table
  9. 17.Array rotation and the commutative property within a fact family
Unit 3: Place Value to 10,000 and Rounding9 lessons
  1. 18.Place value of digits in numbers up to 10,000 (thousands, hundreds, tens, ones)
  2. 19.Expanded form of numbers to 10,000
  3. 20.The open number line as a tool for locating a whole number between two benchmarks
  4. 21.Rounding to the nearest 10 using distance on a number line
  5. 22.Rounding to the nearest 100 using distance on a number line
  6. 23.The dependence of a rounded answer on the chosen rounding unit and purpose
  7. 24.Multiplying a one-digit number by a multiple of 10 using place value
  8. 25.Using rounded estimates to check the reasonableness of an exact sum or difference
  9. 26.Choosing between exact computation and estimation based on the purpose stated in a problem
Unit 4: Area and Perimeter: Two Questions About One Shape9 lessons
  1. 27.Area of a rectangle found by counting unit squares
  2. 28.The equivalence between counting tiled unit squares and the rows x columns array picture
  3. 29.The area formula length x width applied to whole-number rectangle dimensions
  4. 30.The distinction between area (square units, interior count) and perimeter (linear units, distance around)
  5. 31.An unknown rectangle side length derived from a given perimeter and one known side
  6. 32.Area and perimeter recorded for rectangles built from a fixed tile count
  7. 33.The relationship between fixed area and variable perimeter across different rectangle shapes
  8. 34.Rectangle dimension choices applied to an unfamiliar real-world area or perimeter scenario
  9. 35.Rounding rectangle side lengths to estimate area
Unit 5: Unit Fractions and Fractions on the Number Line9 lessons
  1. 36.Partitioning a whole shape into b equal parts
  2. 37.Fraction bar model of a/b as a shaded parts of b equal parts
  3. 38.Equal versus unequal partitioning of a shape into b parts
  4. 39.The requirement of equal-sized parts for a fraction to be defined
  5. 40.Unit fractions as equal-length partitions of the 0-1 segment on a number line
  6. 41.A fraction a/b as a point on the number line reached by counting a hops of size 1/b
  7. 42.Equivalence between the fraction bar shading and the number line hop-point for the same fraction
  8. 43.The dependence of a fraction's actual size on the size of its whole
  9. 44.Transferring equal-partitioning and number-line placement to a new real-world context
Unit 6: Comparing Fractions with Models8 lessons
  1. 45.Comparison of fractions with the same denominator using a bar model
  2. 46.Comparison of fractions with the same numerator using piece size
  3. 47.Fractions as points and distances on a number line
  4. 48.Equivalent fractions shown on matched fraction bar and number-line models
  5. 49.Benchmark comparison strategy using 1/2
  6. 50.The limits of comparing fractions by number alone, without equal wholes
  7. 51.Whole numbers written as fractions with denominator 1
  8. 52.Selecting and constructing a fraction model to justify a comparison
Unit 7: Telling Time to the Minute and Elapsed Time9 lessons
  1. 53.The correspondence between a minute-hand position and its 5-count value on a clock face
  2. 54.Clock reading to the nearest minute, including unlabeled single-minute ticks
  3. 55.The structural analogy between a linear number line and the circular clock face
  4. 56.A timeline model of elapsed time as a distance between two clock times, within a single hour
  5. 57.Elapsed-time word problems that cross an hour boundary
  6. 58.Elapsed time as an invariant distance independent of the specific start and end clock times
  7. 59.Elapsed time across compound boundary crossings in a novel schedule context
  8. 60.The skip-count-by-5 sequence to 60
  9. 61.Structural features of elapsed-time problems that determine solution difficulty
Unit 8: Scaled Picture Graphs and Bar Graphs8 lessons
  1. 62.The multiplication relationship between symbol count and total quantity on a scaled picture graph
  2. 63.The multiplication relationship between bar length in grid units and total quantity on a scaled bar graph
  3. 64.The two-step procedure of multiplying each bar or symbol group by the scale before subtracting to compare quantities
  4. 65.The idea that scale is a stand-in for equal groups, so raw bar length or symbol count is meaningless without it
  5. 66.The construction of a scaled bar graph, including axis labels, scale key, and correctly proportioned bars
  6. 67.The invariance of underlying quantities across different visual scale choices for the same data
  7. 68.The use of rounding to the nearest ten (from Unit 3 place value) as a check on a multiplication-derived graph total
  8. 69.The terms scale, key, and axis as applied to picture and bar graphs

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